Dyscalculia: Action plans for successful learning in mathematics

Glynis Hannell

Routledge | 2013 - 2ª edição | 137 páginas | rar -pdf | 682 kb

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Based on expert observations of children who experience difficulties with maths this book gives a comprehensive overview of dyscalculia, providing a wealth of information and useful guidance for any practitioner. With a wide range of appropriate and proven intervention strategies it guides readers through the cognitive processes that underpin success in mathematics and gives fascinating insights into why individual students struggle with maths. Readers are taken step-by-step through each aspect of the maths curriculum and each section includes:

• Examples which illustrate why particular maths difficulties occur

• Practical ‘action plans’ which help teachers optimise children’s progress in mathematics

This fully revised second edition will bring the new research findings into the practical realm of the classroom. Reflecting current knowledge, Glynis Hannell gives increased emphasis to the importance of training ‘number sense’ before teaching formalities, the role of concentration difficulties and the importance of teaching children to use strategic thinking. Recognising that mathematical learning has a neurological basis will continue to underpin the text, as this has significant practical implications for the teacher.

Contents

Section 1: Introduction to dyscalculia 1
1 Understanding dyscalculia 3
Section 2: Effective teaching, effective learning 15
2 The biological basis of learning 17
3 Making mathematical connections 22
4 Assessment 30
5 Individual differences and mathematics 34
6 Confidence and mathematics 40
Section 3: Understanding the number system 45
7 Introduction to understanding the number system 47
8 Number sense 50
9 Counting 56
10 Using number patterns 62
11 Understanding place value 65
12 Composition and decomposition of numbers 69
Section 4: Understanding operations 73
13 Dyscalculia and operations 75
14 Understanding algorithms 77
15 Addition 81
16 Subtraction 88
17 Multiplication 92
18 Division 95
19 Learning number facts 98
Section 5: Measurement and rational numbers 101
21 Rational numbers 106
Section 6: Teacher resources 111
22 Parent information sheets 113
References 123
Index 125

Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin

(Sources and Studies in the History of Mathematics and Physical Sciences)

Jens Høyrup

Springer | 2002 | 462 páginas 

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In this examination of the Babylonian cuneiform "algebra" texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens Høyrup proposes that the traditional interpretation must be rejected. The texts turn out to speak not of pure numbers, but of the dimensions and areas of rectangles and other measurable geometrical magnitudes, often serving as representatives of other magnitudes (prices, workdays, etc...), much as pure numbers represent concrete magnitudes in modern applied algebra. Moreover, the geometrical procedures are seen to be reasoned to the same extent as the solutions of modern equation algebra, though not built on any explicit deductive structure.

Introduction to Inequalities

(New Mathematical Library)

Edwin F. Beckenbach, R. Bellman

Mathematical Association of America (MAA) | 1975 | 133 páginas | rar - pdf| 4,1 Mb

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| djvu | 949 kb

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Descrição: Most people, when they think of mathematics, think first of numbers and equations-this number (x) = that number (y). But professional mathematicians, in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that areequal. This book provides an introduction to the fascinating world of inequalities, beginning with a systematic discussion of the relation "greater than" and the meaning of "absolute values" of numbers, and ending with descriptions of some unusual geometries. In the course of the book, the reader wil encounter some of the most famous inequalities in mathematics.

The Abel Prize 2008-2012

Helge Holden e Ragni Piene 

Springer | 2014 | 561 páginas | rar - pdf | 6,5 Mb

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The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/).
The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/).

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize:

·         John G. Thompson and Jacques Tits, 2008
·         Mikhail Gromov, 2009
·         John T. Tate Jr., 2010
·         John W. Milnor, 2011
·         Endre Szemerédi, 2012.

The book also presents a  history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau.
This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners.

