• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.483-500
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• 2019

This study compared and analyzed the van Hiele levels of geometry contents in middle school mathematics textbooks and those of students' thinking. As the mathematics curriculum was revised recently, the amount of contents in the geometry area were reduced, but the van Hiele level did not change much, and the gap between the van Hiele level of geometric contents presented in the textbooks and the level of students' geometric thinking still remained unchaged. The van Hiele levels of the geometric contents in the textbooks were distributed in the levels of 1, 2, 3 in the first grade, and 2, 3, 4 in the second and third grade. In the case of the first grade, 69% of the students were less than or equal to level 2, and 73.7% and 47.6% of the students in the second and third grades were less than or equal to level 3, respectively. Especially, in the case of the second and third grade, the ratio of the 4th level of the contents presented in the textbook is higher than the problem, which can cause difficulties for the students.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.435-452
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• 2016

This study was designed to explore students' instrumentalization in relation to the van Hiele's teaching method within a technology environment using GeoGebra. To carry out the study, a total of 4 lesson units was developed based on van Hiele teaching method for two slow learners in Gyeonggi province, Korea. The results of study were as follows. Instrumentalization of students was actualized from preparation, to adaptation, and to application stages. In preparation, and adaptation stages, depending on visualization, students used a trial-and-error method a lot, however in application stage the role of GeoGebra was just to check the solution of what they conjectured. Therefore, a teacher should prepare geometric tasks according to the processes of instrumentalization based on geometric teaching method. During instrumentalization and instrumentation of users, usage scheme(US) and instrumented action scheme(IAS) should be concrete.