Number Theory in Mathematics Education: Perspectives and Prospects

by Zazkis; Rina

• ISBN13: 9780805854084
• ISBN10: 0805854088
• Format: Nonspecific Binding
• 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 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 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
Number Theory in Mathematics Education Research: Perspectives and Prospects	1	(18)
Rina Zazkis
Stephen R. Campbell
Understanding Elementary Number Theory in Relation to Arithmetic and Algebra	19	(22)
Stephen R. Campbell
What Makes an Example Exemplary: Pedagogical and Didactical Issues in Appreciating Multiplicative Structures	41	(28)
John Mason
For the Beauty of Number Theory	69	(30)
Nathalie Sinclair
On the Path to Number Theory: Repeating Patterns as a Gateway	99	(16)
Rina Zazkis
Peter Liljedahl
Learning by Teaching: The Case of Sieve of Eratosthenes and One Elementary School Teacher	115	(26)
Roza Leikin
Learning Elementary Number Theory Through a Chain of Discovery: Preservice Teachers' Encounter with Pentominoes	141	(32)
Peter Liljedahl
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
Jose Guzman
Learning Number Theory Concepts Via Geometrical Interactive Computerized Setting	201	(22)
Ilana Lavy
Overlooking Number Patterns in Algorithmic Problem Solving	223	(26)
David Ginat
Revisiting Algebra in a Number Theoretical Setting	249	(36)
Jennifer Christian Smith
Author Index	285	(6)
Subject Index	291