Re-thinking ‘Concrete to Abstract’ in Mathematics Education: Towards the Use of Symbolically Structured Environments

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 has 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.