The calculator as a cognitive tool: Upper-primary pupils tackling a realistic number problem

This paper examines the idea that the arithmetic calculator can act as a cognitive tool, supporting the amplification or reorganisation of systems of thought. It analyses how a structured sample of pupils in the last year of English primary education, with differing degrees of experience of a 'calculator-aware' number curriculum, tackled a realistic number problem, focusing on their use of calculator, written and mental modes of computation. Examples were found in which use of the calculator helped pupils to work with unusual problem representations, and to adopt solution strategies in which they focused on planning and monitoring computations executed by the machine. For most pupils, however, other issues were more salient. First, there was an important dissonance between pupils' conception of division and the calculator's operationalisation of it, although some cases showed how further experiment or computation with the machine could help to make appropriate connections. Second, while the calculator made it possible to redistribute computation from human to machine, important limitations arose from the transience of the calculator's record of operations and results. The observations suggest the importance of developing pupils' skill in making effective use of the calculator beyond single, simple computations; and the need to help pupils apprehend the relationship between mathematical concepts and their operationalisation in the machine.