Abstract
In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this entails for life chances. We propose working in “symbolically structured environments” as an alternative way of characterising students’ direct engagement with the abstract and exemplify two such environments, both of which involve early number learning. We additionally propose some roles for the teacher working in a symbolically structured environment.
| Original language | English |
|---|---|
| Pages (from-to) | 465 |
| Number of pages | 480 |
| Journal | Canadian Journal of Science, Mathematics and Technology |
| Volume | 19 |
| Issue number | 4 |
| Early online date | 18 Nov 2019 |
| DOIs | |
| Publication status | Published - Dec 2019 |
Structured keywords
- SoE Centre for Teaching Learning and Curriculum
Keywords
- manipulatives
- concrete and abstract
- learning mathematics
- symbolically structured environment
- tens chart
- TouchTimes
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Profiles
-
Professor Alf T Coles
- School of Education - Professor of Mathematics Education
- Educational Futures Network
- Centre for Teaching, Learning and Curriculum
- Cabot Institute for the Environment
- Artful Narrative Inquiry Network (Ani-net)
- Mathematics Education Research Network (MERN)
Person: Academic , Member, Group lead