International Commission On Mathematical Instruction Research Articles

Rethinking history and epistemology in mathematics education*

For a long time, mathematics educators have shown interest in the use of history of mathematics in mathematics teaching. This article discusses some interesting reasons put forwards by the supporters of this use and their epistemological assumptions. The initial part of the article provides a short account of the setting in which the first discussions and the first experiments concerning the use of history in mathematics teaching took place. Afterwards, the article outlines the development of the community of scholars interested in the relationship between history and pedagogy of mathematics, which in 1976 was officially established as the group HPM (History and Pedagogy of Mathematics) affiliated to ICMI (International Commission on Mathematical Instruction). The materials produced in this context constitute a background and a source for researchers and for mathematics teachers wishing to explore the opportunity offered by history in their teaching. About the introduction of history of mathematics in the classroom, the article focuses on two main streams of action: – history for promoting the image of mathematics as a vivid discipline with links with reality and culture, – history for dealing with mathematical concepts. An efficient introduction of history in teaching entails adequate teachers’ historical knowledge. Then a part of this article is dedicated to discuss the role of this knowledge and to present how history may be used in teacher training programs. At the end of the article, some frequent objections put forwards by teachers about the possibility of introducing history in their teaching are presented. The conclusion is that, though there are difficulties and some contexts are not favourable to this introduction, in suitable contexts, the effort required for facing this endeavour will be rewarded by significant improvements in the classroom life.

Educação, educação matemática e teoria cultural da objetivação: uma conversa com Luis Radford

Luis Radford é professor titular da Laurentian University em Sudbury, Ontário, no Canadá. Desde 1992, leciona no programa de formação de professores da École des Sciences de l’Éducation, onde é atualmente diretor e coordenador do Laboratório de Pesquisa em Semiótica Cultural e Pensamento Matemático. Professor de Educação da Universidade de Manchester, no Reino Unido, é presidente do Grupo Internacional de Estudos sobre as relações entre a História e a Pedagogia da Matemática, afiliado à International Commission on Mathematical Instruction (ICMI). Autor de diversos artigos científicos nos quais relaciona temas complexos como história, cultura, ensino e aprendizagem, Luis Radford é internacionalmente reconhecido como pesquisador da área da educação matemática, tendo recebido em 2011 a Medalha Hans Freudenthal do ICMI. Na entrevista concedida durante sua estadia no Brasil, em março de 2014, Luis Radford revela alguns de seus caminhos de formação e sintetiza alguns dos elementos e princípios que orientam a Teoria Cultural da Objetivação sobre os processos de ensino e aprendizagem e, em particular, de que forma essa concepção teórica se relaciona com o campo de pesquisa da educação matemática. Na entrevista, são abordadas ainda algumas estratégias e técnicas metodológicas de pesquisa com professores e alunos, em projetos longitudinais que permitem traçar o desenvolvimento cultural da criança. Por fim, o professor Luis Radford aborda questões gerais relacionadas às orientações curriculares no Brasil, compreendido como um país com importante diversidade cultural e social. A leitura dessa entrevista remete à atualidade das pesquisas sobre os processos de ensino e aprendizagem, de forma específica daqueles relacionados ao conhecimento matemático, bem como oferece elementos para a discussão sobre os processos de formação de professores que visem à formação do sujeito em suas máximas potencialidades, ainda que condicionado por determinantes sociais e culturais.

The twenty-third ICMI study: primary mathematics study on whole numbers

A new study on the teaching and learning of whole number arithmetic in primary school and pre-school will be conducted by the International Commission on Mathematical Instruction (ICMI). The study is organized around themes concerning foundational aspects of whole number arithmetic (cultural, historical, epistemological, as well as (neuro)cognitive), the teaching and learning of whole number arithmetic, and the connection of whole number arithmetic with other mathematical topics. The International Program Committee invites papers for the new study.

