COGNITIVE MODELS AND PROCESSES IN MATHEMATICS EDUCATION
This chapter presents the cognitive processes that are involved in three aspects of mathematics. These are: the process of understanding, the way in which understanding assists the child in developing procedures and strategies for performing mathematics, and how the complexity of mathematical concepts and tasks affects performance.
The essence of understanding a concept is to have a mental representation or mental model that faithfully reflects the structure of that concept. Number is the core of mathematics, and to understand number is to have a mental model of it that includes all the essential relations of numbers, at least within the domain where the concept is used. A 5-year-old's concept of number is presumably much more restricted than that of a pure mathematician, but the 5-year-old may still have a representation of those number relations that are important within the particular domains in which she uses number. Our first purpose then is to consider what is involved in mental models of number.
A mental model is not normally based on formal definitions but rather on concrete properties that have been drawn from life experience. Mental models are typically analogs, and they comprise specific contents, but this does not necessarily restrict their power to deal with abstract concepts, as we will see. The important thing about mental models, especially in the context of mathematics, is the relations they represent. We will use diagrams to depict mental models for a variety of concepts, and it is important to keep in
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Publication information: Book title: Mathematics Education:Models and Processes. Contributors: Lyn D. English - Author, Graeme S. Halford - Author. Publisher: Lawrence Erlbaum Associates. Place of publication: Mahwah, NJ. Publication year: 1995. Page number: 57.
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