PME

International Group for the Psychology of Mathematics Education

A brief history of the International Group for the Psychology of Mathematics Education (PME)

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  1. A brief history
  2. Citations
  3. Numbers of members of PME and participants at conferences
  4. PME Group Presidents: Past and Current
  5. Publications Encouraged by the PME Group
  6. Participants (84) in 1977 Utrecht, The Netherlands
  7. PME members in 1977


Written and complied by
Cynthia Nicol and Steve Lerman with assistance from Joop van Dormolen, Carolyn Kieran, Gerard Vergnaud, Kath Hart and Heinrich Bauersfeld - March 2008.

A brief history

The International Group for the Psychology of Mathematics Education was born in 1976 with approximately 100 participants under the guidance and inspiration of Efraim Fischbein. The impetus to develop an organization with a psychological focus on mathematics education began much earlier when, in 1969 at the first International Congress on Mathematics Education ([ICME], Lyons, France), Fischbein was invited by then ICME president Hans Freudenthal to chair and organize a round table on the psychological problems of mathematics education. Fischbein, a cognitive psychologist and, at that time head of the department of Educational Psychology at the University of Bucharest (later he served as head of the Science Education Department at Tel Aviv University), was keen to take up Freudenthal's call to improve mathematics education in schools by going beyond philosophical discussions of mathematics teaching and learning to advocating empirical scientific research in the field.
The Group has a name
Professor Fischbein proposed to members in 1976 that the group be called "The International Group for the Psychology of Mathematics Education" (IGPME) to distance it from Professor Zoltan Dienes' group that was called "The International Study Group for Mathematics Learning". In 1979 Professor Hartwig Meissner proposed that the abbreviation be IPM. Official acceptance of the abbreviation PME occurred at the Group meeting in 1980, (Berkeley, USA) with the final version of the Constitution.

Participants attending this first round table were keen to continue the discussion on psychological aspects of mathematics education. A working group dedicated to the psychology of mathematics education was organized and offered at the second ICME in 1972 (Exeter, Great Britain). Hundreds of participants attended that workshop recognizing, as Fischbein did, "that the psychological problems of mathematical learning and reasoning are scientifically exciting and at the same time genuinely relevant for mathematics education" (Fischbein, 1990, p. 4). Four years later at ICME in 1976 (Karlsruhe, Germany) participants decided to organize a permanent group that would meet yearly to discuss and explore issues related to the psychology of mathematics education. And so began the International Group for the Psychology of Mathematics Education (PME) with Fischbein as first president and Richard Skemp as second president four years later in 1980.
Freudenthal's psychology of mathematics education
The kind of psychology of mathematics education Freudenthal had in mind was influenced by his mathematical and logical experiments and experiences with grandson Bastiaan. At his opening address at the first PME in Utrecht he defined this kind of psychological research: You need a strategy of observing - a highly sophisticate strategy, but which can be expressed in one principle: Look and listen with an open mind and have the courage to notice and to report events that most people would consider as too silly to be noticed and to be reported - there might be a minority who can appreciate them, and this minority will be right." (Freudenthal, Opening Address of PME 1, Utrecht, The Netherlands 1977)

Guidelines for the development of the PME International Committee were agreed upon in 1978 at PME 2 (Osnabrück, Germany). It was decided that (i) the Committee should consist of 16 elected members, 4 of whom should retire each year, (ii) that retiring members should not be eligible for re-election for the subsequent year, (iii) that the Officers (e.g. President, Treasurer, Secretary) should be chosen by the Committee from among its elected members and (iv) that members retire upon 4 years of service. This continues to be the guideline for the international organization of the Group. The first PME Constitution was adopted by the Annual General Meeting in 1980 (Berkeley, USA) with a focus on "the following categories of communications:
  1. General theoretical problems concerning the relation between psychology as a science and mathematics education
  2. Communications presenting experimental interdisciplinary research
  3. Psychological training for teachers.
These themes focused on an international exchange of knowledge in the psychology of mathematics education, promotion of interdisciplinary research with psychologists, mathematicians and mathematics teachers, and development of the psychological aspects of teaching and learning mathematics and its implications.

PME 1979, Warwick
PME 1979, Warwick. On the left: Ben Knip, Gérard Vergnaud, who together with Alan Bell and Hartwig Meissner designed the constitution of PME, an unknown lady, Dick Lesh, David Tall, Josette Adda, Uwe Bong. Inside, at the time were Hans Freudenthal, Shlomo Vinner, Francis Loewenthal and others.
Each conference had a theme and by 1979 PME 3 (Warwick, United Kingdom) the number of conference themes had doubled from 1977 PME 2 and now included a coordinator and a contributor. As early as PME 3 themes that focused on the social dimensions of learning and issues of teaching were present.

