Children's mathematics: making marks, making meaning
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Sage
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 243-252) and indexes |
| Physical Description: | XIX, 260 S. Ill. |
| ISBN: | 9781412922821 9781412922838 |
Staff View
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| 264 | 1 | |a London [u.a.] |b Sage |c 2006 | |
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Record in the Search Index
| _version_ | 1804137591058989056 |
|---|---|
| adam_text | Contents
About the Authors
ix
Acknowledgements
xi
Foreword by John Matthews
xiii
Foreword by Chris Athey
xv
Preface
xvii
1
Who takes notice of children s own written mathematics?
1
•
Children s mathematical graphics
2
•
International findings
3
•
Studies that relate to mathematical literacy
9
•
Enquiring into children s mathematics
11
2
Making marks, making meaning
13
•
Children making meaning with marks
13
•
Different literacies: mathematical literacy
14
•
Children represent their mathematical actions and understanding
on paper
14
•
Learning theories
20
•
Reading and using mathematical graphics
25
•
Socio-cultural contexts in Early Years settings
31
•
Teachers beliefs
32
•
Creativity in mathematics
34
•
Summary
34
3
Mathematical
schemas
36
•
What is a schema?
36
•
Schemas
and mathematics
40
•
Schemas
and mark-making
41
•
Observing
schemas
in a school setting
44
•
Mapping patterns of schema exploration
51
vi
Children s Mathematics
4
Early writing, early mathematics
56
•
The significance of emergent writing
57
•
Young children explore symbols
58
•
Early writing and early mathematical marks
63
•
Early (emergent) literacy is often misunderstood
66
•
Conclusion
68
5
Bridging the gap between home and school mathematics
69
•
Disconnections
69
•
Understanding symbols
72
•
Mathematics as a foreign language
77
•
Becoming bi-numerate
79
•
Teachers difficulties
82
•
Conclusion
83
6
Making sense of children s mathematical graphics
84
•
The evolution of children s early marks
84
•
Categories of children s mathematical graphics
86
•
Common forms of graphical marks
87
•
Early development of mathematical meaning
91
•
Early explorations with marks
93
•
The beginning is everything
95
•
Early written numerals
96
•
Numerals as labels
99
•
Representations of quantities and counting
100
•
The development of early written number, quantities and counting
105
7
Understanding children s developing calculations
106
•
Practical mathematics
106
•
The fifth dimension: written calculations
108
•
Representations of early operations
108
•
Counting continuously
109
•
Narrative actions
112
•
Supporting children s own mathematical marks
114
•
Separating sets
117
•
Exploring symbols
118
•
Standard symbolic calculations with small numbers
123
•
Calculations with larger numbers supported by jottings
126
•
The development of children s mathematical graphics:
becoming bi-numerate
130
•
Conclusion
132
Contents
vii
8 Environments
that support children s mathematical graphics
134
•
Rich mathematical environments for learning
134
•
The balance between adult-led and child-initiated learning
136
•
Role-play and mark-making
139
•
The physical environment
140
•
Practical steps
145
•
Graphics areas
149
•
Conclusion
161
9
Case studies from early childhood settings
162
•
The birthday cards
162
•
A number line
164
•
No entry
166
•
Carl s garage
167
•
Children s Centres: The Cambridge Learning Network project
169
•
The spontaneous dice game
172
•
Young children think division
174
•
A zoo visit
177
•
Mathematics and literacy in role-play: the library van
178
•
Aaron and the train
181
•
Multiplying larger numbers
185
•
Nectarines for a picnic
187
•
Conclusion
190
10
Developing children s written methods
192
•
The assessment of children s mathematical representations on paper
192
•
The problem with worksheets
194
•
Assessing samples of children s own mathematics
197
•
Examples of assessment of children s mathematics
199
•
The pedagogy of children s mathematical graphics
204
•
Modelling mathematics
205
11
Involving parents and families
216
•
Children s first and continuing educators
216
•
The home as a rich learning environment
217
•
What mathematics do young children do at home?
218
•
What mathematics do parents notice at home?
221
•
Parents observe a wealth of mathematics
225
•
Helping parents recognise children s mathematical marks
225
•
Parents questions about children s mathematical graphics
226
•
Conclusion
227
viii
Children s Mathematics
12
Children, teachers and possibilities
229
•
Inclusion
229
•
Children s questions
230
•
Teachers questions
231
•
It s all very well
-
but what about test scores?
234
Reflections
236
Appendix: our research
238
Glossary
240
References
243
Author Index
253
Subject Index
256
|
| adam_txt |
Contents
About the Authors
ix
Acknowledgements
xi
Foreword by John Matthews
xiii
Foreword by Chris Athey
xv
Preface
xvii
1
Who takes notice of children's own 'written' mathematics?
1
•
Children's mathematical graphics
2
•
International findings
3
•
Studies that relate to mathematical literacy
9
•
Enquiring into children's mathematics
11
2
Making marks, making meaning
13
•
Children making meaning with marks
13
•
Different literacies: mathematical literacy
14
•
Children represent their mathematical actions and understanding
on paper
14
•
Learning theories
20
•
Reading and using mathematical graphics
25
•
Socio-cultural contexts in Early Years settings
31
•
Teachers'beliefs
32
•
Creativity in mathematics
34
•
Summary
34
3
Mathematical
schemas
36
•
What is a schema?
