Topic Study Groups

New developments and trends in mathematics education at preschool level

Aims and focus

Topic Study Group 1: New developments and trends in mathematics education at pre-school level

In Topic Study Group 1 we will discuss contemporary developments in mathematics education at the preschool and initial years of primary level (approximately ages 0 through 7 years). Our aim is to promote cross-fertilization between theory and practice, research and developmental activities. To this end, researchers and educators are strongly encouraged to participate and consider the mutual challenges that stem from their different activities in their own countries.

Our presentations and discussions will focus on a diversity of issues related to young children’s learning. Among these, we want to discuss young children’s intuitive and informal knowledge of mathematics, the cognitive basis and challenges for young children in learning mathematics, their interest in learning mathematics, the needs of young children at-risk for mathematics difficulties, early interventions that promote their understanding and learning of mathematics, what sort of mathematics can young children be taught and what sorts of assessment are appropriate for young learners of mathematics. Papers focusing on smaller or larger samples, using quantitative or qualitative methods are welcome.

Young children’s intuitive and informal knowledge of mathematics is currently of great interest. There are researchers who assert that children have some innate knowledge of mathematics, others suggest that mathematics knowledge is constructed by children in their cultural context. Our group would like to examine the mathematics that children bring to the classroom, what they need to know in order to learn the curriculum that they are taught, and their interest in mathematical ideas and symbols. Some children may be at risk for mathematics difficulties because they have not developed this informal mathematical knowledge when they start school. Whatever the explanations for this, pre-schools could give them this opportunity.

What sort of mathematics can young children be taught is also a focal point for our group. This discussion includes issues such as activities that promote learning and interest in mathematics among young children, language and thinking in mathematics, problem solving, learning with different kinds of tools (concrete materials, the number line, computers, drawings etc.) and in different types of classroom environments. It would also be of interest to discuss monitoring and assessing young children’s mathematical learning.

Speakers will have a limited amount of time for their presentations but most will bring papers for distribution. The sessions will offer participants the opportunity to form networks for further communication and collaboration.

Program

Tuesday 8th July 12:00 – 13:00

Welcome to TSG1 – Terezinha Nunes

Presentations

1. The role of logic in young children’s mathematics learning Terezinha Nunes Department of Education, University of Oxford, Oxford, UK

2. Preschoolers’ Problem Solving Processes and Strategies Related to Accuracy While Solving Reversibility and Missing Addend Problems Luz Stella López Universidad del Norte & Marymount School, Barranquilla, Colombia

3. What is teaching early mathematics? A case study from Big Math for Little Kids Miriam Amit University Ben-Gurion, Israel

Wednesday 9th July 12:00 – 13:30

Presentations

1. How do you teach nursery children mathematics?’ In search of a mathematics pedagogy for the early years Sue Gifford University of Roehampton, UK

2. Young children counting at home Rose Griffiths University of Leicester, UK

3. Avoiding Ten, a Cognitive Bomb Allan Tarp The MATHeCADEMY.net, Hornslets Alle 27, DK-8500 Grenaa, Denmark

4. Learning Mathematics in the First Two Years at School. The New Zealand Experience Pamela Perger Faculty of Education, The University of Auckland, New Zealand

5. Building Integers in Preschool: A Cooperative Learning Experience Jose Manuel Serrano Universidad Complutense de Madrid, Madrid, Spain

6. Pre-school teachers’ mathematics knowledge and its implication for educational policy Miguel Friz Carrillo, Universidad del Bío-Bío, Chile Marjorie Sámuel Sánchez, Universidad Católica del Maule, Chile Susan Sanhueza Henríquez, Departamento Psicología de la Salud, Universidad de Alicante, España

Friday 11th July 12:30 – 13:30

Presentations

1. Discovering geometry at preschool level Catherine Taveau Université Paris-Sorbonne – IUFM de Paris – IREM paris 7- France

2. Keys for using picture books to support kindergartners’ learning of mathematics Sylvia van den Boogaard FIsme, Utrecht University, the Netherlands Marja van den Heuvel-Panhuizen, FIsme, Utrecht University, the Netherlands & IQB, Humboldt University Berlin, Germany

3. Technology use and geometry development in the early years- an analysis based on the human-media-geometry unit Anna Chronaki Department of Early Childhood Education, University of Thessaly, Volos, Greece

4. Mathematics Within Early Childhood – A New Zealand Case Study Shiree Lee School of Sciences, Mathematics and Technology Education, The Faculty of Education, The University of Auckland, New Zealand

Saturday 12th July 12:00 – 13:30

Presentations

1. Scaling Up TRIAD: Teaching Preschool Math with Trajectories and Technologies Douglas H. Clements & Julie Sarama University at Buffalo, The State University of New York, Department of Learning and Instruction, Graduate School of Education

2. Relating Spatial Structures to the Development of Kindergartner’s Number Sense Fenna van Nes & Jan de Lange Freudenthal Institute for Science and Mathematics Education, Utrecht University, The Netherlands

3. Exploring children’s informal knowledge in the teaching of fractions Ema Mamede University of Minho, Braga, Portugal

4. Teaching Mathematics at the beginning of the school Esther Grossi GEEMPA, Porto Alegre, Brazil

5. The Division Process at Kindergarden Hugo Rodriguez Carmona Mexican Society of Geography and Statistics Email: hugo_rodriguezc@yahoo.com.mx

6. Adapting a School Numeracy Programme for Early Childhood Play-based Learning Shiree Lee, Gregor Lomas, Pamela Perger Faculty of Education, The University of Auckland, New Zealand

Closing remarks: Douglas Clements

Abstracts

Tuesday 8th July

The role of logic in young children’s mathematics learning Terezinha Nunes Department of Education, University of Oxford, Oxford, UK

Abstract It has often been claimed that children’s understanding of mathematics is based on their ability to reason logically. This presentation will provide evidence for this claim, which has been so far accepted by many but not supported by research. Two studies will be described. One was a longitudinal study in which we showed (a) that measures of 6-year-old children’s logical abilities and of their working memory both predict their mathematical achievement over a period of 16 months even after controls for differences in age and intelligence, and (b) that the logical scores continued to predict mathematical levels after appropriate controls had been taken into account. In the second study we improved the logical reasoning of a group of children at risk for underachieving in mathematics and showed that they made more progress in mathematics than a similar group of children from the same schools who were not given this teaching. Together these studies showed a strong link between logical reasoning and mathematical development and also established that it is possible to improve mathematics learning in children at risk by improving their logical reasoning in their first year of school.

Preschoolers’ Problem Solving Processes and Strategies Related to Accuracy While Solving Reversibility and Missing Addend Problems Luz Stella López Universidad del Norte & Marymount School, Barranquilla, Colombia.

Abstract This presentation will examine research on the effects of the use of processes and arithmetic strategies on accuracy, in 162 children, ages 4, 5, and 6, while solving Reversibility and Missing Addend problems. The research questions were: Which are the processes and strategies most used? Are different types of processes and strategies used depending upon the type of problem solved? Are children likely to succeed when using different types of processes and strategies? Do the processes and strategies that predict accuracy vary in relationship to the problem solved? A Semi- Structured Clinical Interview was designed and validated as a method to gather data. Results show that there is a tendency for the reports on the use of processes to vary in increasing mean percentages by age. The reports of the use of arithmetic strategies also vary by age, reflecting changes from the more concrete to the more mental ones, as age increases. The processes and strategies accessed do not vary by problem type, yet these do vary when predicting accuracy. Certain processes and strategies interact to predict success. Results will be analyzed in relationship to the literature on problem solving processes and arithmetic strategies.

What is teaching early mathematics? A case study from Big Math for Little Kids Miriam Amit University Ben Gurion, Israel

Abstract There now appears to be widespread agreement that early childhood mathematics education (ECME) should be implemented on a wide scale, particularly for disadvantaged children. Yet little is known about the teaching of early mathematics. The goal of this paper is to demystify the process. We analyze one early childhood teacher’s work as she attempts to implement an extended activity on mapping. Her efforts reveal the myriad activities involved in teaching mathematics to young children. Her teaching entails all the processes involved in teaching mathematics to older children, including profound knowledge of the subject matter, pedagogical content knowledge, lecturing, introduction of symbolism, and connecting everyday experience to abstract ideas. Teaching early mathematics to young children is essentially the same as teaching it to older children. The implications of this observation for professional development are enormous: extensive pre-service and in-service education is necessary to train a new generation of effective teachers of mathematics.

Wednesday, 9th July

How do you teach nursery children mathematics?’ In search of a mathematics pedagogy for the early years Sue Gifford University of Roehampton, UK

Abstract Recent concerns with underachievement have focused attention on mathematics education in pre-school. Evidence points to the effectiveness of mathematics focused, adult led activities, yet little is known about the nature of effective mathematics ‘teaching’ for such young children. With a view to establishing principles for appropriate pedagogy, this paper reviews current research on how young children learn, including evidence from neuroscience, pre-school interventions and home learning. This evidence points to the importance of planning cumulative experience, building on children’s spatial memory, combining kinaesthetic, visual, and verbal learning, and providing opportunities for problem solving and discussion. Close relationships with teachers and working in friendship pairs are important for learning. Children’s views of themselves as mathematical learners are crucial, alongside their interests and mathematical purposes, home learning environments and parental pedagogy. The variation in children’s experience and attitudes indicates the importance of working with families and of helping children make connections. Recommended activities include repetitive routines, rhymes, games and stories which involve problem solving. Resources include a range of computer software and apparatus providing schematic visual images. Interactive adult strategies include modelling, indirect questions and challenges, using errors, puppets and humour and praising effort over performance. Effective staff development includes involvement in mathematics focused activities to foster confidence and the use of learning trajectories in formative assessment. Current developments point to the need to create mathematical communities of practice in pre-school with raised teacher expectations for young children’s mathematical learning.

Young children counting at home Rose Griffiths University of Leicester, UK

Abstract This presentation examines the contribution made by family members to children’s early learning about counting, and discusses the ways in which children develop their understanding of counting in everyday situations. It describes a research project where children’s counting practices at home were filmed in twelve families with children aged two, three or four. Five of the families were multilingual, and children were learning to count in two (or more) languages. It explores the variety of contexts in which children’s skills were extended, as they counted toys, apples, fingers and toes, stairs and how many times they swung on a swing. The families were able to provide children with frequent, meaningful and enjoyable opportunities to count over a long period, often only for a few minutes at a time but with a high level of individual attention, in a way that is more difficult to manage in an educational setting. The challenge for practitioners is to value what families achieve, to use good ideas from home where appropriate in our settings, and to provide support and advice to families, including helping parents and carers to share good ideas from common family practice. A selection of film clips from the project have been used to make a DVD for parents, carers and practitioners.

Avoiding Ten, a Cognitive Bomb Allan Tarp The MATHeCADEMY.net, Hornslets Alle 27, DK-8500 Grenaa, Denmark, +45 8632 1899

Abstract Being the only number with a name but without an icon, ten easily becomes a cognitive bomb to young brains. While ten is the follower of nine by nature, 10 is the follower of 9 by a pastoral choice hiding its alternatives: with 8 as bundle-size 10 is the follower of 7, and the follower of nine is 12. Using anti-pastoral sophist research searching for alternatives to pastoral choices presented as nature, this paper shows that the root of mathematics is the study of multiplicity; that the root of numbers is counting by bundling & stacking using cup-writing and decimal-numbers to report the resulting stacks of bundles and unbundled; that the root of operation is the bundling & stacking process where’7-2’ means ‘from 7 take away 2’, ‘7/2’ means ‘take away 2s’, ‘3×2’ means ‘3 2-bundles’, and ‘5+2’ means ‘juxtaposing 2 1s to 1 5s’; that the root of formulas is the recount formula T = (T/b)x b telling that a total T is counted by taking away bs T/b times, thus predicting the counting result with numbers entered: T = 9 = (9/4)x 4 = 2.1 4s; that the nature of equations is reversed calculations performed by reversing the calculation sign of the numbers, so if zx3+2 = 8 then z = (8-2)/3; that the nature of calculus is adding stacks by uniting their bundles-sizes asking 3 4s + 2 5s = ? 9s. Finally the paper shows how the core of mathematics can be learned by using 1digit numbers alone.

Learning Mathematics in the First Two Years at School. The New Zealand Experience Pamela Perger Faculty of Education, The University of Auckland, New Zealand

Abstract By the time a child in New Zealand reaches their seventh birthday they have experienced at least two mathematical learning environments. One where mathematical concepts are learnt as the child makes sense of the world around them, the other a more formal school environment. The New Zealand curriculum document states that children should learn mathematics through the use of meaningful contexts (Ministry of Education, 2007) yet these contexts are very different to the contexts the child has experienced prior to starting school. With the introduction of the Numeracy Development Project [NDP] the teaching of number has become more separated from other subject areas. The basis of the NDP is a framework of strategies and knowledge that children are facilitated through to increase their numeracy capacity. The framework is divided into two categories, knowledge (numeral identification, counting sequence [forward and backwards], place value, basic facts) and strategy (addition and subtraction, multiplication and division, and proportion and ratio). As well as the frameworks a diagnostic interview was developed enabling teachers to make more specific analysis of children’s mathematical knowledge and strategy. Support material was developed and collated to aid teachers in planning for the specific needs identified through the diagnostic interview. Young children viewed many of these specially developed activities as games, thus providing a meaningful context for learning mathematics. This presentation explores the diagnostic interview (NumPa), the specifically developed activities and the Strategy Teaching Model that supports the teaching and learning of knowledge and strategies identified within the New Zealand Numeracy Frameworks.

Building Integers in Preschool: A Cooperative Learning Experience Jose Manuel Serrano Universidad Complutense de Madrid, Madrid, Spain

Abstract The present work is an experience conducted in a classroom of Infantile Education (preschool)with children of five years old in order they managed to construct the set of integer numbers and were able to operate with the law of composition (+) in the interval [- 9, +9] because notion of ten is not included in the curricular contents of these students. The experience took place in the center’s gymnasium. Purpose was having a larger space, where we could obtain a suitable representation of the numerical straight line for the cognitive structure of the students, so the classroom was insufficient for the correct development of the activities. A train was used as material. The train was made with panels (two wagons) whose wheels can be connected. As well, two set of piston rod with a flag (stations) that took numbers from one to nine. And a drawer as the point always the train left. The drawer represented the origin so it was designated with letter “O” (origin). The activity was a game that demanded the displacement of the train. Children knew the only rule was the train only could go forwards or backwards, that is to say, the train could change of sense, but not of direction. The methodology was cooperative, with interdependence of objectives, division of the task, and differentiation and alternation of rolls. The initial task consisted of differentiating what stations went in front of the drawer and what stations went behind the drawer. It was established, for mutual agreement, to mark the flags of the numbers. The following tasks consisted of problems situations of displacements towards ahead or backwards of both wagons that composed the train. Purpose was the dominion of those displacements. Next a group of tasks was developed to reach a consensus about the representation of the displacements (numbers and marks) in order that they had an exact and equivalent knowledge of which it became at every moment. Finally, inverse activities were made. Students had to translate a representation (numbers and signs) into the real situation. All the students ended up solving situations such as (3-7), that is to say, they went three stations towards ahead (3) and soon they went backwards seven stations (-7), so the train located four station behind the origin. With these activities it was obtained children had a representation, of the content and the task, which are necessary condition for the construction of the meaning and the attribution of sense.

A study of preschool teachers’ the mathematical knowledge and its implications for educational policy Miguel Friz Carrillo, Universidad del Bío-Bío, Chile Marjorie Sámuel Sánchez, Universidad Católica del Maule, Chile Susan Sanhueza Henríquez, Departamento Psicología de la Salud, Universidad de Alicante, España

Abstract The research aims to assess the mathematical knowledge that preschool teachers have. The methodology is determined by a quantitative approach, non-experimental descriptive, survey type. The results indicate that high level of knowledge and skills are found in elementary logic (notion of time, symbolic function, similarities and differences) whereas numbers and space concepts and their functions need to be worked in further depth by teachers. One major obstacle is the gap that stands between the informal mathematical language and the discipline systematized language. Although there are no significant differences in the responses provided by teachers from private and state-supported schools, it is necessary to consider the training models of teachers, since the evidence shows that these programs do not impact significantly on the way in which teachers approach mathematical knowledge.

Friday 11th July

Discovering geometry at preschool level Catherine Taveau Université Paris-Sorbonne – IUFM de Paris – IREM de Paris 7 – France

Abstract In France, all three-year-old children are at preschool. During their schooling, the French young children have to learn the following knowledge: number sense, space and time sense, shapes and magnitudes. At preschool, the syllabus give a key and crucial role to the use of language by placing it at the center of the overall acquisition. In this paper, I will mainly focus on geometry which is more difficult to teach at this school level. Some geometrical activities have been worked out based on didactic tools (Duval’s representation registers and Houdement-Kuzniak’s geometrical paradigms). These activities have been used by teachers and their implementation have been analyzed in teachers’ training with video recordings. Then we have improved these activities to make them available to the teachers’ community via booklets, multimedia package (DVD, CD-ROM) or professional websites. In our proposal, some examples of such activities are given and students’ difficulties are analyzed.

Keys for using picture books to support kindergartners’ learning of mathematics Sylvia van den Boogaard FIsme, Utrecht University, the Netherlands Marja van den Heuvel-Panhuizen, FIsme, Utrecht University, the Netherlands & IQB, Humboldt University Berlin, Germany

Abstract Picture books can offer children a meaningful context for learning mathematics, and provide them with an informal experience base for mathematical operations, objects and structures that can be a springboard for a more formal level of understanding. The “PIcture books and COncept development in mathematics” (PICO-ma) project intends to generate more knowledge on the working and the effect of picture books on the learning of mathematics by young children. Among other things, the project is aimed at identifying what characteristics of picture books that have not been written to teach mathematics, can contribute to the development of mathematical concepts in kindergartners, and at finding out how to read the books to children so that these learning-supporting characteristics of picture books are strengthened. In the presentation, we zoom in on the keys we have developed to elicit children’s thinking and talking about the mathematical concepts that appear in the books. These keys include teacher behavior such as (1) asking oneself a question, (2) playing ignorant, and (3) showing an inquiring expression. Using these keys in reading sessions, we found that they make children cognitively engaged during the reading session. We will illustrate our findings with video clips addressing examples from number (with special attention to “structuring numbers”), measurement (in particular the theme “growth”), and geometry (with the focus on “taking a point of view”).

Technology use and geometry development in the early years- an analysis based on the human-media-geometry unit Anna Chronaki Department of Early Childhood Education, University of Thessaly, Volos, Greece

Abstract Lev Semonovich Vygotsky has repeatedly claimed through his writings that understanding the development of scientific concepts in childhood supports our attempt for devising successful teaching methods. Within this realm, the interrelation of scientific and spontaneous concepts is linked with school instructional practices, child’s development and social interactions. With particular reference to mathematical concepts, he points out, that when a child learns some mathematical operations, ‘the development of that operation or concept has only begun’, and continues arguing that ‘…the curve of development does not coincide with the curve of school instruction; by and large, instruction, precedes development’ (p. 102). Τhe present paper attempts to address the above, by discussing the particular case of geometry teaching and learning as mediated by technology-based tools and interactions. A series of episodes are analyzed with an eye to trace and interpret scientific development as part of evolving interactions amongst educator-children-technology. This perspective relates the studying of the development of scientific concepts with a type of analysis that is based on units. The term ‘unit’ is used here to emphasize that the product of analysis is not about the single elements of a situation but mainly about its wholeness. For example, a word meaning can be the unit of verbal thought and it is in ‘word meaning’ that thought and speech unite into verbal thought. Taking the above into consideration, the present paper takes as a unit of analysis the system children-technology-maths activity. This unit is related to the construct of subject-mediated tool-object as proposed by Leont’ev (1978) and discussed later by Tikhomirov (1981). It enables to interpret child’s mathematical activity and technology use as part of a complex whole and not as isolated and separate actions or operations. And, in parallel, assists to explore how technology (i.e. a dynamic geometry microworld) mediates the development of mathematical concepts (i.e. abstracting geometric properties) by creating an instructional context based on ‘word meanings’.

Mathematics Within Early Childhood – A New Zealand Case Study Shiree Lee School of Sciences, Mathematics and Technology Education, The Faculty of Education, The University of Auckland, New Zealand

Abstract This presentation will discuss examples from a recent case study observing children aged between 12 months and five years as evidence that foundational mathematical learning occurs in children’s play. These examples support the holistic, child-centred and integrated approach to early childhood mathematics promoted within early childhood education in New Zealand. The data collected showed evidence of very young children’s skill and knowledge in rote counting, one to one counting, measuring, addition and subtraction, division, spatial rearrangement, concepts of time, shape recognition, and patterning. Te Whãriki (Ministry of Education [MoE], 1996) New Zealand’s early childhood curriculum document, describes an holistic and open-ended framework for the education of young children from birth to school entry. Learning outcomes for individual subject content areas are stated within this document although the strong emphasis on child-centred and holistic play-based learning remains the fundamental philosophy in implementing these. The pedagogical approaches and understanding that teachers within New Zealand early childhood settings hold, is an essential influence on the mathematical experiences that are offered to children in early childhood settings. Early childhood teachers who understand and articulate the importance of children’s play and create an environment that has potential for hands-on discovery, provide opportunities for children to lay the foundations of their mathematical understanding. This notion of children constructing their own knowledge is espoused clearly within Te Whãriki “To grow up as competent and confident learners and communicators, healthy in mind, body and spirit, secure in their sense of belonging and in the knowledge that they make a valued contribution to society.” (MoE, 1996, p. 9).

Saturday 12th July

Scaling Up TRIAD: Teaching Preschool Math with Trajectories and Technologies Douglas H. Clements & Julie Sarama University at Buffalo, The State University of New York, Department of Learning and Instruction, Graduate School of Education

Abstract Some research-based educational practices have been successful. Unfortunately, there is a “deep, systemic incapacity of U.S. schools, and practitioners Š to develop, incorporate, and extend new ideas about teaching and learning” (Elmore, 1996, p. 1). Fortunately, research provides guidelines to scale up interventions (http://UBTRIAD.org). We used these guidelines to create and test our TRIAD intervention for low-income preschoolers. TRIAD stands for Technology-enhanced, Research-based, Instruction, Assessment, and professional Development. Technology benefits students, teachers, and researchers. Research is the basis for all aspects of TRIAD: The instruction, the assessments, and the professional development. The goal of the TRIAD intervention is to avoid the dilution and pollution that usually plagues efforts to achieve broad success. This presentation will briefly discuss three studies of the internal workings and the empirical evaluations of each of the three components of TRIAD-instruction, assessment professional development. Each one is build around a central core of learning trajectories (descriptions of children’s thinking and learningŠand a related, conjectured route through a set of instructional tasks). Learning trajectories are at the heart of both TRIAD’s math curriculum and its professional development. Learning trajectories help teachers focus on the “conceptual storyline” of the curriculum, a critical element that is often missed. They facilitate teachers’ learning about math, how children think about and learn this math, and how such learning is supported by the curriculum and its teaching strategies. By illuminating potential developmental progressions, they bring coherence and consistency to TRIAD’s three components of assessment, professional development, and instruction.

Relating Spatial Structures to the Development of Kindergartner’s Number Sense Fenna van Nes & Jan de Lange Freudenthal Institute for Science and Mathematics Education, Utrecht University, The Netherlands

Abstract This study is part of a larger interdisciplinary project bridging research from mathematics education with neurosciences to gain insight into how kindergartners’ early spatial and numerical abilities may best be fostered. Regarding the mathematics education component, we are investigating how kindergartners’ spatial structuring abilities may stimulate their number sense and help them to attain more sophisticated numerical strategies. Examples of relevant spatial structures are finger patterns and domino-dot configurations. For this purpose, we developed interactive tasks and classroom activities with which we conducted a teaching experiment in a kindergarten of an elementary school in the Netherlands. The goal of the teaching experiment was (a) to gain insight into kindergartners’ early spatial structuring abilities, and (b) to design an educational setting that can support kindergartners in learning to apply spatial structures as a means to abbreviate numerical procedures. In this presentation, we will share several video clips of activities from the teaching experiment and discuss how they triggered learning opportunities for the children. The significance of such an educational setting is that it may help identify children who have difficulty recognizing spatial structures and who are falling behind in counting ability at such an early stage in formal schooling. It may support children with instructional activities that are tailored to appeal to their interests, their intrinsic motivation and their mathematical strengths rather than just their weaknesses. In this way, the research may contribute to methods for intercepting problems in the development of early, yet fundamental, mathematical abilities of young children.

Exploring children’s informal knowledge in the teaching of fractions Ema Mamede University of Minho, Braga, Portugal

Abstract This paper describes a teaching experiment in which children were introduced to fractions using quotient, part-whole or operator situations. The effects of each of these situations were analysed. Children’s informal knowledge of quantities that are represented by fractions has not been systematically analysed across situations. Differences between situations are analysed by comparing what children learn about this type of quantities and their representations in each of these situations, and whether they transfer this learning across situations. The study involved first-graders (N=37), aged 6 to 7 years, from two primary schools from the city of Braga, in Portugal who had not been taught about fractions before. The children were assigned to work in groups. Two types of tasks were presented to the children: tasks involving the equivalence and ordering of quantities represented by fractions, referred to here as “logical tasks”; and tasks where the children were asked to provide a symbolic representation, referred to as “labelling tasks”. We investigated whether the situation in which the concept of fractions was presented to the children influenced their learning of logical and labelling aspects of fractions. Quantitative analyses showed that children developed a better understanding of equivalence and order of fractional quantities when they were introduced to fractions in quotient situations, but there was no transfer of learning to part-whole or to operator situations. When part-whole and operator situations were used to introduce children to fractions, they only learned how to label fractions and were able to transfer this learning across these two situations.

Teaching Mathematics at the beginning of school Esther Grossi GEEMPA, Porto Alegre, Brazil

Abstract The central idea of this presentation at the Eleventh ICME is based on the Theory of Conceptual Fields of Gérard Vergnaud. The idea that we don’t learn step by step, a set of concepts, but we consider three vectors at the same time. These three vectors are: (1) a set of situations; (2) a set of concepts; and (3) a set of symbolic representation. The set of concepts at the beginning of school are related to five axles: logic, space, structure of numbers, structure of addition and structure of multiplication. In this presentation, it will be argued that the point of departure for children’s understanding of multiplicative structures is division. Division is at the center of mathematics learning for children because it is culturally meaningful: children use partition to solve problems in everyday life more than addition. There is also an affective investment by children in the relation between partition and division: in the majority of real life situations when the need to divide appears, the division is not in equal parts. This is partition and not division. This makes the concept of division attractive for children and adult learners in the initial stages of learning: in mathematics, division is fair.

The Division Process at Kindergarten Hugo Rodriguez Carmona Mexican Society of Geography and Statistics Email: hugo_rodriguezc@yahoo.com.mx

Abstract Fractions are a big issue for students and for teachers as well. At elementary and secondary schools, most teachers see it as a very big challenge to teach their students how to divide fractions and to find word problems that require the use of the division algorithm. It is also difficult to explain to students which kind of situations in real life requires the division of fractions. This presentation will describe manipulative materials called “desquebra/2”, which represent a very easy way for helping teachers to deal with the division process at kindergarten level and presents activities that can help kids understand the division of fractions process.

Adapting a School Numeracy Programme for Early Childhood Play-based Learning Shiree Lee, Gregor Lomas, Pamela Perger Faculty of Education, The University of Auckland, New Zealand

Abstract The New Zealand Early Childhood curriculum is based on a play-based holistic approach to learning centred around supporting, and building on, the child’s interests. This is in contrast to the more formal classroom instruction prevalent in New Zealand primary schools centred on a curriculum that sets out subject specific goals. For school mathematics the development of a research based numeracy teaching/learning programme led to the construction of an oral diagnostic assessment instrument and frameworks setting out detailed progression stages in the knowledge and strategies necessary for children’s numeracy learning. School entry (age five) data gathered using the instrument as part of the implementation of the programme revealed variable levels of knowledge and skills in aspects of numeracy, but more importantly that these were often far more advanced than anticipated by the school curriculum. For example, in the Numeral identification progression 17% of children recognise numbers to 100 and a further 15% numbers to 1000. This data provides clear evidence that current early childhood experiences can and do impact on children’s readiness for further numeracy learning in school environments. The detail gained from the data can be used to indicate particular aspects of numeracy learning that could be enhanced within early childhood settings; firstly, by the linking of the numeracy programme terminology to the mathematics language of the early childhood curriculum for teachers, and secondly, by the use of the activities (eg. games) and the child-centred approaches designed for use within schools which would not compromise the play-based holistic approaches of the early childhood curriculum.

Papers and discussion documents

Final call for papers (27.00 KB)

New developments and trends in mathematics education at primary level

Aims, scope, and goal(s)

The goal of TG2 is to provide highly relevant and interesting presentations of new developments and trends in primary mathematics education from around the world. By sharing our international perspectives, we are confident that all of us will understand more of the highlights and challenges of our respective professional settings and be able to apply what we learn in each of our local contexts. We expect that some papers will be reporting on innovative research, while others may focus on innovative classroom practice, and some papers will be a blend of both.

Proposals by

Name	Country
Tracey Muir	Australia
Sybille Schutte	Germany
Dr Ronald Keijzer	The Netherlands
Jill Cheeseman	Australia
Yukio Sugawara	Japan
Shinya Yamamoto and *Taro Fujita	Japan UK
Prof. Annie Savard Canada
Mary Margaret Capraro, Alma Chavez-Rangel, and Robert M. Capraro	USA
Philippe Skilbecq	Belgium
Jessica Pierson, Luz Maldonado and Erika Pierson	USA

Papers and discussion documents

Cheeseman (72.00 KB)
Keijzer (345.00 KB)
Muir (330.00 KB)
Pierson, Maldonado, & Pierson (255.00 KB)
Savard (64.00 KB)
Skilbecq (251.00 KB)
Sugawara (105.00 KB)
Capraro, Rangel-Chavez, & Capraro (143.00 KB)
Fujita & Yamamoto (254.00 KB)
FINAL SCHEDULE TSG2 JULY 7 (WE NOW START ON TUESDAY NOT MONDAY) (41.00 KB)

New developments and trends in mathematics education at lower secondary level

Aims, scope, and goals

Aims and Focus

The goal of this topic group is to present a cross-section of papers that inform the international community about the new developments and trends in lower secondary mathematics education around the world. It is our hope that through the sharing of our international perspectives the potential to enrich our local contexts will be enhanced.

“New Developments and Trends in Lower Secondary” is a broad topic and one that includes many of the topics explored in other groups. We will use the opportunity of this topic group for exploring the unique nature of the lower secondary context with specific emphasis on resources; curriculum reform; and pedagogy. Papers based on research in mathematics education and papers based on experience from school practice are being presented. We aim at providing opportunities for discussions where theoretical and practical matters in mathematics education can be discussed from various perspectives.

Papers for Topic Study Group III

TSG III will be organised around three themes under the major heading, New developments and trends in mathematics education at lower secondary: 1) Resources; 2) Curriculum Reform: 3) Pedagogy.

Presentations: Auditorio Martínez Carranza 1(Civil) Building H

Tuesday July 8, 12:00 – 13:00

RESOURCES, chaired by Elaine Simmt

Developing an activity based, Mathlab workshop for middle school. Prof. Inder K. Rana, Department of Mathematics, Indian Institute of Technology Bombay, Powai

Olympic Math for lower secondary school. Matthias Ludwig, Department of Mathematics, University of Education, Weingarten, Germany

Wednesday July 9, 12:00-13:30

CURRICULUM REFORM, chaired by Glenda Anthony

Knowledge oriented or competence oriented? Debate on mathematics curriculum standard in China. Binyan Xu, Institute of Curriculum and Instruction, East China Normal University, Shanghai, China

Changing landscapes in New Zealand secondary mathematics classrooms?. Glenda Anthony, Massey University, New Zealand

New developments secondary curriculum in Canada: the Province of Alberta. Elaine Simmt, University of Alberta, Canada

Friday July 11, 12:30 – 13:30

PEDAGOGY, chaired by Binyan Xu

Characteristics of mathematics teaching under the background of the Chinese culture: An investigation in Chinese junior middle school classes. Kong Qiping, The Institute of Curriculum and Instruction, East China Normal University, Shanghai, China

Addressing the ‘dip in lower secondary mathematics learning through school-based projects: a case study of one school’s approach. Judy Anderson, Faculty of Education and Social Work The University of Sydney

Saturday July 12, 12:00 – !3:30

PEDAGOGY cont, chaired by Binyan Xu

Combining share and measure meaning of fractions to facilitate students’ reasoning. Jayasree Subramanian, Eklavya Foundation Bhopal. K. Subramaniam, Tata Institute of Fundamental Research, Mumbai. Shweta Naik, Tata Institute of Fundamental Research, Mumbai. Brajesh Verma, Muskaan, Bhopal.

