The Math Gene

How Mathematical Thinking Evolved And Why Numbers Are Like Gossip

Author: Keith Devlin

Publisher: Hachette UK

ISBN: 0786725087

Category: Science

Page: 352

View: 9747

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Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don't recognize when we're using mathematical reasoning.
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The Elephant in the Classroom

Helping Children Learn and Love Maths

Author: Jo Boaler

Publisher: Souvenir Press

ISBN: 0285643193

Category: Education

Page: 272

View: 5354

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In The Elephant in the Classroom, Jo Boaler outlines what has gone wrong in mathematics education, identifying the problems facing children in classrooms today. How can children be prepared for the mathematics they will need in the future? They need to be taught to be quantitatively literate, to think flexibly and creatively and how to problem solve. Jo Boaler offers concrete solutions for parents and teachers that will revolutionise children's experience with maths. Along with practical teaching activities, strategies and questions that can transform a child's mathematical future, she shares a range of free and accessible online resources. 'We have the research knowledge to make classrooms places where all students are inspired by mathematics' Jo Boaler
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Making the Connection

Research and Teaching in Undergraduate Mathematics Education

Author: Marilyn Paula Carlson,Chris Rasmussen

Publisher: MAA

ISBN: 9780883851838

Category: Mathematics

Page: 319

View: 3580

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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.
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Number Theory in Mathematics Education

Perspectives and Prospects

Author: Stephen R. Campbell

Publisher: Psychology Press

ISBN: 080585407X

Category: Education

Page: 294

View: 1431

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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.
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Planting the Seeds of Algebra, PreK–2

Explorations for the Early Grades

Author: Monica Neagoy

Publisher: Corwin Press

ISBN: 1452279705

Category: Education

Page: 208

View: 438

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Help young minds explore algebraic concepts This book shows teachers how to create a strong foundation in algebra for very young children. Using in-depth math “explorations,” the author unpacks—step by step—the hidden connections to higher algebra. Each exploration contains an elegantly simple grade-banded lesson (on addition, subtraction, patterns, and odd and even numbers), followed by a discussion of the lesson's algebra connections, as well as suggestions for additional problems to explore. Throughout, readers will find: Clear explanations of algebraic connections Specific strategies for teaching the key ideas of algebra Lesson modifications for older or younger students An array of age-appropriate problems and games
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Planting the Seeds of Algebra, 3-5

Explorations for the Upper Elementary Grades

Author: Monica Neagoy

Publisher: Corwin Press

ISBN: 1483379760

Category: Education

Page: 248

View: 5572

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Give your students a foundation of algebra for math success – now and in the future! Students and teachers must become friendly with algebraic foundations, as they have increasingly become the gateway to careers in the STEM fields. Monica Neagoy empowers teachers to embrace algebra and connect it to higher math concepts, tuning you and your students to algebraic thinking, reasoning, and doing. You’ll discover: ?Four explorations to help you weave key algebraic ideas into everyday mathematics Step-by-step lessons from real classrooms that will guide you in teaching concepts and in establishing their relevance and applicability New methods that break down difficult algebraic concepts and build a critical foundation for higher math
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Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 7248

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Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
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The Blank Slate

The Modern Denial of Human Nature

Author: Steven Pinker

Publisher: Penguin

ISBN: 9781101200322

Category: Psychology

Page: 528

View: 770

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A brilliant inquiry into the origins of human nature. "Sweeping, erudite, sharply argued, and fun to read..also highly persuasive." -Time Now updated with a new afterword One of the world's leading experts on language and the mind explores the idea of human nature and its moral, emotional, and political colorings. With characteristic wit, lucidity, and insight, Pinker argues that the dogma that the mind has no innate traits-a doctrine held by many intellectuals during the past century-denies our common humanity and our individual preferences, replaces objective analyses of social problems with feel-good slogans, and distorts our understanding of politics, violence, parenting, and the arts. Injecting calm and rationality into debates that are notorious for ax-grinding and mud-slinging, Pinker shows the importance of an honest acknowledgment of human nature based on science and common sense.
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What Every Principal Needs to Know to Create Equitable and Excellent Schools

Author: George Theoharis,Jeffrey S. Brooks

Publisher: Teachers College Press

ISBN: 0807772267

Category: Education

Page: 241

View: 1063

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School leaders who succeed at creating a high-achieving learning community must also be committed to creating an equitable environment for all students. In this new book, key scholars across the content areas show how to put into practice a commitment to equity and excellence across the Pre-K12 spectrum. Readers learn directly from experts in each of the content domains (literacy, mathematics, science, social studies, music, early childhood, special education, English language learners, world languages, and physical education) how a commitment to social justice and equity can be grounded in core subject areas, why each has a place in the school, and what they need to know and do in each subject area. This book is a critical instructional leadership resource for new and veteran principals who want to see all students succeed. Contributors: Antonio J. Castro, Julie Causton-Theoharis, Virginia Collier, Katherine Delaney, Catherine Ennis, Virginia Goatley, Beth Graue, Rochelle Gutirrez, Kathleen A. Hinchman, Anne Karabon, Christi Kasa, Dave McAlpine, Mitchell Robinson, Victor Sampson, Sherry A. Southerland, and Wayne Thomas
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Apología de un matemático

Author: Godfrey Harold Hardy

Publisher: CAPITÁN SWING LIBROS

ISBN: 8412090624

Category: Mathematics

Page: 160

View: 2404

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G.H. Hardy fue uno de los mejores matemáticos de este siglo, reconocido entre sus contemporáneos como un "matemático auténtico, el más puro entre los puros". Esta Apología, escrita emotivamente cuando su poder creativo matemático estaba ya en su ocaso, es un relato brillante y cautivador de las matemáticas consideradas como mucho más que una ciencia, que nos proporciona una de las mejores visiones de cómo discurre la mente de un matemático en pleno proceso de trabajo. De hecho, este libro está ampliamente considerado como una de las mejores penetraciones en la mente de un matemático profesional, escrita para profanos. En sus páginas, Hardy defiende el valor de la matemática teórica más abstracta y la belleza como valor indispensable de las buenas teorías matemáticas por encima de otros valores como su aplicabilidad o relevancia para los problemas de física. Cuando fue publicada en inglés por primera vez, Graham Greene la aclamó, junto con los cuadernos de notas de Henry James, como "la mejor narración de lo que representa el ser un artista creativo". El prólogo de C. P. Snow a la edición inglesa proporciona algunas claves de la vida de Hardy, incluyendo las anécdotas relativas a su colaboración con el matemático indio Ramanujan, sus aforismos y su pasión por el críquet. Este es un relato único de la fascinación por las matemáticas y de uno de sus exponentes más convincentes de los tiempos modernos.
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