• School Mathematics
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• v.10 no.3
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• pp.339-355
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• 2008

This article tried to review the meaning and implication of six stages theory of learning mathematics suggested by Zoltan Dienes in "Building up Mathematics" in 1971. It was not much concretely known to Korean mathematics education society. In particular, there is no mathematical example which could cover all the stages to know what the theory tells. So this article focused on the example which Dienes developed for learning integers in 2000 to dig the theory. As a result, some critical aspects and problems of six stages theory were found. And finally educational implication was described.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.401-417
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• 2005

Skemp supposed that it is effective to use both examples and non-examples when new concepts which are upper level than learner's schema are introduced. The purpose of this research is to develop a practical process of teaching geometrical concepts based on Skemp's assumption. For this, the related literatures are reviewed and the Korean textbooks(4-ga, 4-na) are analyzed with respect to method of concept formation. The analysis to]Is that the textbook just explains Properties of concepts or present definitions, instead of giving the chance of inquiry. So we design and apply six step process of teaching geometrical concepts to 4th graders focused on students' inquiry using both examples and non-examples.'rho result turns out that using examples and non-examples is highly positive to concept formation.