viii Children’s Mathematics
- 44 EEaarrllyy wwrriittiinngg,, eeaarrllyy mmaatthheemmaattiiccss
- • The significance of emergent writing
- • Young children explore symbols
- • Early writing and early mathematical marks
- • Early (emergent) literacy is often misunderstood
- • Conclusion
- 55 BBrriiddggiinngg tthhee ggaapp bbeettwweeeenn hhoommee aanndd sscchhooooll mmaatthheemmaattiiccss
- • Disconnections
- • Understanding symbols
- • Mathematics as a foreign language
- • Becoming bi-numerate
- • Teachers’ difficulties
- • Conclusion
- 66 MMaakkiinngg sseennssee ooff cchhiillddrreenn’’ss mmaatthheemmaattiiccaall ggrraapphhiiccss
- • The evolution of children’s early marks
- • Categories of children’s mathematical graphics
- • Common forms of graphical marks
- • Early development of mathematical meaning
- • Early explorations with marks
- • ‘The beginning is everything’
- • Early written numerals
- • Numerals as labels
- • Representations of quantities and counting
- • The development of early written number, quantities and counting
- 77 UUnnddeerrssttaannddiinngg cchhiillddrreenn’’ss ddeevveellooppiinngg ccaallccuullaattiioonnss
- • Practical mathematics
- • The fifth dimension: written calculations
- • Representations of early operations
- • Counting continuously
- • Narrative actions
- • Supporting children’s own mathematical marks
- • Separating sets
- • Exploring symbols
- • Standard symbolic calculations with small numbers
- • Calculations with larger numbers supported by jottings
- becoming bi-numerate
- • Conclusion
- 88 EEnnvviirroonnmmeennttss tthhaatt ssuuppppoorrtt cchhiillddrreenn’’ss mmaatthheemmaattiiccaall ggrraapphhiiccss
- • Rich mathematical environments for learning
- • The balance between adult-led and child-initiated learning
- • Role-play and mark-making
- • The physical environment
- • Practical steps
- • Graphics areas
- • Conclusion
- 99 CCaassee ssttuuddiieess ffrroomm eeaarrllyy cchhiillddhhoooodd sseettttiinnggss
- • The birthday cards
- • A number line
- • ‘No entry’
- • Carl’s garage
- • Children’s Centres: The Cambridge Learning Network project
- • The spontaneous dice game
- • Young children think division
- • A zoo visit
- • Mathematics and literacy in role-play: the library van
- • Aaron and the train
- • Multiplying larger numbers
- • Nectarines for a picnic
- • Conclusion
- 1100 DDeevveellooppiinngg cchhiillddrreenn’’ss wwrriitttteenn mmeetthhooddss
- • The assessment of children’s mathematical representations on paper
- • The problem with worksheets
- • Assessing samples of children’s own mathematics
- • Examples of assessment of children’s mathematics
- • The pedagogy of children’s mathematical graphics
- • Modelling mathematics
- 1111 IInnvvoollvviinngg ppaarreennttss aanndd ffaammiilliieess
- • Children’s first and continuing educators
- • The home as a rich learning environment
- • What mathematics do young children do at home?
- • What mathematics do parents notice at home?
- • Parents observe a wealth of mathematics
- • Helping parents recognise children’s mathematical marks
- • Parents’ questions about children’s mathematical graphics
- • Conclusion
- 1122 CChhiillddrreenn,, tteeaacchheerrss aanndd ppoossssiibbiilliittiieess
- • Inclusion
- • Children’s questions
- • Teachers’ questions
- • It’s all very well – but what about test scores?
- RReefflleeccttiioonnss
- Appendix: our research
- Glossary
- References
- Author Index
- Subject Index