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- [Show abstract] [Hide abstract] ABSTRACT: An algebraic model relating the rate of learning to the pace of teaching and to pupil ability is described. The model accounts well for prior data on learning at different speeds and accurately predicts the learning deficit for able pupils taught in heterogeneous classes. The capacity of the model to predict changes of pace and learning from lesson to lesson is described.
- [Show abstract] [Hide abstract] ABSTRACT: The central focus of the paper is the nature of the mental representations of the meaning of the linguistic expressions of mathematics. An information-processing model for the construction of mental representations is presented. The model provides syntactical tree structures as meaning representations. It is argued that the major function of written mathematical language in school mathematics is in the initial presentations of pupil tasks. An information-processing model for the performance of routine mathematical tasks is proposed. The central feature of the model is the major role that transformations of mental representations play. The overall model is related to children's conceptual development, and a series of stages in the acquisition of mathematical language is proposed. Finally, the model is shown to be consistent with a range of current concepts, theories and observational data.
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