# Mathematics for Dyslexics and Dyscalculics: A Teaching Handbook, 4th Edition

# Mathematics for Dyslexics and Dyscalculics: A Teaching Handbook, 4th Edition

ISBN: 978-1-119-15998-8

Jan 2017, Wiley-Blackwell

360 pages

$43.99

## Description

A seminal handbook in the field for more than 20 years, this new and updated edition of *Mathematics for Dyslexics**and Dyscalculics* contains the latest research and best practices for helping learners with numerical and mathematical difficulties.

- Provides a complete overview of theory and research in the fields of dyslexia and dyscalculia, along with detailed yet pragmatic methods to apply in the classroom
- Contains enhanced coverage of place value and the role of the decimal point, why fractions can challenge a developed logic for arithmetic, and the complexity of time along with new material on addressing anxiety, fear, motivation, and resilience in the classroom; and links to new resources including standardized tests and recommended reading lists
- Written by two mathematics teachers with 50 years of teaching experience between them, much of it in specialist settings for students with specific learning difficulties
- Offers effective teaching strategies for learners of all ages in a structured but accessible format

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