Analogical reasoning and overgeneralization in mathematics learning: Implications for teaching effectiveness

Yui Kin NG, Keung Fai Joseph WU

Research output: Chapter in Book/Report/Conference proceedingChapters

Abstract

Good mathematics teachers should at least have some knowledge on how students conceptualize their mathematical experiences and put it into a mental structure, and how they approach and solve relevant mathematical problems within such a mental structure. It has been argued that our ability in finding analogical correspondences is a potent mechanism playing an important role in the evolutionary development of our thinking. This paper will discuss the role of analogical reasoning in learning mathematics and the ways in which students develop their own analogical reasoning skills through tackling mathematical problems. As misuses of analogical reasoning in mathematics may ensue overgeneralization which is an observable and detectable error patterns in doing mathematics, this paper will attempt to identify and analyze students’ common errors in mathematics learning and the relations between analogical reasoning and overgeneralization can thus be revealed. It is anticipated that findings of such analysis would be helpful to mathematics teachers in diagnosing students’ errors and planning appropriate remedial teaching. Copyright © 2000 The Hong Kong Institute of Education.
Original languageEnglish
Title of host publicationProceedings of International Conference on Teacher Education 1999: Teaching effectiveness and teacher development in the new century
Place of PublicationHong Kong
PublisherHong Kong Institute of Education
Pages1-5
ISBN (Print)9629490382
Publication statusPublished - 2000

Citation

Ng, Y. K., & Wu, K. F. (2000). Analogical reasoning and overgeneralization in mathematics learning: Implications for teaching effectiveness. In Proceedings of International Conference on Teacher Education 1999: Teaching effectiveness and teacher development in the new century [CD-ROM] (pp. 1-5). Hong Kong: Hong Kong Institute of Education.

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