Number Theory in Mathematics Education: Perspectives and Prospects, 1st Edition (Paperback) book cover

Number Theory in Mathematics Education

Perspectives and Prospects, 1st Edition

Edited by Rina Zazkis, Stephen R. Campbell


304 pages

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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 of researchers 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 of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing 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 upper-level mathematics education courses.


"There is no extant work on research in number theory that matches the comprehensiveness or currency of this text…It should become a classic in the research literature in mathematics education."

John A. Dossey

Illinois State University

Table of Contents

Contents: Preface. R. Zazkis, S.R. Campbell, Number Theory in Mathematics Education Research: Perspectives and Prospects. S.R. Campbell, Understanding Elementary Number Theory in Relation to Arithmetic and Algebra. J. Mason, What Makes an Example Exemplary: Pedagogical and Didactical Issues in Appreciating Multiplicative Structures. N. Sinclair, For the Beauty of Number Theory. R. Zazkis, P. Liljedahl, On the Path to Number Theory: Repeating Patterns as a Gateway. R. Leikin, Learning by Teaching: A Case of Sieve of Eratosthenes and One Elementary School Teacher. P. Liljedahl, Learning Elementary Number Theory Through a Chain of Discovery: Preservice Teachers' Encounter With Pentominoes. C. Kieran, J. Guzman, The Number Theoretic Experience of 12-to 15 Year Olds in a Calculator Environment: The Intertwining Co-Emergence of Technique and Theory. I. Lavy, Learning Number Theory Concepts Via Geometrical Interactive Computerized Setting. D. Ginat, Overlooking Number Patterns in Algorithmic Problem Solving. J.C. Smith, Revisiting Algebra in a Number Theoretical Setting.

About the Series

Studies in Mathematical Thinking and Learning Series

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Subject Categories

BISAC Subject Codes/Headings:
EDUCATION / Teaching Methods & Materials / Mathematics