Helping Children Learn Mathematics

Robert E. Reys, Mary Lindquist, Diana V. Lambdin e Nancy L. Smith 
Wiley | 2012 - 10ª edição | 461 páginas | rar - pdf | 11,7 Mb

link
password: matav

The new edition of Reys' Helping Children Learn Mathematics examines the forthcoming Common Core Standards and refocuses the themes for the book to make sure they are timely, significant and parallel in form. The three themes threaded throughout the book are: Best Practices, Sense Making and Practical Experiences.

The text strengthens the attention given to diversity by carefully examining the Cultural Connections sections to make sure they address, when appropriate, practical experience suggestions for dealing with diversity. Other updates include new entries in the Book Nooks; an expanded list of Book Nook recommendations; updated references including all research citations; and links from the narrative to appropriate intact lessons that currently are in Teaching Elementary Mathematics: A Resource for Field Experiences.

Table of Contents

Chapter 1:     School Mathematics in a Changing World

Chapter 2:     Helping Children Learn Mathematics with Understanding

Chapter 3:     Planning for and Teaching Diverse Learners

Chapter 4:     Assessment: Enhanced Learning and Teaching

Chapter 5:     Mathematical Processes and Practices

Chapter 6:     Helping Children with Problem Solving

Chapter 7:     Developing Counting and Number Sense in Early Grades

Chapter 8:     Extending Number Sense: Place Value

Chapter 9:     Operations: Meaning and Basic Facts

Chapter 10: Computation Methods: Calculators, Mental Computation, and Estimation

Chapter 11: Standard and Alternative Computational Algorithms

Chapter 12: Fractions and Decimals: Concepts and Operations

Chapter 13: Ratio, Proportion, and Percent: Meanings and Applications

Chapter 14: Algebraic Thinking

Chapter 15: Geometry

Chapter 16: Measurement

Chapter 17: Data Analysis, Statistics, and Probability

Chapter 18: Number Theory

site do manual: wiley.com

Mathematics for Elementary Teachers A Contemporary Approach

Gary L. Musser , Blake E. Peterson e William F. Burger
Wiley | 2013 -10ª edição | 1031 páginas | rar-pdf | 25,9 Mb

link (password: matav)
pdf - 34 Mb - link

Mathematics for Elementary Teachers: A Contemporary Approach, 10th Edition makes readers motivated to learn mathematics. With new-found confidence, they are better able to appreciate the beauty and excitement of the mathematical world. The new edition of Musser, Burger, and Peterson's best-selling textbook focuses on one primary goal: helping students develop a true understanding of central concepts using solid mathematical content in an accessible and appealing format. The components in this complete learning program work in harmony to help achieve this goal. The Tenth Edition features the Common Core Standards to accompany the NCTM standards that are integrated throughout the text.

Contents
1 Introduction to Problem Solving 2
2 Sets, Whole Numbers, and Numeration 42
3 Whole Numbers: Operations and Properties 84
4 Whole Number Computation—Mental, Electronic, and Written 128
5 Number Theory 174
6 Fractions 206
7 Decimals, Ratio, Proportion, and Percent 250
8 Integers 302
9 Rational Numbers, Real Numbers, and Algebra 338
10 Statistics 412
11 Probability 484
12 Geometric Shapes 546
13 Measurement 644
14 Geometry Using Triangle Congruence and Similarity 716
15 Geometry Using Coordinates 780
16 Geometry Using Transformations 820
Epilogue: An Eclectic Approach to Geometry 877
Topic 1 Elementary Logic 881
Topic 2 Clock Arithmetic: A Mathematical System 891
Answers to Exercise/Problem Sets A and B, Chapter Reviews, Chapter Tests, and Topics Section A1
Index I1
Contents of Book Companion Web Site
Resources for Technology Problems
Technology Tutorials
Webmodules
Additional Resources
Videos

