Topic Study Group 38:
The history of the teaching and learning of mathematics
Rooms C201 and C202
  • Ángel Ruiz (Costa Rica)
    angelruizz@racsa.co.cr
  • Renaud d’Enfert (France)
    renaud.denfert@u-psud.fr
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Team members:
  • Luis Carlos Arboleda (Colombia)
    lca@emcali.net.co
  • Rodrigo Cambray (Mexico)
    rcnroc@yahoo.com.mx
  • Wann-Sheng Horng (Taiwan)
    horng@math.ntnu.edu.tw
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Aim and Focus

Aim

The aim of TSG 38 is to provide a forum for participants to share their ideas and findings in the history of the teaching and learning of mathematics.

As decided in the previous ICME, the theme of this group is interdisciplinary and unites different disciplines like the history of mathematics, the history of education and the sociology. At the same time, it introduces many factors that defines the focus of the work to do. For instance, some of the aspects it deals with are:

  • - the evolution of curricula in the various countries,
  • - the evolution of mathematics education as a professional independent discipline,
  • - the cultural and social role of mathematics,
  • - policies in teacher education,
  • - the evolution and roles of teachers’ associations,
  • - the situation of journals on mathematics education,
  • - the role of textbooks in the teaching and learning of mathematics,
  • - general trends in the organizing of the lesson,
  • - the overall impact of digital technologies in the learning and teaching of mathematics.

Even if national studies in the learning and teaching of mathematics are more available, it seems to be appropriate to adopt the broadest international perspective within this TSG and underline comparative approaches. In that sense the work of TSG 38 should contribute to gathering the researchers working in this field, establishing common patterns in the history as well as revealing differences, and especially pointing out research orientations which enhance international perspectives.

Focus

As was stated before, the field for TSG 38 is extraordinarily broad. In accordance with the experience of the past TSG associated to this theme in ICME 10, the focus will therefore be institutionalized forms of teaching and learning in types of schools equivalent to primary and secondary levels. Higher education is very relevant but connected to teacher training in mathematics education.

At this opportunity, we wish to focus TSG 38 on the reforms of mathematics education in primary and secondary schools (19 and 20th centuries), according to the following aspects:

  • - the transformations of the mathematical curricula (changes in content and methods, social and epistemological stakes, cross-cultural comparisons)
  • - new trends in teaching practice (textbooks, methods, technologies as a broad influence, lesson contexts)
  • - the actors involved in the reforms and their motivations (political or ministerial bodies, mathematicians, teachers and their associations, international organizations)
  • - the repercussions on mathematics education teaching training (relation between mathematics and pedagogical components, pedagogical aids offered to teachers).
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Call for papers

Bibliography

Further to the First International Bibliography on the History of Teaching and Learning Mathematics established for ICME 10 by Gert Schubring (http://www.icme-organisers.dk/tsg29/BiblTSG.pdf), we are calling for contributors to gather publications about reforms of mathematics education.
When delivering such data, please forward them in the style for references of ISIS, the well-known journal for history of science: http://www.journals.uchicago.edu/Isis/instruct.html
When the publication includes non-Latin characters, please provide a transliteration of the author’s name and of the title in Latin characters and a translation of the title into English. Short abstracts are welcome. Contributors will be credited for their cooperation.

Contributions

Contributions can be made in 2 ways: oral presentations and presentations by distribution

  • - Oral Presentations: Due to the limited time available, only a relatively small number of contributors will have the opportunity for an oral presentation. The time allowed will be at the most 15 minutes. It is important for participants to provide documents for the website to help participants follow the oral presentation in this short time.
  • - Papers by Distribution: In this case, the full text of the contribution will be available as an electronic file on the web before the Congress.

The TSG 38 aims at developing high quality academic discussion among participants on the basis of short presentations on interesting ideas and findings.

Procedure and Deadlines

  • - January 30, 2007: Submission in digital form of an extended abstract of 1000-2000 words (not including references, pictures, tables etc).
    Abstracts will be reviewed by the members of the Organizing Comittee.
  • - February 15, 2008: Notification of acceptance or rejection, and whether presentation is oral or by distribution. Authors of accepted papers by distribution should submit a full text in electronic form, to be put on the web.
  • - March 10, 2008: Submission of full texts of papers by distribution and of any documents to support oral presentations.
  • - April 1, 2008: The final programme will be announced on the web.
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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: all abstracts, full paper, or any other relevant documents should be submitted by e-mail.

