Children's mathematics: making marks, making meaning
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Sage
2006
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 243-252) and indexes |
| Beschreibung: | XIX, 260 S. Ill. |
| ISBN: | 9781412922821 9781412922838 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV023275156 | ||
| 003 | DE-604 | ||
| 005 | 20080714 | ||
| 007 | t | ||
| 008 | 080424s2006 xxka||| |||| 00||| eng d | ||
| 010 | |a 2006923703 | ||
| 015 | |a GBA636951 |2 dnb | ||
| 020 | |a 9781412922821 |c hbk. |9 978-1-4129-2282-1 | ||
| 020 | |a 9781412922838 |c pbk. |9 978-1-4129-2283-8 | ||
| 035 | |a (OCoLC)65469414 | ||
| 035 | |a (DE-599)BVBBV023275156 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxk |c GB | ||
| 049 | |a DE-355 | ||
| 050 | 0 | |a QA135.6 | |
| 082 | 0 | |a 372.7/044 | |
| 084 | |a DP 4400 |0 (DE-625)19844:12010 |2 rvk | ||
| 100 | 1 | |a Carruthers, Elizabeth |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Children's mathematics |b making marks, making meaning |c Elizabeth Carruthers and Maulfry Worthington |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London [u.a.] |b Sage |c 2006 | |
| 300 | |a XIX, 260 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 243-252) and indexes | ||
| 650 | 7 | |a Basisonderwijs |2 gtt | |
| 650 | 7 | |a Didactiek |2 gtt | |
| 650 | 7 | |a Kleuteronderwijs |2 gtt | |
| 650 | 7 | |a Rekenen |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x Study and teaching (Elementary) |z Great Britain | |
| 650 | 0 | 7 | |a Mathematikunterricht |0 (DE-588)4037949-8 |2 gnd |9 rswk-swf |
| 651 | 4 | |a Großbritannien | |
| 689 | 0 | 0 | |a Mathematikunterricht |0 (DE-588)4037949-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Worthington, Maulfry |e Sonstige |4 oth | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0709/2006923703-d.html |3 Publisher description | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0709/2006923703-t.html |3 Table of contents only | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016460069 | ||
Datensatz im Suchindex
| _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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Carruthers, Elizabeth |
| author_facet | Carruthers, Elizabeth |
| author_role | aut |
| author_sort | Carruthers, Elizabeth |
| author_variant | e c ec |
| building | Verbundindex |
| bvnumber | BV023275156 |
| callnumber-first | Q - Science |
| callnumber-label | QA135 |
| callnumber-raw | QA135.6 |
| callnumber-search | QA135.6 |
| callnumber-sort | QA 3135.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | DP 4400 |
| ctrlnum | (OCoLC)65469414 (DE-599)BVBBV023275156 |
| dewey-full | 372.7/044 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 372 - Primary education (Elementary education) |
| dewey-raw | 372.7/044 |
| dewey-search | 372.7/044 |
| dewey-sort | 3372.7 244 |
| dewey-tens | 370 - Education |
| discipline | Pädagogik |
| discipline_str_mv | Pädagogik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02031nam a2200529zc 4500</leader><controlfield tag="001">BV023275156</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080714 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080424s2006 xxka||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2006923703</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">GBA636951</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781412922821</subfield><subfield code="c">hbk.</subfield><subfield code="9">978-1-4129-2282-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781412922838</subfield><subfield code="c">pbk.</subfield><subfield code="9">978-1-4129-2283-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)65469414</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023275156</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxk</subfield><subfield code="c">GB</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA135.6</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">372.7/044</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DP 4400</subfield><subfield code="0">(DE-625)19844:12010</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Carruthers, Elizabeth</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Children's mathematics</subfield><subfield code="b">making marks, making meaning</subfield><subfield code="c">Elizabeth Carruthers and Maulfry Worthington</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London [u.a.]</subfield><subfield code="b">Sage</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 260 S.</subfield><subfield code="b">Ill.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 243-252) and indexes</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Basisonderwijs</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Didactiek</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Kleuteronderwijs</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Rekenen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield><subfield code="x">Study and teaching (Elementary)</subfield><subfield code="z">Great Britain</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematikunterricht</subfield><subfield code="0">(DE-588)4037949-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="651" ind1=" " ind2="4"><subfield code="a">Großbritannien</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematikunterricht</subfield><subfield code="0">(DE-588)4037949-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Worthington, Maulfry</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0709/2006923703-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0709/2006923703-t.html</subfield><subfield code="3">Table of contents only</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016460069</subfield></datafield></record></collection> |
| geographic | Großbritannien |
| geographic_facet | Großbritannien |
| id | DE-604.BV023275156 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:37:37Z |
| indexdate | 2024-07-09T21:14:43Z |
| institution | BVB |
| isbn | 9781412922821 9781412922838 |
| language | English |
| lccn | 2006923703 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016460069 |
| oclc_num | 65469414 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XIX, 260 S. Ill. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Sage |
| record_format | marc |
| 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 |
| topic_facet | Basisonderwijs Didactiek Kleuteronderwijs Rekenen Mathematik Mathematics Study and teaching (Elementary) Great Britain Mathematikunterricht Großbritannien |
| url | http://www.loc.gov/catdir/enhancements/fy0709/2006923703-d.html http://www.loc.gov/catdir/enhancements/fy0709/2006923703-t.html 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 |
| work_keys_str_mv | AT carrutherselizabeth childrensmathematicsmakingmarksmakingmeaning AT worthingtonmaulfry childrensmathematicsmakingmarksmakingmeaning |