Mathematical Sorcery: Revealing the Secrets of Numbers

Calvin C. Clawson

Basic Books | 1999 | 301 páginas | rar - pdf | 5,5 Mb

link (password: matav)

There are two kinds of people: those who can do mathematics, and then there’s the rest of us.Math is boring.Females have no facility for mathematics (and really don’t need it, anyway).For many people who do not like math, these myths ring true.Calvin Clawson, the celebrated author of Mathematical Mysteries, has a unique talent for opening the door for the uninitiated to the splendors of mathematics. A writer in love with his subject, Clawson offers readers the perfect antidote to the phobias and misconceptions surrounding mathematics in MATHEMATICAL SORCERY. Contending that the power and beauty of mathematics are gifts in which we all can partake, he shows that the field of mathematics holds a bounty of wonder that can be reaped by any one of us in the hopes of discovering new truths.In this captivating quest for pure knowledge, Clawson takes us on a journey to the amazing discoveries of our ancient ancestors. He divulges the wisdom of the Ancient Greeks, Sumerians, Babylonians, and Egyptians, whose stunning revelations still have deep meaning to us today. The secrets of the constellations, the enigma of the golden mean, and the brilliance of a proof are just some of the breakthroughs he explores with unbridled delight.Enabling us to appreciate the achievements of Newton and other intellectual giants, Clawson inspires us through his eloquence and zeal to actually do mathematics, urging us to leap to the next level. He helps us intuitively comprehend and follow the very building blocks that too long have been a mystery to most of us, including infinity, functions, and the limit. As he elegantly states: “Mathematics is pursued not only for the sheer joy of the pursuit, as with the Ancient Greeks, but for the truths it reveals about our universe.” Through MATHEMATICAL SORCERY, we taste the fruit of knowledge that has eluded us until now.

Contents
Acknowledgments ..... ix
Introduction .... 1
Chapter 1: Early Counting ..... 9
Chapter 2: The Incredible Greeks ... 22
Chapter 3: Mathematical Proofs .. 55
Chapter 4: Passing the Torch ... 80
Chapter 5: Opening the Door .. 115
Chapter 6: Functions ... 133
Chapter 7: Stretching Space ... 176
Chapter 8: Extending the Form .... 211
Chapter 9: Isaac Newton ... 228
Chapter 10: Calculus.... 248
Chapter 11: Speculations on the Nature of Mathematics ... 281
Endnotes ... 286
Index ... 291

Understandable Statistics: Concepts and Methods

Charles Henry Brase e Corrinne Pellillo Brase

Cengage Learning | 2011 -10ª edição | 844 páginas | pdf | 54 Mb

link
link1

UNDERSTANDABLE STATISTICS: CONCEPTS AND METHODS, Tenth Edition, is a thorough, yet accessible program designed to help readers overcome their apprehensions about statistics. The authors provide clear guidance and informal advice while showing the links between statistics and the world. To reinforce this approach--and make the material interesting as well as easier to understand--the book integrates real-life data from a variety of sources, including journals, periodicals, newspapers, and the Internet. Readers also have opportunities to develop their critical thinking and statistical literacy skills through special features and exercises throughout the text. The use of graphing calculators, Excel, MINITAB, and SPSS is covered for those who wish to learn about these helpful tools

