The scheme of correspondence and its role in children's mathematics
Abstract:Background. There are two theories about the origin of children's understanding of multiplicative reasoning. One is that multiplicative reasoning has its origin in repeated addition. The other is that children's scheme of one-to-many correspondence is the origin of their multiplicative reasoning, while addition and subtraction originate from the schemes of joining and separating. Aim. The aim of this paper was to assess the evidence for these two theories and provide new relevant evidence. Sample. Two studies were carried out with children from state-supported schools that served a varied constituency with respect to socio-economic background. Neither sample had been taught about multiplication or division in school. Method. In the first study, the children's progress in multiplicative reasoning was assessed after one group received instruction on one-to-many correspondences and the other on repeated addition. In the second study, the intervention group was shown how to use correspondences to solve multiplicative reasoning problems and the control group solved visual non-numerical problems. Results. In the first study, with children aged 67 years, the correspondence group made significantly more progress in multiplicative reasoning problems than the repeated addition group. The second study showed that it is possible to teach young children (aged 45 years) to solve multiplicative reasoning problems. In both studies, additive or multiplicative reasoning in the pre-test was a specific predictor of post-test performance on the same type of task. Conclusions. The results support the theory that the scheme of one-to-many correspondences is the origin of children's multiplicative reasoning. This finding has important educational implications.
Publication date: March 1, 2010
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