36
•
Schemas
and mathematics
40
•
Schemas
and mark-making
41
•
Observing
schemas
in a school setting
44
•
Mapping patterns of schema exploration
51
vi
Children's Mathematics
4
Early writing, early mathematics
56
•
The significance of emergent writing
57
•
Young children explore symbols
58
•
Early writing and early mathematical marks
63
•
Early (emergent) literacy is often misunderstood
66
•
Conclusion
68
5
Bridging the gap between home and school mathematics
69
•
Disconnections
69
•
Understanding symbols
72
•
Mathematics as a foreign language
77
•
Becoming bi-numerate
79
•
Teachers' difficulties
82
•
Conclusion
83
6
Making sense of children's mathematical graphics
84
•
The evolution of children's early marks
84
•
Categories of children's mathematical graphics
86
•
Common forms of graphical marks
87
•
Early development of mathematical meaning
91
•
Early explorations with marks
93
•
'The beginning is everything'
95
•
Early written numerals
96
•
Numerals as labels
99
•
Representations of quantities and counting
100
•
The development of early written number, quantities and counting
105
7
Understanding children's developing calculations
106
•
Practical mathematics
106
•
The fifth dimension: written calculations
108
•
Representations of early operations
108
•
Counting continuously
109
•
Narrative actions
112
•
Supporting children's own mathematical marks
114
•
Separating sets
117
•
Exploring symbols
118
•
Standard symbolic calculations with small numbers
123
•
Calculations with larger numbers supported by jottings
126
•
The development of children's mathematical graphics:
becoming bi-numerate
130
•
Conclusion
132
Contents
vii
8 Environments
that support children's mathematical graphics
134
•
Rich mathematical environments for learning
134
•
The balance between adult-led and child-initiated learning
136
•
Role-play and mark-making
139
•
The physical environment
140
•
Practical steps
145
•
Graphics areas
149
•
Conclusion
161
9
Case studies from early childhood settings
162
•
The birthday cards
162
•
A number line
164
•
'No entry'
166
•
Carl's garage
167
•
Children's Centres: The Cambridge Learning Network project
169
•
The spontaneous dice game
172
•
Young children think division
174
•
A zoo visit
177
•
Mathematics and literacy in role-play: the library van
178
•
Aaron and the train
181
•
Multiplying larger numbers
185
•
Nectarines for a picnic
187
•
Conclusion
190
10
Developing children's written methods
192
•
The assessment of children's mathematical representations on paper
192
•
The problem with worksheets
194
•
Assessing samples of children's own mathematics
197
•
Examples of assessment of children's mathematics
199
•
The pedagogy of children's mathematical graphics
204
•
Modelling mathematics
205
11
Involving parents and families
216
•
Children's first and continuing educators
216
•
The home as a rich learning environment
217
•
What mathematics do young children do at home?
218
•
What mathematics do parents notice at home?
221
•
Parents observe a wealth of mathematics
225
•
Helping parents recognise children's mathematical marks
225
•
Parents' questions about children's mathematical graphics
226
•
Conclusion
227
viii
Children's Mathematics
12
Children, teachers and possibilities
229
•
Inclusion
229
•
Children's questions
230
•
Teachers' questions
231
•
It's all very well
-
but what about test scores?
234
Reflections
236
Appendix: our research
238
Glossary
240
References
243
Author Index
253
Subject Index
256 |
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| index_date | 2024-07-02T20:37:37Z |
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| spelling | Carruthers, Elizabeth Verfasser aut Children's mathematics making marks, making meaning Elizabeth Carruthers and Maulfry Worthington 2. ed. London [u.a.] Sage 2006 XIX, 260 S. Ill. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 243-252) and indexes Basisonderwijs gtt Didactiek gtt Kleuteronderwijs gtt Rekenen gtt Mathematik Mathematics Study and teaching (Elementary) Great Britain Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Großbritannien Mathematikunterricht (DE-588)4037949-8 s DE-604 Worthington, Maulfry Sonstige oth http://www.loc.gov/catdir/enhancements/fy0709/2006923703-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0709/2006923703-t.html Table of contents only Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016460069&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carruthers, Elizabeth Children's mathematics making marks, making meaning Basisonderwijs gtt Didactiek gtt Kleuteronderwijs gtt Rekenen gtt Mathematik Mathematics Study and teaching (Elementary) Great Britain Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4037949-8 |
| title | Children's mathematics making marks, making meaning |
| title_auth | Children's mathematics making marks, making meaning |
| title_exact_search | Children's mathematics making marks, making meaning |
| title_exact_search_txtP | Children's mathematics making marks, making meaning |
| title_full | Children's mathematics making marks, making meaning Elizabeth Carruthers and Maulfry Worthington |
| title_fullStr | Children's mathematics making marks, making meaning Elizabeth Carruthers and Maulfry Worthington |
| title_full_unstemmed | Children's mathematics making marks, making meaning Elizabeth Carruthers and Maulfry Worthington |
| title_short | Children's mathematics |
| title_sort | children s mathematics making marks making meaning |
| title_sub | making marks, making meaning |
| topic | Basisonderwijs gtt Didactiek gtt Kleuteronderwijs gtt Rekenen gtt Mathematik Mathematics Study and teaching (Elementary) Great Britain Mathematikunterricht (DE-588)4037949-8 gnd |
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