Contents
Preface xv
Table of Prerequisite Material 1
1 Getting Started 2
FOCUS PROBLEM: Where Have All the Fireflies Gone? 3
1.1 What Is Statistics? 4
1.2 Random Samples 12
1.3 Introduction to Experimental Design 21
Summary 30
Important Words & Symbols 30
Chapter Review Problems 31
Data Highlights: Group Projects 34
Linking Concepts: Writing Projects 34
USING TECHNOLOGY 35
2 Organizing Data 38
FOCUS PROBLEM: Say It with Pictures 39
2.1 Frequency Distributions, Histograms, and Related Topics 40
2.2 Bar Graphs, Circle Graphs, and Time-Series Graphs 54
2.3 Stem-and-Leaf Displays 63
Summary 71
Important Words & Symbols 71
Chapter Review Problems 72
Data Highlights: Group Projects 75
Linking Concepts: Writing Projects 77
USING TECHNOLOGY 78
3 Averages and Variation 80
FOCUS PROBLEM: The Educational Advantage 81
3.1 Measures of Central Tendency: Mode, Median, and Mean 82
3.2 Measures of Variation 93
3.3 Percentiles and Box-and-Whisker Plots 110
Summary 120
Important Words & Symbols 120
Chapter Review Problems 121
4 Elementary Probability Theory 130
FOCUS PROBLEM: How Often Do Lie Detectors Lie? 131
4.1 What Is Probability? 132
4.2 Some Probability Rules—Compound Events 142
4.3 Trees and Counting Techniques 162
Summary 172
Important Words & Symbols 173
Chapter Review Problems 174
Data Highlights: Group Projects 176
Linking Concepts: Writing Projects 178
USING TECHNOLOGY 179
5 The Binomial Probability
Distribution and Related Topics 180
FOCUS PROBLEM: Personality Preference Types: Introvert or Extrovert? 181
5.1 Introduction to Random Variables and Probability Distributions 182
5.2 Binomial Probabilities 195
5.3 Additional Properties of the Binomial Distribution 210
5.4 The Geometric and Poisson Probability Distributions 222
Summary 239
Important Words & Symbols 240
Chapter Review Problems 241
Data Highlights: Group Projects 244
Linking Concepts: Writing Projects 245
USING TECHNOLOGY 247
6 Normal Curves and Sampling
Distributions 248
FOCUS PROBLEM: Impulse Buying 249
6.1 Graphs of Normal Probability Distributions 250
6.2 Standard Units and Areas Under the Standard Normal Distribution 266
6.3 Areas Under Any Normal Curve 276
6.4 Sampling Distributions 291
6.5 The Central Limit Theorem 296
6.6 Normal Approximation to Binomial Distribution and to Distribution 308
Summary 318
Important Words & Symbols 319
Chapter Review Problems 319
Data Highlights: Group Projects 322
Linking Concepts: Writing Projects 323
USING TECHNOLOGY 325
CUMULATIVE REVIEW PROBLEMS: Chapters 4–6 329
7 Estimation 332
FOCUS PROBLEM: The Trouble with Wood Ducks 333
7.1 Estimating m When s Is Known 334
7.2 Estimating m When s Is Unknown 347
7.3 Estimating p in the Binomial Distribution 360
7.4 Estimating m1 m2 and p1 p2 372
Summary 395
Important Words & Symbols 395
Chapter Review Problems 396
Data Highlights: Group Projects 400
Linking Concepts: Writing Projects 402
USING TECHNOLOGY 404
8 Hypothesis Testing 408
FOCUS PROBLEM: Benford’s Law: The Importance of Being Number 1 409
8.1 Introduction to Statistical Tests 410
8.2 Testing the Mean m 425
8.3 Testing a Proportion p 442
8.4 Tests Involving Paired Differences (Dependent Samples) 452
8.5 Testing m1 m2 and p1 p2 (Independent Samples) 466
Summary 490
Finding the P-Value Corresponding to a Sample Test Statistic 491
Important Words & Symbols 491
Chapter Review Problems 492
Data Highlights: Group Projects 495
Linking Concepts: Writing Projects 496
USING TECHNOLOGY 497
9 Correlation and Regression 500
FOCUS PROBLEM: Changing Populations and Crime Rate 501
9.1 Scatter Diagrams and Linear Correlation 502
9.2 Linear Regression and the Coefficient of Determination 520
9.3 Inferences for Correlation and Regression 541
9.4 Multiple Regression 559
Summary 575
Important Words & Symbols 575
Chapter Review Problems 576
Data Highlights: Group Projects 579
Linking Concepts: Writing Projects 580
USING TECHNOLOGY 581
CUMULATIVE REVIEW PROBLEMS: Chapters 7–9 586
10 Chi-Square and F Distributions 590
FOCUS PROBLEM: Archaeology in Bandelier National Monument 591
Part I: Inferences Using the Chi-Square Distribution 592
Overview of the Chi-Square Distribution 592
10.1 Chi-Square: Tests of Independence and of Homogeneity 593
10.2 Chi-Square: Goodness of Fit 608
10.3 Testing and Estimating a Single Variance or Standard Deviation 618
Part II: Inferences Using the F Distribution 630
Overview of the F Distribution 630
10.4 Testing Two Variances 631
10.5 One-Way ANOVA: Comparing Several Sample Means 640
10.6 Introduction to Two-Way ANOVA 656
Summary 668
Important Words & Symbols 668
Chapter Review Problems 669
Data Highlights: Group Projects 672
Linking Concepts: Writing Projects 673
USING TECHNOLOGY 674
11 Nonparametric Statistics 676
FOCUS PROBLEM: How Cold? Compared to What? 677
11.1 The Sign Test for Matched Pairs 678
11.2 The Rank-Sum Test 686
11.3 Spearman Rank Correlation 694
11.4 Runs Test for Randomness 705
Summary 714
Important Words & Symbols 714
Chapter Review Problems 714
Data Highlights: Group Projects 716
Linking Concepts: Writing Projects 717
CUMULATIVE REVIEW PROBLEMS: Chapters 10–11 718

