This book is a product of the BACOMET group, a group of educators-mainly educators of prospective teachers of mathematics-who first came together in 1980 to engage in study, discussion, and mutual reflection on issues in mathematics education. BACOMET is an acronym for BAsic Components of Mathematics Education for Teachers. The group was formed after a series of meetings in 1978-1979 between Geoffrey Howson, Michael Otte, and the late Bent Christiansen. In the ensuing years, BACOMET initiated several projects that resulted in published works. The present book is the main product of the BACOMET project entitled Meaning and Communication in Mathematics Education. This theme was chosen because of the growing recognition internationally that teachers of mathematics must deal with questions of meaning, sense making, and communication if their students are to be proficient learners and users of mathematics. The participants in this project were the following: Nicolas Balacheff (Grenoble, France) Maria Bartolini Bussi (Modena, Italy) Rolf Biehler (Bielefeld, Germany) Robert Davis (New Brunswick, NJ, USA) Willibald Dorfler (Klagenfurt, Austria) Tommy Dreyfus (Holon, Israel) Joel Hillel (Montreal, Canada) Geoffrey Howson (Southampton, England) Celia Hoyles-Director (London, England) Jeremy Kilpatrick-Director (Athens, GA, USA) Christine Keitel (Berlin, Germany) Colette Laborde (Grenoble, France) Michael Otte (Bielefeld, Germany) Kenneth Ruthven (Cambridge, England) Anna Sierpinska (Montreal, Canada) Ole Skovsmose-Director (Aalborg, Denmark) Conversations about directions the project might take began in May 1993 at a NATO Advanced Research Workshop of the previous BACOMET project in VIII PREFACE

Meanings of Meaning of Mathematics.- ¿Meaning¿ and School Mathematics.- The Meaning of Conics: Historical and Didactical Dimensions.- Reconstruction of Meaning as a Didactical Task: The Concept of Function as an Example.- Meaning in Mathematics Education.- Collective Meaning and Common Sense.- Mathematics Education and Common Sense.- Communication and Construction of Meaning.- Making Mathematics and Sharing Mathematics: Two Paths to Co-Constructing Meaning?.- The Hidden Role of Diagrams in Students¿ Construction of Meaning in Geometry.- What¿s a Best Fit? Construction of Meaning in a Linear Algebra Session.- Discoursing Mathematics Away.- Meaning and Mathematics.