Spectrums: Our Mind-boggling Universe from Infinitesimal to Infinity

 

David Blatner

Bloomsbury Publishing | 2013 | 192 páginas | epub | 7 Mb

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The universe is a mind-boggling place, full of things seemingly too big and too small to understand. How can we visualise the minuscule world of the atom and the vastness of our galaxy? How can we grasp a billionth of a second and a billion years? Or the freezing point of Helium and the heat generated by the blast of an atomic bomb? David Blatner's solution is to put these and many other 'inconceivable' items on six spectrums - numbers, size, light, sound, heat and time - that put them into a human perspective. Full of facts, illustrations and anecdotes, Spectrums proves that we really can make sense of our extraordinary universe. Visit spectrums.com for amazing interactive charts, videos and more

Contents

  Introduction

  Chapter 1 Numbers

  Chapter 2 Size

  Chapter 3 Light

  Chapter 4 Sound

  Chapter 5 Heat

  Chapter 6 Time

  Epilogue

  Acknowledgments

  Table of Prefixes  

  Index

Mathematics: for Elementary School Teacher

Tom Bassarear 

Cengage Learning | 2011 - 5ª edição | 745 páginas | rar - pdf | 23,4 Mb

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Intended for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. Bassarear presents real-world problems, problems that require active learning in a method similar to how archaeologists explore an archaeological find: they carefully uncover the site, slowly revealing more and more of the structure. The author demonstrates that there are many paths to solving a problem, and that sometimes, problems have more than one solution. With this exposure, future teachers will be better able to assess student needs using diverse approaches