Appendix I: Additional Topics A1
Part I: Bayes’s Theorem A1
Part II: The Hypergeometric Probability Distribution A5
Appendix II: Tables A9
Table 1: Random Numbers A9; Table 2: Binomial Coefficients Cn,r A10; Table 3: Binomial
Probability Distribution Cn,r pr qn r A11; Table 4: Poisson Probability Distribution A16;
Table 5: Areas of a Standard Normal Distribution A22; Table 6: Critical Values for
Student’s t Distribution A24; Table 7: The Distribution A25; Table 8: Critical Values
for F Distribution A26; Table 9: Critical Values for Spearman Rank Correlation, rs A36;
Table 10: Critical Values for Number of Runs R A37
Answers and Key Steps to Odd-Numbered Problems A39
Answers to Selected Even-Numbered Problems A74
Index I1

Handbook on the History of Mathematics Education

Alexander Karp e Gert Schubring

Springer | 2014 | 627 páginas | rar - pdf | 4,9 Mb

link (password: matav)

This is the first comprehensive International Handbook on the History of Mathematics Education, covering a wide spectrum of epochs and civilizations, countries and cultures. Until now, much of the research into the rich and varied history of mathematics education has remained inaccessible to the vast majority of scholars, not least because it has been written in the language, and for readers, of an individual country. And yet a historical overview, however brief, has become an indispensable element of nearly every dissertation and scholarly article. This handbook provides, for the first time, a comprehensive and systematic aid for researchers around the world in finding the information they need about historical developments in mathematics education, not only in their own countries, but globally as well.

Although written primarily for mathematics educators, this handbook will also be of interest to researchers of the history of education in general, as well as specialists in cultural and even social history.

Contents

Part I History and Methodology of the Field

1 On Historiography of Teaching and Learning Mathematics .... 3

Gert Schubring

2 The History of Mathematics Education: Developing a Research Methodology ... 9

Alexander Karp

Part II Mathematics Education in Different Epochs and in Different Regions: Antiquity and the Middle Ages

3 Mathematics Education in Antiquity .... 27

Alain Bernard, Christine Proust, and Micah Ross

4 Mathematics Education in Oriental Antiquity and Middle Ages .... 55

Agathe Keller and Alexei Volkov

5 Teaching the Mathematical Sciences in Islamic Societies Eighth–Seventeenth Centuries .... 85

Sonja Brentjes

6 Mathematics Education in the European Middle Ages .... 109

Jens Høyrup

Part III Mathematics Education in Different Epochs and in Different Regions: Premodern Period

