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# Rational Numbers: An Integration of Research

By: Thomas A. Romberg; Elizabeth Fennema et al. | Book details

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Page 239

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USING PRINCIPLES FROM COGNITIVE PSYCHOLOGY TO GUIDE RATIONAL NUMBER INSTRUCTION FOR PROSPECTIVE TEACHERS

Judith T. Sowder, Nadine Bezuk, and Larry K. Sowder San Diego State University

Mathematics content courses for elementary teachers need to be revised to prepare teachers to implement the reforms currently being recommended. The revision of such a course is described. The traditional orientation to rational numbers in courses for prospective teachers focuses on definitions and rules for operations. A review of the recent content analyses of rational numbers and of research on learning of rational numbers indicated needed changes in the curriculum on rational numbers in a course for prospective teachers. Principles from cognitive psychology, useful in determining ways to motivate prospective teachers and assist them in extending their procedural knowledge of rational numbers to knowledge that is adaptive and reflective of rational number sense, guided planning for revising instruction.

Mathematics content courses for prospective elementary teachers traditionally are taught in many universities as lecture courses, often to classes of over 100 students. Manipulative materials are rarely available due to class size; the instructors' lack of familiarity with manipulatives, and/or the belief that using manipulative materials with prospective teachers is appropriate only in a methods course. The coverage of rational numbers is fairly uniform in the textbooks used in these courses: A chapter on fractions defines fractions as ordered pairs, discrete and continuous models are presented, definitions are given for fraction equality and for algorithms for operations, properties are stated, and end-of-the-chapter exercises provide some opportunities to explore the concepts introduced in the chapter and to apply the definitions to comparing and operating on fractions. A similar chapter on decimals follows the one on fractions, and finally, rational numbers are defined and field and order properties are stated formally.

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