Mathematics for Dyslexics and Dyscalculics

Foreword xi

1 Dyscalculia, Dyslexia and Mathematics 1

Introduction 1

Definitions of Dyslexia 3

The Evolution of Definitions of (Developmental) Dyscalculia 5

The Nature of Mathematics and the Ways it is Taught 19

2 Factors that may Contribute to Learning Difficulties in Mathematics 23

Potential Areas of Difficulty in Learning Mathematics 24

General Principles of Intervention 44

Summary 46

3 Cognitive (Thinking) Style in Mathematics 48

Introduction 48

Qualitative and Quantitative Style 49

Cognitive (Thinking) Style in the Classroom 51

Examples 54

Summary 61

4 Testing and Diagnosis 62

A Diagnostic Test Protocol 64

Structure of the Diagnostic Protocol 65

Attitude and Anxiety 73

Thinking Style or Cognitive Style 74

Tests for Dyscalculia 74

Summary of the Test Protocol 74

5 Concept of Number 76

Introduction 76

Early Recognition of Numbers and Their Values 78

The Language of Mathematics (see also Chapter 2) 79

Early Number Work 79

Visual Sense of Number 82

Visual Clues to Number Concept 83

Number Bonds/Combinations 84

Place Value 86

Number Bonds/Combinations for Ten 93

Numbers Near Ten, Hundred or Thousand 94

Summary 95

6 Addition and Subtraction: Basic Facts/Number Combinations 96

Introduction 96

Strategies for Learning/Remembering the Addition and Subtraction Facts 99

Overview 107

Subtraction Facts 108

Extension 109

7 The Times Tables Facts/Number Combinations 110

Introduction 110

Rote Learning Strategies 110

Learning by Understanding 113

The Commutative Property 115

Learning the Table Square 117

Summary 135

8 Computational Procedures for Addition and Subtraction 136

Estimation 138

Addition 138

Teaching Subtraction as a Separate Exercise 147

9 Multiplication 152

Introduction 152

Multiplying by Ten and Powers of Ten 153

Multiplication 157

Estimation 163

Extension 163

10 Division: Whole Numbers 165

Introduction 165

Introduction to Division 166

Estimating 172

Division by Powers of Ten 173

Division by Multiples of Powers of Ten 174

Conclusion 174

11 Fractions, Decimals and Percentages: An Introduction 175

Introduction 175

Fractions 176

Decimals 187

Percentages 195

Overview 203

12 Operating with Fractions 204

Introduction 204

Making Segment Sizes the Same 205

Comparing Fractions 207

Combining Fractions 210

Adding Fractions 212

Subtracting Fractions 216

Combined Additions and Subtractions 219

Multiplying by Fractions 221

Multiplying Mixed Fractions 224

Dividing with Fractions 227

13 Decimals 232

Introduction 232

Addition and Subtraction 232

Multiplication and Division by Powers of Ten 235

Division of Decimals 242

Summary 249

14 Percentages 250

Introduction 250

An Image of Percentage 250

Summary 256

15 Time 257

What are the Potential Problems with Time? 258

Reading the Time 260

Time Problems 264

Summary 268

16 Teaching the Full Curriculum 269

Introduction 269

Some General Principles 270

Teaching the Other Parts of the Curriculum 277

Combining the Parts of the Curriculum 282

Summary 286

17 Attacking and Checking Questions 287

Practice Examples 287

Preliminary Checks 288

Attacking Questions 290

Methods of Attacking Questions 291

Checking 298

18 Important Elements of a Teaching Programme 303

Introduction 303

Consider the Pupils' Needs 303

The Structure of the Course 304

Classroom Management: Making the Lessons Suit the Pupils 308

Evolving Expectations and Emphases 309

Internal Assessment 313

Summary 315

Appendices

Appendix 1: Books, Journals, Tests and Games 316

Appendix 2: Teaching Materials 321

References 324

Index 337