Exploring the Aspects of Sixth Graders’ Logical Explanation for Spatial Figures
2019 Volume 25 Issue 2 Pages 37-53
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2019 Volume 25 Issue 2 Pages 37-53
The purpose of this paper is to examine the aspects of sixth graders’ logical explanation for spatial figures by proposing the theoretical framework and by analyzing the interviews for the students in terms of the framework.
We first set the theoretical framework which consists of the relationships among three dimensional objects, two dimensional representations, and the languages. Moreover, we distinguished two-dimensional representation into sketch, net, and projection in order to analyze the students’ explanation in more detail and reconstructed the framework as the tetrahedron model. The model constitutes the inner and inter relationships among the three-dimensional object and three two-dimensional representations.
Next, we qualitatively analyzed the interview data conducted for sixth graders based on our theoretical framework.
The main findings of this paper are as follows.
1. Sixth graders’ logical explanation can be better examined through our theoretical framework, particularly along the arrows showed in the framework.
2. About half of six graders have their abilities to explore the challenging problem of spatial figures and to explain them logically under the conditions where they can image three-dimensional object dynamically. It suggests a possibility to reconstruct secondary curriculum in spatial geometry towards more exploratory learning which can evoke students’ logical explanation.
