Re-thinking 'concrete to abstract': Towards the use of symbolically structured environments

Alf Coles, Nathalie Sinclair

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
10 Downloads (Pure)


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 languageEnglish
Pages (from-to)465
Number of pages480
JournalCanadian Journal of Science, Mathematics and Technology
Issue number4
Early online date18 Nov 2019
Publication statusPublished - Dec 2019

Structured keywords

  • SoE Centre for Teaching Learning and Curriculum


  • manipulatives
  • concrete and abstract
  • learning mathematics
  • symbolically structured environment
  • tens chart
  • TouchTimes

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