Students’ geometric thinking with cube representations: Assessment framework and empirical evidence
Fujita, T; Kondo, Y; Kumamura, H; et al.Kunimune, S
Date: 2017
Journal
Journal of Mathematical Behavior
Publisher
Elsevier
Publisher DOI
Abstract
While representations of 3D shapes are used in the teaching of geometry in lower
secondary school, it is known that such representations can provide difficulties for
students. In order to assess students’ thinking about 3D shapes, we constructed an
assessment framework based on existing research studies and data from G7-9
students ...
While representations of 3D shapes are used in the teaching of geometry in lower
secondary school, it is known that such representations can provide difficulties for
students. In order to assess students’ thinking about 3D shapes, we constructed an
assessment framework based on existing research studies and data from G7-9
students (aged 12-15). We then applied our framework to assess students’
geometric thinking in lessons. We report two cases of qualitative findings from a
classroom experiment in which Grade 7 students (aged 12-13) tackled a problem
in 3D geometry that was, for them, quite challenging. We found that students who
failed to answer given problems did not mentally manipulate representations
effectively, while others could mentally manipulate representations and reason
about them in order to reach correct solutions. We conclude with the proposition
that this finding shows the framework can be used by teachers in instruction to
assess their students' 3D geometric thinking.
School of Education
Faculty of Humanities, Arts and Social Sciences
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