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 : 42,6 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 : 52,5 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.

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 : 52,9 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.

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 : 40,8 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.

Developing Mathematical Thinking

Jonathan D. Katz
Developing Mathematical Thinking Book PDF

Author : Jonathan D. Katz
Publisher : Rowman & Littlefield
Page : 145 pages
File Size : 50,5 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 : 292 pages
File Size : 44,8 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.

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 : 47,6 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.

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 : 42,5 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.

Advanced Mathematical Thinking

Annie Selden,John Selden
Advanced Mathematical Thinking Book PDF

Author : Annie Selden,John Selden
Publisher : Routledge
Page : 112 pages
File Size : 41,8 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.

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 : 48,7 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.

A First Course in Topology

Robert A Conover
A First Course in Topology Book PDF

Author : Robert A Conover
Publisher : Courier Corporation
Page : 276 pages
File Size : 51,8 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9780486780016

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A First Course in Topology by Robert A Conover Pdf

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

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 : 42,6 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.

Learning Over Time

Alan P. Maloney,Jere Confrey,Kenny H. Nguyen
Learning Over Time Book PDF

Author : Alan P. Maloney,Jere Confrey,Kenny H. Nguyen
Publisher : IAP
Page : 288 pages
File Size : 48,9 Mb
Release : 2014
Category : Education
ISBN : 9781623965693

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Learning Over Time by Alan P. Maloney,Jere Confrey,Kenny H. Nguyen Pdf

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics-how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings-and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories. A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.) This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children's mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories' evolution--from small-scale day-to-day conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.

Expertise in Mathematics Instruction

Yeping Li,Gabriele Kaiser
Expertise in Mathematics Instruction Book PDF

Author : Yeping Li,Gabriele Kaiser
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 49,7 Mb
Release : 2010-12-15
Category : Education
ISBN : 9781441977076

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Expertise in Mathematics Instruction by Yeping Li,Gabriele Kaiser Pdf

Accumulated research findings in past decades have led to the common knowledge that teachers’ professional knowledge is essential to effective classroom instruction. However, there is still very limited understanding about the nature of teachers’ expertise in mathematics instruction. Expertise in Mathematics Instruction addresses this need clearly and concisely. In particular, it examines all aspects of emphases employed to characterize the nature of expertise in mathematics instruction from both researchers’ and practitioners’ perspectives. Moreover, with research contributions from both the East and the West, this book also examines ideas pertinent to fostering and demonstrating expertise in mathematics instruction within different system contexts. This book will raise questions and issues for mathematics education researchers to guide a critical examination of what can be learned from other education systems. Expertise in Mathematics Instruction builds on its theoretical and methodological approach with contributions from international experts in the field. Additionally, a review of related research from mathematics education serves as an introduction to the new research in both Eastern and Western settings. Concluding this resource is a reflection on the benefits of this international collaboration and possible research directions for the future. The final chapter cohesively joins traditional and current research for action. Expertise in Mathematics Instruction is of interest to researchers in mathematics education, mathematics teacher educators, and mathematics educators.

Advanced Mathematical Thinking

David Tall
Advanced Mathematical Thinking Book PDF

Author : David Tall
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 40,9 Mb
Release : 2006-04-11
Category : Education
ISBN : 9780306472039

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Advanced Mathematical Thinking by David Tall Pdf

This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.