| Contents | 6 |
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| Contributing Authors | 8 |
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| Chapter 1 Introduction | 13 |
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| 1. INTRODUCTION | 13 |
| 2. MATHEMATICS | 14 |
| 3. KNOWLEDGE | 15 |
| 4. SITUATED PERSPECTIVES: POWER AND LIMITATION | 16 |
| 5. WHY SITUATED PERSPECTIVES? | 18 |
| 6. THIS BOOK | 20 |
| REFERENCES | 23 |
| Chapter 2 School Mathematics As A Developmental Activity1 | 25 |
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| 1. INTRODUCTION | 25 |
| 2. IMPLICIT EPISTEMOLOGY: WHAT DOES IT MEAN TO BE DOING MATHEMATICS ? | 27 |
| 3. LEARNING CLOSE TO PRACTICAL CONTEXTS AND SITUATIONS | 30 |
| 4. LEARNING IN THE SCHOOL CONTEXT | 32 |
| 4.1 Utilitarian vs. epistemic attitude to the world and to language | 33 |
| 4.2 Unreflected, or not consciously developed vs. planned and conscious procedure | 35 |
| 4.3 Learning as a relation of operations, tasks and the object of cognitive activity | 37 |
| 5. PERFORMANCE IN THE SITUATION VS. DEVELOPMENT | 39 |
| REFERENCES2 | 41 |
| Chapter 3 Participating In What? Using Situated Cognition Theory To Illuminate Differences In Classroom Practices | 43 |
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| 1. INTRODUCTION | 43 |
| 2. OUR POSITION ON SITUATED COGNITION | 47 |
| 3. CASE STUDIES | 48 |
| 3.1 Case 1: Norma | 49 |
| 3.2 Case 2: Roisin | 51 |
| 3.3 Case 3: Susan | 52 |
| 4. ANALYSIS OF CLASSROOM SEQUENCES AS LOCAL COMMUNITIES OF PRACTICE | 55 |
| 4.1 How do students seem to be acting in relation to mathematics? What kind of participants do they seem to be within the lesson? | 56 |
| 4.2 What developing mathematical competence is publicly recognised, and how? | 57 |
| 4.3 Do learners appear to be working purposefully together on mathematics? With what purpose? | 57 |
| 4.4 What are the shared values and ways of behaving in relation to mathematics: language, habits, tool- use? | 58 |
| 4.5 Does active participation of students and teacher in mathematics constitute the lesson? | 59 |
| 4.6 Do students and teacher appear to be engaged in the same mathematical activity? What is the activity? | 60 |
| 5. ANALYSIS OF THE AFFORDANCES, CONSTRAINTS AND ATTUNEMENTS OF MATHEMATICAL ACTIVITY IN EACH SITUATION | 61 |
| 6. INFLUENCE OF STUDENTS CONTRIBUTIONS | 64 |
| 6.1 Susan s class on Equations | 65 |
| 7. CONCLUSION | 67 |
| ACKNOWLEDGEMENTS | 68 |
| REFERENCES | 68 |
| Chapter 4 Social Identities As Learners And Teachers Of Mathematics | 70 |
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| The situated nature of roles and relations in mathematics classrooms. | 70 |
| 1. INTRODUCTION | 70 |
| 2. PUPILS SOCIAL IDENTITIES AS LEARNERS OF MATHEMATICS | 71 |
| 3. LEARNERS SOCIAL IDENTITIES | 72 |
| 4. FROM IDENTITIES TO RELATIONS | 75 |
| 5. CHANGING CLASSROOM RELATIONS | 77 |
| 6. CLASSROOM RELATIONS | 79 |
| 6.1 Parallel calculation chains | 81 |
| 6.2 Solver and recorder | 82 |
| 6.3 Clue problems | 83 |
| 7. DISCUSSION | 86 |
| 8. CONCLUSION | 87 |
| REFERENCES | 88 |
| Chapter 5 Looking For Learning In Practice: How Can This Inform Teaching | 90 |
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| 1. INTRODUCTION | 90 |
| 2. IDENTITY-CHANGING COMMUNITIES OF PRACTICE | 94 |
| 3. A TEACHING MOMENT | 96 |
| 3.1 Methodology: the teaching moment | 97 |
| 3.2 Three stories including the teaching moment | 98 |
| 4. A LEARNING EXPERIENCE | 105 |
| 4.1 Methodology - the biology story | 106 |
| 5. DISCUSSION: WHAT DOES THIS HAVE TO SAY ABOUT TEACHING AND LEARNING? | 108 |
| 5.1 The learning of school students | 108 |
| 5.2 The conceptualisation of teaching | 110 |
| ACKNOWLEDGEMENTS | 112 |
| REFERENCES | 112 |
| Chapter 6 Are Mathematical Abstractions Situated? | 114 |
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| 1. INTRODUCTION | 114 |
| 1.1 Empiricist views on abstraction | 115 |
| 1.2 Situation and context | 117 |
| 1.3 Contextual views of abstraction | 119 |
| 2. THE STUDY, THE TASKS AND PROTOCOL DATA | 122 |
| 2.1 Protocol data | 124 |
| 3. ABSTRACTION: MEDIATION, PEOPLE AND TASKS | 128 |
| 3.1 Mediation | 128 |
| 3.2 People | 131 |
| 3.3 Tasks | 134 |
| 4. CONCLUSIONS | 136 |
| REFERENCES | 136 |
| Chapter 7 We Do It A Different Way At My School | 139 |
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| Mathematics homework as a site for tension and conflict | 139 |
| 1. INTRODUCTION | 139 |
| 2. RYAN, HIS MOTHER AND HIS HOMEWORK | 143 |
| 2.1 The practice of homework | 150 |
| 2.2 Ryan s school and home identities | 152 |
| 2.3 Ryan s mother and mathematics | 153 |
| 2.4 Tensions and conflicts during the homework event | 154 |
| 3. DISCUSSIO
|