Number Theory in Mathematics Education: Perspectives and Prospects

by Zazkis; Rina

• ISBN13: 9780805854077
• ISBN10: 080585407X
• Format: Hardcover
• Copyright: 2006-03-21
• Publisher: Routledge

Summary

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 toaha!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 Prospectsis 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.

Table of Contents

List of Contributors	vii
Preface	ix
1 Number Theory in Mathematics Education Research: Perspectives and Prospects	1	(18)
Rina Zazkis and Stephen R. Campbell
2 Understanding Elementary Number Theory in Relation to Arithmetic and Algebra	19	(22)
Stephen R. Campbell
3 What Makes an Example Exemplary: Pedagogical and Didactical Issues in Appreciating Multiplicative Structures	41	(28)
John Mason
4 For the Beauty of Number Theory	69	(30)
Nathalie Sinclair
5 On the Path to Number Theory: Repeating Patterns as a Gateway	99	(16)
Rina Zazkis and Peter Liljedahl
6 Learning by Teaching: The Case of Sieve of Eratosthenes and One Elementary School Teacher	115	(26)
Roza Leikin
7 Learning Elementary Number Theory Through a Chain of Discovery: Preservice Teachers' Encounter with Pentominoes	141	(32)
Peter Liljedahl
8 The Number-Theoretic Experience of 12- to 15-Year-Olds in a Calculator Environment: The Intertwining Coemergence of Technique and Theory	173	(28)
Carolyn Kieran and José Guzmán
9 Learning Number Theory Concepts Via Geometrical Interactive Computerized Setting	201	(32)
Ilana Lavy
10 Overlooking Number Patterns in Algorithmic Problem Solving	233	(16)
David Ginat
11 Revisiting Algebra in a Number Theoretical Setting	249	(36)
Jennifer Christian Smith
Author Index	285	(6)
Subject Index	291