Introduction .... 125

7 Mathematics Education in Europe in the Premodern Times .. 129

Alexander Karp and Gert Schubring

8 History of Mathematics Education in East Asia in Premodern Times... 153

Andrea Bréard and Annick Horiuchi

9 Mathematics Education in America in the Premodern Period.. 175

Ubiratan D’Ambrosio, Joseph W. Dauben, and Karen Hunger Parshall

Part IV Mathematics Education in Different Epochs and in Different Regions: Modern Period

Introduction ... 197

10 Secondary School Mathematics Teaching from the Early Nineteenth Century to the Mid-Twentieth Century in Italy ... 201

Livia Giacardi and Roberto Scoth

11 Mathematics Education in France: 1800–1980 

Hélène Gispert

12 Mathematics Education in Germany (Modern Times).. 241

Gert Schubring

13 Mathematics Education in the United Kingdom.....257

Geoffrey Howson and Leo Rogers

14 Mathematics Education in Spain and Portugal ... 283

Elena Ausejo and José Manuel Matos

15 Mathematics Education in Russia .... 303

Alexander Karp

16 Mathematics Education in the United States and Canada... 323

Jeremy Kilpatrick

17 Mathematics Education in Latin America .... 335

João Bosco Pitombeira de Carvalho

18 Mathematics Education in Modern Asia.... 361

Joseph W. Dauben, Lee Peng Yee, Dhruv Raina, and Yibao Xu

19 Mathematics Education in Africa ... 391

Alexander Karp, Charles Opolot-Okurut, and Gert Schubring

20 Mathematics Education in Islamic Countries in the Modern Time:Case Study of Tunisia .. 405

Mahdi Abdeljaouad

Part V History of Teaching Mathematical Subjects in School

21 History of Teaching Arithmetic ... 431

Kristín Bjarnadóttir

22 Notes for a History of the Teaching of Algebra .... 459

João Pedro da Ponte and Henrique Manuel Guimarães

23 History of Teaching Geometry .. 473

Evelyne Barbin and Marta Menghini

24 History of Teaching Calculus ... 493

Luciana Zuccheri and Verena Zudini

25 History of Teaching Vocational Mathematics .... 515

Rudolf Sträßer

26 Mathematics Teaching Practices ... 525

Amy Ackerberg-Hastings

Part VI Issues and Processes Across Borders

27 History of International Cooperation in Mathematics Education ... 543

Fulvia Furinghetti

28 History of Tools and Technologies in Mathematics Education .. 565

David Lindsay Roberts

29 History of Mathematics Teacher Education .... 579

Harm Jan Smid

About the Authors .. 597

Name Index ..... 605

Subject Index .625

Problem Solving and Comprehension

Arthur Whimbey, Jack Lochhead, e Ron Narode

 Routledge |  2013 - 7.ª edição | 441 páginas | rar - pdf | 948 kb

link (password: matav)

pdf - 6,8 Mb - link

6.ª edição - 1999

This popular book shows students how to increase their power to analyze problems and comprehend what they read using the Think Aloud Pair Problem Solving [TAPPS] method. First it outlines and illustrates the method that good problem solvers use in attacking complex ideas. Then it provides practice in applying this method to a variety of comprehension and reasoning questions, presented in easy-to-follow steps. As students work through the book they will see a steady improvement in their analytical thinking skills and become smarter, more effective, and more confident problem solvers. Not only can using the TAPPS method assist students in achieving higher scores on tests commonly used for college and job selection, it teaches that problem solving can be fun and social, and that intelligence can be taught.

Changes in the Seventh Edition: New chapter on "open-ended" problem solving that includes inductive and deductive reasoning; extended recommendations to teachers, parents, and tutors about how to use TAPPS instructionally; Companion Website with PowerPoint slides, reading lists with links, and additional problems.

