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Learning And Teaching Number Theory

Author: Stephen R. Campbell
Publisher: Greenwood Publishing Group
ISBN: 9781567506532
Size: 29.38 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: 33.80 MB
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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: 53.45 MB
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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: 15.88 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: 20.20 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: 56.11 MB
Format: PDF
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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: 76.30 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.

How Students Learn

Author: National Research Council
Publisher: National Academies Press
ISBN: 0309074339
Size: 69.55 MB
Format: PDF, Docs
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How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning. How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. The book explores the importance of balancing students’ knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities. How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children’s education.

Mathematics Education As A Research Domain A Search For Identity

Author: Anna Sierpinska
Publisher: Springer
ISBN: 9401151946
Size: 39.33 MB
Format: PDF, Kindle
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No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.

Metacognition In Learning And Instruction

Author: Hope J. Hartman
Publisher: Springer Science & Business Media
ISBN: 9780792368380
Size: 70.21 MB
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.