PME 3 (Warwick UK 1979) conference themes
  • The process of understanding in mathematical learning
  • Instruction and creativity
  • Social dimensions of mathematical learning
  • Learning hierarchies
  • Mathematical thinking
  • Mathematical abilities and their development
  • Space and geometry
  • Attitudes and affective aspects
  • Problem solving
  • Developmental psychology and implications for teaching
Richard Skemp
Richard Skemp
As PME developed, its focus which began with developmental and psychological complexities of learning various mathematical concepts and processes (e.g., number operations, limits, infinity) broadened to include new ways of thinking about learning mathematics. There were periods where particular ideas were prominent in PME research. These included the ideas of Realistic Mathematics Education, constructivism as a theory of knowing, Van Hiele's levels of reasoning, visualization and its connection to technology and geometry, alternative forms of assessment and others. These and other research agendas challenged previous ways of thinking about mathematical activity and provided new implications for instruction. Fischbein in his 1990 introductory chapter of a research synthesis of PME for the ICMI Studies Series offered four trends in mathematics and cognition research of that time. These included the use of the computer and artificial intelligence metaphors for understanding teaching and learning, constructivism and its implications for research and instruction, exploration of the relationship between the formal, algorithmic and intuitive forms of mathematical thinking, and the role and nature of metacognition. With time there was growing discussions on the scientific direction of PME with some members advocating a broadening of the focus of PME to go beyond the psychological considerations to also include the process of teaching and teacher education, epistemology of mathematics from a teaching/learning perspective, and equity and socio-cultural issues of teaching and learning mathematics. In 2005 at the General Meeting (Melbourne, Australia) with recognition that the Group's stated aims over the past 10 years had moved beyond the purely psychological aims of the early years, membership voted to amend the statement of major goals to include the study of other aspects of teaching and learning.
PME 2 (Osnabrück, Germany) conference themes
Themes and committee members that led the PME 2 in 1978:
  1. Acquisition of arithmetical concepts (R. Rees & G. Vergnaud);
  2. Learning of generalisation and proof (A. W. Bell)
  3. Interpersonal aspects of classroom communication (H. Bauersfeld)
  4. Nature of mathematical thinking (A. Vermandel & E. Cohors-Fresneborg)
  5. Intuitive and reflective processes in mathematics (E. Fischbein & R. Skemp)              

Currently the trends and collected research in mathematics education for PME have expanded. The 2006 Handbook of Research on the Psychology of Mathematics Education (Gutiérrez & Boero, 2006) is organized around research areas that have had substantial activity in PME. These main PME research domains include: 1) cognitive aspects of learning and teaching mathematical content such as number, algebra, geometry and measurement as well as research in these areas with respect to young children's thinking, advanced mathematical thinking, and visualization; 2) teaching and learning mathematics with technology; 3) social aspects of mathematics education including socio-cultural research, equity, gender, affect, and constructivism.
Including the social dimensions of learning in PME - Heinrich Bauersfeld Remembers
From the very beginning I was unhappy with the exclusive concentration on Psychology only, which meant focusing on the individual and neglecting the social dimensions of the complex teaching-learning processes. Research on the complex problems of learning/teaching-processes and of teaching teachers to teach mathematics will not arrive at helpful constructive information as long as such vast domains as language, human interaction (not the usual psychological interaction of variables!) and rich case studies are neglected and/or treated by inadequate research methods. Usual refusal sounded like: "We have enough to do with psychology!" Freudenthal was interested, and used to ask me accidentally: "What shall I read about it?" But at that time there was neither easy access available nor were there convincing overviews from sociological perspectives.