Papers and discussion documents: All papers by distribution or documents considered to be appropriate for oral presentations will be included as pdf files in the web page of the TSG on the ICME 11 site around mid April 2008.
Texts should be presented in the following formats: MS Word, Latex, or Adobe Acrobat.

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Program

Tuesday July 8, 12-13 – Reforming Mathematics teaching : commitments and resistances

Renaud D’ENFERT (GHDSO, Université Paris Sud 11, France) & Angel RUIZ (CIMM, Universidad de Costa Rica, Costa Rica) : Introduction

Taro FUJITA (Faculty of Education, University of Plymouth, UK) & Keith JONES (School of Education, University of Southampton, UK) : The process of redesigning the geometry curriculum – A case study of the UK Mathematical Association activity in the early 20th Century.

Livia GIACARDI (Department of Mathematics, University of Torino, Italy) : The School as a “Laboratory”. Giovanni Vailati and the Project for the Reform of the Teaching of Mathematics.

Elisabete Zardo BÚRIGO (Department of Pure and Applied Mathematics, UFRGS, Brazil) : Modern Mathematics in Brazil: the promise of efficient and democratic teaching.

Wednesday July 9, 12-13.30 – Changing Mathematics teaching with textbooks

Nerida F. ELLERTON & M. A. (Ken) CLEMENTS (Illinois State University, USA) : The process of decolonizing school mathematics textbooks and curricula in the United States.

Kristín BJARNADÓTTIR (Iceland University of Education, Iceland) : The History of Public Education in Mathematics in Iceland and its Relations to Secondary Education.

Ildar SAFUANOV (Deparment of mathematics, MADI, Russian Federation) : History of teaching of the concept of a function in Russia.

Maria Cristina ARAÚJO DE OLIVEIRA (UNIBAN/GHEMAT, Brazil) : Modern Mathematics teaching proposals as seen in published textbooks in Brazil

Friday July 11, 12.30-13.30 – Mathematics teaching Reforms and et counter-reforms

Hélène GISPERT (GHDSO Université Paris Sud 11, France) : Two math reforms in their context in 20th Century France: similarities and differences.

Maria Célia Leme DA SILVA & Wagner Rodrigues VALENTE (UNIBAN GHEMAT, PUC/SP, Brazil) : Students’ notebooks as a source of research. On the mathematic education history.

Alexander KARP (Teachers College, Columbia University, USA) : Back to the Future: the Conservative Reform of Mathematics Education in the Soviet Union during the 1930s-1940s.

Saturday July 12, 12-13.30 – Teaching practice

Flávia SOARES (Universidade Severino Sombra, Brazil) : Defining the teachers’ knowledge: a discussion about examinations for primary and secondary school teachers in Brazil in the nineteenth century.

Christopher A.N. KURZ (National Technical Institute for the Deaf, Rochester Institute of Technology, USA) : The struggle of Mathematics Education for the deaf during the late nineteen century.

Gert SCHUBRING (Institut für Didaktik der Mathematik,Fakultät für Mathematik, Universität Bielefeld, Germany) : Comments on the presented papers and on recent developments in related research.

General discussion

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Abstracts

Taro FUJITA (Faculty of Education, University of Plymouth, UK) & Keith JONES (School of Education, University of Southampton, UK) : The process of redesigning the geometry curriculum – A case study of the UK Mathematical Association activity in the early 20th Century.

This paper examines a key period of change in geometry teaching in England. Our focus is the character and nature of the recommendations of the geometry report of the UK Mathematical Association in 1902. We analyse historical documents of the Mathematical Association using a theoretical framework developed from Cooper’s model. Our analysis shows that the character and recommendations of the Mathematical Association report was influenced by various factors including: that the Mathematical Association members still respected the traditional Euclidean approach to geometry as a basis for school geometry; that the academic and power resources available to the Mathematical Association at the time were not sufficient for a complete change from the traditional approach; that conflicts between the various members of the Mathematical Association prevented a complete consensus; and that the climate outside the teaching committee of the Mathematical Association was not ready for radical reform at that time.

Livia GIACARDI (Department of Mathematics, University of Torino, Italy) : The School as a “Laboratory”. Giovanni Vailati and the Project for the Reform of the Teaching of Mathematics.

