How to Be a Math Genius

Mike Goldsmith

DK CHILDREN |  2012 | 130 páginas | rar - pdf | 27,7 Mb

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In this clever guide, young readers previously daunted by algebra, logic, algorithms, and all things math will discover they are better at it than they thought.

How to be a Math Genius explores the math brain and demonstrates to readers that they use math skills all the time — they just don't know it yet. Packed with math activities and puzzles, compelling stories of math geniuses, math facts and stats, and more, How to be a Math Genius makes the dreaded subject of math both engaging and relevant.

Contents

6 A world of math

MATH BRAIN

10 Meet your brain

12 Math skills

14 Learning math

16 Brain vs. machine

18 Problems with numbers

20 Women and math

22 Seeing the solution

INVENTING NUMBERS

26 Learning to count

28 Number systems

30 Big zero

32 Pythagoras

34 Thinking outside the box

36 Number patterns

38 Calculation tips

40 Archimedes

42 Math that measures

44 How big? How far?

46 The size of the problem

MAGIC NUMBERS

50 Seeing sequences

52 Pascal’s triangle

54 Magic squares

56 Missing numbers

58 Karl Gauss

60 Infinity

62 Numbers with meaning

64 Number tricks

66 Puzzling primes

SHAPES AND SPACE

70 Triangles

72 Shaping up

74 Shape shifting

76 Round and round

78 The third dimension

80 3-D shape puzzles

82 3-D fun

84 Leonhard Euler

86 Amazing mazes

88 Optical illusions

90 Impossible shapes

A WORLD OF MATH

94 Interesting times

96 Mapping

98 Isaac Newton

100 Probability

102 Displaying data

104 Logic puzzles and paradoxes

106 Breaking codes

108 Codes and ciphers

110 Alan Turing

112 Algebra

114 Brainteasers

116 Secrets of the Universe

118 The big quiz

120 Glossary

122 Answers

126 Index

128 Credits

Probability and Statistics: A Didactic Introduction

José I. Barragués, Adolfo Morais e Jenaro Guisasola

CRC Press | 2014 | páginas | rar - pdf | 6,35 Mb

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With contributions by leaders in the field, this book provides a comprehensive introduction to the foundations of probability and statistics. Each of the chapters covers a major topic and offers an intuitive view of the subject matter, methodologies, concepts, terms, and related applications. The book is suitable for use for entry level courses in first year university studies of Science and Engineering, higher level courses, postgraduate university studies and for the research community.

Contents
Preface vii
1. Descriptive Statistics 1
Nicholas Watier, Claude Lamontagne and Sylvain Chartier
2. Probability 38
José I. Barragués, Adolfo Morais and Jenaro Guisasola
3. Random Variables 124
Verônica Y. Kataoka, Irene M. Cazorla, Hugo Hernandez and
Claudia Borim da Silva
4. Sampling 176
Giovanni Boscaino and Ornella Giambalvo
5. Point Estimation and Statistical Intervals 210
Martin Griffiths
6. Tests of Hypotheses 252
Martin Griffiths
7. Analysis of Variance 293
David L. Trumpower and Sait Atas
8. Factor Analysis 330
Marta B. Quaglino and José A. Pagura
9. Discriminant Analysis 384
T. Ramayah, Joshua Ignatius, Jasmine Yeap Ai Leen and Lo May Chiun
10. Multiple Regression Analysis 416
María V. López, María C. Fabrizio and María C. Plencovich
Index 469
Color Plate Section 475

Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem

Al Cuoco e Joseph J. Rotman

Mathematical Association of America | 2013 | 480 páginas | rar - pdf | 2,8 Mb

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Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.
This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard."
The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalizations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the more general work of Galois and Abel on roots of polynomials. Results and proofs are motivated with specific examples whenever possible, so that abstractions emerge from concrete experience. Applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions. While such applications are integrated throughout, each chapter also contains a section giving explicit connections between the content of the chapter and high school teaching.

Contents
Early number theory
Induction
Renaissance
Modular arithmetic
Abstract algebra
Arithmetic of polynomials
Quotients, fields, and classical problems
Cyclotomic integers
Epilog
Appendices.

Computers and Exploratory Learning

Andrea A. DiSessa, Celia Hoyles, Richard Noss e L.D. Edwards

Springer | 1995 | 483 páginas | pdf | 30 Mb

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link1

Computers are playing a fundamental role in enhancing exploratory learning techniques in education. This volume in the NATO Special Programme on Advanced Educational Technology covers the state of the art in the design and use of computer systems for exploratory learning. Contributed chapters treat principles, theory, practice, and examples of some of the best contemporary computer-based learning environments: Logo, Boxer, Microworlds, Cabri-Géomètre, Star Logo, Table Top, Geomland, spreadsheets, Function Machines, and others. Emphasis is on mathematics and science education. Synthetic chapters provide an overview of the current scene in computers and exploratory learning, and analyses from the perspectives of epistemology, learning, and socio-cultural studies.