As of 2008 the major goals of PME are:
  1. to promote international contacts and exchange of scientific information in the psychology of mathematical education;
  2. to promote and stimulate interdisciplinary research in the aforesaid area;
  3. to further a deeper and more correct understanding of the psychological and other aspects of teaching and learning mathematics and the implications thereof.
PME meetings include plenary lectures, a plenary panel, research forums, working groups, discussion groups and poster sessions. Each of these research venues provides different opportunities for members to share, present, and engage in discussion of mathematics education. PME meetings during the early years were structured around plenary lectures and working and discussion groups. This was followed in later years by the introduction of a plenary panel that involved a panel presentation and audience discussion around a significant issue.
Tensions developing the constitution
There were some tensions amongst those drafting the Constitution between 1979 and 1980. Issues that troubled the committee were:
  • whether all the officers (President, Vice-President, Treasurer and Secretary) should be elected by the Annual General Meeting (AGM) or just some of those officers. The decision was made to elect the President only at the AGM and the other three officers would be elected by the International Committee (IC).
  • whether officers could be re-elected after their term of office. It was decided that the President could not be re-elected but that other officers could be elected to offices different from those they had already held.
  • whether the term of office of the president would be for two years or more. It was decided that all officers would serve for two years. This was changed to three years for the President during the term of office of Professor Kath Hart between1990 and 1992. Professor Carolyn Kieran was the first to be President for a three year term.
  • whether each IC member would be elected for three years or four, with 3 leaving each year or four. The decision was made in favour of four years.
The principles and wording of the Constitution had to be negotiated by committee members by letter; hence the decision to call a face-to-face meeting in Paris in June 1980. One concern, that seems to have been resolved by the elections for President in 1980, was Professor Nesher's that the arrangements for four members of the IC to step down each year to allow for election of four new members would mean that Professors Skemp, Bell, Fischbein and Freudenthal would all leave the IC at the same time

There are currently two forms of groups: working groups that allow for presentations of more established research programs and discussion groups that support discussions of developing research ideas. PME has encouraged working groups to continue their work during the year between Group meetings, and has when possible provided modest funding to support administrative expenses for this work. Working groups receiving such support were encouraged to publish their work (see list of publications below). An interest of the PME International Committee has and continues to include exploring new discussion formats that offer members possibilities for more personal and interactive involvement.
PME 1979, Warwick
PME 1979, Warwick. On the bus. Among others Shlomo Vinner, and Dina Tirosh
Membership during the beginning years of PME consisted mainly of mathematicians, mathematics educators, and psychologists from a small number of members from Europe and North America. Gradually membership grew so that by the mid 1980s representation also included participants from other countries. Currently members and conference participants represent more than 50 countries all over the world. Membership is open to all persons in active research interested or involved in furthering the Group's direction. Encouraging membership and conference participation by under- or non-represented countries is a crucial activity of PME. Various strategies over the years were implemented including the establishment of a fund, now known as the Skemp Fund (in honor of Richard Skemp and his contributions to the psychology of mathematics), to support representation of scholars from under- and non-represented countries.
A question of language
The Working Group on the Psychology of Learning Mathematics which held a meeting at the 3rd International Congress on Mathematical Education in Karlsruhe in August 1976 was pre-occupied with issues of language. Apparently Professor Hans Freudenthal sat in the front row and translated all his own comments from English into French and German and many of the French and French Canadians had to have the English translated, leading to arguments over the correctness of the translations from those who spoke both. The minutes of the meeting of acting committee the 19th November 1979 included the following: Professor Gerard Vergnaud's proposal that the conference language should be English was accepted. The Grenoble conference in 1981 invited papers in French or English. This possibility was repeated at the 1989 conference in Paris.

In 1994 at PME 18 (Lisbon, Portugal) a sub-group of PME was established to pro-actively strengthen connections and activities with under- and non-represented countries. The sub-group's goals were and continue to include furthering relationships with groups and individuals, providing information about the activities of PME, and facilitating individual participation at PME. Discussion groups at PME conferences over the years examined the political, psychological, financial, linguistic, and scientific issues related to furthering the participation of researchers at under- and non-represented countries. PME continues to be a vibrant organization with over 500 international members contributing to mathematics education worldwide. Published PME conference proceedings are available in hard copy and electronic form. Many proceedings can be retrieved from the Educational Resources Information Centre (ERIC) at www.eric.ed.gov. Future PME conferences include: Morelia Mexico (PME 32 in 2008), Thessaloniki Greece (PME 33 in 2009), and Belo Horizonte Brazil (PME 34 in 2010). For more information please visit the PME website at http://igpme.org/.



Citations


Fischbein, E. (1990). Introduction. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 1-13). Cambridge: Cambridge University Press.
Gutiérrez, A. & Boero, P. (2006). Handbook of research on the psychology of mathematics education: Past, present and future. The Netherlands: Sense Publishers.
PME 1991, Assisi
PME 1991, Assisi From the left: Ted Eisenberg, Jim Kaput, Gontran Ervynck, Dina Tirosh, Tommy Dreyfus, David Tall, Michèle Artigue, Annie and John Selden, Susan Kaput








