A Generative Model of Mathematics Learning.

meaning for mathematics education, this paper will begin with a hypothesis about human learning that has been developed from the investigator's research in cognition, discovery learning, and instruction in schools. It will then present a sample of the empirical studies that led to the generation of the hypothesis. Finally, some of the meaning of this research for mathematics learning will be discussed. The first point to emerge will be that we can be proud of the research in the learning of mathematics, including the development of curricular materials. The second point will be a recommendation that research in mathematics learning should increasingly be devoted to studying the stepby-step specific and higher-order intellectual processes that students engage in when they learn mathematics; such as when they are adding, subtracting, differentiating, and integrating. The hypothesis and empirical studies presented in this paper focus on the cognitive, generative processes that are involved in the learning of mathematics. These processes could perhaps be presented in simpler S-R terminology. The cognitive model emphasizes the learner's active, stepby-step processing of information, and is more compatible with the author's point of view. The data to be discussed will probably arouse recollections of the This is a slightly edited version of a paper commissioned by the ERIC Information Analysis Center for Science, Mathematics, and Environmental Education and presented at a session of the Special Interest Group for Research in Mathematics Education. The session, held 28 February 1973, was in conjunction with the AERA Annual Meeting. The paper was prepared pursuant to a contract with the Office of Education, U.S. Department of Health, Education, and Welfare. Contractors undertaking such projects under government sponsorship are encouraged to express freely their judgment in professional and technical matters. Points of view or opinions do not, therefore, necessarily represent official Office of Education position or policy.

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