A study of seventh-grade students learning fractions in China. Su Hong-Yu, East China Normal University, Shanghai, China

_New developments and Trends in Mathematics Education at the Lower Secondary Level Glenda Anthony, Elaine Simmt, Binyan Xu, session organisers

Papers accepted but will not be presented

Student awareness of analogy: mathematical & ethical implications. Martina Metz, University of Alberta, Canada

Mathematics inquiry learning in China: situation and suggestions. Ru Xin Zhang, Xihu District Teacher Training School, Hangzhou, China

Papers and discussion documents

Qiping Kong (39.00 KB)
Binyan Xu (47.00 KB)
Mathias Ludwig (844.00 KB)
Subramanian et al (90.00 KB)
Glenda Anthony (167.00 KB)
Judy Anderson (235.00 KB)
Metz (98.00 KB)
Hongyu, Su (103.00 KB)

New developments and trends in mathematics education at upper secondary level

Pictures

Aims and focus

Upper Secondary education is becoming more important and facing new challenges because more and more students all over the world are encouraged to study and are effectively studying beyond the compulsory education level (around the age of 15 or 16). This gives rise to many questions: How is Mathematics evolving at the Upper Secondary level? Are all students studying mathematics at this level? Should they? Are all the students studying the same kind of mathematics? Should they? Which different kinds of courses are offered at this level that involve mathematics? How do these courses connect to lower secondary mathematics courses and to higher education courses? How are vocational courses at this level developed and how do they inter-relate with other courses? What ideas are being proposed and implemented in different countries and in different regions of the world? Which are the philosophies behind these proposals? Does change at this level require more research, more professional development for teachers, more curriculum development? Which research in mathematics education being currently conducted might be relevant to shape new curriculum development at this level?

This Topic Study Group intends to study the topics underpinning these questions and others that might be proposed by participants which are connected to the theme of TSG 4: “New developments and trends in mathematics education at upper secondary level”

To discuss these ambitious questions, we propose to organize the topic study group around a set of four inter-related themes as well as to utilize the web page of TSG 4 in advance of ICME 11. The themes proposed are:

(1) Trends in Mathematics at the upper secondary level in different countries: In this theme there will be presentations of recent, developing or planned reforms in the teaching of mathematics at the upper secondary level, focusing on what is happening in the schools with teachers and students.

(2) Advances in Mathematics Courses offered at the upper secondary level meeting the diversity of need: We will focus on specific mathematics courses offered in different countries that diversify the offerings at the upper secondary level, and whether the ones offered now are relevant to the targeted student population, such as Math for the Social Sciences, Math for art courses, math for vocational studies,...

(3) The impact of recent research in mathematics education and the need for more specific research at upper secondary level: When curriculum changes, some of the changes are due to research in mathematics education: which examples can be offered? At other times the change stimulates research: again can we offer examples? Which research seems to be needed? Is classroom based research possible at this level? Do we have examples of new research at this level?

(4) Recent Trends in Philosophies of mathematics education at the upper secondary level: Is mathematics a needed subject for all students throughout schooling/future citizens/workers? Is mathematics a cultural subject that might or might not be studied by all students? Must mathematics be studied beyond the compulsory education level? Should different ways of approaching mathematics be offered? Should mathematics be merged with other subjects for some/all students? At this level should we have more (independent) project work with students elaborating more on some specific content or using mathematics to solve or model some real world problem depending on each project?

Our objective in choosing this thematic approach is to organize ways of reflecting on the topic that might offer different approaches from previous ICMEs in order to intensify the debate.

Papers already accepted

Dindyal, Jaguthsing, Singapore A Diverse Mathematical Landscape at the Junior College Level

Serge Hazanov, Switzerland Evolution of International Baccalaureate Mathematics Program

Jurkiewicz, Samuel, Brazil Discrete Mathematics In The Classroom

Jianyao Zhang, Rongjin Huang, Yeping Li, Peiling Qian, Xuejun Li, China & USA Improving Mathematics Teaching and Learning with a Focus on Core Concepts in Secondary School Mathematics: Introducing a new nation-wide effort in Mainland China

José Carlos Oliveira Costa, Vinício de Macedo Santos, Brazil The Limits and Potentialities of a Competence Based Approach Towards the Restructuring of the Brazilian Educational System in the 1990s

Stripp, C. & Button, T., U K How the Further Mathematics Network’s radical new approach to tuition and support for teachers is widening access to high level mathematics for pre-university students in England

Masuda, Naoyuki, Japan An Approach to Teaching Knot Theory in Schools _ the teaching in senior high school

Roberto Alves de Oliveira, Celi Espasandin Lopes, Brazil Reading and Writing in Mathematics Classes at the Upper Secondary Level

Brown, Jill, Australia Times of Change in Upper Secondary Mathematics Classrooms in Victoria, Australia: Assessment, Content, Technology

zhou chang-jun, China A Case Study of Four Ethnic Minority Excellent Students’ Mathematics Learning Affect in Senior 3 in West Yunnan, China

Gilda de La Rocque Palis, Brazil Development of the function concept at the secondary level. Difficulties at the transition to mathematics based careers at the tertiary level.

Call for papers

The TSG 4 organizing team cordially invites all teachers, researchers, decision makers and other interested people to submit summaries of papers addressing topics related to our “Aims and Focus”. Each summary should be up to 4 pages in length, and outline the key ideas addressed and conclusions reached. Where applicable, journal references or website addresses providing access to fully developed papers should be included. Submission should be electronic to one of the organizing team members with a copy to one of the co-chairs: either as a direct e-mail, or as an attached Word file. Please do not send full papers. Please do not exceed the page guideline.

Summaries should be submitted by December 15, 2007. The organizing team will select the papers to be posted on the website or presented at ICME-11 by January 10, 2008. Those selected will be invited to submit full original papers of no more than 10 pages by March 15, 2008. These papers will be published on this website after being fully refereed by two members of the organizing team to ensure quality and relevance of papers.

The organizing team reserves the right to invite people to submit their work anytime during this process.

The organizing team of TSG 4 will edit Proceedings of the papers and discussions of this Topic Study Group. Depending on the quantity and quality of the papers presented there will be only a digital edition or the Proceedings will be submitted to a publisher.

Please indicate in a cover note with your submission whether or not you wish to be considered for an oral presentation at TSG-4, and if you are otherwise involved in an ICME-11 activity or if you have received any other proposal to contribute to another ICME-11 group or activity, since the number of possible speakers is extremely limited to give opportunity to everybody.

We are anticipating talks of up to 15 minutes each, followed by 5 minutes for discussion.

List of links to relevant material

The organizing team of TSG 4 will publish on this website a list of links to relevant material pertaining to the theme of our TSG. These will include links to pages with mathematics courses and syllabuses, discussions, research papers and other papers around “New developments and trends in mathematics education at upper secondary level”. We invite all interested to submit links to be included in this list.

ICME11 – groups with similar themes:
1. Discussion group 22: Current problems and challenges in upper secondary mathematics education
ICME10 – groups with similar themes:
1. TSG 2: New development and trends in mathematics education at secondary level
2. DG 19: Current problems and challenges in lower secondary mathematics education
Mathematics Curricula in various countries:
1. New HK senior secondary curriculum
Books:
1. Teaching Secondary School Mathematics – Research and practice for the 21st century, Merrilyn Goos, Gloria Stillman, Colleen Vale
Websites:

Papers and discussion documents

The papers will soon be available for downloading here.

New developments and trends in mathematics education at tertiary level

Program

TSG 5 have four sessions, two of one hour each and two of 90 minutes each. More specifically, the first three sessions will address the issues related to theory and practice of mathematics education at tertiary level, including but not limited to pedagogy, curriculum, research and teacher education. Presentations can be both of a theoretical or of an empirical nature. In the fourth session we wish to focus on “visions for 2027”, that is, 20 years after the Monterrey meeting. Since the people who will be active in 2027 are the young researchers in our midst, we would preferably like to turn this session over to the newcomers in the field. Presentations, previsional program and proceedings are now available in the following files.

Papers and discussion documents

Presentation Table (17.00 KB)
Programme as on 30 June 2008 (25.00 KB)
Abstracts (40.00 KB)
Proceedings (7.00 KB)

Activities and programs for gifted students

Introduction

This Topic Study Group is intended to bring together teachers, mathematicians, mathematics educators, mentors and researchers who are interested in identifying and nourishing mathematically gifted students. We would like to gather some information about the theory and practice on the subject and look into the problems related to mathematically gifted students, such as challenges for identifying and providing them with an appropriate education. The web sites are:

ICME-11 website
www.mathhouse.org
www.umoncton.ca/casmi

Program

Program of our sessions:

Time table: version, 3rd of July: http://tsg.icme11.org/document/get/789

Message from the TSG-6 Organizing Team with some more detials of our sessions:

Dear participants of the TSG-6,

We are pleased to welcome you at the ICME-11 TSG-6 sessions Activities and Program for Gifted Students, which are scheduled during the Congress. The TSG -6 group work will be organized during 4 sessions for the total of 6 hours. You may like to connect your presentation to other papers. All papers are now available online on this page in the papers section. You are invited to read all the papers and prepare questions for the discussion.

The first session is scheduled on July, 8 (please double-check it upon registration), at 12:00 pm – 1:00 pm. It aims to set up the Topic Study Group goals. This session will start with invited expert panel presentations that will address focal points of Activities and Programs for Gifted Students. The panel will include —Summary from ICME 10 TSG-4 : www.math.toronto.edu/barbeau/tsg4.pdf

presented by Viktor Freiman

—The Effects of Government and Professional Policies on Expectations, Challenges, Assessment and Curriculum for Gifted Students:

A Brief View from the United States : For the last fifty years, from Sputnik through No Child Left Behind, the government and professional societies such as NCTM in the United States have had varying policies and support for mathematically promising students. A few of the effects of these along with questions raised, http://tsg.icme11.org/document/get/593“

presented by Linda Sheffield

—Closer look at challenging practices in and beyond the classroom:< Clearly the ICMI Study-16 highlights challenge as an important issue in education and the learning process generally, which has never been documented or studied overtly as it should. Traditionally the learning process probably contained more challenge than it does today. However, particularly in Western countries, like mine, syllabi have become more and more refined, and available time for teaching mathematics has so significantly declined, that many teachers have time only to deliver knowledge and not to challenge. Since people need to react to challenging situations during their careers and everyday life, a vital part of the learning process may be lost … read the whole text …

presented by Peter Taylor

—Overview of the field complexity and related research agenda

Following Schoenfeld (2000), who enlightened two main purposes of research in mathematics education, I argue that in the field of mathematical giftedness and creativity research has two interrelated purposes:

• The theoretical purpose: To understand the nature of mathematical giftedness and mathematical creativity from the perspectives of thinking, teaching, and learning;

• The applied purpose: To use such understandings to improve mathematics instruction that will realize mathematical giftedness encourage mathematical creativity.

read the whole text …

presented by Roza Leikin

All the participants will be involved in the discussion with panelists.

The second session takes place on July, 9 at 12:00 pm – 1:30 pm During this session participants will work in three small groups

Group 1: Activities and programs for gifted Group 2: Identification and learning of gifted Group 3: Teaching issues and resources.

Each group will include 4-5 paper presentations associated with the topic of the small group. Duration of the paper presentations will be 15 minutes following the discussing of the audience with the authors.

The third and the fourth sessions will be organized on July, 11, at 12:30 pm – 1:30 pm and on July, 12, at 12:00 pm – 1:30 pm. These sessions will be run in the form of general presentations following by the whole group discussion. At the last session we plan to discuss further collaboration of the participants after the Congress.

Please see the time table of the group in the attached document. Please, verify the day and time of your presentation, it may be different from the preliminary time. Moreover, some on-site adjustment may still be necessary. The room numbers for general sessions should be given to you upon the registration. The room numbers for the parallel sessions will be announced at the first session of the TSG-6.

We are looking forward seeing you very soon and we wish you a nice and safe trip to Monterrey.

Ali, Arne, Mark, Pablo and Viktor,

TSG-6 Organizing Team members

Questions that might be addressed

Our group will continue the study of the topic undertaken by TSG-4 at the ICME-10 in Copenhagen. We are going to follow up main issues identified and discussed by the group (http://www.icme10.dk/ ,(look for Topic Study Group 4) :

Characteristics of giftedness and how such students can be identified.
Having identified the group of gifted students, it is now necessary to consider how such students should be met both inside and outside of the classroom.
Considering are materials that was presented to gifted students, and discussed in particular, technology that might be of use.
Specific examples of problems and investigations.

Further, this group may consider:

a) Literature on the subject of mathematically gifted students? (We welcome survey articles on the subject).

b) Who is a mathematically talented student? What are her or his characteristics? What are the differences between the terms “mathematically gifted, mathematically promising, mathematically talented, mathematically able, mathematical genius, and others used by researchers and practicioners? How does it vary from one country to another?

(c) How can we identify them? What are the ways to search for mathematically gifted students at different ages and settings?

(d) How do we deal with students and kids who think they are (or their family think they are) mathematically gifted, but they are not according to identification criteria?

(e) What is the societal phenomenon of overreacting to mathematically gifted student and how it may affect the life and the future of these students?

(f) How do mathematically gifted students work with mathematics ? What are their strengths and weaknesses on the subject? What are their attitudes and performances? How should we take all this into account in our teaching and assessment practices?

(g) What are special needs for mathematically gifted students (additional trainings, their school and everyday life experiences, their works at home, participation in extracurricular activities such as problem solving, mathematics clubs, mathematics houses, competitions, etc?)

(h) What educational systems should do in order to meet the needs of mathematically gifted? What are the (positive or negative) effects of curriculum as well as its implementation in practice inside or outside school on the development of mathematically gifted students?

(i) How should we teach mathematically gifted students (at different levels) and provide extra curriculum activities for them? How can we as educators or teachers help them to be more creative?

(j) How should we prepare teachers to work with mathematically gifted students?

(k) What are the challenges for gifted students and their mentors and how these challenges can be addressed?

(l) What is the future of a mathematically gifted students and how to help them realize their potential?

(m) What are the resources on the subject? What role may technology play in providing additional resources for mathematically gifted?

(n) Other subjects not identified by the organizers but useful for further studies on the subject.

How to join the group (Call for papers)

The deadline is now extended: new deadline is January, the 3rd Those wishing to join the study group are requested to submit a paper of between 1500 and 2500 words in length that describes their interest in the topic. This contribution should be sent to each of the five members of the committee no later than January 3, 2008 by e-mail. The organizing group expects to make its selection of participation no later than January 20, 2008.

The final schedule of the study group at ICME 11 is expected to be announced by April 1, 2008, when all the accepted and revised papers are published on the web. We look forward to receive your contributions and kindly ask all researchers who are interested on the subject to share their knowledge and experiences on the subject with other members of the group.

Useful links

www.amt.canberra.edu.au/icmis16.html
ICMI Study 16 on Challenging Mathematics in and beyond the Classroom

Presenters (in alpahbethical order)

Bicknell, Brenda, Massey University, New Zealand b.a.bicknell@massey.ac.nz

Title: Who are the Mathematically Gifted? Student, Parent, and Teacher Perspectives

Abstract:

“This paper reports on student, parent and teacher perspectives of the characteristics of the mathematically gifted. The data are extracted from a two-year qualitative study that examined multiple perspectives, school policy documents and programme provision for 15 mathematically gifted and talented students aged from 10 to 13 years.” To read the full text: http://tsg.icme11.org/document/get/575

Mitchell, Peter, Newcastle upon Tyne, UK pm@meikleriggs.co.uk

Title: Summer School Mathematics

Paper (first paragrpah)

‘For the past four years I have been one of a team gathered in the University of Durham which has mounted a two weeks’ summer school in mathematics. This is one of several such schools run in different locations during the summer holidays for senior high school children (Years 9 to 11 in English schools, corresponding to ages 14 to 16).

The National Academy of Gifted and Talented Youth (NAGTY – http://www.nagty.co.uk) was set up by the UK government in 2002 on an American model as a way of fostering provision for gifted and talented school children.’ To read a full paper:

http://tsg.icme11.org/document/get/579

Pandelieva, Valeria University of Ottawa valeria.pandelieva@sympatico.ca

Title: Mathematical giftedness and the need of Math specialists in elementary grades

Abstract:

“The change of the developed countries to highly technological societies continuously requires that they nurture and use the full potential of mathematically and scientifically talented people. As this is a process that should start early in order to be efficient, the main responsibility of identifying and addressing the specific needs of these people is assigned to public school systems and, in particular, to elementary teachers. In this regard, three significant areas of concern arise and are discussed in this paper: (a) The complexity in identifying mathematically promising and mathematically talented elementary students;(b) The highly responsible and difficult task for elementary teachers to differentiate and serve the mathematically promising students within an inclusive classroom; (c) The need of teachers with specialized training and math knowledge in pre-high school grades. The last one should be considered predominantly as a logical consequence of the first two. The main goal and, hence, the purpose of the paper is to promote understanding of this crucial necessity of math specialists and to advocate for a change in this direction.” To read the full text:

http://tsg.icme11.org/document/get/578

Soifer, Alexander, University of Colorado 1420 Austin Bluffs Pkwy Colorado Springs, CO 809006, USA asoifer@uccs.edu

Title: A QUARTER A CENTURY OF DISCOVERING & INSPIRING YOUNG GIFTED MATHEMATICIANS: All the Best from Colorado Mathematical Olympiad

Paper (first paragraph)

‘I. THE EVENT There are many types of mathematical competitions throughout the world. Some expect participants to merely state “good” answers, others are multiple-choice competitions. Some competitions are oral, and completed in a matter of a couple of hours. Others go on for a week or weeks. Over the past 100+ years throughout the world, the word “Olympiad” came to mean the particular type of competition where complete essays-solutions are expected for every problem and an adequate time is offered for solving them. The First Colorado Springs Mathematical Olympiad took place 25 years ago, on April 27, 1984.’ To read the full paper:

http://tsg.icme11.org/document/get/577

1. Rosario, Héctor Associate Professor Department of Mathematical Sciences University of Puerto Rico, Mayagüez Campus PO Box 9018 Mayagüez, PR 00681 sanskritam@gmail.com

Beautiful Minds Need Able Beholders Preparing Middle School Teachers to Identify and Nurture Mathematical Talent

2. Arne Mogensen Aarhus University College of Education, Denmark Arne.Mogensen@skolekom.dk

The proficiency challenge An action research program on teaching of gifted math students

3. HARVEY B. KEYNES JONATHAN ROGNESS Institute of Technology Center for Educational Programs, University of Minnesota, Vincent Hall 4, 206 Church St. SE, Minneapolis, MN 55455 rogness@math.umn.edu

HISTORICAL PERSPECTIVES ON A PROGRAM FOR MATHEMATICALLY TALENTED STUDENTS

Papers and discussion documents

Activities and programs for students with special needs

Programme

In TSG 7 the presentations and discussions are structured in the following themes: TU 8 1200 – 1300Definition of special needs. Identifying students’ needs and early intervention WE 9 12.00-13.30 The view of minority students. Programmes and activities for visually impaired students FR 11 12.30 – 13.30 Activities and materials for visually and hearing impaired students. SA 12.00 – 13.30 Intervention experiences and results

Tuesday 8 1200 – 1300

Theme: Definitions of special needs Lindenskov, Lena & Vianna, Claudia (2008). How to define special needs and students with special needs in relation to learning mathematics’. Welcome by the Organising team. Danish university School of Education, Aarhus University & Federal University of Rio de Janeiro (UFRJ) One of the tasks to be done in the TSG 7, according to the international committee, is to discuss and formulate a definition of what is meant by ‘students with special needs in relation to learning mathematics’. An overview is given and critically reflected, and a proposal for a systematic definition is presented to be discussed during the four time slots of TSG 7.

Theme: Identifying students’ needs and early intervention Gervasoni, Ann (2008). Insights About Identifying and Assisting Children Who Have Difficulty Learning Mathematics. Australian Catholic University, Ballarat. [ann.gervasoni@acu.edu.au] This paper explores three issues associated with assisting Australian children who have difficulty learning mathematics in regular classrooms. The first issue is how to identify these children. The second issue is the diverse instructional needs of this group of children who have difficulty. The third issue is providing assistance for children. In this regard, this paper describes one approach used in Australian Primary Schools that is based on providing children with a 20 week intervention program conducted by a specialist teacher.

Kotagiri, Tadato (2008). Theory and Practice of Educational Intervention in the Learning of Numbers and Arithmetic Operations by Special Needs Children. University of the Ryukyus, Japan [Kotagiri@edu.u-ryukyu.ac.jp] This is an empirical study of educational intervention for children with learning difficulties regarding numbers and calculations. My research began with such questions as “In what situations and what ways does a child become aware of or discover mathematical ideas?” and “In what situations and what ways does his/her mathematical cognition develop?” To answer these questions, a hypothesis has been made: There can be a way or a set of steps to obtain mathematical concepts and skills. Based on this hypothesis, a remedial form of education has been carried out for children with serious difficulties in learning numbers and calculations. The results of educational intervention suggest answering the hypothesis positively. This study has focused on the skill acquisition phase of the practical education process by the Suido Method, specifically on the cognitive modes, e.g. on real world conditions, concrete pictures, schematic figures, and mathematical symbols. I call them “Real World,” “World of Models,” “World of Schemas,” and “Mathematical World”, respectively. The hypothesis is that we can set the steps for acquisition of numerical concepts and arithmetic skills. I then have conducted remedial education for children who experience severe difficulties with acquiring basic mathematical skills, continuously observing their aptitude for basic mathematical skills over a period of several years (Kotagiri 1993, 1999, 2002). The children being studied in this research are considered slow learners, developmentally disabled children including those with global-type learning disabilities, children who have suffered physical brain damage due to high fever and/or cardiac arrest stemming from meningitis, hydrocephalus, etc., and children afflicted by mental disabilities such as mentally retarded children or those with Down syndrome. One can consider that the above hypothesis has been validated or is in the process of being validated. Of course, many children with special needs may be afflicted by a wide range of disabilities, and I am aware that they may not all be covered.

Dalvang, Tone (2008). The compass model – a possible tool for dialogue, reasoning and understanding of situations in which learners experience difficulties in their mathematical education. Forum for mastering mathematics at Sørlandet Centre for Special Needs Education, Agder, Norway. The presentation has four parts: An introduction about the official Norwegian support system in special needs education, and a case concerning a 12 year-old girl presented with learning difficulties in mathematics. The compass model is then applied as a tool for dialogue and reasoning about the present situation, and to make plans for future interventions. In the end purposes of the model are discussed.

Plenary discussion and reflections.

Wednesday 9 12.00-13.30

Theme: The view of minority students. Lange, Troels (2008). Homework and minority students in difficulties with learning mathematics: the influence of public discourse. Aalborg University, Denmark In this paper, I contrast an immigrant 10 year old girl’s perception of her home support and her mathematics teacher’s rather different perception. According to the girl, her big sister who is in Year-10 helps her with her homework in mathematics. However, the teacher believes that she has no support from home. I show how the girl tries to align her perception of her home support with middle class Danish family values, and how the public discourse about immigrants apparently frames the teacher’s perception of the resources that are available or not available to the girl. The analysis becomes an example of how mathematics teaching and learning is embedded in a wider socio-political field. On one hand, the analysis illustrates that the family resources called upon by homework are very differentially available to children with different backgrounds. On the other hand, it suggests that sometimes resources could be available that schools do not see because students are constructed as disadvantaged.

Theme: Programmes and activities for visually impaired students. Vianna, Claudia Segadas– Federal University of Rio de Janeiro (UFRJ); Barbosa, Paula Marcia – Benjamin Constant Institute (IBC); Rocha, Denise Felippe – Brigadeiro Newton Braga School; Silva, Beatriz – student of Federal University of Rio de Janeiro (UFRJ). (2008). Teaching geometry for blind and visually impaired students. Brazil. This research is concerned with the difficulties that blind and visually impaired students face to construct some concepts in geometry and how we can help them to develop these concepts. The focus will be on the teaching of symmetry. Activities were designed and used with lower secondary students from a specialized school for the blind and visually impaired students in Rio de Janeiro – Brazil (Benjamin Constant Institute). Twelve students took part in this research, six were blind and six had low vision, ages varying from twelve to eighteen years old. The same activities were used to a blind student included in a regular school in Rio de Janeiro (Brigadeiro Newton Braga School) This paper describes these activities and students’ reactions to them. The results show how important the previous preparation of materials is in order to help these students to focus on the contents themselves and not in making or understanding drawings.

Kohanova, Iveta (2008). The ways of teaching mathematics to visually impaired students. Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia. In this paper we present overview of actual situation of teaching mathematics to visually impaired students at each level of education (primary, secondary, university) in Slovakia. Problem of accessibility of mathematics to visually impaired students has the solution in linear notation. One of the possibilities to access math is the Lambda editor, which besides the linear notation in Lambda code offers also the graphic visualization for sighted people. Hence in the second part we briefly describe the effort to integrate Lambda editor in to the teaching and study of mathematics, which is an initiative of Support Centre for Visually Impaired Students.The Lambda editor is considered as tool within the material milieu of didactical situation.

Borges, J. A. – Federal University of Rio de Janeiro, BARBOSA, P. M. – Federal University of Rio de Janeiro; JANSEN, L. R. – Universidade Federal Fluminense, LYRIO, S. B. – Universidade Estadual de São Paulo. (2008). DESENVOX – computer tools to teach basic geometry and drawing for the visually disabled in Brazil. Brazil. This paper shows that computer technology is able to assist people who are visually disabled to access and communicate about geometrical information. A computer program, DESENVOX, that allows that blind students can create, edit and print tactile graphics is discussed. It is also shown that for geometrical knowledge to be constructed – which includes the ability to use this computer tool – the students first need some physical experiences with 3D models and Geoboards.

Plenary discussion and reflections.

Friday 11 12.30 – 13.30

Theme: Activities and materials for visually and hearing impaired students. Vita, Aida C; Henriques, Afonso; Cazorla, Irene M.; Salazar, Jesus V. Flores (2008) Reflections about the use of the soroban with blind students within the Brazilian school system. Santa Cruz National University, Brazil. In Brazil, the Decree number 1.010 from Ministry of Education instituted Soroban as a calculator tool for visual disability, but its use in primary, secondary and high school teaching is so far to being reality. This paper intends to reflect about this process and from the idea that Soroban can contribute in the learning of Decimal Numerical System-DNS and the four Mathematic Basic operations, not only for blind people, but for every one. In order to understand Soroban utilization as mediation tool for learning we took Rabardel’s instrumentation approach. We hope to raise some research questions and acting strategies witch can contribute in Soroban’s use institutionalization for primary, secondary and high school. Key-words: Special Education, blind students, Soroban, Basic Mathematical Operations.

Movilio-Chacón, Virginia (2008). Mathematics for Students with Special Educational Needs: Touching and Shaping Mathematics with Deaf Students. Special education school for the deaf, Venezuela. Deaf people can come to be understood not as a disability group but as the possessors and protectors of a great cultural heritage, a beautiful language, numerous art forms and an eloquent history. Harlan Lane, 2003 Just before the sixties, W. Stokoe commented with his colleagues at Gaulladet College on the possibility of the existence of a signed language used by deaf students. At the time, this idea was unacceptable to many deaf educators in the United States. According to his personal experience, the deaf students were using routinely a language, which was structurally different from English. As a result of these observations, in 1960 he published an article titled “Sign Language Structure” and in 1965, with the help of two deaf colleagues, the first dictionary of American Sign Language (ASL) (Stokoe, 2004). In Venezuela the education of the deaf and hard of hearing is done within a bilingual context. The deaf must acquire sign language at the earliest possible time as a first language then afterwards learn how to use written Spanish in order to guarantee their integration into the subsequent educational levels (Oviedo, 2000). Venezuelan Sign Language and, in general, Spanish-American sign languages, have very few signs for mathematical concepts, terms and procedures (Larreal, 2006), so that frequently teachers must create or coin specific signs in order to teach Mathematics to Deaf students. In this paper, we present some experiences in the creation of approximately 250 signs for mathematics. The experience began in 2003 with high school students whose ages ranged from 13 to 26 years, and was developed within the framework of constructivist learning principles at the special education school for the deaf at Maturín, Monagas, in eastern Venezuela. The creation process is developed during class with the help of the math teacher who is also a sign language interpreter. When there is a lack of signs in the mathematical subject studied, new signs are coined in a collaborative process with the active participation of the Deaf students.

Madiha, Hassan Mohamed. (2008). The Effectiveness of a suggested Program in Mathematics to develop the visual thinking of deaf pupils in third grade. Beni Suif University, Egypt. The present research aims at designing a suggested program in mathematics to develop the visual thinking of deaf pupils. The research reviews theoretical studies, develops a Pilot Program, carry out a pilot study for this program on a small sample of deaf pupils, and then modify the program. The effectiveness of this program is measured after applying the program with third grade pupils on elementary stage. This program consists of 69 visual activities related to the basic mathematical concepts, which the deaf pupils are studying in third grade. The quantitative analysis of the results of the program shows the effectiveness of the program to develop the visual thinking for the sample of the deaf pupils. The results also indicated that there are no significant differences between males and females in their visual thinking after the implementation of the program. On the background of the pilot program recommendations are made for programs and textbooks in Egypt.

Plenary discussion and reflections.

Saturday 12 12.00 – 13.30

Theme: Intervention experiences and results Dowker, Ann. (2008). Individualized interventions for children with arithmetical difficulties. University of Oxford, Great Britain. This talk will discuss findings with regard to the incidence of mathematical difficulties; and their common characteristics. It will discuss the important fact that arithmetical ability is not a single entity, but is made up of many components; and therefore arithmetical difficulties are varied and heterogenous. It will discuss their relationships to other abilities: i.e. general cognitive abilities, language, reading and spatial abilities. It will then discuss some of the methods of intervention that have been used over the years,with a focus on individualized interventions, that target children’s specific strengths and weaknesses. Some forms of individualized, component-based techniques of assessing and remediating mathematical difficulties have been in existence for over 60 years (e.g. Buswell and John, 1927; Williams and Whitaker, 1937; Tilton, 1947). However, they have not been in frequent use until recently. Recent programs such as Wright et al’s (2000) Mathematics Recovery program will be discussed, and the talk will conclude with a discussion of my Numeracy Recovery program, now undergoing further development as Catch Up in Numeracy.

Pearn, Catherine. (2008). Mathematics Intervention: The importance of building on success. School of Education – The University of Melbourne, Australia. An Australian national plan requires education authorities to support teachers to identify students not achieving adequate literacy and numeracy skills and to provide early intervention for these students. One such intervention program, Mathematics Intervention, aims to identify and assist, students in Year 1 at risk of not coping with the mathematics curriculum. The program incorporates mathematical activities and strategies based on recent research about student’s early arithmetical learning (Steffe, von Glasersfeld, Richards & Cobb, 1983; Wright, 1991) and about the types of strategies used by students to demonstrate their mathematical knowledge (Gray & Tall, 1994). Mathematics Intervention features elements of both Reading Recovery (Clay, 1987) and Mathematics Recovery (Wright, 1991) and offers students the chance to experience success in mathematics by developing the basic concepts of number upon which they build their understanding of mathematics. The author continues to refine the assessment instruments designed to identify students mathematically “at risk” and support attempts to provide the most appropriate programs for students mathematically ‘at risk’.

Plenary discussion and reflections: What did we achieve? Which next steps are relevant?

Aims, Scope and Goals

Activities and programs for students with special needs

The topic in TSG 7 is of growing importance as skills, knowledge, sense-making, and competences which include mathematics have been seen as relevant for all people. Furthermore policies in several countries stress that all children should be offered opportunities to engage in mathematics in broad and rich ways. Fortunately, more emphasis is at the same time put on the topic both in different kinds of educational practice and in different branches of research as well. Moreover, reviews and edited books are produced more frequently than before, with contributions from mathematics educators as well as from other sorts of professionals. Still a lot of issues are unsolved, and still the awareness towards the topic lies far behind similar awareness regarding reading and literacy. The topic cries for focused exchange of ideas, viewpoints, and experiences, and for common discussion and reflection on questions like:

1.How are special needs in mathematics defined and delimited from other phenomena?

2.What are the characteristics of students with special needs in mathematics and how can such students be identified?

3.What kinds of early identification exist around the world and with which means?

4.What kinds of intervention projects take place around the world and with which means

5.Which activities seem to give promising results, and which do not?

6.Which kinds of programs are offered: mathematics content and organization for which groups of students by which groups of teachers?

7.How can you support maintaining and developing students’ creativity and optimistic attitudes towards mathematics learning in students with special needs?

8.Which identifications, activities and programs for adolescent and adult students with special needs exist and with which results?

9.Which are the available, high quality reviews and edited books to be recommended?

10.With which kinds of theoretical positions are background and characteristics of special needs in mathematics approached, as for instance from psychology, neuro-biology, sociology, and education?

11.How are the qualifications and competences of people working in research and practice?

12.Which voices are being heard in practice and in research on students with special needs?

The Organizing Team of TSG 7 is in close contact with the TSG 6: Activities and programs for gifted students in order to possible exchange viewpoints on the concept of creativity for gifted and special needs students.

Abstracts and papers requirements

The Organizing Team of TSG 7 was inviting the submission of papers for presentation and distribution at ICME-11. The TSG has been allocated four sessions during the conference. The sessions will include invited speakers and papers selected through the submission procedures described here.

Papers may be proposed for two formats: • oral presentation; • presentation-by-distribution in the TSG, without an oral presentation but with a time slot for discussion. For either format, proposals include an abstract (up to 1,000 words plus references), which have been read by the referees. Abstracts reporting research findings should contain a description of the aim of the presentation, background, methods, results, and conclusions. Abstracts reporting theoretical analyses should state clearly why the issue is important, what evidence supports the claims made, and what the implications are for students with special needs in mathematics. Abstracts reporting activities and programs should describe these clearly and concisely and provide some evidence to show that these have been successfully implemented and what kinds of outcome have been documented. Authors should indicate for which format the paper is proposed: • oral presentation; • presentation-by-distribution in the TSG. When making this choice, authors should consider which medium is best for their presentation. Many of us do not have English as a first language and feel more comfortable with a written than an oral presentation.

Authors of accepted abstracts proposals have been invited to submit full papers (length 4 to 12 pages).

