How Does a Dynamic Geometry System Mediate Students’ Reasoning on 3D Linear Transformations?
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In this chapter, I discuss the integration of the Dynamic Geometry System (DGS) with the teaching and learning of two (2D) and three-dimensional (3D) linear transformations. To do this, certain tools and functions of the DGS, in particular, the dragging, slider and grid functions, and the Rotate and move 3D Graphics and ApplyMatrix construction tools of GeoGebra are focused on. Through semiotic potential analysis, a task is designed for students’ construction of mathematical relationships among the characterization of the transformation matrix, determinant of the transformation matrix, and area and volume of given and transformed figures. A task-based clinical interview was conducted with a pair of undergraduate linear algebra students. Data from video records, student production and field notes was analysed within a semiotic lens with reference to the theory of semiotic mediation. The results appear to confirm that the DGS can be considered as an effective tool of semiotic mediation for characterizing 3D linear transformations. Such an approach to the data also provides a detailed understanding for students’ reasoning steps from the use of artifact to creating mathematical meaning.
KeywordsSemiotic mediation Teaching-learning linear algebra DGS 3D linear transformations
I would like to thank my supervisor Prof. Dr. P.H.M. (Paul) Drijvers for his kind and countless contributions to the project and insightful comments on this paper. I also thank the Scientific and Technological Research Council of Turkey (TUBITAK), under the 2219-International Post-Doctoral Research Fellowship Programme (grant no: 1059B191401098), which supported this research. Finally, thanks go to anonymous reviewers and Christine Andrews-Larson for making constructive suggestions, which substantially improved the presentation of the paper.
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