**Manuel Santos**(Mexico)

msantos@cinvestav.mx**Yoshinori Shimizu**(Japan)

yshimizu@human.tsukuba.ac.jp

**Olive Chapman**(Canada)

chapman@ucalgary.ca**Uldarico Malaspina**(Peru)

umalasp@pucp.edu.pe**Hugo Barrantes**(Costa Rica)

habarran@cariari.ucr.ac.cr

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.

Top of pageProblem 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?

© **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.

**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

**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)

- Teaching mathematics in the classroom through problem solving (88.00 KB)
- The method of problem solving based on the Japanese and Polya´s models. A classroom experience in Chilean schools (571.00 KB)
- Problem Posing Performance of Grade 9 Students in Singapore on an open-ended stimulus (178.00 KB)
- Future directions and perspectives for problem solving research and curriculum development (130.00 KB)
- The decision-making as a school activity (83.00 KB)
- Methodologies for investigating relationships between concept development and the development of problem solving abilities (130.00 KB)
- The computer tool for verification hypotheses in parametrical problems solving (604.00 KB)
- A Technology-Based Investigation of United States High School Student Mathematical Problem Solving (73.00 KB)
- Teachers’ beliefs about mathematical problem solving, their problem solving competence and the impact on instruction: A case study of three Cypriot primary teachers (113.00 KB)
- An ICT environment to assess and support students’ mathematical problem-solving performance in non-routine puzzle-like word problems (171.00 KB)
- Formulating mathematical conjectures in learning activities, assisted with technology (818.00 KB)
- Cognitive and metacognitive processes of pre-service mathematics teachers while solving mathematical problems (124.00 KB)
- Strategies for Solving Word Problems on Speed: A Comparative Study between Chinese and Singapore Students (112.00 KB)
- Beyond Show and Tell: Neriage for Teaching through Problem-Solving - Ideas from Japanese Problem-Solving Approaches for Teaching Mathematics - (1.00 MB)
- Instructional Practices to Facilitate Prospective Mathematics Teachers’ Learning of Problem Solving for Teaching (103.00 KB)