Those who submitted abstracts and papers have been required to fill in and send a form with their data and specific interests and experiences by clicking at http://www.inquisiteasp.dk/cgi-bin/qwebcorporate.cgi?idx=VR6K5H

The closing date for abstracts was March 15st, 2008 sent to Lena Lindenskov and Claudia Segadas Vianna (lenali@dpu.dk and claudia@im.ufrj.br)

Deadline for decision was April the 8th.

Deadline for full paper (of a length between 4 and 12 pages) was May the 2nd.

After reviewing and adaptations all the accepted papers are made available here on the TSG 7 website. Also one paper is accepted for distribution of paper copies.

The list of invited speakers with their titles and the detailed program for the two one-hour and two ninety-minute sessions in the congress timetable at the disposal of TSG 7 is also avaiable here at the website.

Looking forward meeting you in Monterrey, Lena Lindenskov and Claudia Segadas Vianna

Papers and discussion documents

Adult mathematics education

Aims and focus

TSG 8 brings together Congress participants who are interested in presentations and discussions of important new trends and developments in research and practice in adult mathematics education.

The Study Group encompasses all mathematics and numeracy education undertaken by adults for the purposes of personal, social, political or economic development, and as a course of study in its own right, or in support of learning another subject, developing a skill or furthering an activity.

‘Adult’ is interpreted as referring to people who start, resume or continue their education in formal, informal or non-formal settings, beyond the normal age of schooling in their societies.

The TSG 8 sessions will include presentations and discussions of important new trends and developments in research or practice in adult mathematics education. They will provide both an overview of the current state-of-the-art in adult mathematics education, and expositions of significant recent contributions to the field, as seen from our various international perspectives.

Call for papers

Invitation

The TSG 8 Organising Team welcome proposals from all those who are interested in participating in TSG 8. We shall compose the programme based on the proposals we receive, subject to final approval by the IPC of ICME-11.

Proposals for Papers should be in English and have the following content:

• name(s) and title(s) of the author(s)

• institution, address, country, email, phone, fax (with international dial code)

• title of presentation

• abstract with up to four references (maximum 500 words)

Proposals should be sent to the Chairs of the TSG 8 Organising Team. All proposals we receive will be acknowledged with thanks. All members of the Organising Team are willing to give informal advice to anyone preparing a proposal. Our addresses are listed below.

Proposals must reach the Organising Team by 30 November, 2007.

Proposers will be informed of the Organising Team’s decision by 18 January, 2008.

The deadline for the Organising Team to receive a full paper is 14 March, 2008.

Organisation and presentation

All proposals received by the due date (see above) will be reviewed by the Organising Team, leading to one of the following outcomes:

(a) The proposal is accepted for the full paper to be published on the TSG 8 website before the Congress, plus ‘hard-copy’ distribution during the TSG 8 meetings (if desired, this may be done by the contributor) – this is the normal outcome for successful proposals;

(b) The proposal is accepted as a 20-minute oral presentation in TSG 8 during the Congress – the outcome for a small subset of the proposals accepted;

(d) The proposal is rejected.

The group will meet for four sessions (two one-hour and two ninety-minute sessions) in the Congress timetable. TSG 8 participants are expected to stay with their group throughout the four sessions. These will be organised by the Organising Team so as to maximise focus, discussion and participation. Parallel sessions may be used.

All papers accepted will be published on the TSG 8 website before the Congress.

The Organising Team intend to edit a special issue of an international peer reviewed journal with selected papers accepted for TSG 8.

Please consult the ICME-11/TSG 8 website, which will be updated continuously and will include background papers.

We look forward to hearing from you!

The TSG 8 Organising Team

Papers and discussion documents

Mathematics education in and for work

Call for papers

Mathematics education in and for work

This TSG will focus on two issues which, although intimately related, we will consider separately (to start with!). First, what mathematics exists in work? (or alternatively, How do people use mathematics and mathematical thinking in their work? This question has many sub-questions including: What are the methodological difficulties of identifying mathematics in work? How can we characterise mathematics in work, when it typically looks so very different from the mathematics that is taught in schools and universities? How explicit are the requirements for mathematics for work, and how do they vary across work contexts? How do employers determine whether or not prospective employees have the mathematical skills required for a specific position? How does the mathematics required in work relate to the nature of the workplace, its demographics?

The second issue focuses on mathematics for work. That is, what mathematics should be taught in order to prepare individuals and communities for work? Again, numerous sub-questions arise, including: Who needs what kinds of mathematics in workplaces? Who is or should be responsible for teaching mathematics for work? What is the relation between current mathematical content as taught in schools and colleges, and the mathematics required for work? What teaching/learning strategies should be incorporated into mathematics classes to prepare future workers for the ways in which they will be expected to function in the workplace (this might include group work and developing skills needed to find and use resources in workplace-related problem solving)?

We would like our sessions to be open, inclusive, and productive. In order to achieve this, we now call upon potential contributors to let us have an abstract of their proposal of no more than one page. This might be a potential paper, a ‘position statement’, an outline of a current or completed research project or simply a provocative comment on one or both of the themes (or a related theme).

The closing date for abstracts is March 1^st, 2008. Please send your proposal to Richard Noss and Susan Forman (r.noss@ioe.ac.uk and sforman2@nyc.rr.com) including the ‘front page’ below.

ABSTRACT

Name(s): Institution: Country: Email: URL

Title of proposal:

Nature of proposal (i.e. project report, research, policy initiative, comment etc.)

One sentence summary:

Proposals by

Erhan Bingolbali, Fatih Ozmantar, Hatice Akkoc – Turkey

Helen Burn – USA

Celia Hoyles, Richard Phillip Kent – England and Arthur Bakker – Netherlands

Nirmala Naresh – India and Norma Presmeg – USA

Hamsa Venkat and Mellony Graven – South Africa

Papers and discussion documents

Venkat (35.00 KB)
Hoyles,Noss,Kent&Bakker (33.00 KB)
Helen Burn (36.00 KB)
Naresh & Presmeg (31.00 KB)
Bingolbali Ozmantar& Akkoc (32.00 KB)
Gomes & Frant (24.00 KB)
Romo Vázquez (30.00 KB)
van der Kooij (43.00 KB)

Research and development in the teaching and learning of number systems and arithmetic

Aims and focus

The purpose of this group is to gather congress participants who are interested in research and development in the teaching and learning of number systems and arithmetic, including operations in the number systems, ratio and proportion, rational numbers. Any current issue related to the main theme of TSG 10 may be considered in discussion. Examples of such issues are the development of ‘number sense’ in students, the role of contexts and models in teaching and learning about number and arithmetic, and the development of teaching/learning units that connect basic arithmetic skills with higher order thinking skills. From an international perspective, we will study and discuss advances in research and practice, new trends, and the state-of-the-art. The focus is all levels from primary through tertiary level.

TSG participants are expected to stay with their group throughout the four sessions. We find this very important if the group is to be able to exchange experience, built networks as well as form collaborations for future research.

Programme

Tuesday, July 8. 12:00-13:00

Session 1: Key note speakers: “State-of-the-art”. Session Chair: Dirk de Bock

(1) Dr. Zalman Usiskin, Professor of Education, University of Chicago, USA: The Arithmetic Curriculum and the Real World

Abstract: The relationships between abstract arithmetic and the real world are dealt with inconsistently in most curricula. Each of the common arithmetic operations is a mathematical model for counting and measure situations found in the real world. These models parallel the theoretical properties of the operations and provide the basis for more sophisticated models found in algebra, geometry, analysis, and statistics. The absence of explicit instruction in these models may explain why many children have difficulty applying arithmetic.

(2) Dr. Darcy Hallett, Assistant Professor, Memorial University, Canada: Effects of Fraction Situations and Individual Differences: A Review of Recent Research Regarding Children’s Understanding of Fractions

Abstract: The goal of this paper is to provide a review of the recent and promising research regarding children’s ability to work with fractions. I have chosen to focus on fractions because many researchers have claimed that children have especial difficulty in learning them. Streefland (1991) has even stated that fractions are “without doubt the most problematic area in mathematics education” (p. 6).

Wednesday, July 9. 12:00-13:30

Session 2: Short oral paper presentations. Session Chair: Bernardo Gómez

Theme: Multiplication, division, fraction

(1) Susanne Prediger: Discontinuities for Mental Models: A Source for Difficulties with the Multiplication of Fractions

Abstract: Different theoretical approaches offer different ways of explaining students’ welldocumented difficulties with arithmetical operations like multiplication of fractions. The article recalls a conceptual framework that integrates approaches focusing on meanings of operations into conceptual change approaches. It offers first results from an empirical study on discontinuities and continuities of models for the multiplication of fractions.

(2) Rose Elaine Carbone & Patricia T. Eaton: Prospective Teachers’ Knowledge of Addition and Division of Fractions

Abstract: This study reports the initial findings of two collaborating mathematics educators from the United States and Northern Ireland on their prospective elementary teachers’ understanding of rational numbers. Prospective elementary teachers were evaluated on their ability to create appropriate real life problems illustrating the addition and division of fractions. The similarity of the misunderstandings that these prospective teachers exhibited offers ways for mathematics educators to inform and improve their teaching. This research also expands international collaborations.

(3) Marta Elena Valdemoros: Planning Fraction Lessons: A Case Study

Abstract: We are doing a case study with three basic education teachers who have joined a master degree focused on a professional strengthening of their teaching experience. In the current research phase we explore how they plan activities for teaching fractions and what kind of difficulties they confront in such planning. In this document we will only make reference to the case of Delia, a fifth grade teacher at an elementary school who has decided to plan her fraction lessons relying on the meaning of measure as the planning’s didactic object. This case study has been done from two fundamental methodological instruments: the observation that took place at a master degree seminar (where the activities proposed by Delia for teaching fractions as a measure were presented) and the interviews, where the aforementioned teacher reflected about the obstacles she experienced through the didactic design process.

(4) Wim van Dooren; Dirk De Bock; Marleen Evers & Lieven Verschaffel: The Role of Number Structures on Pupils’ Over-Use of Linearity in Missing-Value Problems

Abstract: This study builds on previous research showing that primary school pupils over-rely on proportional methods when solving non-proportional missing-value word problems. It is hypothesized that when the numbers in word problems form integer ratios, this will stimulate pupils to apply proportional methods, even if this is inappropriate. It is furthermore expected that the effect will diminish from grade 4 to 6 (with pupils’ age and proportional reasoning experience). The results confirm both hypotheses.

(5) Fátima Mendes & Elvira Ferreira: Developing Multiplication

Abstract: The research project “Developing number sense: curricular demands and perspectives” 1 studies the development of number sense in children from 5 to 11 years old. The project team included classroom teachers and researchers that developed and experimented tasks and task chain that intended to foster number sense. This paper focuses on one of the project case studies. This case study analyses the implementation in a 2nd grade class (7-8 years old) of a task chain related with multiplication. We will center the discussion on the strategies used by children in one particular task.

(6) Issic K. C. Leung; Cho Paul & Regina M. F. Wong: Learning Alternate Division Algorithm in Enhancing the concept of Rates and Density

Abstract: The traditional long division algorithm assumes that users can apply a guess-andmatch type mental process of searching for a maximum that is not greater than the dividend at the initial stage of this algorithm. This optimization process requires heavy cognitive load on metal calculation on applying rules and regulations that does not correlate to life experience of sharing objects. By introducing the special method of learning the concept of division, the Partition of Quotient (POQ), we find that it can enhance the effectiveness of learning the concept of rate in science, in particular, the concept and property of density of an object.

Friday, July 11. 12:30-13:30

Session 3: Short oral paper presentations. Session Chair: Chun Chor Litwin Cheng

Theme: Addition and integers

(1) Bny Rosmah Hj. Badarudin & Madihah Khalid: Using the Jar Model to Improve Students’ Understanding of Operations on Integers

Abstract: The focus of this paper is to report on a study that assess students’ knowledge and understanding of integers before and after the intervention teaching using the ‘jar model’. The paper will concentrate on the kind of errors students make in learning integers and how the ‘jar model’ was supposed to enhance students’ understanding instead of memorising rules like ‘negative times negative gives positive’ etc. Analyses from interviews and performance data of the pre and postintervention stage revealed that most of the students can understand the jar model and thus improvement can be seen from the result of the post-test.

(2) Patricia Baggett & Andrzej Ehrenfeucht: A New Algorithm for Column Addition

Abstract: We show a modern version of an old “dot algorithm” for column addition of whole numbers and decimals. This new “dot” algorithm is at least as efficient as the “standard” written algorithm currently taught in schools, but has 2 advantages: It is easier to use, especially for adding more than two numbers; and it is not “mechanical”. Users can develop their own strategies based on patterns of digits in 1 column, making computation faster and easier. This makes the new algorithm more challenging and interesting. Theoretical underpinnings of the algorithm, historical data, and comments of people who have already learned it will be given.

(3) Mária Slavíčková: Experimental Teaching of the Integers by Using Computers

Abstract: This paper deals with using computer on the mathematical lessons. It is focused on the teaching of the integers by simple program based on the Theory of Constructivism. We provide an experiment in 3 classes and compare their results. There were no significant difference between them, but we find important result – pupils, which use educational software based on the theory of constructivism have better results in context tasks than the pupils, which do not use this kind of software.

(4) Raisa Guberman: A Framework for Characterizing the Development of Arithmetical Thinking

Abstract: Based on a previous study and the Van Hiele Model about levels of geometrical thinking development, I propose a framework for characterizing the development of arithmetical thinking. The framework is based on the profile of students’ reasoning and explanations of arithmetical activities. Data were collected from 190 questionnaires. The quantitative analysis of the results of the questionnaires included calculations of the relative frequencies of levels of arithmetical thinking in the population surveyed. What is outlined in the present paper may provide a possible tool to be used by mathematics teachers.

Saturday, July 12. 12:00-13:30

Session 4: Short oral presentations by the TSG 10 team members. Session Chair: Bettina Dahl Søndergaard

The members of the organizational team of TSG 10 present their point of view on important issues for further research in the field of TSG 10 or reflections on the issues related to TSG 10. This is followed by a general discussion with the audience.

(1) Dirk De Bock: Operations in the number systems: Towards a modelling perspective

Abstract: Elementary mathematics education often focuses one-sidedly on the technically correct and fluent execution of basic operations like addition, multiplication, and direct and inverse proportionality. As a drawback, children tend to perform these operations also beyond their proper range of applicability. In this discussion paper we first provide some research-based illustrations of this phenomenon. Second, we formulate some recommendations for the improvement of educational practice by bringing the modelling perspective more to the forefront of mathematics education.

(2) Bettina Dahl Søndergaard: A Brick in the Wall of Mathematics Education Research in Number Systems and Arithmetic

Abstract: This paper reflects on the state of the research and development of teaching and learning of number systems and arithmetic. This includes a discussion of the descriptive/ explanatory and normative dimensions of mathematics education research in relation to the ten papers in the proceeding. I also refer to an example of a normative statement about standard algorithms in Danish primary education. I conclude that we have reached far but we are not finished yet.

(3) Bernardo Gómez: Models, Main Problem in TSG10

Abstract: The models are present in several of the contributions from the TSG10, who are concerned about the difficulties presented in teaching and learning fractions. Some of the difficulties are related to the generalisation of multiplying and dividing operations. In this study, the alternative historical approaches to tackle this generalisation are analysed. In one of them, connections are sought between models of operations with natural numbers and those with fractions, in order to facilitate the conceptual change, and in the other this conceptual change is avoided.

(4) Chun Chor Litwin Cheng: Concepts Acquisition in Addition and Place Value (ICME-11 TSG10)

Abstract: The concept of place value and addition are presented in several of the contributions in TSG10, and the learning difficulties and possible concepts formation in learning addition are addressed. Many researches showed that children’s learning experience in addition is not as easy is we thought. Most of the time, we teach addition according to textbook material and many textbooks are algorithm-teaching based. Algorithm teaching resulted in systematic error and lack of focus on the development of place value, which hindered children to understand algorithm in multi-digits addition. Also, the representation used in carrying in addition does not relate to the concept of place value or addition. In this paper, the process of addition learning and formation of place value is analysed.

Papers and discussion documents

Valdemoros presentation (1.00 MB)
Mendes presentation (910.00 KB)
Leung presentation (2.00 MB)
De Bock presentation (410.00 KB)
Cho presentation (4.00 MB)
Carbone presentation (7.00 MB)
Slavickova presentation (888.00 KB)
Baggett & Ehrenfeucht presentation (791.00 KB)
Khalid presentation (447.00 KB)
Guberman presentation (847.00 KB)
Usiskin key note presentation (84.00 KB)
Hallett key note presentation (1.00 MB)
Prediger presentation (169.00 KB)
Download the proceeding as pdf here. A few copies of the paperback edition of the Proceedings of TSG10 (book of 150 pages) are still available for the price of 10 euro/book. For more information or for buying a copy, please contact Dirk De Bock, dirk.debo (2.00 MB)
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Picture 1 - all pictures are taken by Bernardo Gomes (912.00 KB)

Research and Development in the Teaching and Learning of Algebra

Focus and outcomes

Focus questions

Within the framework set out above we would like to consider the following questions:

Can algebraic notation and reasoning take on a ‘life of its own’, by the end of secondary schooling, if we introduce young learners to algebra as a means for summarizing observed patterns and making empirical generalizations?
What does research tell us about (the early introduction of) algebraic notation?
How does one shift from using algebra (a) to express mathematical relationships (especially with regard to extra-mathematical phenomena) and (b)to derive additional expressions?

Outcomes

Deeper shared understanding of the Topic Questions, new methodologies (approaches and methods and how they shape the work) as well as emerging knowledge/understanding
Exemplars of research-grounded and research-generative practice
Post-ICME report/publication: a report of the working of the group that will include a subset of accepted papers, as well as overview comments and discussion written by the organizers.

DISCUSSION SESSIONS-Overview

DISCUSSION SESSIONS OVERVIEW

Topic Study Group 11 has a total time of 5 hours to meet during the Congress. The programme and schedules are shown below:

Session	Focus	Issues	Readings
I—Tuesday June 8 12-13 PM	Contexts for learning algebra	Can a) Observing and formulizing rules about patterns b) Making empirical generalizations and c) Thinking about relations among variable quantities provide solid foundations algebra? Or are these likely to lead instruction the wrong direction? What empirical evidence supports your claim(s)?	Dekker, Wijers, van den Zwaart, Spek; Egodawatte; Zhang
II—Wednesday June 9 12-13:30 PM	Early Algebra	What does research tell us about the early introduction of algebraic notation and the syntactic rules of algebra? Does the equals sign in arithmetic mean something fundamentally different from in algebra? Is this necessary or an artifact of limited instruction?	Carraher, Schliemann, & Brizuela; Schliemann, Goodrow,Caddle, Porter & Carraher; Cusi & Malara; Nogeira de Lima; Maranhao
III—Friday June 11 12:30-13:30 PM	Semantics and syntax	How do students shift from using algebra to express extra-mathematical relationships to derive additional statements?	Huang; Martinez; Campos & DeSouza; Groenwald & Becher
IV—Saturday June 12 12-13:30 PM	Special discussion: Puig, Rojano, & Filloy	Within this session Rosamund Sutherland will lead a conversation with Teresa Rojano, Eugenio Filloy and Luis Puig about their recently published book “Educational Algebra”. The focus will be on the question: What is the role of algebraic notation in the development of algebraic understanding? Rojano, Filloy and Puig will also be asked to comment on the main issues that have been raised in the previous sessions of the working group.	Tarp; Linsell; Vieira da Silva

How can I prepare for the discussion sessions?

1-If your name is listed next to one of the discussion sessions, you should: (a) try to prepare some thoughts on how your paper is related to the issues that will be the focus of discussion for that day; (b) Prepare no more than 3 Powerpoint slides to make your points; and© read the papers of the other authors who are listed for that day.

2-If your name is not listed for the session then: (a) read the papers of those whose names ARE listed and (b) think about the relations of those papers (and your own understanding of the research literature) to the issues of the day.

SESSION I- Tuesday: Contexts for Learning Algebra

Time	Focus	Issues	Readings
I—Tuesday June 8 12-13 PM	Contexts for learning algebra	Can (a) Observing and formulizing rules about patterns (b) Making empirical generalizations and (c ) Thinking about relations among variable quantities pave the way for algebra? Or are these likely to lead instruction the wrong direction? What empirical evidence supports your claim(s)?	Zwaart; Egodawatte; Zhang

Authors	Title	Abstract
Dekker, Truus; Wijers, Monica; van der Zwaart, Pieter; Spek, Wim	Learning Lines: From arithmetic to algebra, from elementary towards secondary education	In the Netherlands a discussion is going on about the role of arithmatical and algebraic skills in the ongoing learning lin form primary education to acadamic education and to vocational education. In this line especially the transition from arithmetics to algebra gives interesting possibilities for mantaining and expanding the arithmecal skill in the learning of algebra. The ReAL-project investigated these posibilties and constructed three (of many possible) learning lines from arithmetics to algebra. These learning lines are described in overview in this paper. The learning lines are based on gaps that were found in the most commonly used schoolbooks for mathematics. The gaps were translated into changes for improving the learning of algebra and by doing that giving a constructive role to the maintenance of arithmetic skills in secondary education. This translation resulted in the learning lines mentioned above.
Zhang, Guang-xiang	On Pattern Intuition and Symbol Intuition in Teaching and Learning Algebra	Abstract Geometric intuition is important in mathematical thinking. However, we rely on intuition even when we deal with algebraic problems in which no diagrams are present. Geometric thinking relies heavily on diagrams, and geometric discovery and reasoning arise naturally from intuitional observations. This would appear not to be the case for algebraic operations, which are relatively abstract. Nevertheless, if we investigate the details, we may also find that intuition plays a major role in algebraic reasoning and furthermore that it is an important task for teachers to introduce algebraic concepts and algorithms in intuitionistic ways. Here we put forth the concept of pattern intuition as it applies to algebra and discuss teaching approaches based on pattern intuition. We also provide examples to show the value of pattern intuition in mathematical reasoning.

SESSION II-Wednesday: Early Algebra

Time	Focus	Issues	Readings
II—Wednesday June 9 12-13:30 PM	Early Algebra	What does research tell us about the early introduction of algebraic notation and the syntactic rules of algebra? Does the equals sign in arithmetic mean something fundamentally different from in algebra? Is this necessary or an artifact of limited instruction?	Carraher, Schliemann, & Brizuela; Schliemann, Goodrow, Caddle, Porter & Carraher; Cusi & Malara; Nogueira de Lima

Authors	Title	Abstract
Carraher, David; Schliemann, Analúcia D.; Brizuela, Bárbara M.	Algebra in Early Mathematics: a Longitudinal Intervention	We report on partial results of a study aimed at introducing algebra in elementary school. We describe the main findings of the longitudinal study for a first cohort of students, from grades 3 to 5, taught by the researchers, and for a second cohort, grades 3 to 4, taught by their regular classroom teachers. The quantitative analysis of the data shows that, throughout the grades, students in the experimental group performed significantly better than the control group on written assessments developed by the research team and on standard measures.
Schliemann, Analúcia D.; Goodrow, A.; Caddle, Mary; Porter, Megan; Carraher, David	From Functions to Equations in Elementary School	We report on a study aimed at introducing algebra, including equation solving, from grades 3 to 5. We describe how students learn to work with functions and express relationships between quantities in narratives, tables, graphs, and equations, and how they come to understand and work with equations as the setting equal of two functions. Equations were challenging but within reach of participants
Cusi, Annalisa & Malara, Nicolina	Games of interpretation, anticipating thought and coordination between verbal and algebraic register: key-aspects in the analysis of students’ proofs in elementary number theory	This work is part of a wide-ranging long-term project aimed at fostering students’ acquisition of symbol sense through teaching experiments on proof in elementary number theory (ENT). Our aim is to analyze the use and the role of algebraic language in the development of such proofs. In this paper we present the analysis and classification of students’ behaviour in facing the proof of a conjecture while working in small groups. The analysis of students’ protocols was made by reference to the following interpretative-keys: the application of specific conceptual frames, the games of interpretation between different frames, anticipatory thoughts, the use of conversions and treatments and coordination between different registers of representation. Our analysis highlights the incidence of anticipatory thoughts and of the flexibility in the coordination between different frames and different registers of representation in the development of proof in ENT. Moreover our work testifies the effectiveness of the analysis of students’ discussions during small group activities as a methodological instrument to highlight all these aspects.
Nogueira de Lima, Rosana	Procedural embodiment & quadratic equations	In this paper, we present the results of a research study involving 77 14-15 year-old students working with quadratic equations. Data were analysed in the light of a theoretical framework that considers three different worlds of mathematics (Tall, 2004; Lima, 2007). Evidence shows that students give to equations and the solving methods they use meanings related to procedural embodiments (Lima & Tall, 2008), taking symbols as physical entities that can be moved around, “putting them on the other side” of the equation, with the additional magic of, for example, “changing signs”, or “transforming the exponent in a square root” in the case of quadratics. Procedural embodiments may be effective in some cases, but it is necessary to relate them to their underlying mathematical concepts, in order to make it possible for students to relate the meanings they give to equations to the algebraic principles they should be connected.

SESSION III-Friday: Syntax and Semantics

Time	Focus	Issues	Readings
III—Friday June 11 12:30-13:30 PM	Semantics and syntax	How do students shift from using algebra to express extra-mathematical relationships to derive additional statements?	Huang, Cai, & Ye; Martinez; Campos & Giusti De Souza; Groenwald & Becher; Ribeiro

Authors	Title	Abstract
Huang, Rongjin; Cai, Jinfa; Ye, Lijun	Mathematical tasks implementation in the U.S. and Chinese classrooms	This paper investigates the features of classroom instruction in the U.S. and China through examining the cognitive demands of mathematical tasks and the strategies used to implement the tasks. Based on find-grained analysis of 10 consecutive lessons in each of the two countries, we came to the following conclusions: the U.S. and Chinese teachers tried their best to implement high level cognitive demands in the classrooms through effectively demonstrating high level performance, appropriate soliciting and use of students’ answers, and appropriately organized exploratory activities; the Chinese teacher seems to be successful at maintaining a high level when implementing the tasks while the U.S. teacher had some difficulties in doing so.
Martinez, Mara	Integrating Algebra and Proof in High School: The Case of the Calendar Sequence	Previous studies (Friendlander & Hershkowitz, 1997; Harel & Sowder, 1998; Healy & Hoyles, 2000) set the stage for the need to conduct more research in the integration of algebra and proof in the high school curriculum. Given the evidence provided by Barallobres’ (2004) work, my hypothesis is that an integrated approach can provide meaning to students’ learning of both algebra and proof. The goal of this paper is to report on the challenges that students (9th and 10th graders in a public school in Massachusetts, USA) faced in their work with variables and equivalent expressions when engaged in producing and proving conjectures, and how these challenges were overcome. Students worked on problems from the Calendar Sequence, a didactical sequence (Brousseau, 1997) of twenty problems that was engineered (Artigue, 1988, 1994; Douady, 1997) to promote a specific algebraic functioning: the production of new knowledge about a system (Chevallard, 1985, 1989) such as the calendar.
Groenwald, Claudia Lisete Oliveira & Becher, Ednei Luis	The characteristics of the algebraic thinking of school students using first degree equations	This work presents the results of a pilot experiment implementation; with high school students of a public school in Rio Grande do Sul, a Brazilian state, using the SCOMAX system (Student Concept Map Explore), and the first degree equation content. The SCOMAX is a very intelligent system developed by The Educational Technologies group of La Laguna University in agreement with the Curricular Studies of Mathematics Education group of Universidade Luterana do Brasil, in Canoas-Brazil, which aims to model the students’ knowledge, in any knowledge area. The objective of this work was to investigate the characteristics of the algebraic thinking, developed by the Elementary School, in first degree equations, with High School students.
Alessandro Ribeiro	The multimeanings of equation	The present work discusses different meanings that can be given to the notion of equation in teaching and learning of Mathematics and their potentialities in the construction of mathematical knowledge. It is a theoretical work, as it summarizes and amplifies the arguments presented by the author’s doctorate thesis (Ribeiro, 2007). Grounded in the epistemological study developed in such thesis, it is presented, as can be seen from history of Mathematics facts analysis, different ways of understanding equation. Besides, Research studies on the subject have also been analyzed, showing other ways of explaining the notion of equation. The author validates such results with Semiotic Representation Registers Theory (Duval, 1993, 2003). Afterwards, it is presented and discussed possibilities and potentialities that multimeanings of equation approach can bring to Algebra teaching and learning processes. Among the final conclusions it is pointed out the importance of discussing Elementary Education subjects in teacher training courses without doing it as a simple review of mathematics contents. It is also discussed the relevance that the articulation of multimeanings of equation can provide to teacher and students´ conception enlargement on the notion of equation.

SESSION IV-Saturday: Special discussion of Puig, Rojano, & Filloy

Time	Focus	Issues	Readings
IV—Saturday June 12 12-13:30 PM	Special discussion: Puig, Rojano, & Filloy	Within this session Rosamund Sutherland will lead a conversation with Teresa Rojano, Eugenio Filloy and Luis Puig about their recently published book “Educational Algebra”. The focus will be on the question: What is the role of algebraic notation in the development of algebraic understanding? Rojano, Filloy and Puig will also be asked to comment on the main issues that have been raised in the previous sessions of the working group.	Tarp; Linsell; Vieira da Silva

Authors	Title	Abstract
Tarp, Allan	Pastoral algebra deconstructed	Presenting its choices as nature makes modern algebra pastoral, suppressing its natural alternatives. Seeing algebra as pattern seeking violates the original Arabic meaning, reuniting. Insisting that fractions can be added and equations solved in only one way violates the natural way of adding fractions and solving equations. Anti-pastoral grounded research identifying alternatives to choices presented as nature uncovers the natural alternatives by bringing algebra back to its roots, describing the nature of rearranging multiplicity through bundling & stacking.
Linsell, Chris	Exploring Connections Between Numeracy and Algebraic Thinking: Some Current Directions in New Zealand	At present there are initiatives to extend the New Zealand Numeracy Development Projects from number into algebra. This paper describes an approach to linking numeracy with students’ strategies for solving linear equations. Preliminary data from diagnostic interviews with 500 Year 7 to Year 10 students suggests that there is a hierarchy of sophistication of strategies. The most sophisticated strategy that a student is able to use is associated with the stage of numeracy of the student.
Vieira da Silva, Magda	Influence of intuition and analytical thinking on graphic representaton of problem situations	This work aims to report the results of a research carried out with beginners from the Bachelor’s degree (BA) course in Mathematics to verify the most common errors in the graphic representation of problem situations. Different activities were applied to 23 students and each of them involved: 1) graphic representations and intuitive thinking; 2) graphic representation, exploring intuitive and analytical thinking; 3) graphic representation, exploring intuitive and analytical thinking through more complex situations. In general, intuition and analytical thinking were observed for this study. 33.09% of correct answers were obtained from the overall average, in percentage, among the activities. Such figure is considered very low given the fact it refers to real problem situations. It can be noticed that most learners have difficulty in perceiving what is being proposed and, many times, they perceive it, their intuitive thinking is equivocated, preventing them from getting to a correct analytical thinking.

POSTER

Authors	Title
Ibarra Lidia, Formeliano Blanca, Alurralde Florencia, Silvia Baspiñeiro, Graciela Méndez, Mirta Velásquez	Successions stand always, but what about generalization?

Test

Papers and discussion documents

Research and development in the teaching and learning of geometry

Aims and Focus

The Group is concerned with the teaching and learning of geometry from pre-school through college and university teaching, including any type of geometry, like a non-Euclidean geometry, for example. The Group will incorporate short presentations on, and discussions of, important new trends and developments in research or practice, providing an overview of the current state-of-the-art in geometry teaching and learning, and expositions of outstanding recent contributions to it, as seen from international perspectives.

Though any proposals of relevance to the general focus of the group will be considered, we will be particularly interested in theoretical, empirical, or developmental papers related to the following themes:

1. Curriculum studies and new curriculum implementation.
2. Geometry education and the “real world”: geometrisation and applications.
3. Instrumentation: artefacts, such as computers, and the way they are used.
4. Explanation, argumentation and proof in geometry education.
5. Spatial abilities and geometric reasoning about two-dimensional and three-dimensional shapes.
6. Teacher preparation in geometry education.

The issues raised will be considered from the following points of view: historical and epistemological, cognitive and semiotic, educational related to students’ difficulties and related to the design of teaching and curricula.

Call for Contributions

The organizers of the Topic Study Group welcome proposals from both researchers and practitioners and encourage contributions from all countries with different economic contexts and cultural backgrounds. Reflecting the diversity of the contributions is a major concern of the group organizers.

The submitted contributions will be reviewed by the organizing team of the Topic Study Group. The accepted contributions will be published on the ICME website before the congress. During the session, it is expected that the contributors will be available to present and discuss their work with the other group members. Contributors will also be invited to bring copies of accepted papers, including expanded versions.

Submission Guidelines

The first version of submissions can be a short proposal of 3 pages, clearly indicating the aims and the nature of the work, synthesizing its content and results. Authors of accepted submissions will send later a longer version for publication of 7 pages on the Web site of the congress, presenting the aims and the nature of the work, the underlying theoretical frameworks or assumptions, the ways it was carried out or the methods that were used, and provide the results and/or questions coming from the work.

Submissions could report on research work as well as teaching work in classrooms, or on the design of computer environments or of teaching units integrating technology. They also could address theoretical issues by reporting on advances made in the development of theoretical frameworks or approaches.

