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Thinking Mathematically

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Thinking Mathematically

Thinking Mathematically Book
Author : John Mason,Leone Burton,Kaye Stacey
Publisher : Pearson College Division
Release : 2010
ISBN : 9780273728917
Language : En, Es, Fr & De

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Book Description :

'Thinking Mathematically' seeks to turn this familiar statement into a promise of opportunity and exploration. The examples provided offer both a contextual and procedural base that students can easily build upon.

Thinking Mathematically

Thinking Mathematically Book
Author : Robert F. Blitzer
Publisher : Pearson College Division
Release : 2007-08-14
ISBN : 9780131752153
Language : En, Es, Fr & De

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Book Description :

Summary: The MathXL� Tutorials on CD delivers all of MathXL's algorithmically generated practice exercises in an off-line format. Exercises are correlated at the objective level to the exercises in the textbook, and each exercise is accompanied by an example and a guided solution designed to involve students in the solution process. Selected exercises may also include a video clip to help students visualize concepts. The software provides helpful feedback for incorrect answers and can generate printed summaries of students' progress. Not available for courses in Calculus and Statistics. Visit www.mathxl.com for more information or contact your sales representative for more information.

Thinking Mathematically

Thinking Mathematically Book
Author : Thomas P. Carpenter,Megan Loef Franke,Linda Levi
Publisher : Heinemann Educational Books
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic

How Humans Learn to Think Mathematically

How Humans Learn to Think Mathematically Book
Author : David Tall
Publisher : Cambridge University Press
Release : 2013-09-02
ISBN : 1107035708
Language : En, Es, Fr & De

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Book Description :

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.

Introduction to Mathematical Thinking

Introduction to Mathematical Thinking Book
Author : Keith J. Devlin
Publisher : Unknown
Release : 2012
ISBN : 9780615653631
Language : En, Es, Fr & De

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Book Description :

"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.

Thinking Mathematically

Thinking Mathematically Book
Author : Robert Blitzer
Publisher : Unknown
Release : 2003
ISBN : 9780130499110
Language : En, Es, Fr & De

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Book Description :

Bob Blitzer's books are highly acclaimed for their well-conceived, relevant applications and meticulously annotated examples. This highly anticipated revision achieves the difficult balance between coverage and motivation, while helping readers develop strong problem-solving skills. This book provides readers with the skill building and practice that is so crucial as well as the applications and technology necessary to foster an appreciation of the myriad uses of mathematics. This expanded edition covers voting and apportionment and graphing theory, in addition to a wide range of topics that include set theory, logic, number theory, algebra, consumer mathematics and financial management, geometry, measurement, probability theory and statistics. For anyone interested in refreshing his/her fundamental math skills.

How Not to Be Wrong

How Not to Be Wrong Book
Author : Jordan Ellenberg
Publisher : Penguin Press
Release : 2014-05-29
ISBN : 1594205221
Language : En, Es, Fr & De

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Book Description :

The columnist for Slate's popular "Do the Math" celebrates the logical, illuminating nature of math in today's world, sharing in accessible language mathematical approaches that demystify complex and everyday problems.

Building Thinking Classrooms in Mathematics Grades K 12

Building Thinking Classrooms in Mathematics  Grades K 12 Book
Author : Peter Liljedahl
Publisher : Corwin Press
Release : 2020-09-28
ISBN : 1544374844
Language : En, Es, Fr & De

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Book Description :

A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

Mathematical Thinking

Mathematical Thinking Book
Author : Masami Isoda,Shigeo Katagiri
Publisher : World Scientific
Release : 2012-01-27
ISBN : 9814458716
Language : En, Es, Fr & De

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Book Description :

Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties to develope it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples. Contents:Introductory Chapter: Problem Solving Approach to Develop Mathematical ThinkingMathematical Thinking: Theory of Teaching Mathematics to Develop Children Who Learn Mathematics for Themselves:Mathematical Thinking as the Aim of EducationThe Importance of Cultivating Mathematical ThinkingThe Mindset and Mathematical ThinkingMathematical MethodsMathematical IdeasMathematical AttitudeQuestioning to Enhance Mathematical ThinkingAppendix for the List of Questions for Mathematical ThinkingDeveloping Mathematical Thinking with Number Tables: How to Teach Mathematical Thinking from the Viewpoint of Assessment:Example 1: Sugoroku: Go Forward Ten Spaces If You Win, or One If You LoseExample 2: Arrangements of Numbers on the Number TableExample 3: Extension of Number ArrangementsExample 4: Number Arrangements: Sums of Two NumbersExample 5: When You Draw a Square on a Number Table, What Are the Sum of the Numbers at the Vertices, the Sum of the Numbers Along the Perimeter, and the Grand Total of All the Numbers?Example 6: Where Do Two Numbers Add up to 99?Example 7: The Arrangement of MultiplesExample 8: How to Find Common MultiplesExample 9: The Arrangement of Numbers on an Extended CalendarExample 10: Development of the Arrangement of Numbers in the Extended CalendarExample 11: Sums of Two Numbers in an Odd Number TableExample 12 When You Draw a Square on an Odd Number Table, What Are the Sum of the Numbers at the Vertices and the Grand Total of All the Numbers? Readership: Mathematics educators of teacher training colleges, mathematics teachers, prospective teachers (elementary and secondary school) and undergraduate students in mathematics. Keywords:Lesson Study;Problem Solving;Mathematical Thinking;Teacher Education;Elementary Schools;Junior High Schools;Senior High Schools and GuidebooksReviews:“This extraordinarily important monograph has the potential to make a significant positive contribution to elementary education.”Zentralblatt MATH “This book has the potential to make a significant positive contribution to elementary education and the practice in the classroom.” European Mathematical Society

