Learning and Teaching Number Theory

Author: Stephen R. Campbell
Publisher: Greenwood Publishing Group
ISBN: 9781567506532
Format: PDF
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Essential to developing deeper understandings of mathematics, number theory has received scant attention in mathematics education research. This volume redresses this matter and serves as a launch point for further research in this important area.

Making the Connection

Author: Marilyn Paula Carlson
Publisher: MAA
ISBN: 9780883851838
Format: PDF
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The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.

Number Theory in Mathematics Education

Author: Stephen R. Campbell
Publisher: Psychology Press
ISBN: 080585407X
Format: PDF, Docs
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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.

Transfer of Learning

Author: Robert E. Haskell
Publisher: Academic Press
ISBN: 0123305950
Format: PDF, ePub
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Educators and educational psychologists recognize transfer of learning as a significant issue in various fields of instruction. Transfer of learning cuts across various educational domains, curricula, and methods. This book shows that transfer of learning is not just a technique of learning or instruction, but a way of thinking and knowing.

Metacognition in Learning and Instruction

Author: Hope J. Hartman
Publisher: Springer Science & Business Media
ISBN: 9780792368380
Format: PDF
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Contributions by leading experts and others to understanding the crucial role of metacognition in relation to broad areas of education make this collection a uniquely stimulating book. It encompasses metacognition in both the neglected area of teaching and the more well-established area of learning. The twelve chapters contribute to our understanding of the construct of metacognition and to its role in both teaching and learning. It addresses domain-general and domain-specific aspects of metacognition, including applications to the particular subjects of reading, speaking, mathematics, and science. It is organized into four major sections which address metacognition in relation to students' learning, motivation, and culture; and to teachers' metacognition about instruction. This collection spans theory, research and practice related to metacognition in education at all school levels, from elementary through university. Dr. Robert J. Sternberg, IBM Professor of Psychology at Yale University, is the discussant.

Mathematics and Cognition

Author: Pearla Nesher
Publisher: CUP Archive
ISBN: 9780521367875
Format: PDF, ePub, Mobi
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This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.

Dimensions of Thinking and Cognitive Instruction

Author: Beau Fly Jones
Publisher: Routledge
ISBN: 1134746067
Format: PDF
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By establishing a conceptual framework and a common language for educators to work together, this volume attempts to answer the challenge facing all teachers -- how can students improve the quality of their thinking? Methods of strengthening the thought process include: helping students learn to monitor their attention and commitments; asking questions that require students to organize, analyze, and integrate information; setting tasks that involve complex processes such as problem solving and research; and modeling and reinforcing fair-mindedness.

Cognitive Science and Mathematics Education

Author: Alan H. Schoenfeld
Publisher: Psychology Press
ISBN: 9780805800579
Format: PDF, Kindle
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This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.

Educational Neuroscience

Author: Kathryn E. Patten
Publisher: John Wiley & Sons
ISBN: 144434580X
Format: PDF, Docs
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Educational Neuroscience provides an overview of the wide range of recent initiatives in educational neuroscience, examining a variety of methodological concerns, issues, and directions. Encourages interdisciplinary perspectives in educational neuroscience Contributions from leading researchers examine key issues relating to educational neuroscience and mind, brain, and education more generally Promotes a theoretical and empirical base for the subject area Explores a range of methods available to researchers Identifies agencies, organizations, and associations facilitating development in the field Reveals a variety of on-going efforts to establish theories, models, methods, ethics, and a common language

Cognitive and Instructional Processes in History and the Social Sciences

Author: Mario Carretero
Publisher: Routledge
ISBN: 1136483586
Format: PDF, ePub
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This volume is a direct result of an international conference that brought together a number of scholars from Europe and the United States to discuss their ideas and research about cognitive and instructional processes in history and the social sciences. As such, it fills a major gap in the study of how people learn and reason in the context of particular subject matter domains and how instruction can be improved in order to facilitate better learning and reasoning. Previous cognitive work on subject matter learning has been focused primarily upon mathematics and physics; the present effort provides the first such venture examining the history and social science domains from a cognitive perspective. The different sections of the book cover topics related to comprehension, learning, and instruction of history and the social sciences, including: *the development of some social sciences concepts, *the teaching of social sciences -- problems and questions arising from this cognitive perspective of learning, *the comprehension and learning from historical texts, *how people and students understand historical causality and provide explanations of historical events, and *the deduction processes involved in reasoning about social sciences contents. This volume will be useful for primary and secondary school teachers and for cognitive and instructional researchers interested in problem solving and reasoning, text comprehension, domain-specific knowledge acquisition and concept development.