Sending submissions Submissions in their short form (3pages) or in their final form (7 pages) should be sent by November 30, 2007 as an email attachment to both chairs of the Topic Study Group at the following addresses: Alain KUZNIAK alain.kuzniak@orleans.tours.iufm.fr and Fou‑Lai LIN linfl@math.ntnu.edu.tw

Information about acceptance of the submissions with recommendations for the final version will be available by the end of January. Final versions of accepted submissions should be sent by March 31, 2008.

*Scheme for paper presentation *Final texts should be 7 pages (Times 12, single‑spaced lines) and fit into an outline of 16 cm x 25 cm. Each submission must: ‑ be in .doc or .pdf file ‑ be written in English ‑ have a title (bold, capital, centered, Times 16) ‑ indicate below the title, the name of the author(s), affiliation and country, email address (centered, Times 14) ‑ underline the name of the participating author(s) ‑ include a 200‑word abstract (Times 10) ‑ indicate whether the paper is research or practice oriented ‑ mention the main theme of the presentation (if possible chosen from among the themes listed in the call for contributions).

Papers and discussion documents

Aims and Focus (19.00 KB)
Abstracts and Schedule (92.00 KB)

Research and development in the teaching and learning of probability

Aims and focus of the topic study group

The organizing team:

Carmen	Manfred

Dave	Yingkang

Aims and Focus

Probability and statistics education are relatively new disciplines. Both have only recently been introduced into main stream school curricula in many countries. While application- oriented statistics is undisputed in its relevance, discussion about probability is more ambivalent. When probability is reduced to its classical conception, mainly based on combinatorics or its formal treatment in higher mathematics, it can be seen as irrelevant, and may be abandoned to leave only the statistical element of the stochastics discipline. However, we believe that there are some powerful arguments in favour of a strong role for probability within stochastics curricula:

Sound probabilistic judgements support people’s rational decision-making in important situations, such as medical tests, jury verdicts, investments, assessment, etc.
Equally, reasoning about uncertainty is an important everyday skill. For example, the concepts of risk (not only in financial markets) and reliability impact on our everyday decision-making. Clearly, these concepts are closely related to and dependent upon probability.
Probability is essential in understanding any inferential procedures in statistics.
Probability offers a tool for modelling and “creating” reality. For example, modern physics cannot be formulated without reference to probability concepts.

Thus, the challenge is to teach probability through designing materials and tools that encourage understanding. The focus has to be on creating approaches to probability that are more accessible and motivating, utilising practical applications as appropriate. Pedagogy should embrace schools of thought such as the frequentist and subjective views of probability.

We see the emergence of approaches that promote the visualisation of abstract concepts. Simulation is one such strategy but there are many others. The use of technology also enables a change in emphasis from the technicalities of calculation to conceptual underpinning. At the same time, we recognise the fundamental importance that pedagogy addresses personal attitudes and intuitions in its approach.

With these challenges in mind, we have encouraged in our call papers and presentations at ICME 11 that will help us to share the diversity of endeavours in research on understanding and teaching of randomness, chance and probability. May future teaching take advantage of this exchange, which we expect will initiate new research projects on the teaching and learning of probability.

Call for Papers

We encourage submissions related to the following topics:

Individuals’ corner

Ideas of probability in young children
Students’ understanding and misunderstanding of fundamental probabilistic concepts

Impact of technology

The use of technology for students’ learning of probability
Using software (Fathom, probability explorer, etc.) to study probability and sampling distributions
Special issues in e-learning

Teacher’s corner

Teacher education on the topic of probability
Teachers’ conceptions about teaching probability

Fundamental ideas

The probabilistic idea of random variable – distribution – expectation
The central limit theorem – convergence
Bayes theorem and conditional probability – independence – exchangeability
Probabilistic modelling – a probabilistic look at distributions

Submissions of proposals and papers

Individuals may submit a paper for consideration by the Organizing Team of the Topic Study Group to be accepted for oral presentation in the TSG or as a paper presented by distribution within the group.

Send proposals to Manfred Borovcnik (with the reference “ICME 11 proposal” to filter the mail accordingly).

Format of proposals and papers
Length of proposal: 2 pages plus references; length of final paper: 6-8 pages plus references. Typing should be done according to the formatting template, which you may download from this site. The documents should be delivered in MS-Word (with possibly an extra file in Adobe pdf format for checking the layout). – The layout terms for the final paper are still subject to alterations (there is some discussion within the IPC on common formatting prescriptions for all groups).

Accepted papers will also be published on the website of the conference and on a conference CD. If you do not specify presentation by distribution, we will assume that you wish your paper to be considered for oral presentation. Because only a limited number of papers can be presented orally, you may be asked to accept presentation by distribution. The time for presentation will be limited to 15 minutes; some few talks of general interest may have 30 minutes.

Preliminary time schedule

Short outline/proposal (2 pages)	January 1, 2008
Answer to the authors	January 22 , 2008
Paper Submitted	February 25, 2008
Papers reviewed by the organizing team	March 15, 2008
Final paper submitted and posted on the TSG website	April 13, 2008

Note: Late submissions will be considered, but only for presentation by distribution. Any proposals to be considered for this must be submitted no later than April 15, 2008.

TSG #14: Research and development in the teaching and learning of statistics at ICME-11

More information:	http://tsg.icme11.org/tsg/show/15
Team chairs:
Rolf Biehler (Germany)	biehler@mathematik.uni-kassel.de
Mike Shaughessy (U.S.A.)	mikesh@pdx.edu

Joint ICMI/IASE Study

This conference takes place at the ITESM, Monterrey, June 30 – July 4, 2008 (the week before ICME)

More information:	ICMI/IASE Study
Chair: Carmen Batanero (Spain)	batanero@ugr.es

ELEE: Latin American Statistics Education Meeting
(in Spanish and Portuguese)

This meeting specifically directed to Latin American Statistics Educators takes place at the ITESM, Monterrey, July 4-5, 2008.

More information:	Latin American Statistics Meeting
Cileda Coutinho (Brazil)	cileda@pucsp.br

Programme, papers, and presentations in powerpoint

You find here the schedule of the presentations of this topic study group. By clicking the title, you get the full paper. By clicking the pdf logo, a pdf version of the presentation in powerpoint is opened. This might be useful to get an overview on the key ideas; furthermore, it gives an authentic impression of the group`s work.

Tue, 8th		12.00-13.00
Chair: Yinkang Wu		Issues in Probability Teaching and Learning
Ramesh Kapadia		Chance Encounters – 20 years later Fundamental ideas in teaching probability at school level
Robert Peard		Teaching the Mathematics of Gambling to Reinforce Responsible Attitudes towards Gambling
Seth Ireland & Jane Watson		Concrete to Abstract in a Grade 5/6 Class
Santiago Inzunsa		Probability Calculus and Connections between Empirical and Theoretical Distributions through Computer Simulation
Sofia Anastasiadou & Th. Chadjipantelis		The Role of Representations in the Understanding of Probabilities in Tertiary Education

Wed, 9th		12.00-13.30
Chair: Carmen Batanero		Informal Conceptions
Dor Abrahamson		Bridging Theory: Activities Designed to Support the Grounding of Outcome-Based Combinatorial Analysis in Event-Based Intuitive Judgment – A Case Study
Francesca Chiesi & Caterina Primi		Primary School Children’s and College Students’ Recency Effects in a Gaming Situation
Knut Ole Lysoe		Strengths and Limitations of Informal Conceptions in Introductory Probability Courses for Future Lower Secondary Teachers
Dave Pratt		Shaping the Experience of Young and Naïve Probabilists
Susanne Prediger & Katrin Rolka		Betting As a Pathway to the Law of Large Numbers – Self-Construction of Strategies for Initiating Conceptual Change
Lucia Zapata Cardona		How Do Teachers Deal with the Heuristic of Representativeness?

Fri, 11th		12.30-13.30
Chair: Manfred Borovcnik		Panel discussion: “Fundamental ideas in probability teaching at school level?”
Discussants: Manfred Borovcnik , Ramesh Kapadia , Jane Watson , and Yingkang Wu . More recent trends in school curricula have removed probability at early stages in favour of data analysis techniques. This brings with it a loss of possibilities to prepare a qualitative understanding of probability and related concepts, the possibility to confront children with guided situations with random ingredients where they could get more directed experience necessary to develop their own intuitive strategies for randomness. The panel discussion will focus on the following topics: Relative merits and the potential of probabilistic and data analysis approaches What are fundamental ideas in probability? Which are relevant for teaching? How to extend intuitive strategies of the young students? Approaches to probability (subjectivist, classical, frequentist) Learning environments to engage students actively in the learning

Sat, 12th		12.00-13.30
Chair: Dave Pratt		Conditional probability and Bayes’ theorem
Carmen Díaz & Carmen Batanero		Students’ Biases in Conditional Probability Reasoning
M. Pedro Huerta		On Conditional Probability Problem Solving Research – Structures and Contexts
Veronica Y. Kataoka, e.a.		Probability Teaching in Basic Education in Brazil: Assessment and Intervention
Hugo M. Hernández Trevethan, e.a.		A Practical Approach to Probability in the Context of a Science Fair
Laura Martignon & Stefan Krauss		Hands-on Modelling with Wason Cards and Tinker Cubes: First Steps in Logical and Bayesian Reasoning in Fourth Grade
Ödön Vancsó		A Parallel Discussion of Classical and Bayesian Ways as Introduction to Statistical Inference

The authors come from Europe, USA, Australia and Latin America, the English, the Spanish world, and the “rest” are distributed “evenly”. Some graphs illustrate the variety of approaches in the accepted papers.

Papers and discussion documents

Formatting template and description for writing papers (312.00 KB)

Research and development in the teaching and learning of statistics

Aims and Focus

Statistics education is a growing field of research and development at school and university level. The topic group will focus on presenting and discussing recent research.

Statistics at school level is usually taught in the mathematics classroom in connection with learning probability. Inferential statistics is based on basic understandings of probability. Our topic includes probabilistic aspects in learning statistics, whereas research with a specific focus on learning probability is being discussed TSG 13 of ICME.

We are open to all kinds of relevant research papers, but our specific focus will be on the following topics

Students’ thinking and reasoning about distributions (including variability, comparing distributions)
Students’ making inferences from data (from informal inference to more formal inference, inference from sample to population or process, from data to context, role of models and probability)
Statistical literacy
Role of technology (tools, applets, internet)
Research on teachers and teaching of statistics

Submissions and proposals

Individuals are encouraged to submit a paper for consideration by the Organizing Team to be accepted for oral presentation in the TSG or as a paper presented by distribution within the group.

Please send proposals to Rolf Biehler (biehler@mathematik.uni-kassel.de) AND to Mike Shaughnessy (mikesh@pdx.edu) with the subject ICME 11 proposal. Accepted papers will be published on the website of the conference and on a conference CD. If you do not specify presentation by distribution, we will assume that you wish your paper to be considered for oral presentation. Because only a limited number of papers can be presented orally, you may be asked to accept presentation by distribution. The time for presentation will be limited to 15 minutes; some few talks of general interest may have 30 minutes.

Preliminary schedule

Short outline/proposal (2 pages) — Dec 10, 2007

Answer to the authors — Jan 22, 2008

Paper Submitted —Mar 1, 2008

Papers reviewed by the organizing team — Apr 15, 2008

Final paper submitted and posted on the TSG website — May 15, 2008

Practical information

Length of proposal: 2 pages plus references – Length of final paper: 8 pages including references. Templates with format suggestions will be downloadable from the website.

Long presentation

Influencing Statistical Literacy in the Middle Years of Schooling: The First Year of the StatSmart Project

Rosemary Callingham, University of New England, Australia; Jane M. Watson, University of Tasmania, Australia; Julie Donne, University of Tasmania, Australia

Who will teach them about data? — The responsibility of mathematics and statistics educators to support the integration of data analysis across all subjects

Bill Finzer and Vishakha Parvate, KCP Technologies, Emeryville, CA, USA

Revealing the Notion of Statistical Literacy within the Pisa Results

Karen François, Free University Brussels, Belgium; Carlos Monteiro, Federal University of Pernambuco, Brazil; Stijn Vanhoof, Catholic University Leuven, Belgium

‘Using models and representations in statistical contexts’ as a sub-competency of statistical literacy – Results from three empirical studies

Sebastian Kuntze, Anke Lindmeier, Kristina Reiss, University of Munich, LMU, Germany

Introductory and Intermediate Students’ Understanding and Misunderstanding of P-values and Statistical Significance

Sharon Lane-Getaz, Saint Olaf and Macalester Colleges, USA

Dynamic Technology Scaffolding: A Design Principle with Potential for Supporting Statistical Conceptual Understanding

Sandra R. Madden, Western Michigan University, USA

Building Sampling Concepts for Statistical Inference: a case study

Maxine Pfannkuch, The University of Auckland, New Zealand

Pedagogical content knowledge of a novel teacher: A case from the teaching of graphical representation

Jesús E. Pinto Sosa, University Autónoma of Yucatán, Mexico; María Teresa González Astudillo, University of Salamanca, Spain

Mapping New Statistical Literacies and Iliteracies

Jim Ridgway, James Nicholson and Sean McCusker University of Durham, DH1 1TA, UK

Short presentation

How do students reason about the concepts of sample and population in the context of hypothesis testing?

Birgit Christina Aquilonius, University of Stockholm, Sweden; Mary E Brenner, University of California, Santa Barbara, USA

What about the P in the PPDAC Cycle? An Initial Look at Posing Questions for Statistical Investigation.

Pip Arnold, The University of Auckland, New Zealand

The contribution of statistics in teaching the concept of mathematical function

Irene Cazorla, Universidade Estadual de Santa Cruz, Brazil; Claudia da Silva, Universidade São Judas Tadeu, Brazil; Miriam Utsumi, Universidade de São Paulo, Brazil

Informal Inference: The Science Connection

Tim Erickson, Epistemological Engineering, Oakland, California, USA

Using real data in statistics classrooms – evaluating its effectiveness

Sharleen Forbes, Statistics New Zealand; John Harraway, University of Otago; Rachel Cunnliffe, University of Auckland, New Zealand

Who failed the introductory statistics examination? A study on a sample of psychology students

Silvia Galli, Matteo Ciancaleoni, Francesca Chiesi, Caterina Primi University of Florence, Italy

Conceptions and misconceptions of average: a comparative study between teachers and students

Sandra Magina, Irene Cazorla, Verônica Gitirana and Gilda Guimarães

Teaching and learning of statistics: the project approach

Maria Manuel da Silva Nascimento, Universidade de Trás-os-Montes e Alto Douro, Department of Mathematics, Portugal; José Alexandre dos Santos Vaz Martins, Instituto Politécnico da Guarda, Portugal

How Not to Lose a Student in One Semester: e-Portfolio at the Learning and Teaching Process in Statistics

José Vicente Novegil Souto, Department of Statistics and Operational Research, University of Vigo, España; Bruno C. de Sousa, Department of Mathematics for the Science and Technology, University of Minho, Portugal

Presentation by distribution

Statistics in applied math project development done by Graduate engineering students

Patricia E Balderas Cañas, Universidad Nacional Autónoma de México, Facultad de Ingeniería

Statistics teaching and learning: The New Zealand experience

Frankcom-Burgess Gillian, Senior Lecturer, Faculty of Education

Probability and statistics teaching in brazilian elementary education

Celi Aparecida Espasandin Lopes, Universidade Cruzeiro do Sul – UNICSUL SP – Brazil

Application of item response theory in the attitudes evaluation

Claudette Maria Medeiros Vendramini, Marjorie Cristina Rocha da Silva, Universidade São Francisco, Brazil

Schedule

Monday 7th July
13:00 -14:00 (1 h)

A: Overview/Introduction

B: 2 long presenations:
Finzer & Parvate;
Ridgway & Nicholson

C: short introduction of authors of paper presentation by distribution (all 4 authors are present and bring some copies of papers)

Wednesday 9th July
12:30 -14:00 (1,5 h)

9 short presentations of 8 minutes each:
Aquilonius
Arnold
Cazorla-Silva-Utsumi-Brazil
Erickson
Harraway_Forbes
Galli
Magina-Cazorla-Gitirana-Guimaraes
Nascimento_Martins
Novegil_deSousa

Friday 11th July
12:30 – 13:30 (1 h)

3 long presentations:
Callingham & Watson;
Pinto & Gonzales;
Pfannkuch

Saturday 12th July
12:00 – 13:30 (1.5 h)

A: 4 long presentations:
Kuntze et al;
Francois et al;
Lane-Getaz,
Madden

B: closing

Papers and discussion documents

The papers will soon be available for downloading here.

Research and development in the teaching and learning of discrete mathematics

Discrete mathematics occupy a rather variable place in math education : in some countries, only a very small number of discrete mathematics concepts are taught, except perhaps those related with combinatorics and the basics of number theory. In a few other countries, for example in Hungary (as far as Europe is concerned), there has been a long tradition to introduce graph theory in secondary schools.

The TSG-15 group aims at collecting researches on math education in its aspects pertaining to discrete mathematics : teaching and learning strategies, for students at different levels, and training of teachers. Discrete mathematics can be introduced, either as a mathematical theory, or as a set of tools to solve problems (a graph is a basic and intrinsic modelling tool). For example, mathematical games are often based on problems in discrete mathematics.

The group will try to assess and analyze collectively the state-of-art of curricula in discrete mathematics. This leads to two general and fundamental questions :

- Why and how introduce discrete maths in schools ?

- How can discrete mathematics contribute to make students acquire the fundamental skills involved in defining, modelling and proving, at various levels of knowledge ?

The TSG-15 group will try to focus on short presentations which present original considerations about number theory, discrete geometry, or graph theory, in a didactical point of view, accompanied, wherever possible, by experimental results concerning student productions and the difficulties encountered.

call for papers

The group will be particularly interested in papers related to the following themes :

-number theory at the elementary school level and for pre-service education of teachers,

-combinatorics and graph theory in the current training of junior college teachers,

-the use of the concept of graph in problems which involve defining, modelling and proving,

–the rôle of discrete maths in mathematical games.

Deadlines

The deadline for submissions is the end of January. Information about acceptance of the submissions, with recommendations for the final version(8-10 pages), will be available by the end of February. Final versions should be sent by April, 20th, 2008.

references (to initalizing the discussion...)

Grenier D. (2003) The concept of « induction » in mathematics, Mediterranean Journal For Research in Mathematics Education, vol.2.1, pp.55-64. ed. Gagatsis ; Nicosia Cyprus.

Grenier D., (2002), Different aspects of the concept of induction in school mathematics and discrete mathematics, European Research in Mathematics Education, Klagenfurt, august, 23-27.

Grenier D. (2001), Learning proof and modeling. Inventory of fixtures and new problems. Actes du 9ème International Congress for Mathematics Education,ICME 9, Tokyo, Août 2000.

Zazkis, R., & Campbell, S. R. (Eds.) (2006). Number theory in mathematics education: Perspectives and prospects. In A. H. Schoenfeld (Ed.) Studies in mathematical thinking and learning series. Mahwah, NJ: Lawrence Erlbaum Associates.

Campbell, S. R., & Zazkis, R. (Eds.) (2002). Learning and teaching number theory: Research in cognition and instruction. In C. Maher & R. Speiser (Eds.) Mathematics, learning, and cognition: Research Monograph Series of the Journal of Mathematical Behavior (vol. 2). Westport, CT: Ablex.

Campbell, S. R. (2002). Zeno’s paradox of plurality and proof by contradiction. Mathematical Connections. Series II (1), 3-16.

• Eight others proposals : reviews in progress

•Program

Session 1 : Tuesday,July 8, 12:00-13:00 (60 mn)

Introduction (Jerry Lodder)

Jerry Lodder, Janet BARNETT, Guram BEZHANISHVILI, Hing LEUNG, David PENGELLEY, Desh RANJAN Historical Projects in Discrete Mathematics and Computer Science

QUEK Khiok Seng, TOH Tin Lam, BOEY Kok Leong, TAY Eng Guan and DONG Fengming (Nanyang Technological University, Singapore) Teaching of Discrete Mathematics at Advanced Level in Singapore : Teachers’Perspectives

Ambat VIJAYAKUMAR (Cochin University, India ) Teaching and learning of Discrete mathematics – The Indian scenario

Session 2 : Wednesday,July 9, 12:00-13:30 (90 mn)

Michel SPIRA (Universidade Federal de Minas Gerais, Brazil) The role of the bijection principle on the teaching of combinatorics

Ulrich KORTENKAMP (University of Education Schwäbisch Gmünd, Germany) A technology-based approach to discrete mathematics in the classroom.

Stephan HUBMANN (Dortmund University, Germany) Doing mathematics -authentically and discrete. A perspective for teacher training

Cécile OUVRIER-BUFFET (DIDIREM et Paris 12, France) Discrete mathematics : a mathematical field in itself but also a field on experiments. A case study : displacements on a regular grid

Session 3 : Friday, July 11, 12:30-13:30 (60 mn)

Thierry DANA-PICARD (Jerusalem College of Technology, Israel) Graph isomorphism, matrices and a Computer Algebra System : switching between representations

Léa CARTIER & Julien MONCEL (Joseph Fourier University, Grenoble, France) Learners’ conceptions in different class situations around Königsberg’s bridges problem

Session 4 : Saturday, July 12, 12:00-13:30 (60 mn)

Nicolas GIROUD (Joseph Fourier University, Grenoble, France) Learning experimental approach by a discrete mathematic problem

Denise GRENIER (Institut Fourier and IREM, Grenoble University I, France) Some specific concepts and tools of discrete mathematics

Conclusion (Michel Spira, Jerry Lodder and Denise GRENIER)

Research Situations for classrooms, an example : tiling polyminos, by Maths-à-Modeler-team, University Grenoble 1, France.

Papers and discussion documents

Research and development in the teaching and learning of calculus

Aim and Focus

The aim of the group is to support the improvement of the teaching and learning of Calculus, taking into account differences due to cultural context.

The group will focus on how the traditional Calculus curriculum is being influenced by such phenomena as:

1) Results of research in mathematics education;

2) Recent approaches to mathematics

3) New technological resources; and

4) Several “reform” movements in teaching Calculus.

We hope to encourage reflection and discussion among participants, and, perhaps, disagreement among participants whose views of the discipline are different. We will invite both short talks on a specific domain of research and a sharing of ideas about the teaching-learning interface of Calculus. Among particular questions to be addressed:

• What are the proper objectives of a Calculus course?

• What are the connections between Calculus courses and courses in Precalculus, Mathematical Analysis, Discrete Mathematics and Differential Equations?

• Which conceptions of the content of the Calculus and of its teaching are at the base of teaching experiments?

• How has new technology affected the teaching of Calculus?

• What does “understanding” mean in the Calculus domain?

Call for papers

Any paper that contributes to at least one of the following mathematical educational issues will be considered:

(i) Studies on affect, attitude, or socioepistemological aspects of mathematics education as they relate to teaching and learning of Calculus.

(ii) Cognitive studies that examine students’ mental processes in the doing of mathematics related to Calculus.

(iii) Pedagogical studies at the preuniversity and university level concerning specific mathematical concepts and processes related to Calculus.

(iv) Studies that examine the role that teaching experiments, with or without technology, can play in enhancing the teaching and learning of Calculus topics.

Submissions and proposals

Researchers interested in presenting a paper should send an abstract of length between 500 and 1000 words. The abstracts submitted will be reviewed by the organizing team in order to select those individuals who will make presentations. The abstracts will also be used to help the organizing team to structure the sessions of the presentations. The abstract must be in English or/and Spanish, the main official languages of ICME-11.

Provisional Program

The program of the group’s activities is:

A) One of the four sessions will be in the form of a panel of several invited speakers. These speakers will have the same brief to select and to illustrate what they see as the most dynamical and most pertinent issues currently concerning the theme of this group. The members of the panel will be chosen such that their backgrounds will be as diverse as possible.

B) The others three sessions will be reserved for the presentation of submitted papers. It is envisaged that each speaker will have 20 minutes to deliver a paper (including discussion).

Important dates

Please send your abstract by January 27, 2008 through e-mail to e-mail addresses:

rcantor@cinvestav.mx with copies to chrisraz@sciences.sdsu.edu, yudariah@mel.fs.utm.my, carmen.azcarate@uab.es

Authors will be notified by February 18, 2008 concerning the status of acceptance. All authors whose abstracts have been accepted must complete a full paper by June 1, 2008 to be placed on the official web-site of the ICME-11. Depending on the response, contributed papers may be published in a special issue of a journal or as an edited book.

Papers and discussion documents

01 Alanis (108.00 KB)
02 Arcos_Diaz_Vera (404.00 KB)
03 Baggett_Ehrenfeucht (73.00 KB)
04 Briceno_Cordero (146.00 KB)
05 Castañeda (251.00 KB)
06 Cuesta_Deulofeu_Mendez (178.00 KB)
07 Dray_Edwards_Manogue (85.00 KB)
08 Díaz Moreno (279.00 KB)
09 Frota (166.00 KB)
10 Hernandes_Silva (186.00 KB)
11 Henriques (120.00 KB)
12 Herrera_Preiss_Riera (210.00 KB)
13 Hohenwarter_et_al (399.00 KB)
14 Martínez-Sierra (73.00 KB)
15 Parra_Cordero (131.00 KB)
16 Jeschke_et_al (120.00 KB)
17 Rondero (84.00 KB)
18 Suárez_Cordero (659.00 KB)
19 Tuyub_Cantoral (462.00 KB)
20 Vazquez_Cordero (68.00 KB)
21 Quesada_Renker (112.00 KB)
22 Tarp (139.00 KB)
23_Rondero (77.00 KB)
Accepted papers TSG16 (108.00 KB)
Timetable TSG 16 (74.00 KB)

Research and development in the teaching and learning of advanced mathematical topics

Aims and scope

Educational aspects covering students’ interaction with tertiary level mathematics are vast in number. At this level, the amount of mathematical content and the complexity of concepts spirals; techniques, lines of thinking and mental processes have to be developed either to cope with specific mathematical theory or to generate kinds of argumentation that transverses theories. Also, many general educational frameworks, models or perspectives retain significance at this level, further adding to the plurality of educational angles that can be taken. Despite (or perhaps due) to this diversity, we (the organizing team) have decided not to specialize the range of the material the Group will consider. Our stance is that any researcher working on educational issues on the ‘doing’ of University mathematics should be conversant with the whole gamut of the field, beyond particular personal interests. In this light, we believe that the success of the group’s output will not depend on the output’s cohesion, but rather how it brings out ‘ground – breaking’ material on sundry fronts. To promote this, we plan to include a panel of experienced and open-minded researchers with the agenda to identify issues brought up by recent educational research literature that they deem to be particularly fruitful, and a main speaker to suggest directions that research should undertake in the future. The inclusive manner of the Group’s scope is reflected in the Call for Papers stated below, but we encourage authors to include components in their exposition reflecting relatively novel ideas or approaches. Lastly, we take a slight bias towards educational output that refers to mathematical significance as well as psychological and cognitive aspects. This is partly motivated by the appearance of the term ‘Advanced Mathematical Topics’ in the title of the Group’s subject (in contrast to the more usual term ‘Advanced Mathematical Thinking’), and by our wish that the body of participants will be a mixture of educators and mathematicians with educational interests.

Provisional programme

Monday 7 July 2008 : 13:00 – 14:00

13:00 – 13:05	Ted Eisenberg and Joanna Mamona	Opening
13:05 – 13:15	Johann Engelbrecht	Adding structure to the transition process to advanced mathematical activity
13:15 – 13:30	Pierre Arnoux and Alain Finkel	Using mental imagery processes for teaching mathematics
13:30 – 13:45	Anesa Hosein et al	Mathematical thinking of undergraduate using three types of software
13:45 – 14:00	Deonarain Brijlall and Aneshkumar Maharaj	Applying APOS theory as a theoretical framework for collaborative learning

Wednesday 9 July 2008 : 12:30 – 14:00

Panel discussion

Ed Dubinsky, Derek Holton, Boris Koichu, Jean-Baptiste Lagrange

Friday 11 July 2008 : 12:30 – 13:30

12:30 – 12:45	Annie Selden et al	The interrelation of affect and reasoning in the proving process
12:45 – 13:00	Jean-Ph. Drouhard	Epistemography: How to know what students know and are supposed to know
13:00 – 13:15	Leigh Wood	Graduate capabilities in mathematics: putting high level technical skills into context
13:15 – 13:30	Jae Hee Park	Roles of teacher’s revoicing in inquiry oriented mathematics class: The case of undergraduate differential equations

Saturday 12 July 2008 : 12:00 – 13:30

12:00 – 12:15	Martine de Vleeschouwer	Contribution to the study of duality in Linear Algebra
12:15 – 12:30	Sepideh Stewart and Michael Thomas	Linear Algebra thinking: Embodied, symbolic and formal
12:30 – 12:45	Analia Berge	Students’ perceptions of the property of completeness of the set of real numbers
12:45 – 13:00	Elena Nardi et al	Beyond the ‘formalistic nonsense’: The impact of symbolisation and previously held images on students’ sense -making of formal definitions
13:00 – 13:15	Oleksiy Yevdokimov	Advanced problem solving activities: pro and contra in students’ terra incognita
13:15 – 13:30	Ted Eisenberg and Joanna Mamona	Conclusion

Brief CVs of panelists

Ed Dubinsky

Current professional interests Extension of Piagetian and related theories of learning to the acquisition of abstract concepts in mathematics. Effect of computer experiences in learning abstract mathematics. Cooperative learning in post secondary mathematics education. Development of instructional materials for post-secondary mathematics courses using specific computer experiences based on the theoretical analyses and cooperative learning. Calculus project – Development of a new approach to calculus based on research in learning and using computers, cooperative learning and alternatives to lecturing. Algebra Project – Development of a new approach to abstract algebra based on research in learning and using computers, cooperative learning and alternatives to lecturing. Building a community of researchers in undergraduate mathematics education.

Derek Holton Professor of Mathematics University of Otago, Dunedin, New Zealand

My main interests in mathematics education are bright students and how to help them have a deeper understanding of mathematics. This has led me to look at ideas around problem solving and what mathematics is. In recent years I have become interested in matters relating to tertiary maths education and I am currently spending a great deal of time looking at recruitment and retention issues in undergraduate maths courses (with the ICME 11 Survey Team). In mathematics I have worked with permutation patterns and with cycles and matchings in graphs.

Boris Koichu Senior Lecturer, Mathematics Education Technion – Israel Institute of Technology Haifa, Israel http://edu.technion.ac.il/faculty/bkoichu

My research interests focus on problem solving, with special reference to the issue of transfer of learning, promoting mathematical giftedness and teaching and learning of university mathematics. In relation to advanced mathematical topics, these interests are reflected in the following studies. One study with gifted high school students has explored their heuristic behaviors while looking for new theorems in spatial Euclidian geometry, difference equations and calculus. An on-going research with undergraduate students is aimed at characterizing their conceptual understanding in linear algebra. I am also engaged in a study on incorporating advanced methods of evaluation in mathematics curriculum at pre-university level.

Jean-Baptiste Lagrange Team of Didactics of Didactics (University of Paris 7) and IUFM (University of Reims) http://jb.lagrange.free.fr/site/ Jean-baptiste.Lagrange@univ-reims.fr

My involvement in research and development in the teaching and learning of advanced mathematical topics is at upper secondary level before university. In France, at this level, students have to consolidate their algebraic proficiencies in order to tackle pre-calculus.

The curriculum recommends non formal approaches of calculus concepts, but also that students should be introduced to abstraction and demonstration. It is then not easy to think of the role of algebraic techniques with regard to conceptualization. Rehearsing “rote” techniques certainly does not help, but it is important that students understand the equivalence of expressions and the benefit of algebraic transformations. They should also be able to perform basic transformations without too much difficulty in order to handle problems with inventiveness, intelligence and rigour.

My research group is developing and experimenting a Dynamic Geometry and Computer Algebra tool (Casyopée). This tool can be described as a symbolic calculator of functions and it is also designed to help students deal mathematically with problems of geometrical dependencies (for instance the area of a figure against a length of a segment). We are currently experimenting on a series of lessons with this tool at 11th grade. We prepared specific tasks for helping students to develop algebraic techniques and reflect on these. We expect to learn about the role these development and reflection can play in students’ conceptualisation of advanced notions.

Call for papers

We solicit both theoretical and empirical papers to be presented at the sessions for TSG 17. Any paper that contributes to at least one of the following mathematical educational issues will be considered:

Cognitive studies that examine students’ mental processes in the doing of mathematics (such as in proof, in problem solving and in definition making). Such studies must explain their relevance to ‘advanced thinking’.

Cognitive and pedagogical studies at the tertiary level concerning specific mathematical concepts and theories.

Studies on how an expert’s reflection on the nature of specific mathematical topics leads to the identification of some crucial thinking processes that are imperative for students to master. Such studies preferably would include suggestions about suitable channels of student support in attaining these processes.

(iv) Studies that investigate affect, attitude, and / or socio-epistemological aspects of mathematics education as they relate to Advanced Mathematical Thinking. Also studies on specific approaches towards general teaching at this level are encouraged.

(iv) Studies that examine the role that digital technologies play either in enhancing the teaching and learning of advanced mathematical topics or in how students can mediate unfamiliar mathematical issues on their own.

Researchers that are interested in presenting a paper, should send an abstract of between 500 and 1000 words. The abstracts submitted will be reviewed by the organizing team in order to select those individuals who will make presentations. The abstract must be in English. Please send your abstract by January 20, 2008 through e-mail to both e-mail addresses: eisenbt@013.net and mamona@upatras.gr

Authors will be notified by February 15, 2008 concerning the status of acceptance. Authors whose abstracts have been accepted must complete a full paper by June 1, 2008 to be placed on the official web-site of the ICME-11. Depending on the response, it is hoped that the papers contributed may be published in a special issue of a journal or as an edited book.

