This study investigated the representations and strategies for subtraction used by a sample of 65 students, in Years 4 to 6, in two Brisbane primary schools. Children were presented individually with operations represented symbolically and as word problems. They were asked to solve tasks and explain their procedures. Teachers of the 65 students were interviewed to determine their objectives and strategies. The results of the study show in decreasing order of frequency, use of materials, mental, then written strategies in all Years. Use of recalled facts increased and of calculators decreased over the Years. The results are discussed in terras of informationprocessing capacity and teaching.The intention of the research described in this paper was to determine how children in Years 4, 5, and 6 would represent and solve subtraction algorithms presented symbolically and as word problems. This was in order to assess the strategies that the children would choose to employ, with or without concrete materials as representations, and to compare those with the strategies and representations that the teachers introduced. Teachers were interviewed to determine the objectives, strategies, and representations they intended to use, for teaching subtraction. The hypothesis was that some of the strategies and representations used by teachers and children might differ.
RepresentationsIt is recommended that a variety of non-proportional manipulatives such as counters, buttons and beans, as well as embodiments of the base ten number system such as bundles of tens, Multibase Arithmetic Blocks in base ten (MAB), and Unifix cubes, be used to establish the understanding of place-value and its use in algorithms (