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.
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.
"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