Papers and discussion documents

Arnoux and Finkel (Full paper) (321.00 KB)
Berge (Full paper) (74.00 KB)
Engelbrecht (Full paper) (99.00 KB)
Hosein, Aczel, Clow and Richardson (Full paper) (112.00 KB)
Selden, McKee and Selden (Full paper) (79.00 KB)
Stewart and Thomas (Full paper) (2.00 MB)
Vleeschouwer (Full paper) (211.00 KB)
Wood (Full paper) (73.00 KB)
Yevdokimov (Full paper) (295.00 KB)
Nardi, Biza and Iannone (Full paper) (235.00 KB)
Mamona - Downs and Downs (Abstract) (29.00 KB)
Oh Nam Kwon et al (Abstract) (31.00 KB)
Holton (Panellist summary) (111.00 KB)
Koichu (Panellist summary) (20.00 KB)
Lagrange (Panellist summary) (24.00 KB)
Dubinsky (Panellist summary) (24.00 KB)
Drouhard (Full paper) (94.00 KB)
Brijlall and Maharaj (231.00 KB)

Reasoning, proof and proving in mathematics education

Aims and focus

The ICME 11 Topic Study Group on « Reasoning, proof and proving in mathematics education » will serve a dual role: Present an overview of the current state of art in the topic “Reasoning, proof and proving in mathematics education (RPP),” and expositions of outstanding recent contributions to it, as seen from an international perspective Sharing of ongoing work and perspectives

The topic will be considered at all levels – elementary, secondary, university, and teacher knowledge. Participants could report on research work, on classroom teaching, or on the design of teaching environments or of teaching units for RPP. They also could report on advances made in the development of theoretical frameworks or approaches. The work of this TSG will focus on four broad themes.

1) Epistemological / historical aspect

What is the role of RPP in the history of mathematics?
What is the role of RPP in the developmental processes of mathematics as a discipline?
What is the status of RPP in mathematics as an academic subject?
What is the role of experimentation?
To what extent should mathematical proofs in the empirical sciences, such as physics, figure as a theme in mathematics teaching so as to provide an adequate and authentic picture of the role of mathematics in the world?

2) Curriculum and textbook aspect

A description of the status of RPP at school, at different grade levels, and in various countries
International comparison of the above status of RPP among countries
Discussion of the mathematical contexts and developmental progression of RPP in curriculum and textbooks

3) Cognitive aspect

Students’ and teachers’ views or concepts of RPP
Students’ main difficulties in learning RPP
Describing and interpreting students’ behaviors in RPP tasks

4) Teaching aspect

Approaches to the teaching of RPP, at different grade levels, and in various mathematical subject areas
What do teachers need to know for the teaching of RPP?
Design of appropriate teaching interventions to overcome students’ difficulties in coping with RPP tasks
Instructional approaches to RPP that have shown some success
What is the role of dynamic software in the teaching of proof?

Call for contributions

TSG 18 « Reasoning, proof and proving in mathematics education » invites the submission of contributions related to the topic of the group, as described by the questions, problems and issues listed above. The organizers of the Topic Study Group welcome proposals from both researchers and practitioners and encourage contributions from all countries, representing all economic contexts and cultural backgrounds. Reflecting this diversity is a major goal of the TSG 18 organizers.

The submitted contributions will be reviewed by the TSG 18 organizing team. The accepted contributions will be published on the TSG18 website (http://tsg.icme11.org/tsg /show/19) prior to the congress and presented in poster format during the congress sessions of the group. In the poster presentation it is expected that the contributors will be available to discuss and share their work with the other group members. In addition, authors of some papers, to be selected by the organizing team of the TSG, will be invited to have a paper presentation to the whole group, as a focus for collective discussions. All contributors will be invited to bring copies of accepted papers, including expanded versions and CDs, to be presented-by-distribution during the TSG sessions.

If the circumstances make it practical and desirable, the organizing team will publish a conference book as on the work of TSG 18. Should this happen, the editors, editorial process, and content will be the subject of discussion among the TSG 18 organizing team.

Submission specifications

The first version of a submissions can be a short proposal of 3 pages, clearly indicating the aims and the nature of the work, and giving a synopsis of its content and results. Authors of accepted submissions are then invited to send a longer version (8-10 pages) for publication on the Web site of the congress. This published version should present the aims and the nature of the work, the underlying theoretical frameworks or assumptions, the ways it was carried out or the methods that were used, and provide the results and/or questions that arise from the work.

Sending submissions

Initial submissions (3pages) should be sent by December 15, 2007, as an email attachment to both chairs of the Topic Study Group at the following addresses:

Hans Niels Jahnke (Germany)

njahnke@uni-due.de

Hee-chan Lew (Korea)

hclew@knue.ac.kr

Information about acceptance of the initial submissions, with recommendations for the final version(8-10 pages), will be available by the end of January. Final versions of accepted submissions should be sent by March 31, 2008.

Guidelines for publication

Final texts should be 8 pages (Times 12, single-spaced lines) and fit into an outline of 16 cm x 25 cm. Each submission must have a title (bold, capital, centered, Times 16), be in .doc or .pdf file and be written in English. Indicate below the title, the name of the author(s), affiliation and country and email address (centered, Times 14). Underline the name of the participating author(s) and include a 200-word abstract (Times 10). Indicate whether the paper is research or practice oriented and mention the main theme of the presentation (if possible chosen from among the themes listed in the call for contributions).

Links

International Newsletter on the Teaching and the Learning of Mathematical Proof.

Preliminary Program

ICME 11; Topic Study Group 18 Preliminary Program

Session 1: Epistemology (60 minutes)

Maria G. Bartolini Bussi (long presentation 30 minutes): Experimental mathematics and the teaching and learning of proof

Maria C. Cañadas & Encarnación Castro & Enrique Castro (short presentation 10 minutes): An inductive reasoning model in linear and quadratic sequences

Michael Meyer (short presentation 10 minutes): From discoveries to verifications – theoretical framework and inferential analyses of classroom interaction

Margarida Rodrigues (short presentation 10 minutes): Reasoning and proof in classroom (9th grade)

Session 2: The Teaching of Proof (90 minutes)

Hagar Gal & Hee-Chan Lew (long presentation 30 minutes): Is a rectangle A parallelogram? – towards A bypass of van Hiele level 3 decision making

Hagit Sela (short presentation 10 minutes): Coping with tasks that lead to mathematical contradictions with peers

Hector Rosario (short presentation 10 minutes): Puzzles and Proofs: Informal Arguments and the mathematical Mind

Naoyuki Masuda (short presentation 10 minutes): A study of Jogai Toda’s Deductive Method – including the teaching in senior high school

Stefan Ufer & Aiso Heinze (long presentation 30 minutes): The development of geometric proof competency from grade 7 to 9: a longitudinal study

Session 3: Curriculum (60 minutes)

Behiye Ubuz (long presentation 30 minutes): Proof in Elementary Mathematics: A Turkish Perspective

Ildikó Pelczer & Cristian Voica (short presentation 10 minutes): Proof in Romanian high school introductory analysis textbooks – a historical overview

Sharon L. Senk, Denisse R. Thompson & Gwendolyn Johnson (short presentation 10 minutes): Reasoning and Proof in High School Textbooks from the U.S.A

Yi-Yin Ko, Eric Knuth & Haw-Yaw Shy (short presentation 10 minutes): Taiwanese Undergraduates’ Performance Constructing Proofs and Generating Counterexamples in Differentiation

Session 4: The Teaching of Proof (90 minutes)

Andreas J. & Gabriel J. Stylianides (long presentation 30 minutes): Supporting student learning in the area of proof

Kazuhiko Nunokawa & Toshiyuki Fukuzawa (short presentation 10 minutes): Operating on and Understanding of Problem Situations in Proving

Kai-Lin Yang & Li-Wen Wang (short presentation 10 minutes): Propositions Posed under a Proof without its Proposition

John Selden, Annie Selden & Kerry McKee (short presentation 10 minutes): Improving Advanced Students’ Proving Abilities

Takeshi Miyakawa & Patricio Herbst (long presentation 30 minutes): Why some theorems are not proven in geometry class: Conditions and constraints

Papers and discussion documents

Research and development in problem solving in mathematics education

Aims

This Topic Study Group aims to provide a forum for those who are interested in aspects of problem solving research and development at any educational level, to share recent findings or to exchange ideas. It will also provide an opportunity for the general participants to become acquainted with the progress and current issues of the field, as well as its foreseen future directions. A further goal of the organizing team is that the meetings of this TSG should promote communication and instigate collaborations among the participants. That is, the themes and ideas addressed during the development of the sessions will provide the basis to structure a proposal to write a book on the field.

Call for papers

Problem solving is the heart of mathematics. The teaching and learning of problem solving has a long history in mathematics education. Problem solving is an activity, which provides students with opportunities to construct and experience the power of mathematics. It is also an instructional approach, which provides a consistent context for students and teachers to learn and apply mathematics.

The primary focus of this TSG will be to identify and discuss the current status of research and development in problem solving in mathematics education around the world. More specifically the following areas will be explored:

To understand the complex processes involved in mathematical problem solving;
To explore the process in which students learn and make sense of mathematics via problem solving activities, and how can the teacher facilitate this process;
To discuss ways to evaluate problem solving competencies;
To discuss the role of using computational tools in problem solving approaches;
To identify and discuss future directions of problem-solving research and development.

We plan to have round-table discussions, individual presentations, small group presentations and plenary discussions during the development of the sessions. Thus, contributions from individuals who want to present a talk on these themes are particularly welcome.

We solicit papers on any subject relevant to problem solving, but we shall endeavor to place each contribution in one of the following domains.

(a) Foundations of problem solving. Here, we are interested in discussing issues around the principles or tenets that are important in problem solving activities. Questions that can guide the discussion include: What are the main principles or tenets that distinguish a problem solving approach in research and practice? What does it mean to learn mathematics in terms of problem solving activities? What is the role of routine or nonroutine tasks in problem solving approaches? To what extent the practice of development mathematical knowledge is consistent with problem solving approaches? How perspectives like models and modelling or those that emphasize models in general relate to problem solving? To what extent the principles and tenets associated with problem solving have evolved in accordance with the development of computational tools?

(b) Studies in students’ behavior during mathematical problem solving. These will mostly concern with cognitive, metacognitive, social, and affective aspects of problem solving; accessing knowledge effectively and the interaction in collaborative work are of particular interest. Some relevant questions around these themes involve: How students’ problem solving approaches can be characterized? How have problem-solving approaches evolved in terms of research questions and methods? What are the current trends? What theoretical frameworks have been developed in mathematical problem solving? What is a suitable methodology for studying problem solving processes? How should students’ problem solving competencies be evaluated?

(c) Instructional approaches: Learning and teaching in problem solving. What exactly does the student learns from problem solving experiences? Do we wish to be able to teach mathematical facts or even theories through problem solving? Are present teaching practices effective for all purposes? How to tackle some practical problems, e.g. training teachers, extra time that the problem solving seems to involve. Questions related to the issues include; what makes a task a “good” problem? How can a problem be used for teaching mathematical topics? and to what extent should we expect students to pose and solve their own problems? What types of assessment are consistent with problem solving approaches? To what extent, international assessments like PISA or TIMSS actually evaluate problem-solving competencies?

(d) Research and development in problem-solving with ICT technology. The development and availability of computational tools have influenced not only the development of the discipline; but also the way students construct their mathematical knowledge. In this context, we are interested in discussing questions that involve: How can we effectively use technologies (e.g., internet, calculators, computers etc) to facilitate problem solving? How can we effectively use technology to advance problem-solving research? Do computer representations take away some of the initiative from the solver? What types of mathematical reasoning, including mathematical arguments, do students or problem solvers develop as a result of using various computational tools? What types of strategies and problem representations become important in problem solving environments that promote the use of computational tools?

(e) Curriculum proposals and problem solving. Some curriculum frameworks (NCTM, 2000) recognize the relevance of problem solving activities. However, there is still a need to discuss ways in which fundamental tenets associated with problem solving need to be organized to support a particular curriculum. How should a curriculum proposal, that enhances a problem solving approach, be organized or structured? What fundamental mathematical ideas and processes should be central in a proposal that promotes problem-solving approaches?

This Topic Study Group seeks papers dealing with the above issues or any other aspects of problem solving in mathematics education. If you are interested in presenting your papers, please send an abstract of length between 500 and 1000 words. The abstracts submitted will be reviewed by the organizing team in order to select those individuals who will make presentations. The abstracts will also be used to help the organizing team structure sessions of the presentations. The abstract must be in English, the main official language of ICME-11. Please send your abstract by December 15, 2007 through e-mail to all five organizing team members listed below. Mail or fax can be used for sending your abstract to Dr. Manuel Santos or Dr. Yoshinori Shimizu. Individuals will be notified by February 1, 2008 for the status of acceptance. All selected individuals must complete a full paper by June 1, 2008 to be placed on the official web-site of the ICME-11. All papers selected in this way will be acknowledged in the report of this Topic Study Group. Depending on the response, it is hoped that the selected papers may be published in a special issue of a journal or as an edited book.

Presentations Full Papers

Teaching mathematics in the classroom through problem solving

Norma S. G. Allevato, Universidade Cruzeiro do Sul – UNICSUL/ São Paulo/Brazil; Lourdes R. Onuchic, Universidade Estadual Paulista Julio de Mesquita Filho – UNESP/Rio Claro/Brazil

The method of problem solving based on the Japanese and Polya´s models. A classroom experience in Chilean schools

Aravena D. Maria and Caamaño E. Carlos, Mathematics Department, Basic Sciences Institute, Catholic University of Talca – Chile

Formulating mathematical conjectures in learning activities, assisted with technology

Fernando Barrera Mora and Aarón Reyes Rodríguez, Universidad Autónoma del Estado de Hidalgo

Problem Posing Performance of Grade 9 Students in Singapore on an open-ended stimulus

Chua, Puay Huat and Yeap, Ban Har, National Institute of Education, Nanyang Technological University, Singapore

Future directions and perspectives for problem solving research and curriculum development

Lyn English, Queensland University of Technology; Richard Lesh, Indiana University and Thomas Fennewald, Indiana University

The decision-making as a school activity

María Candelaria Espinel Febles, University of La Laguna; Ana Teresa Antequera Guerra, IES Luis Cobiella Cuevas

Cognitive and metacognitive processes of pre-service mathematics teachers while solving mathematical problems

Omar Hernández Rodríguez, Ed.D. and Wanda Villafañe Cepeda, Ed.D. University of Puerto Rico

An ICT environment to assess and support students’ mathematical problem-solving performance in non-routine puzzle-like word problems

Angeliki Kolovou, FIsme, Utrecht University, the Netherlands; Marja van den Heuvel-Panhuizen, FIsme, Utrecht University, the Netherlands and IQB, Humboldt University Berlin, Germany; Arthur Bakker, FIsme, Utrecht University, the Netherlands; Iliada Elia, Department of Education, University of Cyprus

Methodologies for investigating relationships between concept development and the development of problem solving abilities

Richard Lesh, Indiana University; Lyn English, Queensland University of Technology; Thomas Fennewald, Indiana University

The computer tool for verification hypotheses in parametrical problems solving

D. Mantserov, D. Petrichenko, S. Pozdnyakov

A Technology-Based Investigation of United States High School Student Mathematical Problem Solving

Pamela L. Paek, Charles A. Dana Center, The University of Texas at Austin, Austin, Texas, United States

Teachers’ beliefs about mathematical problem solving, their problem solving competence and the impact on instruction: A case study of three Cypriot primary teachers

Constantinos Xenofontos and Paul Andrews, University of Cambridge

PRESENTATIONS

Tuesday July 8 (12:00hs-13:00hs)
Focus on: Problem Solving and Teachers Education.

Presenters:
Olive Chapman (15 minutes)
Lyn English, Dick Lesh & Thomas Fennewald (15 minutes)
Zahra Gooya (15 minutes)
O. Hernández-W. Villafañe; Constantinos Xenofontos and Paul Andrews (15 minutes)

Wednesday 9 (12:00-13:30Hs)
Round Table: Foundations and Needed Research and Developments in Mathematical Problem Solving.

Brief Introduction (group members)

Panelists:
Lyn English (Australia)
Dick Lesh (USA)
Luis Moreno-Armella (Mexico)
Akihiko Takahashi (Japan)

Friday July 11 (12:30-13:30)
Focus on Students Problem Solving Approaches, Curriculum, Assessment.

Presenters:
Pamela L. Paek (15 minutes)
Chua Puay Huat & YEAP, Ban Har (10 minutes)
Maria Espinel & Ana Antequera (10 minutes)
Norma S.G Allevato, Lourdes R. Onuchic (10 minutes)
Aravena D. Maria and Caamaño E. Carlos (10 minutes)

Saturday 12 (12:00-13:30 Hs).
Focus on: Computational Tools and Future Developments

Presenters:
Jean Marie Laborde, Barbara Pence (20 minutes)
Dick Lesh, Lyn English & Thomas Fennewald (20 minutes)
Fernando Barrera (10 minutes)
Angeliki Kolovou, Marja van den Heuvel-Panhuizen & Arthur Bakker (10 minutes)
D. Mantserov, D. Petrichenko, S (10 minutes)

Conclusions and Summary of the TSG19:
What is the Next? (20 minutes)

Papers and discussion documents

Visualization in the teaching and learning of mathematics

WELCOME!

TSG 20 is designed to promote scholarship on the topic of visualization in the teaching and learning of mathematics. This topic has been gaining increasing attention in the mathematics education community over the last few decades. A broad range of related topic areas fall under this general heading. These may include the roles of external and internal representations (sometimes designated inscriptions and mental imagery respectively), metaphor, metonymy, and gesture, dynamic computer programs, and other aspects of visualization in the teaching and learning of mathematics. Both theoretical papers and reports of empirical research in these and related areas will be considered for inclusion in the program.

CALL FOR PROPOSALS

The Organizing team of TSG 20 is accepting papers for presentation and distribution at ICME-11. The TSG has been allocated four sessions during the conference. The first and last of these will be joint sessions, and the second and third will be organized in smaller subgroups according to the interests of participants. The last session will allow time for general discussion. Papers will be assigned to one of three formats:

joint session papers, of outstanding and general interest;

subgroup session papers, related to specific topic areas (see below);

‘presentation-by-distribution’ in the TSG and on its website (no oral presentation).

For any of the formats, manuscripts must conform to the formal standards of PME research reports (see the link “TSG20 Template” at the end of the web page) except that the maximum length of papers is 12 pages. Authors should indicate that the paper submitted to TSG 20 has not been submitted to another TSG.

Deadline for submission: November 20, 2007.

Based on a careful refereeing process, the Organizing Team will decide on whether to accept the paper in one of the indicated formats, and (if relevant) in what subgroup the paper is to be presented. Notification of this decision will be given by January, 2008.

Specific topic areas may include, but are not confined to, the following:

 The strengths and difficulties associated with visualization in mathematics.

 Pedagogy and classroom cultures that promote visualization in learning mathematics.

 The roles of metaphor, metonymy, and gesture in mathematical visualization.

 Promoting connections amongst registers that include visualization in mathematics.

 The roles of computer technologies in promoting mathematical visualization.

 Components of a theoretical model of visualization in mathematics education.

For preliminary enquiries, contact any of the members of the Organizing Team. Submission of papers should be directed to one of the co-chairs.

TSG20 Template

Please make use of the Template below in preparing your proposal

Program

Monday, July 7 (1 hour) Introduction and 2 plenary papers. Chair: Abraham Arcavi

1. Norma Presmeg: An overarching theory for research in visualization in mathematics education.

2. Fernando Hitt, Alejandro S. González-Martin, & Christian Morasse: Visualization and students’ functional representations in the construction of mathematical concepts. An example: The concept of co-variation as a prelude to the concept of function.

Wednesday, July 9 (1.5 hours) 3 parallel threads, A, B, and C

A. Visual representations and conversions. Chair: Athanasios Gagatsis

1. Athanasios Gagatsis, Areti Panaoura, Iliada Elia, Nicolaos Stamboulidis, & Panayiotis Spyrou: The axis of reflective symmetry as representation in mathematics learning.

2. Flor Rodriguez, Gisela Montiel Espinosa, Ricardo Cantoral Uriza: Visualization in iterative processes.

3. Allen van Blerk, Iben Maj Christiansen, & Trevor Anderson: Learner’s visual recognition of geometry theorems.

4. Orlando Monsalve Posada: Monstrations as a complementary concept for visual thinking: Implications in the teaching and learning of geometry.

B. Aspects of visualization, including technology issues. Chair: Patricia Salinas

1. Patricia Salinas & Angeles Dominguez: Simcalc mathworlds as a tool to support visualization in a calculus course.

2. Thiago Maciel de Oliveira, Rafael Garcia Barbastefano, & Luiz Carlos Guimarães: A discussion about the role of the computer in representation and understanding of 3D objects’ mathematical properties.

3.Eleni Deliyianni, Iliada Elia, Areti Panaoura, & Athanasios Gagatsis: The role of representations in the understanding of fractions in elementary and secondary education.

4. Ricardo Pulido & Patricia Salinas: A visual approach to the graph of a two variable function and to the idea of partial derivative.

C. Issues of teaching involving visualization. Chair: Fatimah Saleh

1. Gonzalo Zubieta & Rafael Meza: Visualization in the teaching/learning of mathematics.

2. Patricia Marchand: Visualization: From sports’ training experiences to school teaching’s practices.

3. Sofia Anastasiadou: Representations and learning in statistics: A comparative study between Greek primary school students and immigrants.

4. Vimolan Mudaly: Visual literacy in mathematics education.

Friday, July 11 (1 hour) 3 parallel threads, A, B, and C

A. Visual representations and conversions. Chair: Athanasios Gagatsis

5. Annita Monoyiou & Athanasios Gagatsis: A coordination of different representations in function problem solving.

6. Jorge Soto-Andrade: Mathematics as the art of seeing the invisible…

B. Aspects of visualization, including technology issues. Chair: Patricia Salinas

5. Sofia Agathangelou, Veronika Papakosta, & Athanasios Gagatsis: The impact of iconic representations in solving mathematical one-step problems of the additive structure by primary second grade pupils.

6. Claudia Acuña Soto & Victor Larios Osorio: Prototypes and learning of geometry: A reflection on its pertinence and its causes.

C. Issues of teaching involving visualization. Chair: Fatimah Saleh

5. Vassiliki Farmaki & Petros Verikios: Function representations as problem solving strategies: The case of inequality.

6. Hui-Yu Hsu: Learning opportunities of reasoning: The interplay between gestures and diagram properties.

Saturday, July 12 (1.5 hours) Chairs: Abraham Arcavi & Norma Presmeg

Discussion in theme groups, chaired by committee members:

Visualization and representations.

Roles of icons, pictures, simulations.

Visual reasoning, visual operations.

Visual literacy.

Visualization and geometry.

Status of visualization.

Creativity.

Papers and discussion documents

TSG20 Template (50.00 KB)
Plenary paper: Presmeg (85.00 KB)
Plenary paper: Hitt, Gonzales-Martin, and Morasse (3.00 MB)
Paper: Acuna Soto and Larios Osorio (128.00 KB)
Paper: Agathangelou et al. (296.00 KB)
Paper: Anastasiadou (131.00 KB)
Paper: Deliyianni et al. (214.00 KB)
Paper: Farmaki and Verikios (387.00 KB)
Paper: Gagatsis et al. (123.00 KB)
Paper: Hsu (585.00 KB)
Paper: Monoyiou and Gagatsis (130.00 KB)
paper: Mudaly (115.00 KB)
Paper: Posada (1.00 MB)
Paper: Pulido and Salinas (261.00 KB)
Paper: Salinas and Dominguez (175.00 KB)
Paper: Zubieta and Meza (168.00 KB)
Paper: Rodriguez (647.00 KB)
Paper: Marchand (227.00 KB)
Paper: Soto-Andrade (1.00 MB)
Paper: van Blerk (115.00 KB)

Mathematical applications and modelling in the teaching and learning of mathematics

Aims and Focus

The aim of the study group is to present and discuss recent research within the area of teaching and learning mathematical modelling and applications and its role in mathematics education. The scope of this endeavour includes all levels and branches of mathematics teaching – elementary school, secondary or high school, college and university level as well as the transitions between levels.

In particular we welcome contributions that

 survey the current state of our knowledge concerning students development of modelling competency through the teaching of application and modelling

 review our knowledge of if and how the students’ learning of mathematics can be enhanced through the teaching of applications and modelling

 discuss mathematical modelling and its role in mathematics teaching from various perspectives such as mathematical, epistemological, learning, pedagogical-didactical perspectives and critical-societal perspectives.

 report recent research or developmental projects with thought provoking findings within the realm of our topic.

Some notes on the demarcation of TSG 21 in relation to closely related TSGs might be helpful for guiding potential contributors. First of all in TSG 21 our common focus of interest is the teaching and learning of modelling and the applications of models understood as the use of mathematics as a tool to understand, formulate, structure, and solve non-mathematical problems or situations occurring in the real world. Hereby TSG 21 distinguishes itself from TSG 19 that focuses on problem solving. It is no doubt that mathematical modelling often involves mathematical problem solving but in our understanding modelling also involves other types of processes with specific aspects of teaching and learning.

The inclusion of modelling is perhaps, together with the integration of information technology, the most wide spread and common feature in recent curriculum developments especially at secondary level. Therefore it is relevant to consider the demarcation to TSG 35. Research on the implementation of mathematical modelling in curricula and its effects is of interest to TSG 21 only if it includes analyses of specific cases of teaching and learning mathematical modelling.

Despite this attempt to clarify the demarcation of TSG 21 we expect to receive quite a few contributions that could be submitted to other TSGs with the same right, and in cases of doubt we will communicate with the organisers of the relevant TSGs in order to suggest the best placement of the contribution.

Types of contribution

In a TSG there are three different types of contributions suggested by the IPC of ICME-11. Papers published on the web page of the TSG before the congress to be used as a basis for surveys and discussions during the congress, papers distributed to the participants as printed handouts at the congress prior to a TSG session and papers presented orally and discussed in one of the four TSG sessions during the congress. All three last types of papers will be made available on the web before the congress.

Programme

The OT of TSG21 has accepted fifteen papers as contributions to our group. Below, you find the final versions of thirteen of these papers listed in the order they appear in the programme. The remaining two papers will be uploaded as soon as we have the final versions.

During our four TSG sessions the presentation and discussion of papers will be structured according to the following three themes:

1. Conceptualizations of mathematical modelling in different theoretical frameworks and for different purposes.

2. Cultural differences and the importance of international co-operation in research and development on the teaching and learning of mathematical modelling.

3. Design of curricular experiments and didactical reflections on the teaching of mathematical modelling.

For each theme there will be a short introduction, oral presentations of a few selected papers and a short general discussion to round off the theme. Papers introducing each of the three themes will be uploaded only shortly before the congress, intentionally on July 1.

The paper presentations will have the format of 15 minutes presentation followed by 5 minutes for questions. The presenters should assume that all participants have read the papers beforehand and the participants are urged to fulfil their part of this assumption and be prepared to discuss all the papers published on the web-page.

Tuesday, July 8, 12.00-13.00: Introduction and Theme 1

12.00-12.15 Introduction to the programme for TSG21 (Morten Blomhøj and Susana Carreira)

12.15-12.35 Introduction to theme 1. Different perspectives on mathematical modelling in educational research – categorising the TSG21 papers, Morten Blomhøj.

12.40-13.00 Mathematical modelling, the socio-critical perspective and the reflexive discussion. Jonei Cerqueira Barbosa, Brazil

Wednesday, July 9, 12.00-13.30: Theme 1, continued

12.00-12.20 Mathematical models in the context of sciences. Patrica Camarena Gallardo, Mexico

12.20-12.40 Differential equations as a tool for mathematical modelling in physics and mathematics courses. Ruth Rodríguez Gallegos, France/Mexico

12.40-13.00 On the development of mathematical modelling competencies – The PALMA longitudinal study. Rudolf vom Hofe & Alexander Jordan et al., Germany

13.00-13.20 Reinforced bonds between modelling and reflecting. Mette Andresen, Denmark

13.20-13.30 Closing discussion on theme 1.

Friday, July 11, 12.30-13.30: Theme 2

12.30-12.50 Introduction to theme 2. Challenges with international collaboration regarding teaching of mathematical modeling. Thomas Lingefjärd, Sweden.

12.50-13.10 A comparative study on mathematical modelling competences with German and Chinese students. Matthias Ludwig, Germany & Binyan Xu, China

13.10-13.30 Mathematical modelling in a European context – A European network-project. Stefanie Meier, Germany.

Saturday, July 12, 12.00-13.30: Conclusion of Theme 2 and Theme 3

12.00-12.15 Closing discussion on theme 2.

12.15-12.35 Introduction to theme 3. Didactical Reflections on the teaching of mathematical modelling – Suggestions from concepts of “time” and “place”. Toshikazu Ikeda, Japan.

12.35-12.55 Formatting real data in mathematical modelling projects. Jussara de Loiola Araújo, Brazil

12.55-13.15 Simple spreadsheet modelling by first-year business undergraduate students: Difficulties in the transition from real world problem statement to mathematical model. Djordje Kadijevich, Serbia

13.15-13.30 Closing discussion on theme 3 and what did we accomplish in TSG21? Closing remarks by Susana Carreira.

All the papers accepted for publication on the TSG21 web-page are organised according to their relations to the three themes. Supplementary to the papers presented orally and mentioned in the programme above the following papers will be published at the web-page:

Papers related to theme 1: Conceptualizations of mathematical modelling in different theoretical frameworks and for different purposes.

Applying mathematics: Metamatics or Mathematism? Allan Tarp, Denmark

The teachers’ tensions in the practice of mathematical modelling. Andréia Maria Pereira de Oliveira & Jonei Cerqueira Barbosa, Brazil

Papers related to theme 2: Cultural differences and the importance of international co-operation in research and development on the teaching and learning of mathematical modelling.

No additional papers.

Papers related to theme 3: Design of curricular experiments and didactical reflections on the teaching of mathematical modelling.

Mathematical modelling: From classroom to the real world. Denise Ferreira & Otavio R. Jacobini, Brazil

Prograph Diagrams – a new old system for teaching functional modelling. Hans-Stefan Siller, Austria

Mathematical models in secondary Chilean education. Maria Aravena Díaz & Carlos Caamaño Espinoza, Chile

Mathematical modelling and environmantal education. Ademir Donizeti Caldeira, Brazil

Submissions

Papers and presentations

Below you find pdf of the papers accepted for TSG21 in the order of their appearance in the programme and related to the three themes of the study group. The last three papers are the papers that introduced each of the three themes in the programme.

After the papers, also you find pdf of the power point presentations given orally at the TSG sessions during ICME-11 in the order of their appearance in the programme.

Papers and discussion documents

New technologies in the teaching and learning of mathematics

Aims, scope, and goals

The ICME 11 Topic Study Group « New Technologies in the Teaching and Learning of Mathematics » will serve a dual role:

- overview of the current state of art in the topic and expositions of outstanding recent contributions to it, as seen from an international perspective
- sharing of ongoing work and perspectives

Technology is understood here in a broad sense and encompasses in particular, computers of all types, calculator technology, the use of the Internet, and distance technology. The use of technology includes implementation for students of all ages, teacher education, and all mathematical topics. Thus, establishing coherence will be a major challenge of the TSG.

Research and innovative projects in learning with technological tools have indeed been showing much promise with respect to their use in the generation of learning environments where students have richer opportunities to construct mathematical meanings, to explore and experiment with mathematical ideas, and to express these ideas using a wealth of representations. However, actual use of these tools in schools is still very sparse despite the abundance of governmental funding and interest around the world. The use of technologies has simply not expanded and the changes promised by the case-study experiences have not really been noticed beyond the empirical evidence given by the studies themselves. The changes in classroom practices involved in the use of technology seem to pose a real challenge to administrators, curriculum designers, teachers and students. Thus, there is a great need for a deeper understanding of how the potential suggested by research in the 80s and the 90s can be grounded both in classroom practices with respect to systemic schooling, in other institutional environments such as the workplace, and in informal situations for children and adults. In recent years, the focus has also been on teaching methods and on ways of supporting teachers to use technological tools. The perturbation posed to traditional teaching has become an avenue for reflection and professional development for teachers rather than an implicit obstacle to implementing technologies in the classroom.

The issues addressed at this TSG will focus on three broad themes.

1) Integration of technology into school and other learning environments : This theme refers both to research studies and the innovative development of technology-based curricula or units. It includes the study of learning processes with technology and the impact of technology on the learning of mathematics. It also addresses the issue of assessing mathematics with and through technology. Connectivity and virtual networks for learning mathematics is also part of the topic.

2) Issues related to the use of technology by teachers: How do teachers cope with perturbations introduced by technology? How do they succeed in the ordinary types of usage? What are teachers’ conceptions of the use of technology? How do these conceptions evolve? How are they taken into account to promote changes in teacher practice? The topic also includes issues about mathematics teacher preparation and professional development in the use of technology.

3) Design of technology for the learning and teaching of mathematics: This theme refers to the design choices of technology environments related to epistemological and cognitive aspects of mathematics and of the learning of mathematics, as well as to the features aimed at assisting teaching.

Call for contributions

TSG 22 « New Technologies in the Teaching and Learning of Mathematics » invites the submission of contributions related to the topic of the group. In particular, any contribution addressing questions, problems and issues related to the presentation of the topics listed above can be submitted. The organizers of the Topic Study Group welcome proposals from both researchers and practitioners and encourage contributions from all countries with different economic contexts and cultural backgrounds. Reflecting the diversity of the contributions is a major concern of the group organizers.

