Windows on mathematical meanings: learning cultures and computers
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Mathematics education library
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 275 S. graph. Darst. |
| ISBN: | 0792340736 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Foreword viii
Chapter 1. Visions of the mathematical 1
1. Reshaping mathematics, revisioning learning 2
2. Computers... 5
3. ...and cultures 7
4. Windows on methodologies 9
Chapter 2. Laying the Foundations 12
1. Introduction 12
2. Meanings in mathematics education: a brief survey 14
2.1. Meanings from mathematical objects 14
2.2. Meanings from problem solving 15
2.3. Meanings constructed by the individual learner 17
2.4. From enactive to reflective mathematical knowledge:
spirals of abstraction? 19
3. Vignette: The N-task 22
4. The influence of setting on mathematical behaviour 30
4.1. Problematising children s performance 31
4.2. Into the cul-de-sac: situated mathematical expression 33
5. Street mathematics 36
5.1. Meaning mathematically in the street and in school 36
5.2. The role of representations 38
6. A way out of the cul-de-sac? 41
6.1. Language and tools 42
6.2. Abstract versus concrete? 43
6.3. Returning to the vignette 47
7. Rethinking abstraction 48
Chapter 3. Tools and technologies 52
1. Computers and educational cultures 52
2. A preliminary case for programming 54
2.1. Computers and conviviality 57
3. The development of a programming culture 59
3.1. The development of a literature 59
3.2. The development of a research community 60
3.3. Summing up the case for programming 61
4. Microworlds: the genesis of the idea 63
v
vi CONTENTS
5. Opening windows on microworlds 65
5.1. The issue of transfer 65
6. Objects and structures 67
6.1. The question of pedagogy 69
Chapter 4. RatioWorld 74
1. What do we - and learners - know? 74
2. Building an alternative methodology 77
2.1. The written tasks 78
2.2. The computational objects 80
3. The data set 82
3.1. The students 83
3.2. Data collection 83
4. The microworld activities and student responses 84
4.1. Meanings of similarity 84
4.2. Broadening the notion of multiplication 85
4.3. The imperative of formalisation 87
4.4. Towards a consistent approach 90
5. Quantitative windows on learning 92
5.1. Gross trends 92
5.2. A step towards the individual 95
5.3. The baseline group 97
5.4. Individual student response profiles 97
6. Reflections 100
Chapter 5. Webs and situated abstractions 105
1. Reviewing the foundations 105
2. Webs of meaning 107
2.1. Flagging 110
2.2. Adjusting 112
2.3. Sketching 115
2.4. Patterning 117
3. Domains of situated abstraction 119
3.1. Situated abstraction 122
3.2. Webs and abstractions 125
3.3. Connecting drawing to geometry 126
3.4. Towards a theory of mathematical meaning 129
Chapter 6. Beyond the individual learner 134
1. Extending the web 134
1.1. Some theoretical background 135
2. Collaborative activity in mathematics 137
2.1. Knowledge domain, task and medium 138
2.2. The role of language in mathematical learning 141
CONTENTS vii
3. A study of groupwork 143
3.1. The tasks 144
3.2. A complementarity between quantitative
and qualitative data 145
3.3. Gross trends 146
3.4. What was happening inside the groups? 147
3.5. Individual learning 148
3.6. Summing up the study 150
4. Opening new windows 152
Chapter 7. Cultures and change 156
1. Innovation and inertia 156
2. Visions of Logo 159
2.1. Snapshots of Logo 159
2.2. Logo in the U.K. 161
3. Myths and methodologies: a case study of Logo research 166
3.1. Pea and Kurland s approach 167
3.2. Methodologies and the Papert-Pea debate 173
3.3. Transformations of meaning: what is
Logo pedagogy? 175
3.4. The creation of conventional wisdom 177
4. The struggle for meanings 179
Chapter 8. A window on teachers 184
1. Investigating teachers attitudes and interactions 186
1.1. Mary - the frustrated idealist 188
1.2. Rowena - the confident investigator 190
1.3. Denis - the controlling pragmatist 190
1.4. Fiona - the anxious traditionalist 192
1.5. Bob - the curriculum deliverer 193
2. Teachers making meanings 195
2.1. Reshaping school mathematics 196
2.2. Reshaping the microworlds innovation 197
2.3. Reshaping pedagogy 198
3. Connections and cultures 199
3.1. The social construction of change 200
Chapter 9. A window on schools 203
1. The background to the case study 204
2. The teachers voices 206
2.1. The head teacher 206
2.2. Two teachers: Colin and John 208
2.3. The advisory teacher 211
3. The students voices 214
viii CONTENTS
3.1. Meanings of programming 215
3.2. Meanings of LogoMathematics 216
3.3. Teaching and the trajectory of Logo learning 218
3.4. Classroom culture 219
4. Meanings in conflict 222
Chapter 10. Re-visioning mathematical meanings 226
1. Reviewing the scene 226
2. Epistemological revisions: six examples 229
2.1. Small changes in tools afford large changes
in meanings 230
2.2. Programming to reconnect with mathematics 231
2.3. New geometry with new tools 232
2.4. Revisioning number patterns 236
2.5. Convivial mathematics 240
2.6. Connecting mathematics with practice 245
3. Reconnecting mathematics and culture 251
3.1. The invisibility of mathematical meanings 253
3.2. Re-visioning learning cultures 255
References 259
Index 272
|
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| id | DE-604.BV011028246 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:50Z |
| institution | BVB |
| isbn | 0792340736 |
| language | English |
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| physical | XI, 275 S. graph. Darst. |
| publishDate | 1996 |
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| publisher | Kluwer |
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| series | Mathematics education library |
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| spelling | Noss, Richard Verfasser (DE-588)128334738 aut Windows on mathematical meanings learning cultures and computers by Richard Noss & Celia Hoyles Dordrecht [u.a.] Kluwer 1996 XI, 275 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics education library 17 Mathématiques - Étude et enseignement Wiskunde gtt Mathematik Mathematics Study and teaching Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 s DE-604 Hoyles, Celia Verfasser aut Mathematics education library 17 (DE-604)BV000020735 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007384071&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noss, Richard Hoyles, Celia Windows on mathematical meanings learning cultures and computers Mathematics education library Mathématiques - Étude et enseignement Wiskunde gtt Mathematik Mathematics Study and teaching Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4037949-8 |
| title | Windows on mathematical meanings learning cultures and computers |
| title_auth | Windows on mathematical meanings learning cultures and computers |
| title_exact_search | Windows on mathematical meanings learning cultures and computers |
| title_full | Windows on mathematical meanings learning cultures and computers by Richard Noss & Celia Hoyles |
| title_fullStr | Windows on mathematical meanings learning cultures and computers by Richard Noss & Celia Hoyles |
| title_full_unstemmed | Windows on mathematical meanings learning cultures and computers by Richard Noss & Celia Hoyles |
| title_short | Windows on mathematical meanings |
| title_sort | windows on mathematical meanings learning cultures and computers |
| title_sub | learning cultures and computers |
| topic | Mathématiques - Étude et enseignement Wiskunde gtt Mathematik Mathematics Study and teaching Mathematikunterricht (DE-588)4037949-8 gnd |
| topic_facet | Mathématiques - Étude et enseignement Wiskunde Mathematik Mathematics Study and teaching Mathematikunterricht |
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