Ways to Think About Mathematics

Ways to Think About Mathematics Book
Author : Steve Benson,Susan Addington,Nina Arshavsky
Publisher : Corwin Press
Release : 2004-10-05
ISBN : 9780761931058
Language : En, Es, Fr & De

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Book Description :

Funded by the National Science Foundation and successfully field-tested in a variety of settings, the materials presented give teachers the opportunity to grow as learners for the classes they teach.

The Nature of Mathematical Thinking

The Nature of Mathematical Thinking Book
Author : Robert J. Sternberg,Talia Ben-Zeev
Publisher : Routledge
Release : 2012-10-12
ISBN : 1136487506
Language : En, Es, Fr & De

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Book Description :

Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.

Understanding the Mathematical Way of Thinking The Registers of Semiotic Representations

Understanding the Mathematical Way of Thinking     The Registers of Semiotic Representations Book
Author : Raymond Duval
Publisher : Springer
Release : 2017-07-18
ISBN : 3319569104
Language : En, Es, Fr & De

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Book Description :

In this book, Raymond Duval shows how his theory of registers of semiotic representation can be used as a tool to analyze the cognitive processes through which students develop mathematical thinking. To Duval, the analysis of mathematical knowledge is in its essence the analysis of the cognitive synergy between different kinds of semiotic representation registers, because the mathematical way of thinking and working is based on transformations of semiotic representations into others. Based on this assumption, he proposes the use of semiotics to identify and develop the specific cognitive processes required to the acquisition of mathematical knowledge. In this volume he presents a method to do so, addressing the following questions: • How to situate the registers of representation regarding the other semiotic “theories” • Why use a semio-cognitive analysis of the mathematical activity to teach mathematics • How to distinguish the different types of registers • How to organize learning tasks and activities which take into account the registers of representation • How to make an analysis of the students’ production in terms of registers Building upon the contributions he first presented in his classic book Sémiosis et pensée humaine, in this volume Duval focuses less on theoretical issues and more on how his theory can be used both as a tool for analysis and a working method to help mathematics teachers apply semiotics to their everyday work. He also dedicates a complete chapter to show how his theory can be applied as a new strategy to teach geometry. “Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations is an essential work for mathematics educators and mathematics teachers who look for an introduction to Raymond Duval’s cognitive theory of semiotic registers of representation, making it possible for them to see and teach mathematics with fresh eyes.” Professor Tânia M. M. Campos, PHD.

Thinking Mathematically Expd Clast Mnl

Thinking Mathematically Expd Clast Mnl Book
Author : James Wooland
Publisher : Addison Wesley Longman
Release : 2004-04
ISBN : 9780131443730
Language : En, Es, Fr & De

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Book Description :

Download Thinking Mathematically Expd Clast Mnl book written by James Wooland, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mathematical Thinking

Mathematical Thinking Book
Author : Masami Isoda
Publisher : World Scientific
Release : 2012
ISBN : 9814350850
Language : En, Es, Fr & De

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Book Description :

Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.

Primary CAME Thinking Maths Teachers Guide

Primary CAME Thinking Maths Teachers Guide Book
Author : David Johnson
Publisher : Nelson Thornes
Release : 2003-07
ISBN : 1903142296
Language : En, Es, Fr & De

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Book Description :

This folder accompanies the Primary CAME professional development programme. The two-year programme is based on extensive research into how to promote the development of children's mathematical thinking skills. It explores not just what to teach Year 5 and 6 children but how and why.

Understanding Emotions in Mathematical Thinking and Learning

Understanding Emotions in Mathematical Thinking and Learning Book
Author : Ulises Xolocotzin
Publisher : Academic Press
Release : 2017-05-12
ISBN : 0128024895
Language : En, Es, Fr & De

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Book Description :

Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. Covers methodologies in studying emotion in mathematical knowledge Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches Explores the role of anxiety in mathematical learning Synthesizes unifies the work of multiple sub-disciplines in one place

Thinking about Mathematics

Thinking about Mathematics Book
Author : Stewart Shapiro
Publisher : OUP Oxford
Release : 2000-07-13
ISBN : 0192893068
Language : En, Es, Fr & De

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Book Description :

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Advanced Mathematical Thinking

Advanced Mathematical Thinking Book
Author : David Tall
Publisher : Springer Science & Business Media
Release : 1991-11-30
ISBN : 0792314565
Language : En, Es, Fr & De

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Book Description :

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.