Contents
1 Foundations for Learning Mathematics 1
SECTION 1.1 Getting Started and Problem Solving 2
INVESTIGATIONS
1.1A Pigs and Chickens 7
1.1B Coin Problem? 12
SECTION 1.2 Patterns and Communication 14
INVESTIGATIONS
1.2A Sequences and Patterns 15
1.2B Patterns in Multiplying by 11 19
1.2C Pascal’s Triangle 21
1.2D Communicating Patterns in a Magic Square 22
SECTION 1.3 Reasoning and Proof 26
INVESTIGATIONS
1.3A Does Your Answer Make Sense? 26
1.3B Inductive Thinking with Fractions 27
1.3C Deductive Reasoning and Venn Diagrams 32
Data Highlights: Group Projects 123
Linking Concepts: Writing Projects 125
USING TECHNOLOGY 126
1.3D Why Is the Sum of Two Even Numbers an
Even Number? 33
1.3E Darts, Proof, and Communication 34
1.3F The Nine Dots Problem 35
1.3G How Many Games in the Tournament? 36
SECTION 1.4 Representation and Connections 39
INVESTIGATIONS
1.4A How Long Will It Take the Frog to Get out
of the Well? 40
1.4B How Many Pieces of Wire? 44
LOOKING BACK ON CHAPTER1 49
CHAPTER 1 SUMMARY 50
CHAPTER 1 REVIEW EXERCISES 51
2 Fundamental Concepts 53
SECTION 2.1 Sets 54
INVESTIGATIONS
2.1A Classifying Quadrilaterals 54
2.1B Describing Sets 56
2.1C How Many Subsets? 58
2.1D Translating Among Representations 63
2.1E Finding Information from Venn Diagrams 63
SECTION 2.2 Algebraic Thinking 68
INVESTIGATIONS
2.2A A Variable by Any Other Name Is Still a Variable 69
2.2B Baby-sitting 73
2.2C Choosing Between Functions 74
2.2D Matching Graphs to Situations 76
2.2F Looking for Generalizations 79
2.2G How Many Dots? 80
SECTION 2.3 Numeration 87
INVESTIGATIONS
2.3A Relative Magnitude of Numbers 98
2.3B What If Our System Was Based on One Hand? 99
2.3C How Well Do You Understand Base Five? 100
2.3D Base Sixteen 101
LOOKING BACK ON CHAPTER 2 106
CHAPTER 2 SUMMARY 107
CHAPTER 2 REVIEW EXERCISES 108
3 The Four Fundamental Operations of Arithmetic 111
SECTION 3.1 Understanding Addition 112
INVESTIGATIONS
3.1A A Pattern in the Addition Table 116
3.1B Mental Addition 117
3.1C Children’s Strategies for Adding Large Numbers 120
3.1D An Alternative Algorithm 123
3.1E Addition in Base Five 123
3.1F Children’s Mistakes 125
3.1G What Was the Total Attendance? 127
3.1H Estimating by Making Compatible Numbers 128
3.1I Number Sense with Addition 130
SECTION 3.2 Understanding Subtraction 133
INVESTIGATIONS
3.2A Mental Subtraction 137
3.2B Children’s Strategies for Subtraction with Large Numbers 139
3.2C An Alternative Algorithm 141
3.2D Children’s Mistakes in Subtraction 142
3.2E Rough and Best Estimates with Subtraction 143
3.2F Number Sense with Subtraction 143
SECTION 3.3 Understanding Multiplication 148
INVESTIGATIONS
3.3A A Pattern in the Multiplication Table 153
3.3B Mental Multiplication 154
3.3C An Alternative Algorithm 159
3.3D Why Does the Trick for Multiplying by 11 Work? 159
3.3E Multiplication in Base Five 160
3.3F Children’s Mistakes in Multiplication 162
3.3G Developing Estimation Strategies for Multiplication 162
3.3H Using Various Strategies in a Real-life Multiplication Situation 163
3.3I Number Sense with Multiplication 164
SECTION 3.4 Understanding Division 170
INVESTIGATIONS
3.4A Mental Division 174
3.4B Understanding Division Algorithms 175
3.4C The Scaffolding Algorithm 177
3.4D Children’s Mistakes in Division 178
3.4E Estimates with Division 180
3.4F Number Sense with Division 181
3.4G Applying Models to a Real-life Situation 182
3.4H Operation Sense 183
LOOKING BACK ON CHAPTER 3 189
CHAPTER 3 SUMMARY 190
CHAPTER 3 REVIEW EXERCISES 191
4 Number Theory 195
SECTION 4.1 Divisibility and Related Concepts 196
INVESTIGATIONS
4.1A Interesting Dates 196
4.1B Patterns in Odd and Even Numbers 198
4.1C Understanding Divisibility Relationships 200
4.1D Determining the Truth of an Inverse Statement 201
4.1E Understanding Why the Divisibility Rule for 3 Works 202
4.1F Divisibility by 4 and 8 204
4.1G Creating a Divisibility Rule for 12 207
SECTION 4.2 Prime and Composite Numbers 211
INVESTIGATIONS
4.2A The Sieve of Eratosthenes 212
4.2B Numbers with Personalities: Perfect and Other Numbers 217
SECTION 4.3 Greatest Common Factor and Least Common Multiple 220