In Italy at the beginning of the twentieth century, forty years after the Unification, several factors pointed to a pressing need for reform: the evident deficiencies in secondary school teaching; the changed social and historical context; the influence of reform movements in other European countries – especially Felix Klein’s movement in Germany and Gaston Darboux’s in France –; the increasingly active participation of teachers in the political issues of education; and, finally, the remarkable increase in the number of pupils enrolled in secondary schools (from 18,231 to 94,572 between 1861 and 1901). To address this situation, in 1905 Minister Leonardo Bianchi appointed a Royal Commission for the reform of the secondary school system. Despite the difficulties and conflicts within the board itself, in February 1908 the Commission presented a draft law proposing, on the one hand, a professional technical school with three-year courses enabling entry to the technical institutes, and, on the other hand, a three-year course for the scuola media unica (lower secondary school, or middle school, common to all schools), excluding Latin as a subject, which would grant students access to the three different kinds of upper secondary school: liceo classico (with Latin and Greek), liceo scientifico (with two modern languages and a broader science syllabus), and liceo moderno (with Latin and two modern languages).
The syllabi for mathematics, and the instructions on teaching method, original and panoramic in their approach, were written by Giovanni Vailati (1863-1909), a mathematician with a diversity of interests who belonged to the school of Giuseppe Peano.
In may paper, I will concentrate on the following points: Vailati’s criticisms of the schools of the time, the pedagogical and methodological assumptions that he starts from in formulating his project for reform, his concrete proposals for a renovation of the teaching of mathematics, the criticisms of his proposals, and the results effectively achieved.

Elisabete Zardo BÚRIGO (Department of Pure and Applied Mathematics, UFRGS, Brazil) : Modern Mathematics in Brazil: the promise of efficient and democratic teaching.

The modern mathematics movement, originated in Europe and in the United States, reverberated in Brazil, more than in other Latin American countries. In order to understand the local extension of this movement, elements of the reality of secondary education in Brazil are considered as well as the local interpretations and appropriations of the new curricular proposals.
The Grupo de Estudos em Ensino de Matemática (Study Group on Mathematics Teaching – GEEM) was created in 1961 in the city of São Paulo. GEEM discourse promised overcoming an elitist and inefficient education, promoting interest, inquisitiveness, and learning, opposing concept understanding to algorithm mechanization. The intended purpose of a more advanced, correct, and, at the same time, accessible mathematics was supported by the composition of the Group, that brought together mathematicians and licensed secondary teachers, engaged in innovative experiences.
The reach of a movement that promised the “modernization” of teaching, and that identified modernization with democratization must also be understood within a context of optimism and belief in the benefits of technical progress. The teaching of mathematics had to be modern, such as Brazil wanted and expected to be.

Nerida F. ELLERTON & M. A. (Ken) CLEMENTS (Illinois State University, USA) : The process of decolonizing school mathematics textbooks and curricula in the United States.

We define “colonialism” as “an attitude of mind, accepted by leaders and representatives of the colonizing power, and by those being colonized, that what goes on at ‘home’ should also take place in the colonies.” More often than not, this “acceptance” is subconscious – “people behave in a colonialist way because that is the way they have learnt to behave.” Colonialist attitudes usually persist within nations and cultures long after colonies have gained their independence from colonizing powers.
As soon as the United States was legally constituted, in the 1770s and 1780s, the impoverished fledgling nation wanted to avoid expenses associated with importing English arithmetics. It also wanted to show that, as a nation, it was capable of generating texts superior in quality to those from England. However, Pike’s (1788) Arithmetic, the first mathematics text written in English by a US citizen, followed a similar sequence of topics and used a similar approach to texts used during the colonial period. The process of decolonizing school mathematics textbooks and curricula evolved over the next 50 years. This paper will summarise key factors which influenced how this transformation occurred.

Kristín BJARNADÓTTIR (Iceland University of Education, Iceland) : The History of Public Education in Mathematics in Iceland and its Relations to Secondary Education.

Iceland was a Danish colony at the margin of Europe until the 20th century. Legislation acts on knowledge in writing and arithmetic in 1880 and on public education free of charge on the responsibility of the local communities in 1907, were landmarks in the history of public education in mathematics and spurred creation of mathematics textbooks for the general public. However several official decisions of social-democratic origin, made in the period 1920s to 1940s, intended to ensure the right to education for all children, had grave consequences. The decisions hindered natural development of public mathematics education, made it dependent on upper school levels and caused stagnation for decades. The impact of these decisions remained into the 1970s, until the New Math reform wave broke rather harshly on Iceland, but eventually released initiative to a new domestic reform.

