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This book focuses on aspects of mathematical beliefs, from a variety of different perspectives. Current knowledge of the field is synthesized and existing boundaries are extended. The volume is intended for researchers in the field, as well as for mathematics educators teaching the next generation of students.

This book offers an exploration of tools and mathematics and issues in mathematics education related to tool use, from pre-history to future directions in the field. It includes coverage of curriculum, assessment, and policy design.

The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

This is a variegated picture of science and mathematics classrooms that challenges a research tradition that converges on the truth. The book is for educational researchers, research students, and practitioners with an interest in optimizing the effectiveness of classrooms as environments for learning.

This book presents a research focus on diversity and inclusivity in mathematics education. If we in mathematics education seek to challenge that status quo, more research must be focussed not just on diversity but also on the inclusivity, of practices in mathematics education.

In this book, the author discusses a modern concept of general education that then helps to clarify both curricular and pedagogical deficits involved in conventional mathematics instruction.

They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them.

This timely volume raises issues concerning the nature of school mathematics and mathematics at work, and the challenges of teaching valuable mathematics in school and providing appropriate training for a variety of careers. It offers lively commentaries on important `hot' topics: transferring knowledge and skill across contexts;

An innovative contribution to educational research is to be found in this book. The book addresses the need to generate texts that assist educators and future educators in taking up new research and making sense of it. The book will appeal to teacher educators, student teachers, and mathematics education researchers alike.

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended.

The Construction of New Mathematical Knowledge in Classroom Interaction deals with the very specific characteristics of mathematical communication in the classroom.

They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them.

This book is of interest to mathematics educators, researchers in mathematics education, gender, social justice, equity and democracy in education; It thus interrogates and develops theoretical research tools for mathematics education and provides ideas for practice in mathematics classrooms.

An innovative contribution to educational research is to be found in this book. The book addresses the need to generate texts that assist educators and future educators in taking up new research and making sense of it. The book will appeal to teacher educators, student teachers, and mathematics education researchers alike.

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended.

This is a variegated picture of science and mathematics classrooms that challenges a research tradition that converges on the truth. The book is for educational researchers, research students, and practitioners with an interest in optimizing the effectiveness of classrooms as environments for learning.

The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it.

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The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it.

In the first BACOMET volume different perspectives on issues concerning teacher education in mathematics were presented (B. Christiansen, A. G. Howson and M. Otte, Perspectives on Mathematics Education, Reidel, Dordrecht, 1986). Underlying all of them was the fundamental problem area of the relationships between mathematical knowledge and the teaching and learning processes. The subsequent project BACOMET 2, whose outcomes are presented in this book, continued this work, especially by focusing on the genesis of mathematical knowledge in the classroom. The book developed over the period 1985-9 through several meetings, much discussion and considerable writing and redrafting. Our major concern was to try to analyse what we considered to be the most significant aspects of the relationships in order to enable mathematics educators to be better able to handle the kinds of complex issues facing all mathematics educators as we approach the end of the twentieth century. With access to mathematics education widening all the time, with a multi­ tude of new materials and resources being available each year, with complex cultural and social interactions creating a fluctuating context of education, with all manner of technology becoming more and more significant, and with both informal education (through media of different kinds) and non­ formal education (courses of training etc. ) growing apace, the nature of formal mathematical education is increasingly needing analysis.

It is amazing that the usual reply to being introduced to a mathematician is a stumbling apology about how bad someone is at mathematics, no matter how good they may be in reality.

The present publication Three Dimensions has three aims: to give a picture of the goals Wiskobas set for future mathematics education, at the same time to show how such goals can be described, and to show the theoretical framework of the Wiskobas curriculum.

Dialogue and Learning in Mathematics Education is concerned with communication in mathematics class-rooms. Both are considered important for a theory of learning mathematics. Thus a theory of learning mathematics is developed which is resonant with critical mathematics education.

This book focuses on aspects of mathematical beliefs, from a variety of different perspectives. Current knowledge of the field is synthesized and existing boundaries are extended. The volume is intended for researchers in the field, as well as for mathematics educators teaching the next generation of students.

In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory.

Mathematics is in the unenviable position of being simultaneously one of the most important school subjects for today's children to study and one of the least well understood. Everybody knows how important it is and everybody knows that they have to study it.

It gathers texts which give the best presentation of the principles and key concepts of the Theory of Didactical Situations that Guy Brousseau developed in the period from 1970 to 1990.

This timely volume raises issues concerning the nature of school mathematics and mathematics at work, and the challenges of teaching valuable mathematics in school and providing appropriate training for a variety of careers. It offers lively commentaries on important `hot' topics: transferring knowledge and skill across contexts;