Number Theory in Mathematics Education Perspectives and Prospects

Number Theory in Mathematics Education Perspectives and Prospects

by Rina Zazkis
     
 

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

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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.

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Product Details

ISBN-13:
9780805854077
Publisher:
Taylor & Francis
Publication date:
04/30/2006
Series:
Studies in Mathematical Thinking and Learning Series
Pages:
304
Product dimensions:
6.20(w) x 9.00(h) x 0.90(d)

Table of Contents

1Number theory in mathematics education research : perspectives and prospects1
2Understanding elementary number theory in relation to arithmetic and algebra19
3What makes an example exemplary : pedagogical and didactical issues in appreciating multiplicative structures41
4For the beauty of number theory69
5On the path to number theory : repeating patterns as a gateway99
6Learning by teaching : the case of sieve of Eratosthenes and one elementary school teacher115
7Learning elementary number theory through a chain of discovery : preservice teachers' encounter with pentominoes141
8The number-theoretic experience of 12- to 15-year-olds in a calculator environment : the intertwining coemergence of technique and theory173
9Learning number theory concepts via geometrical interactive computerized setting201
10Overlooking number patterns in algorithmic problem solving223
11Revisiting algebra in a number theoretical setting249

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