Tools or crutches? Apparatus as a sense-making aid in mathematics teaching with children with moderate learning difficulties

This paper challenges a view of concrete materials as abstracts used within a rigid instructional sequence that particular children are perceived to require or not, as the case may be. Focussing on mathematics teaching, it contends that it is more useful to consider the function of these materials as tools, artefacts used flexibly and selectively by pupils to make sense of mathematics, rather than as crutches, devices which may support procedural competency in mathematics but with no guarantees of understanding.