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Content: 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