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Learning And Teaching Number Theory

Author: Stephen R. Campbell
Publisher: Greenwood Publishing Group
ISBN: 9781567506532
Size: 23.99 MB
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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
Size: 75.61 MB
Format: PDF, ePub
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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: Rina Zazkis
Publisher: Routledge
ISBN: 1136501436
Size: 71.97 MB
Format: PDF, ePub
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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.

Mathematics And Cognition

Author: Pearla Nesher
Publisher: CUP Archive
ISBN: 9780521367875
Size: 58.76 MB
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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.

How To Think About Analysis

Author: Lara Alcock
Publisher: OUP Oxford
ISBN: 0191035386
Size: 72.96 MB
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Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

Educational Neuroscience

Author: Kathryn E. Patten
Publisher: John Wiley & Sons
ISBN: 144434580X
Size: 27.76 MB
Format: PDF, ePub, 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

The Pragmatics Of Mathematics Education

Author: Tim Rowland
Publisher: Psychology Press
ISBN: 9780750710121
Size: 49.87 MB
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Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.

Cognition In Education

Author:
Publisher: Academic Press
ISBN: 0123877075
Size: 53.20 MB
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Education and cognitive psychology are natural companions—they both are focused on how people think and learn. Although collaborations have occurred for many years, recently there has been a much greater interest in collaborations that bring cognitive principles into classroom settings. This renewed collaborative research has led both to new evidence-based instructional practices and to a better understanding of cognitive principles. This volume contains overviews of research projects at the intersection of cognitive science and education. The prominent contributors—cognitive psychologists, developmental psychologists, educational psychologists, and science educators—were chosen both for the quality of their work and the variety of their contributions—general principles; influence of affect and motivation; and focus on math and science education. This volume contains overviews of research projects at the intersection of cognitive science and education The prominent contributors were chosen both for the quality of their work and the variety of their contributions general principles; influence of affect and motivation; and focus on math and science education.

Classroom Lessons

Author: Kate McGilly
Publisher: MIT Press
ISBN: 9780262631686
Size: 47.94 MB
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"To better understand the authors' messages and to prepare our students for the challenges ahead, we at the local level must assume responsibility for learning how to use these classroom lessons' in our own schools." -- Brian Bottge, "Educational Leadership" A timely complement to John Bruer's Schools for Thought, Classroom Lessons documents eight projects that apply cognitive research to improve classroom practice. The chapter authors are all principal investigators in an influential research initiative on cognitive science and education. Classroom Lessons describes their collaborations with classroom teachers aimed at improving teaching and learning for students in grades K-12. The eight projects cover writing, mathematics, history, social science, and physics. Together they illustrate that principles emerging from cognitive science form the basis of a science of instruction that can be applied across the curriculum. The book is divided into three sections: applications of cognitive research to teaching specific content areas; applications for learning across the curriculum; and applications that challenge traditional concepts of classroom-based learning environments. Chapters consider explicit models of knowledge with corresponding instruction designed to enable learners to build on that knowledge, acquisition of specified knowledge, and what knowledge is useful in contemporary curricula. Contributors: Kate McGilly. Sharon A. Griffin, Robbie Case, and Robert S. Siegler. Earl Hunt and Jim Minstrell. Kathryn T. Spoehr. Howard Gardner, Mara Krechevsky, Robert J. Sternberg, and Lynn Okagaki. Irene W. Gaskins. The Cognition andTechnology Group at Vanderbilt. Marlene Scardamalia, Carl Bereiter, and Mary Lamon. Ann L. Brown and Joseph C. Campione. John T. Bruer. A Bradford Book

Metacognition In Learning And Instruction

Author: Hope J. Hartman
Publisher: Springer Science & Business Media
ISBN: 9780792368380
Size: 10.99 MB
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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.