Number Theory in Mathematics Education Perspectives and Prospects

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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 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 in this book highlight number theory-related topics as a stepping stone from arithmetic toward generalization and algebraic formalism, and as a means forproviding 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 upperlevel mathematics education courses.

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Product Details

Table of Contents

1 Number theory in mathematics education research : perspectives and prospects 1
2 Understanding elementary number theory in relation to arithmetic and algebra 19
3 What makes an example exemplary : pedagogical and didactical issues in appreciating multiplicative structures 41
4 For the beauty of number theory 69
5 On the path to number theory : repeating patterns as a gateway 99
6 Learning by teaching : the case of sieve of Eratosthenes and one elementary school teacher 115
7 Learning elementary number theory through a chain of discovery : preservice teachers' encounter with pentominoes 141
8 The number-theoretic experience of 12- to 15-year-olds in a calculator environment : the intertwining coemergence of technique and theory 173
9 Learning number theory concepts via geometrical interactive computerized setting 201
10 Overlooking number patterns in algorithmic problem solving 223
11 Revisiting algebra in a number theoretical setting 249
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