Special Issue on History and Philosophy of Mathematics in Mathematics Education

Although Science & Education has published papers specifically concerning mathematics over the years—some quite significant for education—mathematics has never received the spotlight. Indeed, when the journal was established it bore the subtitle, Contributions from History, Philosophy and Sociology of Science and Mathematics, but so few papers on mathematics were received in those years that the word ‘‘mathematics’’ was duly dropped. Yet within the community of science and mathematics educators, there is no lack of interest at least in the contributions of history and philosophy of mathematics to mathematics education, particularly the history of mathematics. Besides publications such as those we have listed at the end of this introduction, one can point to the activities of the International Study Group on the Relations between the History and Pedagogy of Mathematics (HPM) which dates back to 1972, and which almost from the start became an affiliated study group of the International Commission on Mathematical Instruction (ICMI), the largest and oldest international organization for mathematics education. International conferences of HPM have been held in Europe, Canada, Australia, Taiwan, Mexico, and Korea in association with the quadrennial International Congress on Mathematical Education (ICME). The European Summer University on History and Epistemology in Mathematics Education (ESU), now held every 4 years as well, is another regular venue for meetings dealing with history in mathematics education, as is the working group on History in Mathematics Education at the biennial Congress of European

ICMI의 역사와 수학교육

There has been an ongoing symbiotic relationship between the history of the International Commission on Mathematical Instruction(ICMI) and the broader history of mathematics education since 1908. Similarly, the International Congress on Mathematical Education(ICME) has played an important role in the direction of Mathematics education since its first congress in 1969. ICME-12 is due to be held in Seoul, Korea from July <TEX>$8^{th}$</TEX> to <TEX>$15^{th}$</TEX> 2012. To date, there has been no research paper concerning the history of the ICMI published in any Korean journal. In readiness for the upcoming ICME-12, this paper aims to provide a comprehensive overview of the history of the IMCI from the perspective of Mathematics education.

Book review: The first century of the International Commission on Mathematical Instruction

The International Commission on Mathematical Instruction (ICMI) celebrated the centennial of its foundation in March 2008. For the occasion, an anniversary symposium, the ICMI Centennial in Rome, was organized. The symposium was held at the Accademia Nazionale dei Lincei in Rome where the foundation event had occurred a hundred years ago. The book reviewed here publishes the texts of the presentations given at the symposium. It takes the form of proceedings that follow the structure of the meeting's program but can also be considered a work dedicated to the activity of the ICMI during its hundred years of existence. The text is organized as a series of chapters by different authors that tackle different facets of this unifying topic. The text begins with a brief introduction to the symposium, provides some information about it, and lists some questions that characterize the symposium's context and goals and the development of the event. It also provides the address of the new ICMI website and gives information about the presence of the symposium on the web http://www.unige.ch/ math/EnsMath/Rome2008/.1 The past, present, and future of the ICMI are three axes that articulate the structure of this book and serve to analyze some of the principal themes connected to the Commission's activity; themes that the editors indicate in their introduction. Following the introduction, the book is organized into three main sections: plenary lectures, short talks, and working groups and panel discussions. Five of the plenary lecture chapters have two parts: presentation and reaction. These chapters alternate historical reflection on the proposal and discussion of the topical problems that the ICMI has worked on along with the considerable tensions created by any lack of balance concerning their

A social perspective on technology-enhanced mathematical learning: from collaboration to performance

This paper documents both developments in the technologies used to promote learning mathematics and the influence on research of social theories of learning, through reference to the activities of the International Commission on Mathematical Instruction (ICMI), and argues that these changes provide opportunity for the reconceptualization of our understanding of mathematical learning. Firstly, changes in technology are traced from discipline-specific computer-based software through to Web 2.0-based learning tools. Secondly, the increasing influence of social theories of learning on mathematics education research is reviewed by examining the prevalence of papers and presentations, which acknowledge the role of social interaction in learning, at ICMI conferences over the past 20 years. Finally, it is argued that the confluence of these developments means that it is necessary to re-examine what it means to learn and do mathematics and proposes that it is now possible to view learning mathematics as an activity that is performed rather than passively acquired.

