Rigorous Mathematical Thinking

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Rigorous Mathematical Thinking

James T. Kinard,Alex Kozulin
Rigorous Mathematical Thinking Book PDF

Author : James T. Kinard,Alex Kozulin
Publisher : Cambridge University Press
Page : 210 pages
File Size : 43,7 Mb
Release : 2008-06-02
Category : Psychology
ISBN : 9781139472395

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Rigorous Mathematical Thinking by James T. Kinard,Alex Kozulin Pdf

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.

Introduction to Mathematical Thinking

Keith J. Devlin
Introduction to Mathematical Thinking Book PDF

Author : Keith J. Devlin
Publisher : Unknown
Page : 0 pages
File Size : 48,9 Mb
Release : 2012
Category : Mathematics
ISBN : 0615653634

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Introduction to Mathematical Thinking by Keith J. Devlin Pdf

"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

An Introduction to Mathematical Reasoning

Peter J. Eccles
An Introduction to Mathematical Reasoning Book PDF

Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 366 pages
File Size : 42,7 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521597188

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An Introduction to Mathematical Reasoning by Peter J. Eccles Pdf

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

How Not to Be Wrong

Jordan Ellenberg
How Not to Be Wrong Book PDF

Author : Jordan Ellenberg
Publisher : Penguin Press
Page : 480 pages
File Size : 42,6 Mb
Release : 2014-05-29
Category : Mathematics
ISBN : 9781594205224

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How Not to Be Wrong by Jordan Ellenberg Pdf

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Developing Mathematical Thinking

Jonathan D. Katz
Developing Mathematical Thinking Book PDF

Author : Jonathan D. Katz
Publisher : Rowman & Littlefield
Page : 145 pages
File Size : 40,9 Mb
Release : 2014-07-07
Category : Education
ISBN : 9781475810585

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Developing Mathematical Thinking by Jonathan D. Katz Pdf

In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

Introduction to Mathematical Thinking

Friedrich Waismann
Introduction to Mathematical Thinking Book PDF

Author : Friedrich Waismann
Publisher : Courier Corporation
Page : 272 pages
File Size : 45,9 Mb
Release : 2012-08-07
Category : Mathematics
ISBN : 9780486167428

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Introduction to Mathematical Thinking by Friedrich Waismann Pdf

Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.

Math Exchanges

Kassia Omohundro Wedekind
Math Exchanges Book PDF

Author : Kassia Omohundro Wedekind
Publisher : Stenhouse Publishers
Page : 216 pages
File Size : 40,6 Mb
Release : 2011
Category : Education
ISBN : 9781571108265

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Math Exchanges by Kassia Omohundro Wedekind Pdf

Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in math workshop become self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges: Guiding Young Mathematicians in Small Group Meetings is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?

Introduction to Mathematical Thinking

Friedrich Waismann
Introduction to Mathematical Thinking Book PDF

Author : Friedrich Waismann
Publisher : Courier Corporation
Page : 292 pages
File Size : 41,8 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0486428044

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Introduction to Mathematical Thinking by Friedrich Waismann Pdf

Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; and more. Includes 27 figures. Index. 1959 edition.

The Heart of Mathematics

Edward B. Burger,Michael Starbird
The Heart of Mathematics Book PDF

Author : Edward B. Burger,Michael Starbird
Publisher : Springer Science & Business Media
Page : 798 pages
File Size : 41,6 Mb
Release : 2004-08-18
Category : Mathematics
ISBN : 1931914419

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The Heart of Mathematics by Edward B. Burger,Michael Starbird Pdf

Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.

Interdisciplinary Perspectives on Math Cognition

Marcel Danesi
Interdisciplinary Perspectives on Math Cognition Book PDF

Author : Marcel Danesi
Publisher : Springer Nature
Page : 344 pages
File Size : 43,9 Mb
Release : 2019-09-14
Category : Mathematics
ISBN : 9783030225377

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Interdisciplinary Perspectives on Math Cognition by Marcel Danesi Pdf

This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.

Daily Math Thinking Routines in Action

Nicki Newton
Daily Math Thinking Routines in Action Book PDF

Author : Nicki Newton
Publisher : Routledge
Page : 241 pages
File Size : 47,7 Mb
Release : 2018-09-05
Category : Education
ISBN : 9781351164269

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Daily Math Thinking Routines in Action by Nicki Newton Pdf

Bring math to life with routines that are academically rigorous, standards-based, and engaging! Go beyond circling ABCD on your bell ringers and do nows and get your students reasoning, modeling, and communicating about math every day! In this new book from bestselling author and consultant Dr. Nicki Newton, you’ll learn how to develop effective daily routines to improve students’ thinking, reasoning, and questioning about math. The book provides a wide variety of rigorous, high-interest routines and explains how to rotate and implement them into your curriculum. Inside, you’ll find: Questioning techniques that encourage students to think beyond the "right vs. wrong" continuum Tips for building a math-learning environment that is friendly and supportive of all students Math vocabulary exercises that are meaningful and fun An assortment of innovative daily activities, including "Fraction of the Day," "Truth or Fib," "Find and Fix the Error," "Guess My Number," "What Doesn’t Belong?" and many, many more. Each chapter offers examples, charts, and tools that you can use immediately. With these resources and the practical advice throughout the book, you’ll increase students’ ability to understand math on a deeper level while keeping them engaged in their own learning processes.

Advanced Mathematical Thinking

Annie Selden,John Selden
Advanced Mathematical Thinking Book PDF

Author : Annie Selden,John Selden
Publisher : Routledge
Page : 112 pages
File Size : 51,7 Mb
Release : 2013-10-15
Category : Education
ISBN : 9781135478452

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Advanced Mathematical Thinking by Annie Selden,John Selden Pdf

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.

Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline

Matthew Inglis,Nina Attridge
Does Mathematical Study Develop Logical Thinking Testing The Theory Of Formal Discipline Book PDF

Author : Matthew Inglis,Nina Attridge
Publisher : World Scientific
Page : 204 pages
File Size : 46,8 Mb
Release : 2016-09-06
Category : Mathematics
ISBN : 9781786340702

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Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline by Matthew Inglis,Nina Attridge Pdf

For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results.Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents.Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy.

How to Think Like a Mathematician

Kevin Houston
How to Think Like a Mathematician Book PDF

Author : Kevin Houston
Publisher : Cambridge University Press
Page : 341 pages
File Size : 41,9 Mb
Release : 2009-02-12
Category : Mathematics
ISBN : 9781139477055

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How to Think Like a Mathematician by Kevin Houston Pdf

Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

Calculus: A Rigorous First Course

Daniel J. Velleman
Calculus A Rigorous First Course Book PDF

Author : Daniel J. Velleman
Publisher : Courier Dover Publications
Page : 737 pages
File Size : 45,9 Mb
Release : 2017-01-18
Category : Mathematics
ISBN : 9780486809366

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Calculus: A Rigorous First Course by Daniel J. Velleman Pdf

Designed for undergraduate mathematics majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on calculus as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of calculus instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of calculus that is deep enough to allow the student to not only find answers to problems, but also achieve certainty of the answers' correctness. No background in calculus is necessary. Prerequisites include proficiency in basic algebra and trigonometry, and a concise review of both areas provides sufficient background. Extensive problem material appears throughout the text and includes selected answers. Complete solutions are available to instructors.