Using structure in young children's mathematics learning

Current research and practice show that many children who experience difficulties in mathematics learning can be assisted through appropriate individual assessment and scaffolded 'instruction' based on their level of cognitive development. While traditional methods have had some success in 'mastery' of key content, usually in number skills, new approaches are more concerned with improving general underlying mathematical processes such as the ability to visualise, represent, or organise mathematical thinking. Suitable learning experiences would need to be regular and systematic where children develop visual memory as they observe, recall and represent numerical and spatial processes such as counting, partitioning, patterning, subitising, grouping and unitising. Learning experiences would be regularly repeated in varied form, including problems in words, pictures and using technology, to encourage generalisation. This is becoming critical in a society that requires students to develop quantitative literacy and problem-solving skills as well as basic number knowledge. Over the past decade researchers at Macquarie University have conducted a number of related studies aiming to find early causes of mathematical difficulty. Their approach shows that low-achieving students of all ages have a poor grasp of mathematical patterns and structures. Rather than dismissing these findings as a characteristic of an immutable 'low ability', low- achieving students can be assisted to seek and recognise mathematical patterns and structures, and the effect on their overall mathematics achievement can be substantial. Low-achievers' representations (drawings, diagrams, notations) tend to be idiosyncratic, focusing on particular features of special interest to them and often varying over time without showing any progress towards use of structure. Low- achievers do not recognise the underlying mathematical similarities between superficially different situations is the first step in effective mathematics learning. This has far-reaching implications, particularly for children's interpretation of problems using technology, in standard tests or in textbook formats.