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The development of multiplicative thinking in primary school children

Jacob, Lorraine (2001) The development of multiplicative thinking in primary school children. Masters by Research thesis, Murdoch University.

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Multiplicative thinking cannot be generalised in any simple way from additive thinking. This would not be a concern if additive thinking was sufficient for children to progress mathematically but it is not. This study investigates the development of multiplicative thinking in children. Its purpose was to investigate how additive and multiplicative thinking differs and the developmental changes children make as they move from thinking additively to thinking multiplicatively. A premise of this study was that unless teachers could actually recognise the difference between additive and multiplicative thinking they would be unlikely to be able to help children develop the latter. There were two parts to this study. The first part was an analytical examination of the research, the second part an empirical study. An analysis of the mathematics of multiplication led to the conclusion that it was identification or construction of the multiplicand and the multiplier within a situation and the simultaneous coordination of these factors that typified multiplicative thinking about a situation. An analysis and synthesis of the existing research literature suggested five broad phases through which multiplicative thinking develops. These were labelled as one-to-one counting, additive composition, many-to-one counting, multiplicative relations and operating on the operators.

The second part of the study was empirical. It investigated the potential of a set of tasks to distinguish between additive and multiplicative thinkers in a way that could be used in classrooms and thus be helpful to teachers. A group of Year Three and Year Four children carried out the eight tasks during individual interviews. This study showed that although it was not easy to discern the difference between an additive and a multiplicative thinker it was possible through such tasks.

Publication Type: Thesis (Masters by Research)
Murdoch Affiliation: School of Arts
Supervisor: Willis, Sue
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