Mathematics Education as a Research Domain: A Search for Identity

1. Front Matter

   Pages i-xiii

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2. The ICMI Study Conference

   1. Front Matter

      Pages 1-1

      PDF

   2. Discussion Document

      • Anna Sierpinska, Jeremy Kilpatrick

      Pages 3-32

   3. Research, Effectiveness, and the Practitioners’ World

      • Alan J. Bishop

      Pages 33-45

3. Mathematics Education as a Research Discipline

   1. Front Matter

      Pages 47-47

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   2. A Glance over the Evolution of Research in Mathematics Education

      • Josette Adda

      Pages 49-56

   3. Balancing Complex Human Worlds: Mathematics Education as an Emergent Discipline in Its Own Right

      • Norma C. Presmeg

      Pages 57-70

   4. A Postmodern Perspective on Research in Mathematics Education

      • Paul Ernest

      Pages 71-85

   5. Mathematics Education as a ‘Design Science’

      • Erich Ch. Wittmann

      Pages 87-103

   6. What is Mathematics Education? A Survey of Mathematics Educators in Canada

      • Roberta Mura

      Pages 105-116

   7. Programs for the Education of Researchers in Mathematics Education

      • Gunnar Gjone

      Pages 117-127

4. Goals, Orientations, and Results of Research in Mathematics Education

   1. Front Matter

      Pages 129-129

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   2. The Aims of Research

      • Gilah C. Leder

      Pages 131-140

   3. Aiming Research Toward Understanding: Lessons We Can Learn from Children

      • James Hiebert

      Pages 141-152

   4. Transforming the International Mathematics Education Research Agenda

      • Nerida F. Ellerton, M. A. Clements

      Pages 153-175

   5. Clarifying the Meaning of Mathematical Objects as a Priority Area for Research in Mathematics Education

      • Juan D. Godino, Carmen Batanero

      Pages 177-195

   6. Research and Results in Mathematics Education: Some Contradictory Aspects

      • Paolo Boero, Julianna Radnai Szendrei

      Pages 197-212

   7. Models in Mathematics Education Research: A Broader View of Research Results

      • Carolyn Kieran

      Pages 213-225

   8. Towards a Cognitive Theory of Practice

      • Gérard Vergnaud

      Pages 227-240

No one disputes how important it is, in today's world, to prepare students to un­ derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda­ mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci­ plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela­ tions between the teacher and the taught, and other general problems in the inter­ face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.

• Mathematica
• evolution
• logic
• mathematics
• sociology

• Concordia University, Montreal, Canada

  Anna Sierpinska

• University of Georgia, Athens, USA

  Jeremy Kilpatrick

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