Ildar SAFUANOV (Deparment of mathematics, MADI, Russian Federation) : History of teaching of the concept of a function in Russia.
Definitions of functions in Soviet school and undergraduate textbooks used in 20-th century will be traced.
The greatest mathematicians such as Luzin, Kolmogorov, Aleksandrov, were the first to realize the necessity of the introduction of the modern definition of a mapping into the scientific and educational literature. Already in 60-s the general concept of a mapping (function) began to enter into curricula of secondary and tertiary school.
Appropriate steps have been undertaken for the preparation of school teachers. Nevertheless, in 80-s the general concept of a mapping has been expelled from school curricula.
The final opinion about the introduction of modern strict definition of a mapping is not reached concerning not only school, but even undergraduate curricula and textbooks.

Maria Cristina ARAÚJO DE OLIVEIRA (UNIBAN/GHEMAT, Brazil) : Modern Mathematics teaching proposals as seen in published textbooks in Brazil.

We can say that Modern Mathematics Movement was the second international movement for renovating Mathematics teaching. The first one was spread out by IMUK (afterwards known as ICMI) when presided by Felix Klein, at the beginning of 20th century.
Modern Mathematics Movement, as we are referring to, corresponds to divulged shifting of course proposals, mainly in the 1960’s, and it was, in a manner of speaking, an attempt to modernise Mathematics teaching, by means of modifying and updating teaching contents and methods at two levels of scholarship: primary and secondary (7-18 years old). One of the principal targets was to bring together teaching contents at secondary (15-18 years old) and tertiary levels (undergraduate courses).
In Brazil, professor Osvaldo Sangiorgi was one of its principal supporters and divulgers. He has acted as a teacher in different teaching levels – secondary and tertiary – and was author of many adopted textbooks between 1950’s and 1970’s.
In this paper we have in mind to expose an analysis of professor Sangiorgi’s appropriations over updating proposals for Mathematics teaching as propagated by his textbooks Matemática curso moderno. We restring ourselves to the study of numerical sets and operations contents at gymnasium initial series (11-12 years old), as presented in his textbooks, and we have focused on methodological proposals as well.

Hélène GISPERT (GHDSO, Université Paris Sud 11, France) : Two mathematical reforms in their context in 20th Century France: similarities and differences.

My talk will focus on two key moments of history of the teaching of mathematics in twentieth century France. The first one took place at the very beginning of the century, when a global reform of secondary instruction , the “1902 Reform” was undertaken. The second one, at the end of the sixties, was the moment of a specific reform of mathematical teaching, the so called “Réforme des mathématiques modernes”.
These two moments, and that is a first similarity, were moments of deep reorganisation of the structures and goals of instruction – secondary instruction for 1902, primary and secondary instruction for the sixties – taking into account new goals and new audiences. In both cases, a major argument for these changes was “modernity” and mathematics had a specific role in the rhetoric which was then developed. Nevertheless we have a first major difference: the way mathematics and modernity were linked was totally different in 1902 and in the sixties, due to different epistemological conceptions of mathematics. This led to major differences in the new mathematical curricula which were then put in place, in particular for pupils 13-14 years old. On the contrary, pedagogical methods which were respectively promoted by the reformers in 1902 and 1960s were far less opposed that the differences in the curricula could have suggested.

Maria Célia Leme DA SILVA & Wagner Rodrigues VALENTE (UNIBAN GHEMAT, PUC/SP, Brazil) : Students’ notebooks as a source of research. On the mathematic education history.

This paper has the purpose to reflect about the first results of the research that has been carried out by GHEMAT – Grupo de Pesquisa de História da Educação Matemática in Brazil, which considers the students’ notebooks as a source of research for the mathematic education history writing. A material rarely used in historical investigations on mathematic education, the students’ notebooks show to be as very rich documents for the analysis of teachers’ pedagogical practices. The results to be presented include considerations about how the curricular proposals of two major international movements that sought to modernize the school mathematics were taken to classrooms. Differently from analyses that consider the innovative proposals as pedagogical failures, the study that takes notebooks as sources of research reveals the dynamics occurred in the classroom, the tactics developed in the school day by day to start the strategies built to alter the school mathematics in the early and middle XX century. The notebooks substantively point that pedagogical practices are cultural practices and, as such, they represent the result of creative consumption of representations imposed to the school environment.

Alexander KARP (Teachers College, Columbia University, USA) : Back to the Future: the Conservative Reform of Mathematics Education in the Soviet Union during the 1930s-1940s.

This presentation will address the radical reforms that took place in Russian (Soviet) mathematics education, and in education in general, during the 1930s-1940s. During this time, post-Revolutionary pedagogical innovations were rejected, and many practices from former, pre-Revolutionary gymnasia—which had been earlier characterized as “the school of rote memorization and routine”—were embraced anew. Soviet history of education subsequently labeled the activists of the 1920s as planners and visionaries, and came to view the changes that had occurred during this time as unequivocally beneficial. There is a need for an impartial analysis of these changes, however. An attempt at such an analysis will be undertaken in this report.