The submitted contributions will be reviewed by the organizing team of the Topic Study Group. The accepted contributions will be published on the ICME website before the congress and presented in a poster session within the slots of the group. During this session, it is expected that the contributors will be available to discuss their work with the other group members. Presentations related to theme 3 may also include live demonstrations of new technologies. Contributors will also be invited to bring copies of accepted papers, including expanded versions, and CDs to be presented-by-distribution during this session.

Submissions

Sending submissions

Submissions in their short form (3pages) or in their final form (7 pages) should be sent by November 15, 2007 as an email attachment to both chairs of the Topic Study Group at the following addresses: Colette.Laborde@imag.fr and kynigos@ppp.uoa.gr

TSG 22 Final Schedule

ICME 11 – TSG 22

Presentation and schedule

The issues addressed at this TSG will focus on three broad themes.

Theme 1: Integration of technology into school and other learning environments:
This theme refers both to research studies and the innovative development of technology-based curricula or units. It includes the study of learning processes with technology and the impact of technology on the learning of mathematics. It also addresses the issue of assessing mathematics with and through technology. Connectivity and virtual networks for learning mathematics is also part of the topic.

Theme 2: Issues related to the use of technology by teachers:
How do teachers cope with perturbations introduced by technology? How do they succeed in the ordinary types of usage? What are teachers’ conceptions of the use of technology? How do evolve these conceptions? How are they taken into account to promote changes in their practice? The topic includes also issues about mathematics teacher preparation and professional development in the use of technology.

Theme 3: Design of technology for the learning and teaching of mathematics:
This theme refers to the design choices of technology environments related to epistemological and cognitive aspects of mathematics and of the learning of mathematics, as well as to the features aimed at assisting teaching.

Monday July 7 – 13.00 -14.00
1st Session – 1h – Plenary Session

KYNIGOS Chronis, University of Athens, Greece, LABORDE Colette, University Joseph Fourier, France
Title: New technologies in the learning and teaching of mathematics: what’s new since last ICME?

CERULLI Michele, University of Genova, Italy,
HOYOS Veronica, National Pedagogical University, Mexico,
JAKUCYN Natalie Glenbrook South High School, Glenview, IL and The University of Chicago School Mathematics Project, Chicago, IL, USA,
LEUNG Allen, University of Hong Kong, Hong Kong SAR, China
Title: Critical Issues addressed by the sessions of the Topic Groups

Wednesday July 9 – 12.30-14.00
2nd Session – 1h30 – Oral Presentations

Group 1 – Theme 1- Integration of technology into school and other learning environments
Chair Allen
1. JAHN A. Paula, UNIBAN, Brazil, FLORES SALAZAR J. Victoria Pontifical Catholic University of Sao Paulo PUC-SP/Brazil
Title: A view of instrumental genesis using Cabri 3D

2. PSYCHARIS Giorgos and KYNIGOS Chronis, Educational Technology Lab, School of Philosophy, Univ. of Athens, Greece
Title: Exploring angle through geometrical constructions in a simulated 3D space

3. OR Anthony, LEUNG Allen Education Bureau, Government of the Hong Kong SAR, University of Hong Kong
Title : Develop a learning and teaching unit in the Cabri 3D environment about concepts of 3-D figures in Hong Kong Secondary Mathematics Curriculum

4. SOURY-LAVERGNE Sophie Laboratoire d’Informatique de Grenoble-LIG, University Joseph Fourier, France
Title: Deductive reasoning and instrumental genesis of the drag mode in dynamic geometry

Group 2 – Theme 1 – Integration of technology into school and other learning environments
1. LU Yu-Wen Allison, University of Cambridge, UK
Title : The use of mathematical software in secondary mathematics teaching– a new challenge for young teachers

2. BRODAHL Cornelia, University of Agder, Norway
Title : Challenges and choices in developing complete digital courses in secondary Mathematics education

3. KARADAG Zekeriya, Ontario Institute for Studies in Education, University of Toronto, Canada
Title : Improving online mathematical thinking

4. DANA PICARD Thierry , Jerusalem College of Technology, Israel
Title : Existence theorems vs Construction of a Solution: An example of a Theoretical- Computational Conflict

Group 3 Theme 2 – Issues related to the use of technology by teachers
1. AMADO Nelia, FCT, University of Algarve, Portugal
Title: Communities of practice and mentoring relationships in beginner teachers’ use of technology in the classroom

2. FAGGIANO Eleonora, University of Bari – Italy, FASANO Margherita, University of Basilicata – Italy
Title: Teachers’ perceptions and usage of ICT: an issue for educators to deal with.

3. GARCIA-CAMPOS Montserrat & ROJANO Teresa, CINVESTAV, Mexico
Title: Computer Algebra Systems: A teacher centered study on the cognitive, epistemological and didactic dimensions.

4. SINCLAIR Margaret, WIDEMANN Herbert, KALLISH Lindsay, FIORONI Marcella, York University, Canada
Title: Symbolic calculators in mathematics education for future engineers: linked hand-held technology in early secondary mathematics

Group 4 – Theme 3 – Design of technology for the learning and teaching of mathematics
1. CONFREY Jere, MALONEY Alan, NGUYEN Kenny, North Carolina State University, USA
Title : Graphs ‘n Glyphs as Professional Transitional Software to Assist Middle School Students in Rational Number Reasoning Topics

2. YEO SHU Mei, THONG CHEE Hing, & KHO TEK Hong, Ministry of Education, Singapore
Title : Algebra discs : digital manipulatives for learning algebra

3. CERVAL-PEÑA E., SANGWIN C J, HERMANS Dick, School of Mathematics, University of Birmingham, UK
Title : Developing automatic assessment of steps in students’ work

Group 5 Theme 3- Design of technology for the learning and teaching of mathematics
1. DICK Thomas, Oregon State University, Corvallis, USA
Title : Exploiting next generation handheld technology: TI-Nspire as “Microworld Maker”

2. LABORDE Jean-Marie, IAM-IMAG Grenoble, FRANCE
Title : 3D-environment, Dynamic Math: Design issues. The case of Cabri 3D

3. BORBA de Souza Rute E., LEITE Maici D. , GOMES Alex S., Universidade Federal de Pernambuco, Brazil
Title : Contributions from the Theory of Conceptual Fields: help and feedback messages in educational software for deaf students

4. ROWE Leanne, The Learning Federation, Australia, WAY Jenni, University of Sydney, Australia
Title : The Role of Scaffolding in the Design of Multimedia Learning Objects

Friday July 11 – 12.15 -13.15
3rd Session – 1 h- Poster and demo Session

Group 1 Theme 1 – Integration of technology into school and other learning environments
1. ACELEJADO Maxima J., Philippines
Title : Using Internet: A Teaching Strategy for Sketching Graphs of Equations

2. BUTTON Tom, LEE Stephen, MEI/The Further Mathematics Network, UK
Title : A comprehensive web-based learning environment for pre-university students: encouraging students to become independent learners and promoting good-practice for teachers

3. DE LAS PEÑAS Ma. Louise Antonette N., Ateneo de Manila University, Quezon City, Philippines
Title : On Maximizing Technology Resources and their Benefits In Teaching and Learning Mathematics

5. KORTENKAMP Ulrich, University of Education Schwäbisch Gmünd, Germany
Title : Math Unit Testing – A new approach to the use of technology in teaching

5. MAFFEI Laura , MARIOTTI M Alessandra, SABENA CristinaMathematics Department, University of Siena, Italy,TRGALOVA J., University Joseph Fourier, Grenoble
Title: Different feedbacks for different educational goals: how theoretical assumptions can drive the modes of use of the Aplusix CAS.

6. OZEL Serkan, Turkey , CAPRARO Robert M., USA, YETKINER Ebrar Z., Texas A&M University, Turkey
Title : A technology intervention using multiple representations on mathematics

7. RANA Inder K., I. I. T. Bombay, Powai Mumbai, India
Title : Teaching a Large Class in Technological Setting

8. REYES Araceli, Instituto Tecnólogico Autónomo de México, Mexico
Title: Teaching Advanced Calculus with APOS and Coursecompass

Group 2 Theme 2- Issues related to the use of technology by teachers
1. DUARTE José Antonio, Escola Superior de Educação de Setúbal, Portugal
Title: The ICT in Mathematics Education: From Teachers’ Traning to the classroom practice

2. MILLER Dave, AVERIS Doug Averis Keele University, Keele, Staffordshire, UK
Title : Secondary mathematics and the interactive whiteboard implications for professional development

3. MISKULIN Rosana G. Sguerra, IGCE/RIO CLARO/UNESP/Brazil, PENTEADO Miriam de Godoy,IGCE/Rio Claro/UNESP/Brazil, MARIANO da SILVA Carla Regina Mariano, IGCE/Rio Claro/UNESP/Brazil
Title: Distance Education as a formative scenary of he practice of the mathematics teacher

4. NAVARRO Guevara Douglas, Universidad Nacional de Costa Rica
Title: On Mahematics implications of the incorporation of computer tools

5. SCHREIBER Cristof J. W. Goethe Universität, Frankfurt; Germany
Title: Blended Learning in the Pre- and In-Service Training of Primary Teachers

Group 3 – Theme 3- Design of technology for the learning and teaching of mathematics
1. ANDRADE-ARECHIGA Maria, CICESE, México1, LOPEZ Gilberto Department of Computer Science, CICESE, México, LOPEZ-MORTEO Gabriel, Universidad Autónoma de Baja California, México
Title: Using technology to teach college-level mathematics

2. ARAYA CHACON Andrea, NAVARRO Guevara Douglas, Universidad Nacional de Costa Rica
Title: Three-dimensional objects handling

3. DIBUT TOLEDO Lázaro S., de LEON RODRIGUEZ Narciso R., Universidad de Cienfuegos, Cuba
Title: Mathdev: A resource for the Blended Learning in Mathematics

4. GUZNER Claudia, CIVICO Alejandra, D’AMELIO Adriana, LEON Oscar, POLENTA Cecilia, SCHILARDI Adriana, SEGURA Sandra, Universidad Tecnológica Nacional, Facultad Regional Mendoza y Universidad Nacional de Cuyo, Argentina
Title: Learning styles and environments web design: the case of the derivative

5. KOBAL Damjan, FMF, University of Ljubljana, Slovenia
Title: (E)-mind thinking in e-learning project

6. GOGUADZE George, Universitat des Saarlandes, Saarbrucken, Germany MELIS Erica , German Research Institute for Artificial Intelligence (DFKI)
Title : Feedback in ActiveMath Exercises

7. MONTESSINOS Benoit, KUNTZ Gérard, Sesamath, France
Title: Sesamath: a teachers society, to create and to spread mathematical resources through the Internet.

8. NODELMAN Vladimir, Holon Institute of Technology, Israel
Title: Requirements to the software for learning and teaching of mathematics

9. WANG P., MIKUSA M., AL SHOMRANI S., LAI X., ZOU X., ZELLER D., Kent State University, Kent, Ohio, USA
Title : An Overview of WME: a Web-based Mathematics Education System

Saturday July 12 – 12.00-13.30
4th session – 1h30 – Oral presentations

Group 1 Theme 1- Integration of technology into school and other learning environments
Chair Natalie
1. OWENS Douglas T, The Ohio State University, USA, PAPE Stephen, University of Florida, USA, IRVING Karen E., The Ohio State University, USA, SANALAN Vehbi A., The Ohio State University, USA, BOSCARDIN Christy Kim, Center for Research on Evaluation, Standards & Student Testing, University of California, Los Angeles, USA, ABRAHAMSON Louis, Better Education Foundation, USA
Title: The Connected Algebra Classroom: A Randomized Control Trial

2. PINEAU Kathleen, École de technologie supérieure, Canada CARON France, Université de Montréal, Canada
Title: Teaching Strategies and their effect on students’ performance

3. GEIGER Vince, FARAGHER Rhonda, The Australian Catholic University, Australia, GOOS Merrilyn, The University of Queensland, Australia, LOWE Jim, Redcliffe State High School, Australia
Title: CAS as a Provocative Agent in the Process of Mathematical Modelling

4. LAVICZA Zsolt, University of Cambridge, UK
Title : The use of Computer Algebra Systems in university-level mathematics teaching

Group 2 – Theme 1 – Integration of technology into school and other learning environments
1. MORENO ARMELLA Luis, Cinvestav, Mexico & James J. Kaput Center for Research and Innovation in Mathematics Education, UMass, Dartmouth, USA, TRIGO Manuel Santos, Departamento de Matemática Educativa, Cinvestav, México
Title : Mathematical Practices and new potential instructional trajectories in dynamical environments

2. GRAVINA Maria Alice, Mathematics Institute, RGS Federal University, Brazil
Title : Dynamical visual proof: what does it mean?

3. MANN Markus, University of Education Weingarten, Germany
Title : Video-based learner assistance in learning environments for geometry

4. WONG Ka Lok, University of Hong Kong, China, Hong Kong SAR
Title : Geometry in clicks and drags : an opportunity for integrating technology into classroom teaching and learning of geometry

Group 3 – Theme 3- Design of technology for the learning and teaching of mathematics
1. PRANK Rein, ISSAKOVA Marina, LEPP Dmitri, VAIKSAAR Vahur, TÖNISSON Eno, University of Tartu, Estonia
Title : T-algebra – Intelligent Environment for Expression Manipulation Exercises

2. TRGALOVA Jana, CHAACHOUA Hamid, University Joseph Fourier, France
Title : Development of Aplusix software

3. SILLER Hans Stefan, Universität Salzburg, Austria
Title : Prograph diagrams a new old system to teach functional modeling

Group 3- Theme 2- Issues related to the use of technology by teachers
4. JUAREZ Manuel and RAMIREZ José Luis, CENIDET – MÉXICO
Title : A Review of Teacher Learning in a Distance Course on Discrete Mathematics

Group 4 – Theme 1 – Integration of technology into school and other learning environments
1. PERSSON Per-Eskil, Malmö University, Sweden
Title: Hand held calculators as tools for algebra learning – A literature review

2. BURRIL Gail, Michigan State University, USA
Title: The role of handheld technology in teaching and learning secondary school mathematics

3. KARRER Monica, JAHN A. Paula, Universidade Bandeirante (UNIBAN) – Brazil –
Title: Studying plane linear transformations on a dynamic geometry environment : analysis of tasks emphasizing the graphic register

Group 4 – Theme 2 – Issues related to the use of technology by teachers
1. EVANS Brooke, The Metropolitan State College of Denver, USA , BEAN Hamilton, University of Colorado at Boulder, USA, ROMAGNANO Lew, LOAS Jim and MC KENNA Patricia, The Metropolitan State College of Denver, USA
Title: Community: Metro’s Mathematics for Rural Schools Program

Planing TSG22 final

Papers and discussion documents

Amado COMMUNITIES OF PRACTICE AND MENTORING RELATIONSHIPS (131.00 KB)
Arechiga Using technology to teach college-level mathematics (254.00 KB)
Brodahl Challenges and choices in developing complete digital courses (43.00 KB)
Burrill THE ROLE OF HANDHELD TECHNOLOGY (137.00 KB)
Button et al A comprehensive web-based learning environment (174.00 KB)
Cerval et al Automatic assessment of steps in students (130.00 KB)
Chacon & Guevara Three-dimensional objects (654.00 KB)
Dana-Picard Existence theorems vs. Construction of a Solution (133.00 KB)
DeLasPenas et al On Maximizing Technology Resources (2.00 MB)
Dibut & De Leon MATHDEV_A RESOURCE FOR THE BLENDED LEARNING IN MATHEMATICS (628.00 KB)
Duarte THE ICT IN MATHEMATICS EDUCATION FROM TEACHERS TRAINING TO THE CLASSROOM PRACTICE (1.00 MB)
Evans et al ONLINE MATHEMATICS CONTENT COURSE (94.00 KB)
Faggiano & Fasano TEACHERS’ PERCEPTIONS AND USAGE OF ICT (56.00 KB)
Garcia-Campos & Rojano COMPUTER ALGEBRA SYSTEMS (118.00 KB)
Geiger et al CAS Enabled Devices as Provocative Agents (713.00 KB)
Goguadze & Melis FeedbackinActiveMathExercises (151.00 KB)
Gravina Dynamical visual proof what does it mean (581.00 KB)
Jahn & Flores EXPLORING THREE-DIMENSIONAL OBJECTS (450.00 KB)
Juarez et al Collaborative distant interaction in a course on discrete mathematics (43.00 KB)
Karadag IMPROVING ONLINE MATHEMATICAL THINKING (372.00 KB)
Karrer & Jahn STUDYING PLANE LINEAR TRANSFORMATIONS (183.00 KB)
Lavicza The use of Computer Algebra Systems (104.00 KB)
Lee Developing a digital game for the instruction of fractions (97.00 KB)
Leite et al CONTRIBUTIONS FROM THE THEORY OF CONCEPTUAL FIELDS (535.00 KB)
Luyuwen THE USE OF MATHEMATICAL SOFTWARE IN SECONDARY (281.00 KB)
Maffei DIFFERENT FEEDBACKS FOR DIFFERENT EDUCATIONAL GOALS (1.00 MB)
Miskulin et al DISTANCE EDUCATION AS A FORMATIVE SCENARY (55.00 KB)
Montessinos & Kuntz Sesamath a teachers society (141.00 KB)
Nodelman REQUIREMENTS TO THE SOFTWARE (629.00 KB)
Or Designing a teaching unit in the Cabri 3D environment (1.00 MB)
Owens et al The Connected Algebra Classroom (150.00 KB)
Ozel et al A TECHNOLOGY INTERVENTION USING MULTIPLE (225.00 KB)
Persson HANDHELD CALCULATORS AS TOOLS FOR ALGEBRA (56.00 KB)
Pineau & Caron SYMBOLIC CALCULATORS IN MATHEMATICS (272.00 KB)
Prank et al T-algebra – Intelligent Environment for Expression Manipulation Exercises (124.00 KB)
Ramirez & Juarez A Review of Teacher Learning in a Distance Course on Discrete Mathematics (74.00 KB)
Rana TEACHING A LARGE CLASS IN TECHNOLOGICAL SETTING (211.00 KB)
Reyes Teaching Advanced Calculus with APOS (401.00 KB)
Schreiber BLENDED LEARNING IN THE PRE- AND IN-SERVICE (770.00 KB)
Siller Prograph diagrams-A new old system for teaching (336.00 KB)
Sinclair et al LINKED HAND-HELD TECHNOLOGY (101.00 KB)
Trgalova & Chaachoua Development of Aplusix software (753.00 KB)
Wang et al WME a Web-based Mathematics Education System (245.00 KB)
Way & Rowe The Role of Scaffolding in the Design (188.00 KB)
Yeo et al ALGEBRA DISCS DIGITAL MANIPULATIVES FOR LEARNING ALGEBRA (1.00 MB)
Acelajado Using Internet A Teaching Strategy (85.00 KB)
Moreno-Armella & Santos-Trigo Mathematical practices and new potential instructional (169.00 KB)
Guzner et al LEARNING STYLES AND ENVIRONMENT WEB DESIGN (556.00 KB)
Psycharis & Kynigos Exploring angle through geometrical constructions in 3D space (331.00 KB)
Mann VIDEO-BASED LEARNER ASSISTANCE IN (199.00 KB)
Kobal et al (E-) MIND THINKING IN E-LEARNING PROJECT (515.00 KB)
Soury-Lavergne DEDUCTIVE REASONING AND INSTRUMENTAL GENESIS OF (756.00 KB)
Maloney et al Graphs ’n Glyphs as Professional Transitional Software to Assist (117.00 KB)
Araya & Navarro Three-dimensional objects handling (654.00 KB)
Liu et al Learning Mathematics in a Virtual World (177.00 KB)
Navarro On mathematics implications of the incorporation of computer tools (71.00 KB)
Guzner et al Learning Styles and Environment Web Design (566.00 KB)
Laborde 3D-environment, Dynamic Math: Design issues (176.00 KB)
Dick Exploiting next generation handheld technology (77.00 KB)

The role of history of mathematics in mathematics education

1. Aims and Focus

Nowadays, after the meaningful advance of the dialogue between history and mathematics education in different parts of the world and several aspects, it is possible to distinguish among at least three autonomous research fields led by this debate: the history of mathematics; the history of mathematics education and the history in mathematics education. The focus of the TSG 23 is just about the third of these fields, although the achievements in the first and second of these research fields have been conditioning the development of the specific debate in TSG 23. Thus, there is no doubt that some of the main difficulties for the establishment of dialogues between history and mathematics education, in all of its levels and aspects, are not just the access to historical sources, but also the production of new and more enlightening histories of mathematics and mathematics education. The ways how these dialogues can be established, especially from an educational perspective, are another difficulty. However, some processes and tools – as the edition of original sources and the information and communication technologies (ICT) – seem to contribute partially to attenuate the first difficulty. Concerning the second, it is through researches, experiments, meetings and debates that these dialogues can become relevant and efficient, chiefly to school practices involving mathematics. In fact, the history of mathematics and mathematics education, as well as their use in all levels and aspects of mathematics education, is becoming extensive everywhere in the world. All the meetings, conferences, summer schools, seminars devoted to mathematics education offer opportunities to discuss and debate this topic. Several aims are pointed to the establishment of dialogues between history and mathematics education, and many ways are used to reach these aims. Among them, we can mention:

• to humanize the mathematics education conceiving it as a historical, social and cultural production, as well as a set of particular social activities which are related to other social activities;

• to make student understand the meanings of aims, values, concepts, methods and proofs in different social practices involving mathematics;

• To develop the learners’ citizenship feeling, problematizing school mathematical social practices in a historico-critical point of view and maintaining an open attitude towards the study of mathematical practices in different geopolitical, institutional and chronological contexts.

To reach these aims, researchers and teachers pursue different ways and try to give theoretical and epistemological foundations to the use of the history of mathematics and mathematical education in their teaching. In spite of these efforts, several issues are still open and deserve to be discussed. Among them:

• What kind of proposals, strategies and pedagogical practices have been relevant and useful to the establishment of fruitful dialogues between history and mathematics education in different countries, contexts and levels, chiefly in the mathematics teachers’ education?

• How and why the integration of history of mathematics in mathematics education has been differently valued in the school curricula of several countries and regions?

• On what kind of political, philosophical, sociological, anthropological, psychological and linguistic bases and theoretical perspectives the integration of history in mathematics education has been conceived?

• To what extent the production of new and more enlightening histories of mathematics and mathematics education could contribute and promote new ways of establishing dialogues between history and mathematics education?

• Which place does the history of mathematics occupy in mathematics textbooks of different countries?

• Which place do the historical mathematics textbooks occupy in the mathematics’ teachers education in different countries?

• How the ICT and Internet can help to promote dialogues between history and school mathematics education?

• Which non standards media can be used to promote dialogues between history and school mathematics education? In the sessions devoted to this TSG 23, we hope to gather different actors of mathematics education, researchers, historians, teachers, … to discuss and shed light on these questions.

2. Call for Papers

All contributions that focus on the topics and issues mentioned above are welcome. They could be specific to a school level, a mathematical and/or historical content, a mathematical and/or pedagogical practice, a cultural context and/or mathematics teachers’ education. However, considering the framework and the objectives of this meeting, such contributions should have a global approach and be built upon recent results in that field.

3. Contributions

In accordance with the rules of the ICMI, there will be two kinds of contributions: oral contributions and written contributions.

Oral contributions: Some of the contributions may be more suitable for verbal presentation on the spot. However, given the limited time available and, depending on the number of accepted submissions, only a relatively small number of contributions are expected to be of this kind. No more than fifteen minutes will be allowed for such contributions (See Procedures and Deadlines).

Written contributions: Some contributions may be more suitable through papers. This means that a full text will be available; either as a hard copy to be distributed to the participants on the spot, or as an electronic file on the web. Also, depending on the number of submitted and accepted contributions, occasion for contributors to discuss their papers will be provided for (See Procedures and Deadlines).

In any case, authors are asked to provide an electronic version of their participations (extended abstract or full text) to be put on the website. Additional and useful documents can be also submitted. Clearly, this has great advantages: documents will be available well before the Congress and there is no need to make copies for an unspecified number of participants. Therefore, providing documents on the web is most welcome and will greatly help participants to follow the oral presentation in this admittedly short time. Moreover, this will permit people, who can not attend the Congress or be enrolled in other activities during the Congress, to be widely informed on our TSG activities.

In fact, the success of our TSG will rely on the enthusiastic participation and contribution of all who care for joining us and working together in this international meeting.

NB 1. It is the authors’ responsibility to produce hard copies for distribution among the participants.

NB 2. The TSG23 aims at fostering discussion on the basis over short presentations on recent ideas and results. Therefore, authors who think that their presentations would take too much time or which purposes did not meet the “aims and focus” of this TSG are advised to get information about other related events, mainly:

- ICME11 HPM Satellite Meeting, to be held at Mexico City (Mexico) in 14-18 July 2008, immediately after the ICME-11. More information can be found in http://www.red-cimates.org.mx/HPM2008.htm

- TSG38 – ICME11: The History of the Teaching and Learning of Mathematics

NB 3. Later, the organizers will do their best to ensure a hard copy of the proceedings of the TSG contributions. This can be done in a special edition of a suitable magazine or independently. Additional reviewing may be necessary for such work.

4. Selection Criteria

The contribution must be:

• relevant to the development of the “aims and focus” of TSG-23;

• clear and concise in its purposes;

• consistent and objective in its argumentation;

• original and built upon recent researches.

5. Procedures and Deadlines

January 20, 2008: Electronic-form submission of an extended abstract of up to 2000 words (not including references, pictures, tables etc.) or a full text with an ordinary/ small abstract. Abstracts and full texts will be reviewed by the members of the Organizing Team.

February 29, 2008: Notification of acceptance or not and whether presentation is oral, or by distribution. Eventual adjustments may be suggested.

March 16, 2008: Submission of full texts for written contribution and any documents to support oral contribution.

April 20, 2008: The final programme is announced on the web.

6. Practical Information

Contact: For further information, please contact the Team Chairs. In particular, abstracts, full texts and documents should be addressed to any one of the Team Chairs.

Submission of documents: Authors are kindly requested to submit their abstract, full paper, or any other relevant document, by e-mail prepared using Adobe Acrobat.

7. Programme

Monday 7th Chair Abdellah El Idrissi

13-13:35 Invited talk: Constantinos TZANAKIS (Greece): “Contributions from the study of the history of statistics in understanding students’ difficulties for the comprehension of the Variance”

13:35-14 – Adriana Cesar de MATTOS (Brazil): “The process of recognition in the history of mathematics”

Wednesday 9th Chair Alejandro GARCIADIEGO

12:30 – 13:05 Invited talk: Louis CHARBONNEAU (Canada): “Astronomical and mathematical instruments as pedagogical tools”

13:05 – 13:30 Snezana LAWRENCE (UK): “History of mathematics making its way through the teacher networks: professional learning environment and the history of mathematics in mathematics curriculum”

13:30 – 14:00 Liliana MILEVICICH & Alejandro LOIS (Argentina): “The teaching and learning of integral calculus from a historical perspective”

Friday 11th Chair Constantinos TZANAKIS

12:30 – 13:05 Invited talk: Uffe Thomas JANKVIST (Denmark): “On Empirical Research in the Field of Using History in Mathematics Education”

13:05 – 13:30 Lenni HAAPASALO (Finland): “On instrumental genesis within procedural and conceptual thinking”

Saturday 12th Chair Fulvia Furinghetti

12 – 12:30 Invited Talk: Bjørn SMESTAD (Norway): “Student projects on history of mathematics”

12:30 – 13:15 General discussion

13:15 – 13:30 Invited of Honor: Ubiratan D’AMBROSIO (Brazil) Synthesis

Closure

LIST OF ALL CONTRIBUTORS OF THE TSG23

INVITED SPEAKERS

Louis CHARBONNEAU: “Astronomical and mathematical instruments as pedagogical tools”

Bjørn SMESTAD: “Student projects on history of mathematics”

Constantinos TZANAKIS: “Contributions from the study of the history of statistics in understanding students’ difficulties for the comprehension of the Variance”

Uffe Thomas JANKVIST: “The role of the history of mathematics in mathematics education”

Ubiratan D’AMBROSIO: Synthesis

ORAL CONTRIBUTIONS

Adriana Cesar de MATTOS: “The process of recognition in the history of mathematics”

Lenni HAAPASALO “On instrumental genesis within procedural and conceptual thinking”

Snezana LAWRENCE: “History of mathematics making its way through the teacher networks: professional learning environment and the history of mathematics in mathematics curriculum”

Liliana MILEVICICH & Alejandro LOIS: “The teaching and learning of integral calculus from a historical perspective”

WRITTEN CONTRIBUTIONS

Diego Pareja HEREDIA: “The Huge Gap between Math Education and the front of Mathematics”

Slim MRABET: “The development of Thales theorem throughout history”

Gladys Denise WIELEWSKI: “Two cultures of mathematics in historical and educational perspective”

Papers and discussion documents

Dr Snezana LAWRENCE (271.00 KB)
Liliana Milevicich, Alejandro Lois (190.00 KB)
Uffe Thomas Jankvist (1.00 MB)
Slim MRABET (82.00 KB)
Diego PAREJA (118.00 KB)
Lenni.Haapasalo (290.00 KB)
Adriana Cesar de Matos (150.00 KB)
Gladys Denise Wielewski (129.00 KB)
Louis Charbonneau (76.00 KB)
Kourkoulos Michael / Tzanakis Constantinos (268.00 KB)
SCHEDULE (287.00 KB)

Research on classroom practice

Aims

This Topic Study Group intends to stimulate people’s interest in research on classroom practice in mathematics, and to strengthen the use, knowledge and understanding of that practice. Studies and comparisons of classroom practice in mathematics are clearly one of the goals that Felix Klein proposed to the Union of Mathematicians in connection with the foundation of ICMI. These studies focus on classroom observations and deal with significant events which happen in classrooms, mainly those which depend on teacher’s actions. Thus classroom observations and significant events must be the key base and result of scientific studies on teaching. The central focus of the topics we want to examine in an experimental way in relation to questions about teaching mathematics must be based on arguments resulting from observations of classroom practices. Thus we think it advisable that the major part of that type of studies should be distributed according to the various study topics of ICME. This is the first time that ICME has offered a topic study group for research on classroom practice. We are interested to receive and review all the papers by researchers of ICME, in order to give an informed overview of the field. On the other hand, we want to improve and to discuss ways of organizing observations, means of observation, ways of describing and recognizing teaching-learning phenomena, ways of knowing what can be reproduced, means to identify what we are looking for, what we know, and why we are sure we know it.

Goals

As there are diversified theoretical frameworks and practices in mathematics education between different countries, one of the goals is to help the group understand various practices in different didactical systems and the theories supporting these practices. For this purpose, this group intends to address the following general issues:

• Classroom practices within well-defined didactical systems
• Classroom practices promoted by research projects
• Analytical accounts of empirical lessons based on observations of classroom practices
• Comparison of classroom practices between different systems
• Perspectives (theoretical, socio-cultural, political) informing different classroom practices and analysis of these.

There may also be variations in practices as a result of the mathematical topics and focus of the lessons, e.g., classroom practices in algebra lessons may be very different from those in geometry, classroom practices in promoting problem solving and learning of basic skills. Therefore, we may also consider themes such as:

• Classroom practices for the teaching of specific topics
• Classroom practices for specific mathematical processes such as problem solving, investigation, projects, basic skills.

We want to present contributions which represent current practices and perspectives and to share main tendencies in this topic, to identify needs, to discuss and suggest orientations for future research. We hope to maintain and strengthen this topic for the next ICME.

Other examples and suggestions

There exist many other specific forms of contributions acceptable for presentation such as:

• Conditions of the reproducibility of practices, situations or processes
• Comparison between teachers’ strategies, and didactical or epistemological rules, following different situations and steps of the teaching and learning process
• Use of statistical methods for the analysis of observations in the classroom
• Ethical considerations for classroom observations, examples of violations and their effects
• The reciprocal role of the knowledge to be taught and the tacit knowledge in the didactic interactions
• etc.

Scope

• To gather, document, bring closer and compare studies on classroom practice independently of the reasons for which they were carried out.
• To present and compare classroom practices following different conditions or mathematical topics.
• To present projects of multimedia-library to preserve the observations of classes (video recordings, transcriptions of lessons, collection of pupils’ work, preparation of lessons, etc), to classify them and make analytical accounts of these available to researchers
• To reflect on the bases and the methods which legitimate the contributions of observations of classroom practice in research on mathematics teaching
• To reflect on the uses of these observations and of their results in education systems

Focus

The focus of TSG 24 is a discussion of research related to mathematics classroom practice. Classroom practice includes practices located within the classroom as a system in which activities of learning and teaching processes are embedded. A consideration of the mathematics classroom as a system requires the study of the interactions between: the mathematical content to be taught and learned, the activity of the teacher and the work of the students. In the interaction processes, mathematical content is contextualized through situations and the teacher plays an important role related to his/her knowledge and his/her teaching practice. It is important to understand through research the nature and extent of the interactions in the mathematics classroom, the complexity of the didactic system, the roles of the teacher and students in the interaction processes when the mathematical content is taught and learned and the complexity of the activities in mathematics classrooms.

Submissions and proposals

Authors submitting a paper to this group should specify which of the above issues they are contributing to. TSGs will have scheduled sessions in the program. Therefore, only a limited number of papers can be accepted and presented orally during the conference. Some papers will be accepted for distribution and they will be posted on the website only.