The emergence of women on the international stage of mathematics education

In this article, I consider the history of the International Commission on Mathematical Instruction (ICMI) from its inception until the International Congress on Mathematical Education (ICME) held in 1969. In this period, mathematics education developed as a scientific discipline. My aim is to study the presence and the contribution of women (if any) in this development. ICMI was founded in 1908, but my history starts before then, at the end of the nineteenth century, when the process of internationalization of mathematics began, thanks to the first International Congress of Mathematicians. Already in those years, the need for internationalizing the debate on mathematics teaching was spreading throughout the mathematical community. I use as my main sources of information the didactics sections in the proceedings of the International Congresses of Mathematicians and the proceedings of the first ICME. The data collected are complemented with information from the editorial board of two journals that for different reasons are linked to ICMI: L’Enseignement Mathematique and Educational Studies in Mathematics. In particular, as a result of my analyses, I have identified four women who may be considered as pioneer women in mathematics education. Some biographical notes on their professional life are included in the paper.

ICMI Study 16: Challenging Mathematics in and Beyond the Classroom: Discussion Document

From time to time, the International Commission on Mathematical Instruction (ICMI) mounts studies to investigate in depth and detail particular fields of interest in mathematics education. This paper is the Discussion Document of the forthcoming ICMI Study 16, Challenging Mathematics in and beyond the Classroom.

The International Commission on Mathematical Instruction (ICMI) – The Fifteenth ICMI Study: The Professional Education and Development of Teachers of Mathematics

The International Commission on Mathematical Instruction (ICMI) – The Fifteenth ICMI Study: The Professional Education and Development of Teachers of Mathematics

ICMI Study 14: Application and Modelling in Mathematics Education — Discussion Document

This paper is the Discussion Documentfor a forthcoming ICMI Study on Applications and Modelling in MathematicsEducation. As will be well-known, fromtime to time ICMI (the InternationalCommission on Mathematical Instruction)mounts specific studies in order toinvestigate, both in depth and in detail,particular fields of interest inmathematics education. The purpose of thisDiscussion Document is to raise someimportant issues related to the theory andpractice of teaching and learningmathematical modelling and applications,and in particular to stimulate reactionsand contributions to these issues and tothe topic of applications and modelling asa whole (see Section 4). Based onthese reactions and contributions, alimited number (approximately 75) ofparticipants will be invited to aconference (the Study Conference)which is to take place in February 2004 inDortmund (Germany). Finally, using thecontributions to this conference, a bookwill be produced (the Study Volume)whose content will reflect thestate-of-the-art in the topic ofapplications and modelling in mathematicseducation and suggest directions for futuredevelopments in research and practice.The authors of this Discussion Document are themembers of the International ProgrammeCommittee for this ICMI Study. Thecommittee consists of 14 people from 12countries, listed at the end of Section4. The structure of the Document isas follows. In Section 1, we identifysome reasons why it seems appropriate tohold a study on applications and modelling.Section 2 sets a conceptual frameworkfor the theme of this Study, and Section3 contains a selection of importantissues, challenges and questions related tothis theme. In Section 4 we describepossible modes and ways of reacting to theDiscussion Document, and in the finalSection 5 we provide a shortbibliography relevant to the theme of thisStudy.

ICMI study 14: Applications and modelling in mathematics education —Discussion document

This paper is the Discussion Documentfor a forthcoming ICMI Study on Applications and Modelling in MathematicsEducation. As will be well-known, fromtime to time ICMI (the InternationalCommission on Mathematical Instruction)mounts specific studies in order toinvestigate, both in depth and in detail,particular fields of interest inmathematics education. The purpose of thisDiscussion Document is to raise someimportant issues related to the theory andpractice of teaching and learningmathematical modelling and applications,and in particular to stimulate reactionsand contributions to these issues and tothe topic of applications and modelling asa whole (see Section 4). Based onthese reactions and contributions, alimited number (approximately 75) ofparticipants will be invited to aconference (the Study Conference)which is to take place in February 2004 inDortmund (Germany). Finally, using thecontributions to this conference, a bookwill be produced (the Study Volume)whose content will reflect thestate-of-the-art in the topic ofapplications and modelling in mathematicseducation and suggest directions for futuredevelopments in research and practice.The authors of this Discussion Document are themembers of the International ProgrammeCommittee for this ICMI Study. Thecommittee consists of 14 people from 12countries, listed at the end of Section4. The structure of the Document isas follows. In Section 1, we identifysome reasons why it seems appropriate tohold a study on applications and modelling.Section 2 sets a conceptual frameworkfor the theme of this Study, and Section3 contains a selection of importantissues, challenges and questions related tothis theme. In Section 4 we describepossible modes and ways of reacting to theDiscussion Document, and in the finalSection 5 we provide a shortbibliography relevant to the theme of thisStudy.