Flávia SOARES (Universidade Severino Sombra, Brazil) : Defining the teachers’ knowledge: a discussion about examinations for primary and secondary school teachers in Brazil in the nineteenth century.

In Brazil, training at a higher education level in order to graduate teachers to act in the primary and secondary schools starts with the creation of universities, which took place behindhand from the 1930s on. As there were no institutions which offered specific education for a Mathematics teacher in the 19th century, any professional with technical background could teach. Furthermore, as far as the first grades were concerned, no particular training was required, as very little was expected from the candidates. Even with such a gap, during the 19th century, beginning of the institutionalization of the public instruction in Brazil, other mechanisms regulated the teaching practice and legitimated the range of knowledge necessary for whoever wanted to be a teacher.
It is common sense that a good teacher is essential to the improvement of any subject. But how can one measure the teacher’s “quality”? One of the conditions for the recruitment of teachers for primary and secondary public schools in Brazil is the public contest. Throughout the 19th century, several legal apparatuses regulated the teaching profession and the conditions for public and private teaching practice in Brazil. According to the current regulation, these conditions were altered in many ways, granting more or less freedom to the practice of the profession, as it can be read from the texts of the legislation.
In the light of such items, it is believed that the public contest examinations can reveal the actual requirements for the teaching practice, not to mention other significant questions about the conception related to the teacher’s role, the contents they were supposed to teach, the knowledge they should possess, among other aspects, in those times. In the shape of Lee Shulman (1986)’s article, published in 1986, this text aims at covering aspects of the history of Mathematics teaching in Brazil during the 19th century, discussing the selection of teachers and the evolution of the range of knowledge required from the teaching candidate by making use of exams for admission of teachers applied in Rio de Janeiro. As well as in Shulman (1986), public contest examinations applied in Rio de Janeiro during the 19th century found in the city’s archives are used for analysis so that it can provide researchers in history of the Mathematics teaching with materials for possible comparisons with models from other countries.

Christopher A.N. KURZ (National Technical Institute for the Deaf, Rochester Institute of Technology, USA) : The struggle of Mathematics Education for the deaf during the late nineteen century.

This paper documents historical patterns and issues of mathematics education for the deaf during the late nineteenth century from a historical perspective. Until this time, little has been known about mathematics curriculum and instruction for the deaf since the establishment of the American Asylum for the Deaf and Dumb in Hartford, Connecticut, in 1817, to serve deaf and hard of hearing children whose primary means of relating to the world is visual and who share a language that is visually received and produced (Lane, Hoffmeister, & Bahan, 1996; Ladd, 2003). This research paper contributes new information to the fields of mathematics education and deaf education through a detailed analysis of the mathematics education reforms for the deaf in America during the late nineteenth century. By using primary sources, this historical research study brings to light a new understanding of mathematics instruction and curricula for the deaf in the late nineteenth century.
Long before the 1920 founding of the first professional organization comprised of teachers of mathematics in the United States, the struggle of mathematics education for deaf children in the country continued as their teachers tried to find a perfect one-size-fit-all instructional methodology for teaching mathematics, swinging back and forth between the traditional and modern paradigms of teaching. Such struggle has shown that the evolution of curricular instruction had undergone numerous alterations, attempted innovative pedagogies, controversies on methods and learned concepts, and inquires and illustrations in curriculum development (Kliebard, 2004). In this paper, four focus areas of struggle are: (1) the founding and implementation of a college for the deaf in Washington, D.C. in 1864 brought some calls from college professors and classroom teachers for increased expectation and standardization in the mathematics curriculum for pre-college deaf students across the country; (2) the development of vocational training programs for the deaf as the society experiences an emergence of the Industrial Revolution; (3) potential problems associated with mathematics teaching and learning for deaf children were debated among educational professionals of the deaf; and (4) the pedagogical pendulum shifted between the two tents of teaching paradigms, traditional and modern.
During the late nineteenth century, the majority of the teachers of the deaf concurred that understanding practical mathematical applications was as important as the knowledge of arithmetical concepts for securing a job in the workplace sphere as society moved from the agricultural-business sphere toward the industrial-business sphere. In terms of curriculum and instruction to prepare deaf students for the working sphere, the pedagogical pendulum had kept swinging back and forth.

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