Numbers of members of PME and participants at conferences


Number of participants Number of members
2007 PME31 Seoul, Korea 340 503
2006 PME30 Prague, Czech Republic 687 901
2005 PME29 Melbourne, Australia 357 640
2004 PME28 Bergen, Norway 477 808
2003 PME27 Honolulu, USA 479 803
2002 PME26 Norwich, United Kingdom 478 680
2001 PME25 Utrecht, The Netherlands 600 817
2000 PME24 Hiroshima, Japan 370 602
1999 PME23 Haifa, Israel 414 682
1998 PME22 Stellenbosch, South Africa 387 681
1997 PME21 Lahti, Finland 315 630
1996 PME20 Valencia, Spain 445 693
1995 PME19 Recife, Brazil 242 555
1994 PME18 Lisbon, Portugal 388 655
1993 PME17 Tsukuba, Japan 195 508
1992 PME16 Durham, USA 368 603
1991 PME15 Assisi, Italy 190 189
1990 PME14 Oaxtepec, Mexico 185 185
1989 PME13 Paris, France 262 262
1988 PME12 Veszprem, Hungary 241 240
1987 PME11 Montreal, Canada 309 312
1986 PME10 London, United Kingdom 262 262
1985 PME9 Noordwijkerhout, The Netherlands 217 212
1984 PME8 Sydney, Australia 183 184
1983 PME7 Shoresh, Israel 131 131
1982 PME6 Antwerpen, Belgium 144 143
1981 PME5 Grenoble, France 86 86
1980 PME4 Berkeley, USA 81 79
1979 PME3 Warwick, United Kingdom 45 45
1978 PME2 Osnabrück, Germany 70 70
1977 PME1 Utrecht, The Netherlands 84 84

Note: For the years before 1992 the numbers of participants are uncertain
Budapest 1988
Budapest 1988.
David Tall and Anna Sfard


PME Group Presidents: Past and Current



Efraim Fischbein (Israel) 1977-1980
Richard Skemp (UK) 1980-1982
Gérard Vergnaud (France) 1982-1984
Kevin Francis Collis (Australia) 1984-1986
Perla Nesher (Israel) 1986-1988
Nicolas Balacheff (France) 1988-1990
Kath Hart (UK) 1990-1992
Carolyn Kieran (Canada) 1992-1995
Stephen Lerman (UK) 1995-1998
Gilah Leder (Australia) 1998-2001
Rina Hershkowitz (Israel) 2001-2004
Chris Breen (South Africa) 2004-2007
Fou-Lai Lin (Taiwan) 2007-2010


Publications Encouraged by the PME Group
(e.g., resulting from PME research and working groups)


1990:
Nesher, Pearla & Kilpatrick, Jeremy (Eds.) Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics Education Cognition University Press. ICMI Study Series. Publisher: Cambridge.
1991:
Tall, David (Ed), Advanced Mathematical Thinking. Publisher: Kluwer, Dordrecht
1993:
Bishop, Alan & Hart, Kath & Lerman, Stephen & Nunes, Terezinha Significant Influences on Children's Learning of Mathematics. Document Series No. 47, Education Sector. Publisher: UNESCO, Paris
1997:
Zack, Vicky & Mousley, Judith & Breen, Chris (Eds.) Developing Practice: Teachers Inquiry and Educational Change. Book/Monograph Publisher: Deakin University Press, Melbourne Publication based on PME group: Teachers as researchers.
1998:
Goldin, Gerald & Janvier, Claude (Eds.) PME Working Group on Representations (dedicated to Robert B. Davis). Article in: Journal of Mathematical Behavior (Special Issue), Vol. 17, nos. 1 - 2. Publication based on PME group: Representations.
1999:
Ellerton, Nerida F. (Ed.) Mathematics Teacher Development: International perspectives Book/Monograph. Publisher: Meridian Press. Publication based on PME group: Research on teacher development
1999:
Jaworski, Barbara & Wood, Terry & Dawson, Alexander (Eds.) Mathematics Teacher Education: Critical International Perspectives. Book/Monograph. Publisher: Falmer Press, London. Publication based on PME group: Psychology of inservice.
2000:
Jones, Keith & Gutiérrez, Angel & Mariotti, Maria Alessandra (Eds.) Proof in Dynamic Geometry Environments. PME Special Issue of Educational Studies in Mathematics, 44 (1-2). Publisher: Kluwer, Dordrecht.
2001:
Ainley, Janet & Pratt, Dave (Eds,) Constructing Meaning from Data. PME Special Issue of Educational Studies in Mathematics, 45 (1-2). Publisher: Kluwer, Dordrecht.
2001:
Kieran, Carolyn & Forman, Ellice & Sfard, Anna (Eds.) Bridging the Individual and the Social: Discursive Approaches to Research in Mathematics Education. PME Special Issue of Educational Studies in Mathematics, 46 (1-3). Publisher: Kluwer, Dordrecht (reprinted as a book, Learning Discourse, by Kluwer in 2002). Publication based on plenary panel of 1999 PME Conference.
2002:
English, Lyn & Goodchild, Simon (Eds.) Researching Mathematics Classrooms: A critical examination of methodology. Book/Monograph Publisher: Greenwood. Publishers. Publication based on PME group: Classroom research.
2006:
Gutiérrez, Angel & Boero, Paolo (Eds.) Handbook of research on the psychology of mathematics education: Past, present and futureBook/Monograph. Publisher: Sense Publishers, The Netherlands. Publication based on PME research -- on the occasion of 30th anniversary of PME.