Please send all papers to the co-chairs of the Organizing Team:

Ida Ah Chee Mok (China, Hong Kong SAR) co-chair [iacmok@hku.hk] Guy Brousseau (France) co-chair [guy.brousseau@numericable.fr]

Guidelines:

1. Papers should be about research, be related to mathematics education, and conform to the aims, scope and goals of the TSG 24.

2. To be accepted, articles should meet at least the following criteria:

Empirical or developmental:(a) a clear statement of the purpose of the paper, (b) theoretical framework and related literature, (c) methodology, (c) synthesis and discussion of results and implications, (d) clarity, and (e) relevance to the TSG 24 audience.

Theoretical essays: (a) a statement about the focus of the paper, (b) theoretical framework, reference and related literature, and; (c) a clearly articulated statement of the author’s position on the subject, (d) clarity and (e) relevance to the TSG 24 audience.

3. Papers previously presented at international conferences cannot be accepted.

4. Each participant may propose only ONE paper, although a group of authors may propose several papers, each one to be presented by a different author attending the conference.

The format of papers must be as follows:

1. A maximum of eight pages, including references, tables, figures and appendices.
2. Written in English using Times 12-point font, 12-point line space, and 6 points between paragraphs (except tables: 6 points after paragraphs); Paper size A4 and margins: 25 mm (all sides).
3. The title should be centered (in 14 point bold capitals), author(s) name(s) (in 12 point bold), affiliation(s) of author(s) (in 12 point italics) and email address, in this order; all in Times.
4. The name of the presenting author(s) should be underlined.
5. The paper must begin with an abstract of up to ten lines, single-spaced, in italics.
6. References should be in the style used in Educational Studies in Mathematics (ESM)

Paper review process:

All papers will be reviewed by three reviewers. We will use a peer review process. Authors will be invited to help with the reviewing process. If authors are able to help with the reviewing process, please kindly indicate the number of papers they can help to review while submitting their papers to the co-chairs. Reviewers will recommend acceptance, acceptance with modification, or rejection of a manuscript. The final decision will be made by the co-chairs of the group.

Call for papers

TSG 24 invites contribution of research papers (empirical, theoretical, or developmental). In the papers, the author (s) can obviously be interested in presenting and discussing their research including the following types of information (related to the above general issues):

1. Statements of practices, descriptions of classes, chronicles, and episodes.

2. Research using the statements of practices to answer questions about teaching, or comparisons, for example. Identification and analysis of classroom practices and their conditions…

3. Theoretical and experimental studies on the tools of analysis of the practices in the classroom; on the concept of classroom practice, on their identifiers, their characteristics, on what is observable; their relationship with the school processes, with conditions and situations in which they appear; relations with the results; studies about the methods of research, etc.

How to join the group

TSG 24 will have two one-hour and two ninety-minute sessions in the congress timetable. Participants will be expected to stay in this TSG throughout the four sessions. Based on the reading of the accepted papers, some papers will be accepted for oral presentations which will be divided into some subgroups (themes). Some papers will be accepted for distribution and they will be posted on the website only.

If possible, we will explore the feasibility of organizing a forum, open to all, for discussions by email before the conference. Details of the forum may be posted on the web with the accepted papers.

Important dates

Program

Topic Study Group 24: Research on classroom practice

Timetable

(Each oral presentation have 24 minutes including questioning)

Time	Room A	Room B
Tuesday First session: 1 hour
12h- 12.12	Presentation and organization of TSG24 meeting by Co-chairs
(12.12-13h) 2 presentations de 24 minutes	02 Organization of the study in 10th grade classes analysis of the didactical contracts 08 The explanation of the teachers. An experience study of the notion of similarity in upper middle level	01 Solving Mathematical Word Problems in Primary Grades 05 Confucian Heuristics and Mathematics Teaching in Shanghai: Qifa Shi Teaching
Wednesday Second session: 1h 30
Time	Room A	Room B
(12h -13.30) 3 presentations de 24 minutes	04 Studying arguments in mathematics classroom. A case study 07 A theoretical characterization of service mathematics. 10 The reproducibility phenomenon in the context of teacher-student interactions.	11 Supporting secondary novices’ efforts to implement a Pedagogy consonant with the NCTM teaching standards 12 Motion sensor: a learning tool for reading function graphs 15 Exploring functional relationships to foster Algebraic thinking in grade 8
12 minutes	Questions and debates
Friday Third session: 1hour
Time	Room A	Room B
(12. 30 -13.30) 2 presentations of 24 minutes	14 Communication in the classroom: practice and Reflection of a mathematics teacher 17 Tensions in integrating mathematics and other school disciplines: Cases from classroom teachers in South Africa	16 A glimpse of a mathematical enculturator in Chinese mathematics classrooms: an example from a shanghai lesson 18 A trajectory to generalization: the teacher’s support to pupils’ mathematical investigations in the classroom
(12 minutes)	(All in Room A) 06 Status and methods of observation of classroom practices: Pieces of discussion from the example of the COREM (Chopin presented by Guy)
Saturday Fourth session: 1:30 hour
Time	Room A	Room B
(12 -13.30) 2 presentations of 24 minutes	21 A-didactical situation in multicultural primary school 22 Sharpening Teaching Ability in K-8 Mathematics Classrooms	19 Secondary school students’ understanding of the Concept of function 20 The Impact of Written Reflections in a Geometry Course for preservice Elementary Teachers
30 minutes	Questions and debates (All in Room A)
12 minutes	Perspectives and conclusions Co Chair (Ida) (All in Room A)

Papers and discussion documents

Papers Accepted (91.00 KB)
An, Wu & King (191.00 KB)
Arias & Araya (196.00 KB)
Brousseau (85.00 KB)
Cabañas & Cantoral (143.00 KB)
Cao, Xu & Clarke (154.00 KB)
Gill & O'Donoghue (93.00 KB)
Hesiquio (92.00 KB)
Ho (195.00 KB)
Lezama (114.00 KB)
Lewis (102.00 KB)
Lo Cicero & Spagnolo (202.00 KB)
Mangiante (105.00 KB)
Martinho & Ponte (65.00 KB)
Matos & Ponte (211.00 KB)
Mok (66.00 KB)
Mwakapenda (404.00 KB)
Oliveira (82.00 KB)
Saraiva & Teixeira (137.00 KB)
Soto-Johnson, Wheeler & Cribari (114.00 KB)
Wu & Li (84.00 KB)
Torres & Martinez (110.00 KB)
Chopin (55.00 KB)
Program (278.00 KB)
Spanolo & DiPaola (168.00 KB)

The role of mathematics in the overall curriculum

Aims and scope

Mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.

The purpose of this TSG is to investigate the role of mathematics in the overall curriculum. Due to the wide range of possible issues that could be addressed in this TSG, we plan to organize the papers and accompanying discussions into three key strands.

Firstly, we ask the question: why does mathematics hold such an important and unique place among other subjects? That is, what is the significance of mathematics in the overall school curriculum? As a point of departure we offer a few thoughts on why mathematics should be treated as an important subject in overall curriculum.

- Mathematics has a transversal nature. If we reflect on the history of curriculum in general, then mathematics (geometry and algebra) were two of the seven liberal arts in Greek as well as in medieval times. This historical role supports the notion that mathematics has provided the mental discipline required for other disciplines.

- Mathematical literacy is a crucial attribute of individuals living more effective lives as constructive, concerned and reflective citizens. Mathematical literacy is taken to include basic computational skills, quantitative reasoning, spatial ability etc.

- Mathematics is applied in various fields and disciplines, i.e., mathematical concepts and procedures are used to solve problems in science, engineering, economics. (For example, the understanding of complex numbers is a prerequisite to learn many concepts in electronics.) The complexity of those problems often requires relatively sophisticated mathematical concepts and procedures when compared to the mathematical literacy aforementioned.

- Mathematics is a part of our human cultural heritage, and we have a responsibility to develop that heritage.

Secondly, since mathematics provides foundational knowledge and skills for other school subjects, such as sciences, art, economy, etc., the issue of how mathematics is intertwined with other school subjects deserved to be addressed. In some curricula, mathematics is offered independently to support the study of other school subjects as an ‘instrumental subject’, and in other curricula, integrated courses which combine mathematics and other fields are offered.

Thirdly, we may wish to reflect on the number of hours (proportion of hours) and/or courses allocated to mathematics when compared to the other school subject in the curriculum of each country. In addition to this quantitative analysis, information about the qualitative description of school mathematics in relation to other subjects also needs to be gathered. Although this comparison won’t show us the whole picture of why different countries attach the importance that they do to mathematics, the comparison may nonetheless provoke further discussion.

Call for papers

The TSG 25 organizing team cordially invites all interested researchers and teachers to submit papers related to the topic of this group, in particular to its aims and scope. Any contribution addressing questions, problems and issues related to the topics listed above may be submitted. We welcome proposals from both researchers and practitioners, and encourage contributions from all countries with different cultural backgrounds.

Method of submission: email attachment to the TSG 25 chairs – Aarnout Brombacher (aarnout@brombacher.co.za) or Kyungmee Park (kpark@hongik.ac.kr)

Deadline for submission of abstracts (1-2 pages) – 15 January, 2008

Notification of acceptance of abstracts – 31 January, 2008

Submission of full papers – 15 March, 2008

Notification of acceptance of papers – 31 March, 2008 (i.e. accepted for presentation, accepted for distribution or on the website, rejected)

Program

First session – July 7th (60 min) Monday 13:00 to 14:00h

13:00-13:15h	Introduction to the theme by Aarnout Brombacher
13:15h – 13:40h	Curricular Methodology for the Mathematics In The Engineering Careers Patricia Camarena Gallardo and Alma Alicia Benítez Pérez
13:40h – 13:45h	Critical reaction by Joana Brocardo/Aarnout Brombacher
13:45h – 14:00h	Discussion

Second session – July 9th (90 min) Wednesday 12:30 to 14:00h

12:30 – 12:55h	Using Mathematical Inquiry To Engage Student Learning Within The Overall Curriculum Jill Fielding-Wells and Katie Makar
12:55 – 13:00h	Critical reaction by Joana Brocardo
13:00 – 13: 25h	The Place of Mathematics in the Integrated Curriculum Pamela Perger and Margaret Thomson
13:25 – 13:30h	Critical reaction by Aarout Brombacher
13:30 – 14:00h	Discussion

Third session – July 11th (60 min) Friday 12:30 to 13:30h

12:30 – 12:55h	Mathematics in a New Interdisciplinary Subject for Upper Secondary Education: aSMaT Jenneke Krüger
12:55 – 13:00h	Critical reaction by Kyungmee Park
13:00 – 13:30h	Discussion

Last session – July 12th (90 min) Saturday

12:00 to 13:30h

Structures discussion that follows from the earlier sessions

Papers and discussion documents

Using Mathematical Inquiry to Engage Student Learning Using Mathematical Inquiry to Engage Student Learning within the Overall Curriculum (130.00 KB)
Mathematics in a new interdisciplinary subject for upper secondary education: aSMaT (129.00 KB)
CURRICULAR METHODOLOGY FOR THE MATHEMATIC IN THE ENGINEERING CAREERS (69.00 KB)
The Place of Mathematics in the Integrated Curriculum (107.00 KB)
TSG25 Programme (49.00 KB)

Learning and cognition in mathematics: Students´ formation of mathematical conceptions, notions, strategies, and beliefs

Proposals by

- Mirela Rigo mrigo@cinvestav.mx
- Therese Dooley Therese.Dooley@spd.dcu.ie
- Samuele Antonini samuele.antonini@unipv.it
- Marita Barabash maritab@013.net
- Matsuo Nanae matsuo@faculty.chiba-u.jp
- Silfverberg Harry harry.silfverberg@uta.fi

Program

Monday 13:00-14:00

Introduction and Overview 13:00-13:10 (10 Mins)

Gabriele Kaiser, Bjoern Schwarz, 13:10-13:40 (30 Mins) “Beliefs and Professional Knowledge of Future Teachers – Qualitative Studies on Influences and Relations” (Gabriele Kaiser & Björn Schwarz)

JeongSuk Pang 13:40-13:52 (12 Mins) “Prospective elementary teachers’ beliefs and knowledge: Division of fractions”

* Reflecting 13:52-14:00:(8 Mins) Including any papers on site linking to the day’s sessions

Wednesday 12:00-13:30

Anna Sfard, Dani Ben-Zvi, 12:00-12:30 (30 Mins) Topic associated with “The Learners’ Autonomy”

Gaye Williams 12:30-12:42 (12 Mins) “Optimism-building to increase problem solving capacity”

Thérèse Dooley 12:42-12:50 (8 minutes) “How a performance glitch led to mathematical insight in a primary class

Reflecting and Connecting: 12:50-13:00 (10 Mins) Including today’s sessions, any papers from previous days linking to this, and papers on site linking to the day’s sessions.

Matuso Nanae & Harry Silfverberg 13:00-13:10 (10 minutes) “Similarities and differences between Japanese and Finnish 6th and 8th Graders’ ways to interpret and apply the definitions of geometric concepts”

Reflecting 13:10-13:20: (10 Mins) Including papers on site linking to sessions

* Preliminary Thoughts About Ways to Use Knowledge Gained 13:20-13:30: (10 Mins)

Friday 12:30-13:30

Masami Isoda 12:30-13:00 (30 Mins) “Getting others’ perspectives through Hermeneutic Effort: A theory of understanding for planning the problem solving teaching approach.”

Despina Potari 13:00-13:12 (12 Mins) “Prospective Primary Teachers’ Conceptions of Axial Symmetry”

Irene Biza, 13:12-13:20 (8 mins) “Models of students’ conceptions about tangent lines”

* Reflecting:13:20-13:30 (10 minutes).

Saturday 12:00-13:30

Dick Lesh 12:00-12:30 (30 Mins) “Models & Modeling Perspectives on the Nature of Mathematical Knowledge”

Guershon Harel 12:30-12:42 (12 Mins) “Constituent Elements of Mathematical Knowledge”
Samuele Antonini 12:42-12:50 (8 minutes) “Student use of Reductio Ad Adsurdum”

Reflecting* 12:50-13:00 (10 minutes) Plenary 13:00-13:30 (30 mins) Developing and overview. Where to from here?

Papers and discussion documents

Call For Papers (32.00 KB)
2 Rina Hershkowitz: Abstract (21.00 KB)
3 Terry Wood: Abstract (22.00 KB)
4 Anna Sfard: Abstract (36.00 KB)
5 Richard Lesh: Abstract (40.00 KB)
Numbering Key and Program Overview (23.00 KB)
Despina Portari P Abstract (20.00 KB)
Gaye Williams P Abstract (40.00 KB)
Guershon Harel P Abstract (52.00 KB)
JeongSuk Pang P Abstract (46.00 KB)
Information on Online Discussion (30.00 KB)
Panel_PangJ_Prospective Elementary Teachers’ Beliefs And Knowledge: Division Of Fractions (70.00 KB)
ECR_DooleyT_How A ‘performance glitch’ led to mathematical insight in a primary class (84.00 KB)
ECR_AntoniniS_STUDENTS’ USE OF REDUCTIO AD ABSURDUM (91.00 KB)
ECR_BarabashM_Characterization Of Mathematical-Cognitive Development Using Two Dimensional Model Of Insight (373.00 KB)
CFP_Mevarech & Armani_The Effects of Metacognitive Instruction on Students’ Mathematics Achievement and Regulation of Cognition (42.00 KB)
CFP_Ulep_Student Learning in Mathematical Interactions (83.00 KB)
CFP_Hagen_Raising Levels of Student Engagement through Imaginative Education – The Student Perspective (49.00 KB)
Welcome to TSG26 Online Discussion (2.00 KB)
CFP_Matsuo & Silfverberg_SIMILARITIES AND DIFFERENCES BETWEEN JAPANESE AND FINNISH 6TH AND 8TH GRADERS’ WAYS TO INTERPRET AND APPLY THE DEFINITIONS OF GEOMETRIC CONCEPTS (93.00 KB)
1 Gabriele Kaiser Abstract (20.00 KB)
Discussion Almost Starting (39.00 KB)
TonyGardiner_Uk_220208_RequestInfoGayePaper (26.00 KB)
TonyGardiner220208_Optimism (1.00 KB)
GayeResponseTonyGardiner_Optimism (4.00 KB)
ECR_BizaI_Models of Students' Conceptions About the Tangent Line (96.00 KB)
CFP_White&Mitchelmore_Teaching for Abstraction: Then and Now (74.00 KB)
Discussion:PaulWhite140408 (4.00 KB)
Discussion:Dick Lesh_Response To Paul White 1404 (8.00 KB)
Changes to Expert Team Composition (25.00 KB)
ECR_RigoM_Students’ beliefs within the context of elementary school mathematics classes (80.00 KB)
6. Masami Isoda: Getting Others' Perspectives Through Hermeneutic Effort (279.00 KB)
Program Final as at 5th July 2008 (75.00 KB)
Discussion_GayeWilliams_usage_of_'Insight' (50.00 KB)
Discussion_PamelaHagen_Usage_of_'Engagement' (39.00 KB)
Panel_WilliamsG_Links Between Optimism-Building and Problem Solving Capacity (68.00 KB)

Mathematical knowledge for teaching

Scope

TSG27 complements and is focused differently from the work of Topic Study Groups 28 and 29. These groups are more generally concerned with pre- and in-service teacher education. We are concerned with teacher content knowledge and its relationship to teaching skill. This implies that mathematical knowledge for teachers and mathematical knowledge for professional mathematicians have similarities and also important differences. What are these differences? These differences are not restricted to different amounts and different areas of mathematical knowledge. The differences have to be understood on the basis of different epistemological views on the nature of mathematical knowledge in different contexts and on the function for which the mathematical knowledge is used. The call for papers below is indicative of this focus. We are not concerned with teacher beliefs, the relationship between beliefs and practice, nor with teacher education practice and approaches that do not focus on knowledge of mathematics and its use in teaching. These aspects of mathematics teacher education, although important, are in the background for this Topic Study Group, whereas they are likely to be more in focus on TSG28 and 29.

Focus Questions

TSG 27’s work is framed by the following focus questions:

Q1. What are (and have been) different perspectives about mathematical knowledge for teaching? What are the bases––theoretical or empirical––for these perspectives? Where are areas of overlap and agreement? Where and what are major differences? Do these represent substantially conflicting views, or do they simply reflect giving attention to different aspects of the question?

Q2. What are (and have been) different methods of studying mathematical knowledge for teaching ––what teachers know and use, or what they need to know and know how to use? What are key common and distinct aspects of the methods used to answer these questions?

Q3. What are (and have been) different empirical research fields or contexts e.g. in primary or secondary classrooms, with or without digital technologies, with or without teachers as co-researchers, in mathematics or maths method classes for teachers? How have these shaped the research questions pursued?

Q4. How could research results gained by different research methodologies (quantitative, qualitative, interpretative research methods) support teachers developing their mathematical knowledge and their professional view on the nature of mathematics in teaching?

Q5. What are some distinct approaches to helping teachers develop the mathematical knowledge they need to know and know how to use? What kinds of evidence are there about how these function and with what effects?

The Sessions

PROGRAMME

Day 1, MONDAY 7 July 1 hour: Framing the work of the group

Major issues in the terrain of maths knowledge for teaching -Jill Adler, Deborah Ball An epistemological orientation to the problem of MKT ...Heinz Steinbring

Day 2: WEDNESDAY 9 July 90 mins.

Work in smaller groups on a selection of themes informed by the submitted papers.

We ask that all participants read the papers prior to the Congress. Some of the papers speak to more than one of the themes. We think these are interesting themes that can both inform the discussion, and give scope for those who have contributed papers to talk about their work within a larger theme.

Provisional themes * Are MKT and its components most effectively described and grasped by topic? Big ideas? Mathematical use? (Yasuhiro Sekiguchi and Mercy Kazima) * Are categories or distinctions within MKT useful and for what? (Li Jianhua, Dany Huillet) * Is MKT teachable and in what forms? (Craig Pournara, Raven McCrory). * Is MKT measurable? If so, what kinds of measures are in use and in what contexts, for what purposes? How do such measures interact with environments of high stakes assessments. (Mark HooverThames, Stefan Krauss)

Day 3. FRIDAY 11 JULY, 1 Hour.

Synthesis: What do we seem to agree on, what not, and why?

Brent Davis and Tim Rowland

Day 4 SATURDAY 12 July 90 Mins: Ways forward for this line of work; critical next steps

Outcomes for this Topic Study Group

1. Greater shared understanding of breadth of question, ranging and developing methodologies (approaches and methods and how they shape the work) as well as emerging knowledge/understanding

2. Exemplars of practice

3. Post–ICME report/publication

Call for Papers and Expressions of Interest

Thirty papers have been received and accepted. See details below. We welcome other participants to the sessions at the Congress.

Accepted papers

The papers listed alphabetically below have all been accepted for discussion in the Topic Study Group TSG27.

(Please note the paper by Thames et al. is not in alphabetical order. It has just been received and uploaded on to the site. The paper can be found at the end of the list. Message posted-20 Jun 08.)

(Please note that the papers by Heid and Senk et al. are not in alphabetical order. They have just been received and uploaded on to the site. The papers can be found at the end of the list. Message posted-30 Jun 08.)

(Please note that the paper by Kristjansdottir is not in alphabetical order. It has just been received and uploaded on to the site. The paper can be found at the end of the list. Message posted-05 Jul 08.)

List of Authors and Paper Titles

Authors	Paper Title
Susan Addington, David Dennis & Madeleine Jetter	Measurement and Multiplicative Thinking in Prospective Elementary Teachers
Solange Amorim Amato	Avoiding the Teaching of Mathematics
Sarah Bansilal	Can reform pedagogies be facilitated by teachers who themselves do not have a sound concept image of the crucial mathematics?
Kim Beswick	Middle School Mathematics Teachers’ Knowledge for Teaching
Tim Burgress	Statistical Knowledge for Teaching: Exploring it in the Classroom
Charalambos Y & Charalambous	Mathematical Knowledge for Teaching and Teaching Practices: A Virtual-Design Approach to Study a Complex Relationship
Brent Davis	“Concept Study”: Open vs. Closed Understandings of Mathematical Ideas
Juan D. Godino, Mauro Rivas & Walter F. Castro	Epistemic and Cognitive Analysis of an Arithmetic- Algebraic Problem Solution
Pedro Gomez & Maria Jose Gonzalez	Mathematics Knowledge for Teaching Within a Functional Perspective of Preservice Teacher Training
Raisa Guberman & Dvora Gorev	Learning Mathematics for Teaching: Sources of Subject-Matter Knowledge
Lenni Haapasalo & Jozef Hvorecky	Perspectives on Mathematical Knowledge for Teaching
Danielle Huillet	Mathematics For Teaching: An Anthropological Approach
Mercy Kazima	Investigating Mathematics for Teaching through Probability in Practice
Stefan Krauss, Michael Neubrand, Werner Blum & Jürgen Baumert	The Professional Knowledge of German Secondary Mathematics Teachers: Investigations in the Context of the COACTIV Project
Anna Kristjansdottir	Developing of teachers’ professional knowledge of mathematics. Historical, present and future perspectives
Alexandra Lawson & Wendy Stienstra	Pre-service Students’ Partial Understandings of Elementary Mathematics Concepts and Procedures
Katie Makar	Knowledge for Teaching Mathematics Through Inquiry
Raven McCrory	Resource Use by Instructors of Mathematics Classes for Future Elementary Teachers: Results of a Survey
Shweta Naik	The Measures for Understanding Teachers’ Mathematical Knowledge for Teaching Fractions- How do they really work?
Aihui Peng	Inquiry into Students’ Mathematical Thinking Through Error Analysis as a Means to Teacher Development
Craig Pournara	Developing Mathematical Knowledge for Teaching in a Pre-service Secondary Teacher Education Programme in South Africa
Tim Rowland	The Knowledge Quartet: A Theory of Mathematical Knowledge in Teaching
Allan Tarp	CATS, Count&Add in Time&Space – a Natural Way to Become a Mathematics Teacher
Kazuko Ito West	Japanese High School Mathematics Teacher Competence in Real World Problem Solving
Zhonghe Wu & Shuhua An	Using the Model-Strategy-Application Approach to Developing Pre-service Teachers’ Knowledge and Assessing Their Progress in Math Methods Courses
Mark Hoover Thames, Laurie Sleep, Hyman Bass, and Deborah Loewenberg Ball	Mathematical Knowledge for Teaching (K-8):Empirical, Theoretical, and Practical Foundations
M. Kathleen Heid	Mathematical Knowledge for Secondary School Mathematics Teaching
Sharon L. Senk, Ray Peck, Kiril Bankov, Maria Teresa Tatto	Conceptualizing and Measuring Mathematical Knowledge for Teaching: Issues from TEDS-M, an IEA Cross-National Study1

Papers and discussion documents

Addington_ICME11_TSG27_prop (90.00 KB)
Amato_ICME11_TSG27_fullpaper (91.00 KB)
Bansilal_ICME11_TSG27_fullpaper (105.00 KB)
Beswick_ICME11_TSG27_fullpaper (222.00 KB)
Burgess_ICME11_TSG27_prop (173.00 KB)
Charalambous_ICME11_TSG_27_prop (44.00 KB)
Davis_ICME11_TSG27_prop (103.00 KB)
Godino_ICME11_TSG27_fullpaper (188.00 KB)
Gomez_ICME11_TSG27_prop (104.00 KB)
Guberman_ICME11_TSG27_fullPaper (67.00 KB)
HaapasaloHvor_ICME11_TSG27_prop (275.00 KB)
Huillet_ICME11_TSG27_fullpaper (99.00 KB)
Kazima___ICME11__TSG27_prop (54.00 KB)
Krauss_ICME11_TSG27_fullpaper (131.00 KB)
Lawson_ICME11_TSG27_fullpaper (243.00 KB)
McCrory_ICMI_TSG27_prop (63.00 KB)
NAIK_ICME_TSG27 (127.00 KB)
Peng_ICME11_TSG27_fullpaper (177.00 KB)
POURNARA_ICME11_TSG27_fullpaper (58.00 KB)
Rowland_ICME11_TSG27_fullpaper (60.00 KB)
Tarp_ICME11_TSG27_fullpaper (167.00 KB)
West_ICME11_TSG27_fullpaper (100.00 KB)
Wu_ICME11_TSG27_prop (224.00 KB)
Thames_ICME11_TSG27_fullpaper (152.00 KB)
Heid_ICME11_TSG27_fullpaper (149.00 KB)
Senk__ICME11_TSG27_fullpaper (220.00 KB)
Kristjansdottir_ICME11_TSG27_fullpaper (181.00 KB)
Makar_ICME11_TSG27_Prop_1_ (123.00 KB)

Inservice education, professional life and development of mathematics teachers

AIMS, SCOPE AND GOALS

The professionalization of teaching requires teachers and teacher educators to be involved in a learning process throughout their entire professional life. The complexity of mathematical teaching practices raises a lot of questions for inservice teacher education. Nowadays, schools are confronted with many challenges like the elaboration of new curriculum grounded in learning/teaching paradigms that call into question a number of mathematical teaching practices, the consideration of specific culture contexts to rethink these curriculum and mathematical teaching practices, the integration of historical dimensions into teaching, the development of interdisciplinary projects, the introduction of new technologies into classrooms, or the adaptation of teaching practices for different students and contexts (students with learning difficulties, multicultural classrooms, ESL/teaching mathematics in a second language, underprivileged schools, adults, analphabetism…). The problems encountered differ according to the teacher education systems in place in each country.

These challenges demand serious reflections as to how to support the persons directly concerned by these issues (practicing teachers and other school practitioners) and develop means that take into account the differing problems to educate teachers in each country. Inservice teacher education can take different forms (courses, colloquium, sharing experiences, collaborative practices…) and can be supported by different persons (teachers, pedagogical consultants, teacher educators, researchers, mathematicians…). In the past, this inservice education has often been considered as inappropriate or too distant from real classrooms practices and teachers knowledge. However, in the last decade, different experiences and alternative approaches have been developed worldwide to support the learning process of practitioners for, in and from practice (web communities, teachers working in collaboration, action research, collaborative research, communities of inquiry, teachers research …). Most of these approaches and experiences take seriously into consideration the practitioners’ points of view and their knowledge in the support processes of the practice, mainly through the development of school curriculum, learning/teaching situations and in the construction of mathematical professional knowledge linked to the teaching practice.

What do we know about these different approaches and experiences developed to support the professional development of teachers? How are they characterized and researched? How do they take into account the challenges and complexities of teaching practices in different socio-cultural contexts? What do we know about the sorts of professional learning taking place in these approaches and settings? What do these suggest concerning the initial mathematics teachers education?

Issues and questions to be addressed are:

- What do we mean by teachers’ professional development in mathematics? Which conceptualizations of professional development are emerging from research in mathematics education? What are their different theoretical and epistemological bases?

- When and how does professional development begin and grow along the professional life of a teacher?

- What strategies, practices and processes are identified and described as promoters or catalysts of the teachers’ professional development?

- How is the process of professional development being favored or hindered by the public politics in the different countries?

- How does inservice education address the question of the complexity of practice in mathematics education and the challenges it is confronted with? (searching to take into account this complexity, to address some of these challenges…)

- What do we know of approaches and experiences developed to support the professional development of teachers? Especially, how can we characterize the process developed within and throughout the approach in regard to its relation to practice, to the role of teacher educators and teachers, to the learning taking place?

- How does inservice education take into consideration the contexts of cultural diversity or of specific cultures, and the mathematics developed in given cultural or professional groups ( Bishop, 1988;D’Ambrosio, 2001;Gerdes, 1995;Lave, 1988)?

First session - Lecture of Barbara Jaworski

“Mathematics Teacher Education in a Global Context”

Barbara Jaworski (B.Jaworski@lboro.ac.uk)

“Abstract:” Over the last 2 decades, mathematics teacher education (MTE) has grown as an important sub-discipline of the discipline of mathematics education. I will begin by tracing this development in terms of both the historical dimension and its key elements/instruments. This includes significant papers and working groups at major conferences, the journal JMTE (Journal of Mathematics Teacher Education), a dedicated survey at ICME 10, books and a handbook, and major trends. Research in the area (and in some cases the lack of it) will be a principle focus. I will then address what seem to me to be the current major trends in MTE, particularly with regard to knowledge in teaching, the education of practising teachers and development of teaching. This includes elements of reflective practice, teachers’ engagement in (action) research and partnerships between teachers and academics/educators. The roles and development of mathematics teacher educators is also an important focus. I will end with a perspective on our future within mathematics teacher education.

FORMAT AND ORGANIZATION OF THE TOPIC

In the ICME 11 programme, TSG28 will have two one-hour sessions and two ninety-minute sessions at its disposal, thus 5 hours in total. This is a very short amount of time to deal with such ambitious issues, as well as potentially many contributions.

To take into account this short amount of time, the team made the choice to organize the study group not in terms of oral presentations (of each paper). The dynamics will be the following: for each set of 4 or 5 papers related to a common sub-topic (or sub-theme), a researcher (or critical respondent) will be indicated or invited by the team to make a simple synthesis of the papers and to raise some questions to be discussed by participants together with authors. In addition, in the first session, a lecture will be given that will present an overview of the current state-of-the-art in the topic, and of important questions to discuss.

A panel on important issues linked to the topic of the group will also be organized during the last session of TSG28. This panel will be oriented by questions developed by team leaders.

CALL FOR PAPERS

For TSG28, we invite papers that fit with the aims and the focus outlined above.

- Papers should have a clearly focus on issues relating to inservice education, professional life and development of mathematics teachers;

- In particular, papers should be oriented toward the main focus of the topic study group, that is, approaches and experiences developed to support professional development of teachers FOR, IN and FROM practice, precisely concerning some of the questions and issues pointed above;

- Papers that report research should make very clear the theoretical and methodological positions adopted, as well as an analysis of the approach developed, including an appropriate blend of theory and practice;

- Papers reporting on practical experiences should make very clear the reflective (or theoretical) part of the experience. In other words, papers cannot be mere descriptions of an experience.

These four points will constitute the main criteria for reviewing papers and for recommending acceptance to the group.

PAPER FORMAT AND SUBMISSION

A common format for all papers is required to allow ease of reading and critical judgment across papers. This will also facilitate a publication on the website, in order for the participants to have access to the papers prior to the meeting.

Papers should be of a maximum of 8 pages in length, including references and figures, on “letter” format. They should be written in English. Text should be 12 point Times New Roman, 1 1/2 spaced, with 6 points spacing between paragraphs, and margins of 1 inch (2.54 cm) all around.

Papers should be preceded by an abstract of up to 250 words, single spaced, 10 points Times New Roman.

The title should be in 14 point Times New Roman, bold capitals, followed by the authors’ names, affiliations and country in 14 point Times New Roman Italics. Titles, authors’names and information should be centered in the text; with names of presenting authors underlined. References should follow the APA style.

Papers that do not meet these requirements will not go into the review process.

PLEASE SEND YOUR PAPER BY EMAIL ATTACHMENT TO EACH GROUP LEADER (CHAIRS AND CO-LEADERS) BY NOVEMBER 1ST, 2007. YOU WILL FIND THE FIVE EMAIL ADDRESSES LISTED ABOVE. INDICATE CLEARLY THE NAME OF THE CORRESPONDING AUTHOR AND PROVIDE AN INSTITUTIONAL ADDRESS, EMAIL ADDRESS AND TELEPHONE NUMBER FOR THIS PERSON. INDICATE ALSO WHICH AUTHORS WILL BE ATTENDING TSG28 AT ICME-11 AND PRESENTING THE PAPER, BY UNDERLINING THEIR NAMES ON THE PAPER.

PAPER REVIEW PROCESS

Each paper will be reviewed by three referees, one of the group leader and two experts in the topic that have also submitted papers to the TSG-28.

