Mathematics Education as a Research Domain: A Search for Identity: An ICMI Study Book 1 (Institute for Amorphous Studies Series)

I: The ICMI Study Conference.- Discussion Document.- List of Participants.- What is the Specific Object of Study in Mathematics Education? Report of Working Group 1.- What are the Aims of Research in Mathematics Education? Report of Working Group 2.- What are the Specific Research Questions or Problématiques of Research in Mathematics Education? Report of Working Group 3.- What are the Results of Research in Mathematics Education? Report of Working Group 4.- What Criteria Should Be Used to Evaluate the Results of Research in Mathematics Education? Report of Working Group 5.- Research, Effectiveness, and the Practitioners’ World.- II: Mathematics Education as a Research Discipline.- A Glance Over the Evolution of Research in Mathematics Education.- Balancing Complex Human Worlds: Mathematics Education as an Emergent Discipline in its Own Right.- A Postmodern Perspective on Research in Mathematics Education.- Mathematics Education as a ‘Design Science’.- What is Mathematics Education? A Survey of Mathematics Educators in Canada.- Programs for the Education of Researchers in Mathematics Education.- III: Goals, Orientations and Results of Research in Mathematics Education.- The Aims of Research.- Aiming Research Toward Understanding: Lessons We Can Learn From Children.- Transforming the International Mathematics Education Research Agenda.- Clarifying the Meaning of Mathematical Objects as a Priority Area for Research in Mathematics Education.- Research and Results in Mathematics Education: Some Contradictory Aspects.- Models in Mathematics Education Research: A Broader View of Research Results.- Towards a Cognitive Theory of Practice. 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. 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. Content: Front Matter....Pages i-xiii Front Matter....Pages 1-1 The ICMI Study Conference....Pages 3-45 Front Matter....Pages 47-47 A Glance over the Evolution of Research in Mathematics Education....Pages 49-56 Balancing Complex Human Worlds: Mathematics Education as an Emergent Discipline in Its Own Right....Pages 57-70 A Postmodern Perspective on Research in Mathematics Education....Pages 71-85 Mathematics Education as a ‘Design Science’....Pages 87-103 What is Mathematics Education? A Survey of Mathematics Educators in Canada....Pages 105-116 Programs for the Education of Researchers in Mathematics Education....Pages 117-127 Front Matter....Pages 129-129 The Aims of Research....Pages 131-140 Aiming Research Toward Understanding: Lessons We Can Learn From Children....Pages 141-152 Transforming the International Mathematics Education Research Agenda....Pages 153-175 Clarifying the Meaning of Mathematical Objects as a Priority Area for Research in Mathematics Education....Pages 177-195 Research and Results in Mathematics Education: Some Contradictory Aspects....Pages 197-212 Models in Mathematics Education Research: A Broader View of Research Results....Pages 213-225 Towards a Cognitive Theory of Practice....Pages 227-240