Participants (84) in 1977 Utrecht, The Netherlands


A M
Abele, Albrecht GERMANY Machut, T. GERMANY
Adda, Josette FRANCE Malet, A. SPAIN
Anger, E. SWITZERLAND Marthe, Patrick FRANCE
Audigier, M.N. FRANCE Mètrégiste, R. FRANCE
Avital, Shmuel ISRAEL Moske, M. THE NETHERLANDS
Movshovitz-Hadar, Nitsa ISRAEL
B N
Balacheff, Nicolas FRANCE Nelissen, J. THE NETHERLANDS
Balzer, W. GERMANY Nesher, Pearla ISRAEL
Bauersfeld, Heinrich GERMANY Nimier, J. FRANCE
Bell, Alan UNITED KINGDOM
Bessot, Annie FRANCE
Bong, Uwe GERMANY
Broekman, Harrie THE NETHERLANDS
Brusseau, Guy FRANCE
C R
Chevallard, Yves FRANCE Radatz, Hendrik GERMANY
Cohors-Fresenborg, Elmar GERMANY Rash, B. GERMANY
Colomb, J. FRANCE Rees, Ruth UNITED KINGDOM
Comiti, Claude FRANCE Rouchier, André FRANCE
D S
Darche, N. FRANCE Schmidt, Siegbert GERMANY
de Backer, W. BELGIUM Schuyten-Plancke, Gilberte BELGIUM
de Leeuw, Leendert THE NETHERLANDS Skemp, Richard R. UNITED KINGDOM
Stavy, Ruth ISRAEL
E T
Ervynck, Gontran J. BELGIUM Tall, David UNITED KINGDOM
Troelstra, Rudolf THE NETHERLANDS
F V
Fischbein, Efraim ISRAEL Van Dormolen, Joop ISRAEL
Floyd, Ann UNITED KINGDOM van Eerde, Dolly THE NETHERLANDS
Freudenthal, Hans THE NETHERLANDS van Stern, H. GERMANY
Frommhold, J. GERMANY van 't Riet, S.P. THE NETHERLANDS
van 't Riet, Nol THE NETHERLANDS
van Tooren, Arie THE NETHERLANDS
Vedder, Jaap THE NETHERLANDS
Vergnaud, Gérard FRANCE
Vermandel, Alfred BELGIUM
Vidal-Madjar, Annie FRANCE
Vinner, Shlomo ISRAEL
von Stern, Heino GERMANY
Vuurmans, A. THE NETHERLANDS
G W
Gardiner, John UNITED KINGDOM Weidner, C. GERMANY
Gjone, Gunner NORWAY Weinheimer, B. GERMANY
Glaser, H. GERMANY Welmers, H. THE NETHERLANDS
Gras, Régis FRANCE Winter, Colin F. UNITED KINGDOM
Guillerault, Michel FRANCE Wolters, Miriam A. THE NETHERLANDS
H
Hart, Kath UNITED KINGDOM
Hefendehl, Lisa GERMANY
Holland, Gerhard GERMANY
J
Janvier, Claude CANADA
Jauman, H. GERMANY
K Z
Kayler, Hélène CANADA Zimmermann, Bernd GERMANY
Klukhuhn, W. THE NETHERLANDS
Knip, Ben H. THE NETHERLANDS
Küchemann, Dietmar UNITED KINGDOM
Kündinger, Erika CANADA
L
Laborde, Colette FRANCE
Labrie, Jean Marie CANADA
Laenen, C. BELGIUM
Leonard, François FRANCE
Löttgen, U. GERMANY
Lunkenbein, D. CANADA




PME members in 1977 (The conference was in Utrecht, The Netherlands)


Countries Number of Percentage
BELGIUM 4 5.1
CANADA 4 5.1
FRANCE 19 24
GERMANY 20 25
ISRAEL 6 7.6
NORWAY 1 1.3
SPAIN 1 1.3
SWITZERLAND 1 1.3
THE NETHERLANDS 16 20
UNITED KINGDOM 7 8.9