Reviewers will recommend acceptance, acceptance with modifications, or rejection of a paper. The final decision will be taken by group leaders.

TIMESCALE OF PAPER SUBMISSION AND THE REVIEW PROCESS

November 10th , 2007: An extension of deadline for submission of papers.

November 2007 to December 2007: Review process. Authors are informed of the decision on their paper by December 20th, 2007. Papers rejected at this stage will not be reconsidered.

January, 15th, 2008: Authors with papers accepted with modifications resubmit papers following recommendations. These papers will be read by one of the group leaders who will make a decision about acceptance (on the basis of the authors’ attentive responses to reviewers’ recommendations).

January 22nd, 2008: Final decisions about contributing papers and presentations.

February 2008: Group leaders structure the programme for the topic study group, on the basis of the accepted papers. Papers whose authors have registered for the ICME-11 conference and participation in this study group will be published on-line on the conference website.

Proposals by

- Naomi Chissick (Israel)
- Bracha Kramarski and Tali Revach (Israel)
- Ruth Beatty and Cathy Bruce (Canada)
- Jérôme Proulx (Canada)
- Mario Sanchez (Danemark)
- Christine Suurtamm and Nancy Vezina (Canada)
- Ginger Rhodes and Patricia Wilson (USA)
- Yeping Li, Rongjin Huan, Jiansheng Bao, Yadong Fan (China)
- Dario Fiorentini, Rosana G. S. Miskulin, Regina C.Grando and Adair M. Nacarato, Cármen L.B. Passos, Brazil
- Ana Cristina Ferreira and Maria Angela Miorim, Brazil
- Claudia Canha Nunes, Portugal
- Maria Teresa Menezes Freitas and Dario Fiorentini, Brazil
- Els de Geest, Marie Joubert Gibb, Rosamund Sutherland, Jenni Back, Christine Hirst, England

Papers and discussion documents

Beatty_Bruce (35.00 KB)
Chissick (28.00 KB)
Costa (114.00 KB)
Ferreira_Miorim (25.00 KB)
Fiorentini_Miskulin_Others (89.00 KB)
Freitas_Fiorentini (27.00 KB)
Geest_Joubert_Others (27.00 KB)
Kramarski_Revach (102.00 KB)
Li_Huang_others (29.00 KB)
Murphy (27.00 KB)
Nacarato_Grando (25.00 KB)
Nunes (26.00 KB)
Passos_Lamonato (22.00 KB)
Proulx (144.00 KB)
Rhodes_Wilson (150.00 KB)
Sanchez (134.00 KB)
Suurtamm_Vezina (26.00 KB)
Organization of the papers in sub-themes (12.00 KB)
FINAL SCHEDULE TSG28 (7.00 KB)

The preservice mathematical education of teachers

TSG 29: The pre-service mathematical education of teachers

The Topic Study Group 29 is designed to gather congress participants who are interested in pre-service mathematical education of elementary and secondary teachers. TSG 29 tries to collect, compare and discuss research experiences with the different practices of mathematical teacher education throughout the world. It seems important to discuss how similar/different are these from the certification or licensure examination for teachers as well as a variety of factors that influence the number and the type of teaching adaptations created by preservice teachers. Being aware of the possible ambiguity of the name of the topic, we would define here two basic terms: ‘pre-service teacher’ and ‘mathematical education’, followed by the scope and focus of this topic group.

Basic Definition

(a) Pre-service teachers are undergoing preparation to become qualified teachers. (b) Mathematical education refers to the kinds of mathematical content and knowledge that act as the integral part of the mathematics teacher education.

The Scope

TSG 29 is dedicated to sharing and discussing of significant new trend and development in research and practice about mathematical education of pre-service mathematics teachers. It aims to provide both an overview of the current state-of-the-art as well as outstanding recent research reports from an international perspective.

In order to provide a preliminary orientation to the field of study, some distinctions might be drawn. Above all, there seem to be substantial differences between the mathematical education of elementary and secondary teachers. Other differences relate to forms and sites, to contents and methods, and to agents and aims:

• Forms: Mathematics and mathematics education as consecutive or integrated components of the pre-service education of mathematics teachers.

• Sites: Traditional universities, teacher universities, or teacher training colleges as the providers of the mathematical education of teachers.

• Contents: What kind of mathematics is taught? Is the focus on academic mathematics or school mathematics? Apparently, many secondary mathematics teachers will have studied elements of what has been called ‘advanced mathematics’, whereas most elementary teachers will have studied ‘elementary mathematics’. Mathematics that is labelled as ‘advanced’ can consist of formal and highly abstract mathematics, but it can also be applied mathematics or mathematical modelling. Mathematics that is labelled ‘elementary’ can consist of a systematic introduction into the content knowledge of school mathematics, but it can also be an introduction into current conceptions of school mathematics (e.g. school mathematics as problem solving). Another issue is whether school mathematics is regarded from a higher (or meta-mathematical) advantage point. Is it just knowledge of mathematics or knowledge about mathematics as well, the latter comprising historical, epistemological, philosophical, and sociological knowledge of mathematics?

• Students: Apparently, pre-service teachers enter teacher education programs with quite different mathematical qualifications and expectations as well as social aspirations. Who is attracted and enrolled by teacher education programs? How does mathematical teacher education take these differences into account?

• Instruction methods: The pre-service mathematical education of teachers is often conceived as a transmission of a systematic collection of definitions, theorems, proofs. Alternatively, it might be organised and understood as an introduction into a particular human activity. This issue is strongly related to the weak or strong classification of teachers and learners: Is the mathematics given in lectures or has it to be re-constructed in self-regulated student study groups? How could we engage the relationship between a variety of epistemological position? (e.g. initial pupil position, university students’ position and teacher position).

• Agents: Who is in charge of the pre-service mathematical education of teachers? Mathematicians, experienced mathematics teachers, specialised mathematics teacher educators or didacticians.

• Aims: The particular forms, sites, contents, instruction methods and agents may produce a cumulative effect on the future teachers: In many places, the pre-service mathematical education of secondary teachers shows the tendency to aim implicitly at forming the habits of a mathematician, and not of a mathematics teacher.

Focus of TSG29

The main focus of TSG 29 will be on empirical, as well as theoretical and developmental papers on issues such as: (1) A comparison of mathematical contents or curriculum of pre-service mathematics education in different countries; (2) What kind of mathematics could we present to preservice teacher? What mathematical qualifications and expectations are need to teach? (3) The link or relationship between the kind of mathematics and the role of mathematical experiences of the pre-service mathematical primary and secondary teachers; (4) The impacts and effectiveness of pre-service mathematical education of teachers; (5) Innovative and creative approaches of developing mathematical content knowledge of pre-service mathematics teachers

Call for papers

We welcome proposals that deal with all aspects of the above focus and innovative ideas that promote a better mathematical education for pre-service mathematics teacher preparation program.

If you wish to present a paper, please send a text of 4000 words which present the theoretical framework and precise the relationship between the main focus of the TSG29 and your paper, the methodology, the results and the conclusion. It would be important to submit your text by email as Microsoft Word attachment to before 15 November 2007 to Lim Chap Sam (cslim@usm.my) or Lucie DeBlois (lucie.deblois@fse.ulaval.ca).

The full paper should be submitted as a single file in Microsoft Word format using Times New Roman 11-point font size and single-spacing. Please also include title, author(s), institution, postal address, fax, telephone numbers and email address at the beginning of the abstract. All papers will be peer-reviewed.

Informations

All texts at the end of this page were accepted by a commitee of pairs and were presented

Papers and discussion documents

Abramovich_Brouwer (39.00 KB)
Proulx_Bednarz (53.00 KB)
Ma_Millman_Wells (31.00 KB)
molina_Lupianez_Segovia (163.00 KB)
Dawson (35.00 KB)
Krzywacki-Vainio (43.00 KB)
Gomez, Rico, Gil, Lupiáñez, Marín, Moreno, Romero (173.00 KB)
Schedule TSG-29 (5.00 KB)
Lim Chapsam (93.00 KB)
Sayac (94.00 KB)

Motivation, beliefs and attitudes towards mathematics and its teaching

Aims and Focus

In the tradition of TSG 24 of last ICME, the Topic Study Group 30, “Motivation, beliefs and attitudes towards mathematics and its teaching” addresses researchers working in the field of affect in mathematics education. The constructs motivation, beliefs, and attitudes should be interpreted in the broadest sense of the terms. Consequently, we invite discussion on all areas of affect: attitude, beliefs, emotion, goals, identity, motivation, needs, self-concept, and values as they play a crucial role in mathematics learning and teaching.

Affect has been a topic of interest in mathematics education research for different reasons and from different perspectives for more than thirty years. Today we know that affective variables can be seen as either hidden or explicit factors that influence learning outcomes as well as teaching praxis. The different research perspectives that have been used in the study of affect include psychological, social, philosophical, and linguistic. We welcome all these and as well as other perspectives.

The aim of the TSG30 is to generate discussion around this broad field of related phenomena with a special emphasis on both, the students’ and the teachers’ level.

We would like to engage interested participants in the review process prior to the conference and nominate respondents to all presentations in order to enable deeper levels of critical discussion during the conference. The activities of the group during the conference will include a few lecture-type presentations with most of the time spent in discussions around accepted papers.

Key words: affect, attitude, beliefs, emotion, goals, identity, motivation, needs, self-concept, values.

Call for Papers

The organizers of the Topic Study Group 30, “Motivation, beliefs and attitudes towards mathematics and its teaching” invite research-based papers on affect in mathematics education. We encourage papers from researchers worldwide and are particularly interested in papers that relate theory to practice.

Based on the received proposals the Organizing Team of TSG30 will compose the program. Please keep in mind that Congress policy is that each individual is restricted to one major speaking appearance. The program of TSG30 is thus subject to final approval by the IPC of ICME-11.

The Organizing Team intends to edit a special issue of an international journal with selected papers accepted for TSG30.

Guidelines for proposals

Proposals should be in English and should have the following content:

- Title
- Name(s) and e-mail addresses of the author(s)
- Institution, country
- Abstract (max 10 lines)
- The main text
- References
- Appendices

The length of the paper may be 4–12 pages (including references and appendices). For submissions, please use the same format as for PME:

- A4 paper, size 21 cm x 29.7 cm
- Margins should be set at 2.5 cm top and 2.5 cm bottom; 2 cm left and 2 cm right
- All text should be Times.
- Sizes are 14 point for normal text and 13 point for quotes, transcripts and references
- Use 16 point line spacing and 6 points between paragraphs.
- Use no more than three levels of headings: TITLE uppercase 16 point, HEADING 2 uppercase 14 point, Heading 3 lowercase 14 point

A template is available at

http://www.pme31.org/proposals/proposals_templates.htm

Proposals should be submitted electronically to Team Chairs. Proposals received will be acknowledged upon reception.

If you have further questions, please contact any of the team chairs or team members.

Review Process

In TSG30 we will use a peer review system and provide an opportunity for participants to develop their papers through the review process. All contributors are expected to review 2-3 of the other papers and we welcome non-contributors to volunteer as reviewers. Guidelines for review will be sent to reviewers along with the papers to be reviewed. Based on the reviews, the organizing team will

accept the paper for an oral presentation,
accept the paper for presentation by distribution,
accept the paper for either oral presentation or presentation through distribution, but require the author(s) to revise their paper, or
reject the paper.

In cases 1), 2), and 3), the authors are expected to develop their papers based on the reviews and the paper will be published on the TSG30 website before the Congress. Authors may also bring paper copies to be distributed at the conference.

Important dates

- Submission of proposals 15 December, 2007
- Deadline for reviews 30 January, 2008
- Decision of the organizing team 15 February, 2008
- Submission of revised paper 1 April, 2008

Schedule

Session 1, Monday, 13.00 – 14.00, Overview on Research on Affect, Chairs: Günter Törner, Bettina Rösken, Presenters: Gerald Goldin, Inés Gómez Chacón

Session 2, Wednesday, 12.30 – 14.00, Students and the Affective Domain, Chair: Cristina Frade, Presenters: Miriam Liston, Naomi Ingram, Inés Gómez Chacón

Session 3, Friday, 12.30 – 13.30, Methodological Considerations, Chair: Sung Sook Kim, Presenters: Kirsti Kislenko, Jose M. Diego-Mantecón

Session 4, Saturday, 12.00 – 13.30, Teachers and the Affective Domain, Chairs: Günter Törner, Bettina Rösken Presenters: Cristina Frade, Chen Qian, Katja Maass

Papers and discussion documents

Language and communication in mathematics education

Aims, scope, and goals

TSG 31: Language and communication in mathematics education is a recurrent group in ICME, devoted to the discussion and diffusion of the latest research on language aspects of mathematics education in a broad sense. We strive to organise a fulfilling scientific experience for all participants, and – in consistence with the topic of the group – to maximise participants’ possibilities to communicate and discuss their results and concerns. Along this line, we also wish to point out that, while the official language of the congress is English, we are aware that this is not the native language of most of the participants, so we will do our best to ensure that non-native speakers of English can also follow and participate fully in our work.

Of course, given the breadth of the topic of the group, we face the challenge of organising the sessions in themes that will allow for focus and coherence in the discussions, and to take up issues which are of particular importance in current research. The call explains in more detail how we have chosen to do so. Please do not hesitate to contact the organisers with your concerns and questions.

We look forward to welcome you to our group in Mexico in 2008!

The organising team

Call for papers (expired)

CALL FOR PAPERS

The 11th international congress of mathematical education will held in Monterrey, Mexico, July 6-13, 2008 (see website). As in previous ICME’s, there will be a topic study on “Language and communication in mathematics education”. It will meet in four sessions during the congress (two session of an hour and two sessions of 1½ hour).

The organising team (see below) invites contributions for these sessions in the form of paper proposals pertaining to one or more of the following main themes:

A. What we write and say when teaching and learning mathematics : symbols, natural language, and other semiotic representations – what are their significance for teaching and learning?

B. Learning mathematics in another language : Challenges and approaches in teaching mathematics to students in another language than their mother tongue.

C. The way we justify, argue and prove in mathematics classrooms : Reasoning discourses in the classroom – challenges for learners, strategies for teachers.

Each of these themes will be considered according to three levels of education:

1. Primary level (learners of age about 5 to 12 years)

2. Secondary level (learners of age about 12 to 19 years)

3. Tertiary level and adult education (adults)

This leaves, in principle, the possibility of 9 different subthemes A1, A2, …, C2, C3. Depending on the proposals received, some of these may be merged, but we ask all proposals to identify with one of them as a first approximation. It may be that some papers identify with more than one of the main themes and more (or any) of the levels; still, you should indicate the one that suites best. Please send your contribution to both of the chairs (see below) with the following subject line: “TSG-31 proposal, subtheme Xn” (replace Xn by the subtheme, such as B3). Deadline is January 25, 2008 (NB: this is 10 days later than previously announced, and is due to temporary technical difficulties at this site, which has now been solved). Please notice that proposals can be up to 10 pages and that you must use the style file of PME, which can be found here . Proposals not using this style file, exceeding 10 pages, or arriving late, will be rejected without review.

Review and presentation

Papers will be reviewed by at least two referees and based on their reports, the organising theme will allot the papers to one of the following formats of presentation:

- subgroup discussion (here, the main focus will be on having focused, in-depth discussions on a group of connected papers; authors will present some questions relating to their paper that they wish the subgroup to discuss)

- paper by distribution (not presented, but may be included in subgroup discussions)

The exact planning of the four sessions is given below on this page. You can also download accepted papers below.

Detailed programme for the four sessions

The topic study group has accepted 23 papers: 17 for oral presentation and discussion in parallel sessions (P), and 6 for presentation-by-distribution (D). The accepted papers can be downloaded through the links below (in the section entitled “Papers and discussion documents”, where papers are marked “D” and “P” according to the category in which they have been accepted).

The oral presentation and discussion of papers will take place during our four sessions, as follows: each of the four sessions will have two parallel subgroups, in which a number of papers will be presented (max. 10 minutes for each paper, including if time permits short questions) and discussed (the remaining time). The papers of each subgroup are sufficiently related to enable a common discussion. Each subgroup will be chaired by a member of the organising team, who will be responsible to deliver a short report from the subgroup to the final session. Participants are encouraged to download, print and read the papers of the subgroup they attend, before the conference.

Here is the plan for the four sessions (papers are indicated by author name, see complete title and link to paper below); a more detailed plan, with room numbers for subgroups and so on, will be announced at the first session of the topic study group. Notice that the time slots for TSG’s were recently changed; if they are (again) different in the final congress programme, we will of course have our sessions at the times indicated in that programme, and the times below will have to be read accordingly.

SESSION 1 – TUESDAY JULY 8, 12.00-13.00

12.00-12.15:

Welcome, introduction to the group (B. Barton, C. Winsløw)

12.15-13.00:

Subgroup 1x: Theme C, Argumentation and proof (J. Hunter, D. Won Kim; Chair: I. Ben Kali)

Subgroup 1y: Theme A, Gesture (M. Cestari et al., S. Gerofsky; Chair: B. Herbel-Eisenmann)

SESSION 2 – WEDNESDAY JULY 9, 12.00-13.30

Subgroup 2x: Theme B, Second language (M. NiRiordain, M. Civil, K. Garegae; Chair: B. Barton)

Subgroup 2y: Theme A, Semiotics and representations (R. Rubenstein, N. Hardy, G. Foley; Chair: C. Winsløw)

SESSION 3 – FRIDAY JULY 11, 12.30-13.30

Subgroup 3x: Theme A, Writing and genres (R. de Oliveira, T. Meaney et al.; Chair: S. Gerofsky)

Subgroup 3y: Theme A, Role of teachers and language (F.-J. Hsieh, L. Ejersbo; Chair: B. Herbel-Eisenmann)

SESSION 4 – SATURDAY JULY 12, 12.00-13.30

12.00-12.30:

Subgroup 4x: Theme B, Second language (R. Hunter; Chair: S. Gerofsky)

Subgroup 4y: Theme A, Semiotics and representations (F. Roubicek; Chair: I. Ben Kali)

12.30-13.30:

Reports from subgroups by chairs (2½ minutes per paper, including questions)

Closing (B. Barton, C. Winsløw)

Papers and discussion documents

Gender and mathematics education

Call for papers

Participants in Topic Study Group 32 will focus on issues of gender with respect to the teaching and learning of mathematics for all students, at all levels of education, and in all contexts. Various theoretical and philosophical perspectives will also be examined.

It is recognised that gender differences in mathematics learning outcomes – participation, achievement, and affect – are not uniform across all countries, in all areas of mathematics learning, or for all groups of learners of mathematics. Research examining gender differences and interventions to address them are at different stages, take different forms, and are in receipt of different levels of funding and support around the globe.

AIMS AND ORGANIZATION OF TSG32

There will be four TSG 32 sessions. In the first session an invited speaker will open the deliberations of the TSG and will promote discussion.

In the remaining three TSG32 sessions, papers will be presented. Prospective participants are invited to submit proposals for papers to be included in these sessions. Empirical and non-empirical research studies in which a range of methodological approaches have been adopted are encouraged. Topics might include:

* The situation with respect to gender differences in mathematics learning outcomes – participation, performance, and/or attitudes/beliefs/values – within particular contexts
* Factors contributing to gender issues with respect to mathematics learning outcomes in particular contexts
* Societal, systemic, organisational, and/or cultural dimensions related to gender issues and mathematics teaching and learning
* The role of technology, resources, learning settings, and/or pedagogical approaches in addressing or re-inforcing gender differences in mathematics learning outcomes
* Theoretical and/or philosophical perspectives on gender issues and mathematics education

A diverse range of proposals from researchers representing developed and late developing nations is wanted.

CALL FOR PAPERS

The Proposal

If you are interested in presenting a paper that fit the aims and focus of TSG 32, your proposal is due on January 1, 2008. The following information must be provided:

title
name(s) of the author(s) and email contacts
institution (and location and country)
abstract of 300-500 words (excluding references)

The language used for the abstract must be English, the official language of ICME-11.

Please email your proposal to: Helen Forgasz whose email is Helen.Forgasz@education.monash.edu.au or to Maria Trigueros whose email is trigue@itam.mx

You will receive acknowledgment of receipt of your proposal.

Reviewing and outcomes

Submitted proposals will be reviewed by the organising team of the Topic Study Group (TSG 32).

The outcome of your proposal submission will be provided not later than January 26, 2008. All the accepted contributions will be published on the ICME-10 website before the congress. Depending on the number of submissions, the range of topics and the quality of the proposals, some authors will also be invited to present orally the papers at the congress; the other accepted contributions will be referred to during discussions at the sessions of the Topic Group.

In summary, due to the limited number of sessions for TSG 32 and the time available, papers will be accepted in two ways:

You may be invited to give an oral presentation at the conference and your paper will be uploaded to the TSG 32 website for all to read, OR
Your paper will uploaded to the TSG 32 website without an oral presentation, and will be referred in group discussions.

In both cases the organising team for TSG 32 must find the paper to be of high quality.

Accepted proposals

If your proposal is accepted for TSG 32, the deadline for submitting a full paper will be March 1, 2008. Full papers, in English, should be about 5000 words in length (excluding references), and should be emailed to: Liv Sissel Gronmo l.s.gronmo@ils.uio.no

Please circulate this Call for Papers to individuals who may be interested. If you have any questions about TSG 32, please send an email to: Olof Steinthorsdottir: steintho@email.unc.edu , or to Anna Chronaki: chronaki@uth.gr.

PLEASE NOTE: It is an ICME-11 policy that each individual is restricted to one major speaking appearance at the conference, which includes plenary lectures and panels, and organization of TSGs or DGs.

Papers and discussion documents

Barkatsas (65.00 KB)
Chamdimba (242.00 KB)
Forgasz (721.00 KB)
Hall (65.00 KB)
Kaino (39.00 KB)
Ma (70.00 KB)
Mendick (54.00 KB)
Paek (223.00 KB)
Pálsdóttir (35.00 KB)
Pourkazemi (86.00 KB)
Ramirez (269.00 KB)
Rodriguez (132.00 KB)
Steinthorsdottir (46.00 KB)
Trigueros (34.00 KB)
Vale (31.00 KB)
Knowles (10.00 KB)
Presentations schedule (7.00 KB)

Mathematics education in a multilingual and multicultural environment

Call for Contributions for ICME 11 Topic Study Group 33: Mathematics education in a multilingual and multicultural environment

The purpose of this group is to gather congress participants who are interested in research, development or teaching experiences that focus on mathematics education in multilingual, intercultural and/or multicultural situations.

The two one-hour and two ninety-minute sessions in the congress timetable at the disposal of TSG 33 will include presentations and discussions of the “state-of-the-topic area” and new trends and developments in research and practice in mathematics education in multicultural environment.

Individuals and groups may submit a paper for consideration by the Organizing Team of TSG 33 for an oral presentation during the second, third, or fourth group session.

We invite contributions related to the topics of TSG 33 such as:

Empirical proposals with anthropological, sociological or an educational focus.
Theoretical proposals about multicultural and/or intercultural education and its relation to mathematics.
Descriptions of teaching experiences in multicultural environments.
Syllabi or descriptions of relevant practices regarding the preparation of teachers working in multicultural environments.
Educative resources to support intercultural education (audio-visuals, manipulatives, computer programs, bibliographies, etc.)
Bibliographic surveys related to the group topics with analysis or comments.
Other kinds of related works relevant to the group’s focus areas.

Authors should specifically indicate how their submission aligns to the group’s focus areas; more than two areas may be given.

Important Dates

Proposals (5 pages double-spaced) must be sent by January 27, 2008 to both chairs of TSG 33: Maria Luisa Oliveras [e-mail:oliveras@ugr.es] and Natalia de Bengoechea [e-mail: bengoech@upn.mx]. Please write “ICME 11 TSG 33 proposal” in the subject line. You will receive an email confirming that we have received your paper. If you have not received such an email by January 25, please email again. Submitted proposals will be reviewed by the organizing team of the Topic Study Group 33 and authors will be notified by February 25, 2008 of the team’s decision.

All the accepted contributions will be published on the ICME-11 website before the congress. Depending on the number of submissions and the range of topics of the proposals, the organizing team will provide 10-20 minutes each oral presentation of papers accepted for the congress. Papers may be accepted and referred to during the discussions of the group, but time may not exist for oral presentations of these papers during the congress.

In summary, due to the limited time available for TSGs, accepted papers will have one of two designations:

Your paper will be accepted for an oral presentation at the conference and the paper will be uploaded to the TSG 33 website for all to read, or

Your paper will be accepted without an oral presentation at the conference, but will be referred to during group presentations. The paper will also be uploaded to the TSG 33 website.

For proposals accepted for TSG 33, the deadline for submission of the final full paper is April 1, 2008. Full papers, written in English, should be a maximum of 10 pages in length, and should be emailed to: Natalia de Bengoechea [e-mail: bengoech@upn.mx].

Program

First Session (Tuesday 8, 12:00 – 13:00)

I. Team’s members and speakers introduction. (10 min)

II. Theoretical Studies

PAPER	AUTHORS
Model for Research on Multiculturality in Mathematics Education.	Maria Luisa Oliveras
Study of “The State of the Question about Multiculturality and Mathematics Education”.	Maria Luisa Oliveras. Presents Natalia de Bengoechea
School mathematical discourse in a learning landscape: Broadening the perspective for understanding mathematics education in multicultural settings.	Paola Valero, Tamsin Meaney, Helle Alrø, Uenuku Fairhall, Ole Skovsmose, and Tony Trinick

Second Session (Wednesday 9, 12:00 – 13:30)

III. Teachers and teacher’s training

III.a. Teachers in multicultural classes (45 min)

PAPER	AUTHORS
A Transnational Study of Latino/a Students’ Access to Opportunities to Learn Mathematics.	Richard Kitchen
Mother-tongue of teaching mathematics project.	Eva Norén
Coping with Multicultural & Multilingual mathematics classes.	Salanieta Bakalevu

III.b. Teachers’ training and work in multicultural environments (45 min)

PAPER	AUTHORS
Intercultural education and indigenous education in Mexico, an experience in Oaxaca.	Natalia de Bengoechea
Talking about Multilingual Classrooms: A Critical Discourse Analysis of Mathematics Teacher Educators’ Talk.	Nancy Chitera
Perspectives and challenges of the indigenous teacher education: the teacher educator external to the culture of the “other” in the center of attentions.	Maria do Carmo Domite and Claudia Georgia Sabba

Third Session (Friday 11, 12:30 – 13:30)

IV. Students in multicultural classes

PAPER	AUTHORS
U.S. Latino Students’ Thinking and Communication on National Assessment Educational Progress (NEAP) Measurement Items.	Cynthia Anhalt, Anthony Fernandes and Marta Civil
Reform Mathematics in Bilingual Classrooms: Flexible Thinking and Language Development in Spanish-Speaking First Graders.	Mary Marshall, Sandra Musanti and Sylvia Celedón–Pattichis
An evaluation of the Ayuujk students learning in the Xaam elementary school.	Xaab Nop Vargas–Vásquez
Using Field Trips and Hands-on Activities to Improve Middle School Student Achievement in, and Attitude Toward, Mathematics and Science in a Multilingual and Multicultural Environment.	Kenneth C. Wolff and Mika Munakata

Fourth Session (Saturday 12, 12:00 – 13:30)

V. Culture and mathematics

V.a. Culture and mathematical education

PAPER	AUTHORS
Mayan Mathematics and Standards for Elementary School in Guatemala.	Leonel Morales
The Politics of Language and Schooling in the Mathematics Education of Bilingual Chicana/o Students.	Lena Licón Khisty and Craig Willey
In the lines and abos muiscas, the daily life of the class of mathematics.	Blanca María Peralta and Hilda Milena Ortiz
Learners’ home languages supporting learner engagement in linear programming.	Thulisile Nkambule

V.b. Culture and resources for mathematical education

PAPER	AUTHORS
Mathematics education is in life of Uighur students of Xinjiang of China—To Development Mathematics Textbooks for Depressed and Minority Area by Multi-Resources of Curricula.	Alimu Abulikemu
A multicultural look at mathematics.	Vivian La Ferla, Sinan Olkun, Funda Gönϋlateş and Meltem Ceylan
Microprojets for Intercultural Education.	Ma. Luisa Oliveras
Falta	Florence Glanfield

VI. Conclusions and general discussion on important issues for further work in the topic areas of TSG 33.

Papers and discussion documents

Research and development in task design and analysis

TSG34 Program

ICME-11 TSG 34 Research and development in task design and analysis Programme

Session 1 (60 mins)

- speaker 1 (30 min): Malcolm Swan (University of Nottingham): The design of multiple representation tasks to foster conceptual development.

- speaker 2 (30 min): Orit Zaslavsky (Technion – Haifa): Attention to similarities and differences: a fundamental principle for task design and implementation in mathematics education.

Session 2 (90 mins)

- speaker 1 (30 min): Janet Ainley (University of Leicester): Task design based on Purpose and Utility.

- speaker 2 (30 min): Jean Schmittau (State University of New York): Task design: a cultural-historical perspective.

- reactor (15 minutes): Anne Watson

- discussion (15 minutes): Paul Drijvers to chair

Session 3 (60 mins)

- speaker 1 (30 min): Michal Tabach & Alex Friedlander (Weizmann Institute): Designer concerns versus student work: the case of improving grades.

- speaker 2 (30 min): Viviane Durand-Guerrier (University of Lyon): What we learn from logical analysis of mathematical tasks in a semantic perspective?

Session 4 (90 mins)

- speaker 1 (30 min): Arthur Lee & Allen Leung (University of Hong Kong): Variational tasks in dynamic geometry environment.

- speaker 2 (30 min): Aad Goddijn (Freudenthal Institute): Polygons, triangles and capes: designing a one day team task for senior high school.

- reactor (15 minutes): Paul Goldenberg

- discussion (15 minutes): Anne Watson to chair

Papers and discussion documents

TSG Program (34.00 KB)
TSG34-Swan (610.00 KB)
TSG34-Zaslavsky (260.00 KB)
TSG34-Ainley (23.00 KB)
TSG34-Schmittau (22.00 KB)
TSG34-Tabach-Friedlander (92.00 KB)
ComparisonTF-VDG (14.00 KB)
TSG34-Lee-Leung (756.00 KB)
TSG34-Durand-Guerrier20-05-08 (58.00 KB)
Tsg34_A_Goddijn_PolygonsAndCapes (84.00 KB)
TSG34ComparisonLeeLeung-Goddijn (13.00 KB)
TSG34comparingdesignsGoddijn (15.00 KB)
PPT Ainley (320.00 KB)
PPT Friedlander (562.00 KB)
PPS_Durand-Guerrier (1.00 MB)
PPT_Watson (40.00 KB)
PPT-Goldenberg (1.00 MB)
PPT-Swan (473.00 KB)
PPT-Goddijn (800.00 KB)
LinkPPT-LeeLeung (27.00 KB)

Topic Study Groups

New developments and trends in mathematics education at preschool level

Aims and focus

Program

Abstracts

Papers and discussion documents

New developments and trends in mathematics education at primary level

Aims, scope, and goal(s)

Proposals by

Papers and discussion documents

New developments and trends in mathematics education at lower secondary level

Aims, scope, and goals

Aims and Focus

Papers for Topic Study Group III

Presentations: Auditorio Martínez Carranza 1(Civil) Building H

Papers accepted but will not be presented

Papers and discussion documents

New developments and trends in mathematics education at upper secondary level

Pictures

Aims and focus

Papers already accepted

Call for papers

List of links to relevant material

Papers and discussion documents

New developments and trends in mathematics education at tertiary level

Program

Papers and discussion documents

Activities and programs for gifted students

Introduction

Program

Questions that might be addressed

How to join the group (Call for papers)

Useful links

Presenters (in alpahbethical order)

Papers and discussion documents

Activities and programs for students with special needs

Programme

Aims, Scope and Goals

Abstracts and papers requirements

Papers and discussion documents

Adult mathematics education

Aims and focus

Call for papers

Papers and discussion documents

Mathematics education in and for work

Call for papers

Proposals by

Papers and discussion documents

Research and development in the teaching and learning of number systems and arithmetic

Aims and focus

Programme

Papers and discussion documents

Research and Development in the Teaching and Learning of Algebra

Focus and outcomes

DISCUSSION SESSIONS-Overview

DISCUSSION SESSIONS OVERVIEW

How can I prepare for the discussion sessions?

SESSION I- Tuesday: Contexts for Learning Algebra

SESSION II-Wednesday: Early Algebra

SESSION III-Friday: Syntax and Semantics

SESSION IV-Saturday: Special discussion of Puig, Rojano, & Filloy

POSTER

Test

Papers and discussion documents

Research and development in the teaching and learning of geometry

Aims and Focus

Call for Contributions

Submission Guidelines

Papers and discussion documents

Research and development in the teaching and learning of probability

Aims and focus of the topic study group

Aims and Focus

Call for Papers

Submissions of proposals and papers

Preliminary time schedule

Other activities linked to probability education at and around ICME

TSG #14: Research and development in the teaching and learning of statistics at ICME-11

Joint ICMI/IASE Study

ELEE: Latin American Statistics Education Meeting (in Spanish and Portuguese)

Programme, papers, and presentations in powerpoint

ELEE: Latin American Statistics Education Meeting
(in Spanish and Portuguese)

Monday July 7 – 13.00 -14.00
1st Session – 1h – Plenary Session

Wednesday July 9 – 12.30-14.00
2nd Session – 1h30 – Oral Presentations

Friday July 11 – 12.15 -13.15
3rd Session – 1 h- Poster and demo Session

Saturday July 12 – 12.00-13.30
4th session – 1h30 – Oral presentations