INVESTIGATIONS
4.3A Cutting Squares Using Number Theory Concepts 220
4.3B Methods for Finding the GCF 222
4.3C Relationships Between the GCF and the LCM 227
4.3D Going Deeper into the GCF and the LCM 228
LOOKING BACK ON CHAPTER 4 232
CHAPTER 4 SUMMARY 232
CHAPTER 4 REVIEW EXERCISES 233
5 Extending the Number System 235
SECTION 5.1 Integers 236
INVESTIGATIONS
5.1A Subtraction with Integers 242
5.1B The Product of a Positive and a Negative Number 243
SECTION 5.2 Fractions and Rational Numbers 247
INVESTIGATIONS
5.2A Rational Number Contexts: What Does Mean? 248
5.2B Wholes and Units: Sharing Brownies 250
5.2C Unitizing 251
5.2D Fundraising and Thermometers 253
5.2E Partitioning with Number Line Models 254
5.2F Partitioning with Area Models 255
5.2G Partitioning with Set Models 256
5.2H Determining an Appropriate Representation 257
5.2I Sharing Cookies 260
5.2J Ordering Rational Numbers 262
5.2K Estimating with Fractions 262
SECTION 5.3 Understanding Operations with Fractions 268
INVESTIGATIONS
5.3A Using Fraction Models to Understand Addition of Fractions 268
5.3B Connecting Improper Fractions and Mixed Numbers 270
5.3C Mental Addition and Subtraction with Fractions 271
5.3D Estimating Sums and Differences with Fractions 273
5.3E Understanding Multiplication of Rational Numbers 274
5.3F Division of Rational Numbers 278
5.3G Estimating Products and Quotients 280
5.3H When Did He Run Out of Gas? 282
5.3I They’ve Lost Their Faculty! 283
SECTION 5.4 Beyond Integers and Fractions: Decimals, Exponents, and Real Numbers 288
INVESTIGATIONS
5.4A Base Ten Blocks and Decimals 290
5.4B When Two Decimals Are Equal 291
5.4C When Is the Zero Necessary and When Is It Optional? 292
5.4D Connecting Decimals and Fractions 293
5.4E Ordering Decimals 294
5.4F Rounding with Decimals 296
5.4G Decimals and Language 297
5.4H Decimal Sense: Grocery Store Estimates 300
5.4I Decimal Sense: How Much Will the Project Cost? 301
5.4J How Long Will She Run? 302
5.4K Exponents and Bacteria 302
5.4L Scientific Notation: How Far Is a Light-Year? 304
5.4M Square Roots 306
LOOKING BACK ON CHAPTER 5 312
CHAPTER 5 SUMMARY 313
CHAPTER 5 REVIEW EXERCISES 314
6 Proportional Reasoning 315
SECTION 6.1 Ratio and Proportion 316
INVESTIGATIONS
6.1A Unit Pricing—Is Bigger Always Cheaper? 319
6.1B How Many Trees Will Be Saved? 320
6.1C How Much Money Will the Trip Cost? 321
6.1D Reinterpreting Old Problems 322
6.1E Using Estimation with Ratios 322
6.1F Comparing Rates 324
6.1G Is the School on Target? 327
6.1H Finding Information from Maps 328
6.1I From Raw Numbers to Rates 329
6.1J How Much Does That Extra Light Cost? 330
SECTION 6.2 Percents 335
INVESTIGATIONS
6.2A Who’s the Better Free-Throw Shooter? 336
6.2B Understanding a Newspaper Article 337
6.2C Buying a House 340
6.2D Sale? 342
6.2E What Is a Fair Raise? 343
6.2F How Much Did the Bookstore Pay for the Textbook? 344
6.2G The Copying Machine 345
6.2H 132% Increase? 346
6.2I Saving for College 348
6.2J How Much Does That Credit Card Cost You? 350
LOOKING BACK ON CHAPTER 6 354
CHAPTER 6 SUMMARY 355
CHAPTER 6 REVIEW EXERCISES 355
7 Uncertainty: Data and Chance 357
SECTION 7.1 The Process of Collecting and Analyzing Data 359
INVESTIGATIONS
7.1A What Is Your Favorite Sport? 360
7.1B How Many Siblings Do You Have? 363
7.1C Going Beyond a Computational Sense of Average 368
7.1D How Many Peanuts Can You Hold in One Hand? 369
7.1E How Long Does It Take Students to Finish the Final Exam? 373
7.1F Videocassette Recorders 379
7.1G Fatal Crashes 382
7.1H Hitting the Books 385
SECTION 7.2 Going Beyond the Basics 396
INVESTIGATIONS
7.2A How Many More Peanuts Can Adults Hold
Than Children? 396
7.2B Scores on a Test 399
7.2C Which Battery Do You Buy? 400
7.2D Understanding Standard Deviation 403
7.2E Analyzing Standardized Test Scores 406
7.2F How Long Should the Tire Be Guaranteed? 407
7.2G Comparing Students in Three Countries 412
7.2H Grade Point Average 415
7.2I What Does Amy Need to Bring Her GPA Up to 2.5? 416
SECTION 7.3 Concepts Related to Chance 424
INVESTIGATIONS
7.3A Probability of Having 2 Boys and 2 Girls 427
