Number Theory in Mathematics Education Perspectives and Prospects Studies in Mathematical Thinking and Learning Series

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.

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.