| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1995: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1994: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Research Abstract |
Although mathematical constructs of children often bear inconvenient conceptions or misconceptions that affect negatively their conceptual and procedual understanding in mathematics learning, effective teaching models for resolving their misconceptions have not been addressed. The object of the study is,
(1) to reveal misconceptions of children in test problems of school mathematics,
(2) to identify some of the underlying factors of misconceptions and make up classroom model of mathematics for resolving misconceptions.
We developed test problems to reveal misconceptions of students of sixth, seventh, and eighth grade children and examined responses to the problems. Analyzing test results and protocols, we classified misconceptions into some categories of conceptual and procedural knowledge in mathematics : (1) compartmentalization, (2) oversimplification, (3) self-restriction, and so on.
These misconceptions exist in children's inner psychological schemes, but are inconsistent with logical system of mathematics. Identifying factors of misconceptions obtained in the research, we make up a classroom model of teaching mathematics for resolving misconceptions in mathematics.
It is intended to bring children with misconceptions to the realizations that their ideas are inconvenient and inadequate, and in need of modification. For this intention, two tasks named Critical Task and Assimilation Task were developed. The former consisted of both items with misconceptions and correct responses, and the latter with new scheme which might be formed through critical task for checking its availability. The use of multiple analogies and multiple mental representations with computer graphic seems effective teaching strategies for resolving misconceptions as well as the tasks. Classroom model developed in the study is effective in building connections between conceptual and procedual knowledge in school mathematics.
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