ICMI Study 14: Applications and Modelling in Mathematics Education--Discussion Document.

This paper is the Discussion Documentfor a forthcoming ICMI Study on Applications and Modelling in MathematicsEducation. As will be well-known, fromtime to time ICMI (the InternationalCommission on Mathematical Instruction)mounts specific studies in order toinvestigate, both in depth and in detail,particular fields of interest inmathematics education. The purpose of thisDiscussion Document is to raise someimportant issues related to the theory andpractice of teaching and learningmathematical modelling and applications,and in particular to stimulate reactionsand contributions to these issues and tothe topic of applications and modelling asa whole (see Section 4). Based onthese reactions and contributions, alimited number (approximately 75) ofparticipants will be invited to aconference (the Study Conference)which is to take place in February 2004 inDortmund (Germany). Finally, using thecontributions to this conference, a bookwill be produced (the Study Volume)whose content will reflect thestate-of-the-art in the topic ofapplications and modelling in mathematicseducation and suggest directions for futuredevelopments in research and practice.The authors of this Discussion Document are themembers of the International ProgrammeCommittee for this ICMI Study. Thecommittee consists of 14 people from 12countries, listed at the end of Section4. The structure of the Document isas follows. In Section 1, we identifysome reasons why it seems appropriate tohold a study on applications and modelling.Section 2 sets a conceptual frameworkfor the theme of this Study, and Section3 contains a selection of importantissues, challenges and questions related tothis theme. In Section 4 we describepossible modes and ways of reacting to theDiscussion Document, and in the finalSection 5 we provide a shortbibliography relevant to the theme of thisStudy.

E Pluribus Unum: Challenges of Diversity in the Future of Mathematics Education Research

Our task in preparing this article on the occasion of the 25th anniversary of the Journal for Research in Marhematics Education (JRME) was to look ahead to the future of research in the field and to identify and discuss issues that might be important for the next decade or two in the life of the journal. Rather than merely offering our own opinions and speculations. we decided to interview a number of other researchers, some from the United States and some from other countries, to sample their views regarding the current state of research in mathematics education, the issues that may affect the future of the field, and the role of the JRME in the current and future scene. In particular, we asked these researchers to identify examples of work they considered significant and to comment on its imponant characteristics. We probed their definitions of the field by asking them to identify the types of work (e.g., empirical studies, historical or theoretical analyses) they judged could legitimately be called research in mathematics education. We explored their visions of the future of research over the next few decades. And we questioned them about the role and place of the JRME in the research community and about its impact on the field. In addition, we participated in a conference on Research in Mathematics Education and Its Results in May 1994 that was part of a study conducted by the International Commission on Mathematical Instruction (ICMI). The discussion document framing the study (Sierpinska et al., 1993) and many of the presentations and conversations at the ICMI Research Conference should be acknowledged as sources of ideas for the article. Naturally, we have included our own opinions, analyses, and perspectives.

Living with a new mathematical species

In 1985 the International Commission on Mathematical Instruction (ICMI) convened a meeting in France of mathematicians, computer scientists, and mathematics educators from around the world to discuss the impact of “informatics” (the common European term for computer science) on mathematics—specifically, on mathematical research, on the mathematical curriculum, and on mathematical pedagogy.

International Commission on Mathematical Instruction (I.C.M.I.): First International Congress on Mathematical Education

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