Structural Understanding In Advanced Mathematical Thinking
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Structural Understanding In Advanced Mathematical Thinking
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Author : Naďa Stehlíková
language : en
Publisher: Nada Stehlikova
Release Date : 2004
Structural Understanding In Advanced Mathematical Thinking written by Naďa Stehlíková and has been published by Nada Stehlikova this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Advanced Mathematical Thinking written by David Tall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking – what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students – has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: • the nature of advanced mathematical thinking, • cognitive theory, and • reviews of the progress of cognitive research into different areas of advanced mathematics.
How Humans Learn To Think Mathematically
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Author : David Tall
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-02
How Humans Learn To Think Mathematically written by David Tall and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-02 with Education categories.
How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
Rigorous Mathematical Thinking
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Author : James T. Kinard
language : en
Publisher: Cambridge University Press
Release Date : 2008-06-02
Rigorous Mathematical Thinking written by James T. Kinard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-02 with Psychology categories.
This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.
Making The Connection
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Author : Marilyn Paula Carlson
language : en
Publisher: MAA
Release Date : 2008
Making The Connection written by Marilyn Paula Carlson and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Handbook Of International Research In Mathematics Education
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Author : Lyn D. English
language : en
Publisher: Routledge
Release Date : 2010-04-02
Handbook Of International Research In Mathematics Education written by Lyn D. English and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-02 with Education categories.
The second edition continues the mission of bringing together important new mathematics education research that makes a difference in both theory and practice. It updates and extends the Handbook’s original key themes and issues for international research in mathematics education for the 21st century, namely: priorities in international mathematics education research lifelong democratic access to powerful mathematical ideas advances in research methodologies influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development being an important component of all these aspects. This edition also examines other catalysts that have gained increased import in recent years including a stronger focus on the teacher and teacher practice, a renewed interest in theory development, an increased focus on the mathematics needed in work place settings, and a proliferation of research designs and methodologies that have provided unprecedented opportunities for investigating (and ultimately improving) mathematical teaching and learning. This edition includes ten totally new chapters; all other chapters are thoroughly revised and updated.
Third International Handbook Of Mathematics Education
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Author : M.A. (Ken) Clements
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-15
Third International Handbook Of Mathematics Education written by M.A. (Ken) Clements and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-15 with Mathematics categories.
The four sections in this Third International Handbook are concerned with: (a) social, political and cultural dimensions in mathematics education; (b) mathematics education as a field of study; (c) technology in the mathematics curriculum; and (d) international perspectives on mathematics education. These themes are taken up by 84 internationally-recognized scholars, based in 26 different nations. Each of section is structured on the basis of past, present and future aspects. The first chapter in a section provides historical perspectives (“How did we get to where we are now?”); the middle chapters in a section analyze present-day key issues and themes (“Where are we now, and what recent events have been especially significant?”); and the final chapter in a section reflects on policy matters (“Where are we going, and what should we do?”). Readership: Teachers, mathematics educators, ed.policy makers, mathematicians, graduate students, undergraduate students. Large set of authoritative, international authors.
Advanced Mathematical Thinking
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Author : Annie Selden
language : en
Publisher: Routledge
Release Date : 2013-10-15
Advanced Mathematical Thinking written by Annie Selden and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-15 with Education categories.
This is Volume 7, Issue 1 2005, a Special Issue of 'Mathematical Thinking and Learning' which looks at Advanced Mathematical Thinking. Opening with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. The articles follow the recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices.
Algebra Structure Sense Development Amongst Diverse Learners
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Author : Teresa Rojano
language : en
Publisher: Taylor & Francis
Release Date : 2022-06-07
Algebra Structure Sense Development Amongst Diverse Learners written by Teresa Rojano and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-07 with Education categories.
This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels. Positing algebra structure sense as fundamental to developing students’ broader mathematical maturity and advanced thinking, this text reviews conceptual, historical, cognitive, and semiotic factors, which influence the acquisition of algebra structure sense. It provides empirical evidence to demonstrate the feasibility of linking algebra structure sense to technological tools and promoting it amongst diverse learners. Didactic approaches include the use of adaptive digital environments, gamification, diagnostic and monitoring tools, as well as exercises and algebraic sequences of varied complexity. Advocating for a focus on both intuitive and formal knowledge, this volume will be of interest to students, scholars, and researchers with an interest in educational research, as well as mathematics education and numeracy.
Primary Mathematics Knowledge And Understanding
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Author : Claire Mooney
language : en
Publisher: SAGE
Release Date : 2009-05-27
Primary Mathematics Knowledge And Understanding written by Claire Mooney and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-27 with Education categories.
A secure knowledge of primary mathematics is essential for the trainee teacher. Clear subject knowledge and understanding is the foundation of confident, creative and effective teaching. Written to help trainee primary teachers develop and consolidate their knowledge of mathematics, this fourth edition has been completely revised and updated. The text is structured around the current curriculum and incorporates the Primary National Strategy. All content is linked to the 2007 QTS Standards and new links are made to the Early Years Foundation Stage.