7.3B Probability of Having 3 Boys and 2 Girls 430
7.3C Probability of Having at Least 1 Girl 431
7.3D 50-50 Chance of Passing 432
7.3E What Is the Probability of Rolling a 7? 433
7.3F What Is the Probability of Rolling a 13 with 3 Dice? 435
7.3G “The Lady or the Tiger” 436
7.3H Gumballs 438
7.3I Is This a Fair Game? 440
7.3J What About This Game? 440
7.3K Insurance Rates 442
SECTION 7.4 Counting and Chance 447
INVESTIGATIONS
7.4A How Many Ways to Take the Picture? 447
7.4B How Many Different Election Outcomes? 449
7.4C How Many Outcomes This Time? 451
7.4D Pick a Card, Any Card! 453
7.4E So You Think You’re Going to Win the Lottery? 454
LOOKING BACK ON CHAPTER 7 456
CHAPTER 7 SUMMARY 457
CHAPTER 7 REVIEW EXERCISES 458
8 Geometry as Shape 463
SECTION 8.1 Basic Ideas and Building Blocks 463
INVESTIGATIONS
8.1A Playing Tetris 465
8.1B Different Objects and Their Function 466
8.1C Point, Line, and Plane 472
8.1D Measuring Angles 478
SECTION 8.2 Two-Dimensional Figures 484
INVESTIGATIONS
8.2A Recreating Shapes from Memory 485
8.2B All the Attributes 487
8.2C Classifying Figures 487
8.2D Why Triangles Are So Important 491
8.2E Classifying Triangles 492
8.2F Triangles and Venn Diagrams 494
8.2G Congruence with Triangles 498
8.2H Quadrilaterals and Attributes 500
8.2I Challenges 501
8.2J Relationships Among Quadrilaterals 502
8.2K Sum of the Interior Angles of a Polygon 506
8.2L What Are My Coordinates? 509
8.2M Understanding the Distance Formula 510
8.2N The Opposite Sides of a Parallelogram Are Congruent 510
8.2O Midpoints of Any Quadrilateral 512
SECTION 8.3 Three-Dimensional Figures 518
INVESTIGATIONS
8.3A What Do You See? 520
8.3B Connecting Polygons to Polyhedra 521
8.3C Features of Three-Dimensional Objects 523
8.3D Prisms and Pyramids 526
8.3E Different Views of a Building 528
8.3F Isometric Drawings 529
8.3G Cross Sections 530
8.3H Nets 531
LOOKING BACK ON CHAPTER 8 537
CHAPTER 8 SUMMARY 538
CHAPTER 8 REVIEW EXERCISES 539
9 Geometry as Transforming Shapes 543
SECTION 9.1 Congruence Transformations 546
INVESTIGATIONS
9.1A Understanding Translations 547
9.1B Understanding Reflections 549
9.1C Understanding Rotations 550
9.1D Understanding Translations, Reflections, and Rotations 552
9.1E Connecting Transformations 555
9.1F Transformations and Art 557
SECTION 9.2 Symmetry and Tessellations 563
INVESTIGATIONS
9.2A Reflection and Rotation Symmetry in Triangles 566
9.2B Reflection and Rotation Symmetry in Quadrilaterals 567
9.2C Reflection and Rotation Symmetry in Other Figures 568
9.2D Letters of the Alphabet and Symmetry 568
9.2E Patterns 569
9.2F Symmetries of Strip Patterns 572
9.2G Analyzing Brick Patterns 575
9.2H Which Triangles Tessellate? 580
9.2I Which Regular Polygons Tessellate? 581
9.2J Tessellating Trapezoids 583
9.2K More Tessellating Polygons 585
9.2L Generating Pictures Through Transformations 587
SECTION 9.3 Similarity 595
INVESTIGATIONS
9.3A Understanding Similarity 596
9.3B Similarity Using an Artistic Perspective 598
9.3C Using Coordinate Geometry to Understand
Similarity 599
LOOKING BACK ON CHAPTER 9 601
CHAPTER 9 SUMMARY 602
CHAPTER 9 REVIEW EXERCISES 602
10 Geometry as Measurement 605
SECTION 10.1 Systems of Measurement 606
INVESTIGATIONS
10.1A Developing Metric Sense 611
10.1B Converting Among Units in the Metric System 614
SECTION 10.2 Perimeter and Area 619
INVESTIGATIONS
10.2A What Is the Length of the Arc? 620
10.2B Converting Units of Area 625
10.2C Using the Pythagorean Theorem 626
10.2D Understanding the Area Formula for Circles 627
10.2E A 16-Inch Pizza Versus an 8-Inch Pizza 628
10.2F How Big Is the Footprint? 628
10.2G Making a Fence with Maximum Area 630
SECTION 10.3 Surface Area and Volume 637
INVESTIGATIONS
10.3A Are Their Pictures Misleading? 646
10.3B Finding the Volume of a Hollow Box 647
10.3C Surface Area and Volume 648
LOOKING BACK ON CHAPTER 10 654
CHAPTER 10 SUMMARY 655
CHAPTER 10 REVIEW EXERCISES 655

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

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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