Mathematics Education as a Research Domain: A Search for Identity: An ICMI StudyAnna Sierpinska, Jeremy Kilpatrick In 1978, in the foreword to Weeding and Sowing: A Preface to a Science of Mathematics Education, Hans Freudenthal wrote that his book is a preface to a science that does not exist. Almost 20 years later, does his claim still hold true? The present book is the result of the reflection of many individuals in mathematics education on this and related questions. Is mathematics education a science? Is it a discipline? In what sense? What is its place within other domains of research and academic disciplines? What accounts for its specificity? In the book, the reader will find a range of possible answers to these questions, a variety of analyses of the actual directions of research in different countries, and a number of visions for the future of research in mathematics education. The book is a result of an ICMI Study, whose theme was formulated as: `What is Research in Mathematics Education and What are Its Results?'. One important outcome of this study was the realization of the reasons for the difficulty of the questions that the study was posing, leading possibly to a set of other questions, better suited to the actual concerns and research practices of mathematics education researchers. The book addresses itself to researchers in mathematics education and all those working in their neighborhood who are concerned with the problems of the definition of this new scientific domain emerging at their borders. |
Contents
List of Participants | 9 |
What are the Specific Research Questions or Problématiques | 20 |
ALAN J BISHOP | 33 |
JOSETTE ADDA | 49 |
PRESMEG | 57 |
PAUL ERNEST | 71 |
ERICH CH WITTMANN | 87 |
ROBERTA MURA | 105 |
GILLIAN HATCH CHRISTINE SHIU | 297 |
RUDOLF VOM HOFE | 317 |
STEPHEN LERMAN | 333 |
CLAIRE MARGOLINAS | 351 |
JOHN MASON | 357 |
THOMAS A ROMBERG | 379 |
YASUHIRO SEKIGUCHI | 391 |
GILA HANNA | 399 |
Programs for the Education of Researchers in Mathematics | 117 |
LEDER | 131 |
JAMES HIEBERT | 141 |
NERIDA F ELLERTON M A KEN CLEMENTS | 153 |
GODINO CARMEN BATANERO | 177 |
PAOLO BOERO JULIANNA RADNAI SZENDREI | 197 |
CAROLYN KIERAN | 213 |
GÉRARD VERGNAUD | 227 |
BOOK 2 | 240 |
Mathematics Education and Mathematics | 240 |
Case Study from an International Perspective | 243 |
MARGARET BROWN | 263 |
Developmental Research as a Research Method | 277 |
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action research activity aims analysis approach Balacheff basic ideas Brousseau classroom cognitive Cognitive Science complex concepts concerning construction Constructivist context criteria cultural curriculum Didactics of Mathematics Didactique des Mathématiques Didaktik der Mathematik disciplines discussion domain Educational Studies epistemological Ethnomathematics example experience Fennema field framework Freudenthal Grouws Hans Freudenthal innovation instructional theory interaction International interpretation IREM Journal for Research Kilpatrick Kluwer Academic Publishers learning of mathematics mathe mathematical knowledge mathematicians mathematics education research mathematics teaching matics education meaning methods models National paper paradigm perspective philosophy of mathematics Piaget practice practitioners problems produce programs Psychology of Mathematics questions relevant research in mathematics role school mathematics scientific semiotic Sfard ship of Theseus Sierpinska situated cognition situations social solving specific Studies in Mathematics Teachers of Mathematics teaching and learning teaching units theoretical thinking tion trend understanding University validity