CONTENTS

Preface to the Seventh Edition ix

Preface to the Sixth Edition xi

1. Test Your Mind—See How It Works 1

2. Errors in Reasoning 11

3. Problem-Solving Methods 21

4. Verbal Reasoning Problems 43

5. Six Myths About Reading 139

6 Analogies 143

7. Writing Relationship Sentences 157

8. How to Form Analogies 173

9. Analysis of Trends and Patterns 195

10. Deductive and Hypothetical Thinking Through Days of the Week 223

11. Solving Mathematical Word Problems 241

12. Open-Ended Problem Solving 335

13. The Post-WASI Test 356

14. Meeting Academic and Workplace Standards: How This Book Can Help 364

15. How to Use Pair Problem Solving: Advice for Teachers, Parents, Tutors, and Helpers of All Sorts 383

Appendix 1. Answer Key 400

Appendix 2. Compute Your Own IQ 420

References 421

Cases of Assessment in Mathematics Education: An ICMI Study

Mogens Niss

Springer | 1993 ; edição de 2013 | 215 páginas | pdf | 5,9 Mb

link

This book is one of the first to present a variety of carefully selected cases to describe and analyze in depth and considerable detail assessment in mathematics education in various interesting places in the world. The book is based on work presented at an invited international ICMI seminar and includes contributions from first rate scholars from Europe, North America, the Caribbean, Asia and Oceania, and the Middle East.
The cases presented range from thorough reviews of the state of assessment in mathematics education in selected countries, each possessing `archetypical' characteristics of assessment, to innovative or experimental small or large scale assessment initiatives. All the cases presented have been implemented in actual practice.
The book will be particularly stimulating reading for mathematics educators -- at all levels -- who are concerned with the innovation of assessment modes in mathematics education, as well as everybody working in the field of mathematics education: in research and development, in curriculum planning, assessment institutions and agencies, mathematics specialists in ministries, teacher trainers, textbook authors, frontline teachers.

TABLE OF CONTENTS
MOGENS NISS
Introduction 1
LUIS RICO
Mathematics Assessment in the Spanish Educational System 9
DESMOND R. BROOMES & JAMES A. HALLIDAY
Major Issues in Assessing Mathematics Performance at 16+ Level: A Caribbean Perspective 21
MURAD JURDAK
Assessment in Mathematics Education in the Arab Countries 35
JOHN A. DOSSEY & JANE O. SWAFFORD
Issues in Mathematics Assessment in the United States 43
EDWARD A. SILVER & SUZANNE LANE
Assessment in the Context of Mathematics Instruction Reform: the Design of Assessment in the QUASAR Project 59
MARGARET BROWN
Assessment in Mathematics Education: Developments in Philosophy and Practice in the United Kingdom 71
CHRIS LITTLE
The School Mathematics Project: Some Secondary School Assessment Initiatives in England 85
LUCIANA BAZZINI
The Teaching/Learning Process and Assessment Practice: Two Intertwined Sides of Mathematics Education 99
GUNNAR GJONE
Types of Problems and How Students in Norway Solve Them 107
HANS NYGAARD JENSEN
Assessment of Primary and Lower Secondary Mathematics in Denmark 119
KIRSTEN HERMANN & BENT HIRSBERG
Assessment in Upper Secondary Mathematics in Denmark 129
WIM KLEUNE & HENK SCHURING
Assessment of Examinations in the Netherlands 139
MAX STEPHENS & ROBERT MONEY
New Developments in Senior Secondary Assessment in Australia 155
LEONOR CUNHA LEAL & PAULO ABRANTES
Assessment in an Innovative Curriculum Project for Mathematics in Grades 7-9 in Portugal
WEI CHAO-QUN & ZHANG HUI
Educational Assessment in Mathematics Teaching: Applied Research in China
CHENG ZEMIN & LV SHAOZHENG
The Practice and Study of Evaluating Mathematics Teaching in China
RUTH K. SWEETNAM
Assessment in Mathematics Within the International Baccalaureate 203
Index 213