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Number Theory in Mathematics Education Perspectives and Prospects
     

Number Theory in Mathematics Education Perspectives and Prospects

by Rina Zazkis
 

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ISBN-10: 080585407X

ISBN-13: 9780805854077

Pub. Date: 04/30/2006

Publisher: Taylor & Francis

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these

Overview

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre-K-16 settings and mathematics teacher education.

Topics variously engaged include: understanding particular concepts related to numerical structure and number theory; elaborating on the historical and psychological relevance of number theory in concept development; attaining a smooth transition and extension from pattern recognition to formative principles; appreciating the aesthetics of number structure; exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; reexamining previously constructed knowledge from a novel angle; investigating connections between technique and theory; utilizing computers and calculators as pedagogical tools; and generally illuminating the role number-theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters in this book highlight number theory-related topics as a stepping stone from arithmetic toward generalization and algebraic formalism, and as a means forproviding intuitively grounded meanings of numbers, variables, functions, and proofs.

Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upperlevel mathematics education courses.

Product Details

ISBN-13:
9780805854077
Publisher:
Taylor & Francis
Publication date:
04/30/2006
Series:
Studies in Mathematical Thinking and Learning Series
Pages:
268
Product dimensions:
6.00(w) x 9.00(h) x 0.90(d)

Table of Contents

List of Contributors vii

Preface ix

1 Number Theory in Mathematics Education Research: Perspectives and Prospects Rina Zazkis Stephen R. Campbell 1

2 Understanding Elementary Number Theory in Relation to Arithmetic and Algebra Stephen R. Campbell 19

3 What Makes an Example Exemplary: Pedagogical and Didactical Issues in Appreciating Multiplicative Structures John Mason 41

4 For the Beauty of Number Theory Nathalie Sinclair 69

5 On the Path to Number Theory: Repeating Patterns as a Gateway Rina Zazkis Peter Liljedahl 99

6 Learning by Teaching: The Case of Sieve of Eratosthenes and One Elementary School Teacher Roza Leikin 115

7 Learning Elementary Number Theory Through a Chain of Discovery: Preservice Teachers' Encounter with Pentominoes Peter Liljedahl 141

8 The Number-Theoretic Experience of 12- to 15-Year-Olds in a Calculator Environment: The Intertwining Coemergence of Technique and Theory Carolyn Kieran Jose Guzman 173

9 Learning Number Theory Concepts Via Geometrical Interactive Computerized Setting Ilana Lavy 201

10 Overlooking Number Patterns in Algorithmic Problem Solving David Ginat 223

11 Revisiting Algebra in a Number Theoretical Setting Jennifer Christian Smith 249

Author Index 285

Subject Index 291

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