### Perspectives and Prospects

### 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 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.

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.

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.

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;

*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

*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.

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;

*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

*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.

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;

*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

*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.