Table of Contents
1. Computers and Exploratory Learning: Setting the Scene .... 1
Andrea A. diSessa, Celia Hoyles, Richard Noss, Laurie D. Edwards
Section I: Computers and Knowledge
2. Thematic Chapter: Epistemology and Systems Design .... 15
Andrea A. diSessa
3. New Paradigms for Computing, New Paradigms for Thinking .... 31
Mitchel Resnick
4. From Local to Global: Programming and the Unfolding of Local Models in the Exploratory Learning of Mathematics and Science ... 45
Bruno Vitale
5. East or West-GEOMLAND is Best, or Does the Answer Depend on the Angle? ... 59
Bojidar Sendov, Evgenia Sendova
6. Computational Media to Support the Learning and Use of Functions ... 79
Al Cuoco
7. Knowledge Representation in a Learning Environment for Euclidean Geometry .. 109
Maria Alberta Alberti, Daniele Marini
8. Microworlds as Representations ..... 127
Laurie D. Edwards
9. Visualizing Formal and Structural Relationships with Spreadsheets ... 155
Erich Neuwirth
10. Creating Software Applications for Children: Some Thoughts About Design .... 175
Michael Eisenberg
Section II: Computers and Learning
11. Thematic Chapter: Exploratory Software, Exploratory Cultures? .... 199
Celia Hoyles
12. The Medium and the Curriculum: Reflections on Transparent Tools and Tacit Mathematics ..221
Chris Hancock
13. What About a Learning Environment Where Euclidean Concepts are Manipulated with a Mouse? ..... 241
Colette and lean-Marie Laborde
14. Four Steps to the Right ..... 263
Augusto Chioccariello, Nadia Culotta Leccioli, Chiara Oreste
15. Learning Dynamic Geometry: Implementing Rotations ..... 275
Angel Gutierrez
16. Sketching a Multidisciplinary Microworld: A Collaborative Exploration in Boxer ..... 289
Jeremy Roschelle, John Mason
17. Design of Computer-Based Cognitive Tools ..... 305
Emrah Orhun
18. The Spreadsheet as a Tool for Mathematical Modeling: A Case Study ... 321
João Filipe Matos
19. The Many Faces of a Computational Medium: Teaching the Mathematics of Motion .. 337
Andrea A. diSessa
Section III: Computers and Cultures
20. Thematic Chapter: Computers as Commodities .... 363
Richard Noss
21. Exploring the Sketch Metaphor for Presenting Mathematics Using Boxer .... 383
John Mason
22. Programming as a Means of Expressing and Exploring Ideas: Three Case Studies Situated in a Directive Educational System .. 399
Chronis Kynigos
23. Do Users Inhabit Or Build Their Boxer Environment? .. 421
Liddy Nevile
24. Designing, Exploring and Interacting: Novice Activities in the Boxer Computational Medium .... 443
Kathryn Crawford
25. Learning Opportunities Provided by Domain-Oriented Design Environments ..... 463
Gerhard Fischer
Subject Index ..... 481

The Mathematics Of Sex: How Biology and Society Conspire to Limit Talented Women and Girls

Stephen J. Ceci e Wendy M. Williams

Oxford University Press | 2009 | páginas | rar - pdf |1 Mb

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Nearly half of all physicians and biologists are females, as are the majority of new psychologists, veterinarians, and dentists, suggesting that women have achieved equality with men in the workforce. But the ranks of professionals in math-intensive careers remain lopsidedly male; up to 93% of tenure-track academic positions in some of the most mathematically-oriented fields are held by men.
Three main explanations have been advanced to explain the dearth of women in math-intensive careers, and in The Mathematics of Sex, Stephen J. Ceci and Wendy M. Williams describe and dissect the evidence for each. The first explanation involves innate ability--male brains are physiologically optimized to perform advanced mathematical and spatial operations; the second is that social and cultural biases inhibit females' training and success in mathematical fields; the third alleges that women are less interested in math-intensive careers than are men, preferring people-oriented pursuits. Drawing on research in endocrinology, economics, sociology, education, genetics, and psychology to arrive at their own unique, evidence-based conclusion, the authors argue that the problem is due to certain choices that women (but not men) are compelled to make in our society; that women tend not to favor math-intensive careers for certain reasons, and that sex differences in math and spatial ability cannot adequately explain the scarcity of women in these fields. The Mathematics of Sex represents the first time such a thorough synthesis of data has been carried out to solve the puzzle of women's underrepresentation in math-intensive careers. The result is a readable, engaging account suitable not only for academics in an array of disciplines, but for general readers as well--including educators, science policymakers, parents of daughters, and anyone intellectually curious about a key controversy of our time.

