Application of Generalization Schemas to Solve Figural Pattern Problems on Sixth Graders
Author: Chia-Huang Chen(Department of Mathematics Education, National Taichung University of Education)
Vol.&No.：Vol. 58, No. 1
Date：March 2013
Pages：59-90
DOI：10.3966/2073753X2013035801003
Abstract：
The purpose of this study is to enhance our understanding of the generalization process by examining the generalization schemas of figural pattern problems and capturing the cognitive structure of generalization, and by examining the ways in which to improve the generalization schema transformation to construct models for solving generalization problems and promote the effects of algebraic thinking. Three Grade six students in a teaching activity setting completed 32 tasks related to figural pattern problems, and the worksheets and interviews data were collected. The data were analyzed qualitatively, and three stages were considered: (1) Students used both the “relationship of whole figure” and “elements of part structure” concept schemas for problem-solving planning in the abductive stage; (2) both schemas were applied during the connection stage on the “figural characterizes contrast with figural terms” and “objects count contrast with figural terms” to combine the relationship between figures and terms; (3) students used both the “unit combined” and “figural structure” concept schemas to solve the figural pattern problems during the generalized stage. Students used “addition,” “multiplication,” and “practical” operation schemas to integrate the rules and expressions for resolving the figural pattern problems. The change and transformation of the schemas during generalization were influenced by student knowledge, experiences, and characteristics of the figural structure. Researchers constructed both the “utilize the figural structure” and “utilize the number alley” models for problem-solving generalization learning based on students’ generalization schema operation and development. The findings such as the models of problem-solving generalization support teachers’ instruction, engaging students in algebraic thinking and implementing algebraic teaching with figural pattern problem solving.
Keywords：generalization, algebraic thinking, schema, figural pattern problem
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References：
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