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This study investigated students' understandings of two-dimensional shapes in different orientations. The purpose was to identify to what extent students could identify the two-dimensional shapes included in the K-6 Mathematics Syllabus (NSW Board of Studies 2002), and what role orientation and language have in this process. The design involved an investigation using both quantitative and qualitative methods of data collection to provide a detailed picture of students' understandings. Empirical evidence is provided to explain the difficulties students encounter in understanding two-dimensional shapes in different orientations. The theoretical framework for this study is the van Hiele Theory. The van Hiele Theory provides the most useful, descriptive framework of students' geometric development currently available. Numerous studies have highlighted some inadequacies in the theory, particularly in relation to lower level geometrical understandings. The findings of this study support the need for the adoption of some modifications as suggested by some researchers in this field. In an attempt to describe and track student responses, the SOLO Model has been employed to analyse the students' outcomes because the language used by students and the level of response will give a more accurate picture of the understandings students have of two-dimensional figures. |
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