Contents
Preface: Setting the Stage ix
Introduction: Why care about women in science? 3
Chapter 1 A multidimensional problem 16
Chapter 2 Opening arguments: Environment 28
Chapter 3 Opening arguments: Biology 58
Chapter 4 Challenges to the environmental position 79
Chapter 5 Challenges to the biological position 114
Chapter 6 Background and trend data 146
Chapter 7 Comparisons across societies, cultures, and developmental stages 161
Chapter 8 Conclusions and synthesis 179
Chapter 9 What next? Research and policy recommendations 197
Epilogue 219
Notes 223
About the authors 237
References 241
Index 261

Conception and Characteristics of Expert Mathematics Teachers in China

(Perspektiven der Mathematikdidaktik)

Xinrong Yang

Springer Spektrum | 2014 | 335 páginas | rar - pdf | 1,65 Mb

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The superior performance of East Asian students in recent international studies of mathematics achievement has attracted the attention of educators and policy makers worldwide. Xinrong Yang focuses on exploring how an expert mathematics teacher is conceptualized by mathematics educators in China and the characteristics that expert mathematics teachers share. The author adopts a sociocultural theory and a prototypical view of conception in this study of teacher expertise and shows that some of the roles expected to be played by expert mathematics teachers in China, such as being at the same time a researcher, a mentor, an expert in examination, and an exemplary model, are quite different from the roles expected of an expert teacher in Western cultures. In addition, some characteristics of expert mathematics teachers the author identifies are different from those reported in previous studies. Examples include the expert mathematics teachers´ contemporary-constructivist oriented beliefs about mathematics and its learning and teaching, and their ability to teach with flexibility, balance, and coherence.​

Contents
​​Conception of Expert Mathematics Teachers
Beliefs and Knowledge of Expert Mathematics Teachers.
Classroom Teaching Practice and Sociocultural Influences​.

Making Sense of Mathematics Teacher Education

Fou-Lai Lin e Thomas Cooney

Springer | 2001 | 329 páginas | pdf |10,9 Mb

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This is a research-based book that deals with a broad range of issues about mathematics teacher education. It examines teacher education programs from different societies and cultures as it develops an international perspective on mathematics teacher education. Practical situations that are associated with related theories are studied critically. It is intended for teacher educators, mathematics educators, graduate students in mathematics education, and mathematics teachers.

Contents
SECTION I: PERSPECTIVES ON TEACHER EDUCATION
THOMAS 1. COONEY / Considering the Paradoxes, Perils, and Purposes of Conceptualizing Teacher Development 9
STEPHEN LERMAN / A Review of Research Perspectives on Mathematics Teacher Education 33
SECTION II: MAKING SENSE OF MATHEMATICS
JOAo PEDRO DA PONTE / Investigating Mathematics and Learning to Teach Mathematics 53
DINA TIROSH, RUTH STAVY, and PESSIA TSAMIR / Using the Intuitive- Rules Theory as a Basis for Educating Teachers 73
COLETTE LABORDE / The Use of New Technologies as a Vehicle for Restructuring Teachers' Mathematics 87
SECTION III: MAKING SENSE OF TEACHING
FRED GOFFREE and WIL OONK / Digitizing Real Teaching Practice for Teacher Education Programmes: The MILE Approach 111
PETER SULLIVAN and JUDY MOUSLEY / Thinking Teaching: Seeing Mathematics Teachers as Active Decision Makers 147
KENNETH RUTHVEN / Mathematics Teaching, Teacher Education, and Educational Research: Developing "Practical Theorising" in Initial Teacher Education 165
ANNA SFARD and CAROLYN KIERAN / Preparing Teachers for Handling Students' Mathematical Communication: Gathering Knowledge and Building Tools 185
SECTION IV: MAKING SENSE OF THE CONTEXT OF TEACHING
PAUL COBB and KAY MCCLAIN / An Approach for Supporting Teachers' Learning in Social Context 207
ALAN J. BISHOP / Educating Student Teachers About Values in Mathematics Education 233
CHIEN CHIN, YUH-CHYN LEU, and FOU-LAI LIN / Pedagogical Values, Mathematics Teaching, and Teacher Education: Case Studies of Two Experienced Teachers 247
SECTION V: MAKING SENSE OF THE COMPLEXITY OF TEACHER EDUCATION
KONRAD KRAINER / Teachers' Growth is More Than the Growth of Individual Teachers: The Case of Gisela 271
BARBARA JAWORSKI/Developing Mathematics Teaching: Teachers, Teacher Educators, and Researchers as Co-Learners 295