High school students' learning of 3D geometry using iMAT (integrating Multitype-representations, Approximations and Technology) engineering
Camou, Bernardo Jorge
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A review of high school geometry texts and mathematics curricula indicate that 3D geometry is usually just a small portion of most geometry courses, and the research literature indicates that it is seldom taught. This research study attempted to demonstrate that the approach called iMAT (integrating Multitype-Representations, Approximations, and Technology) could be effective for enabling students to learn 3D geometry in a meaningful and efficient way. This approach was based in the consideration of mathematics as a quasi-experimental science. Therefore, to learn 3D geometry, it is crucial to experiment using different technologies to produce several representations of the same 3D object. Each representation by itself is not enough to provide the necessary support to enable the conceptualization of the geometric object. The researcher designed a 3D geometry unit to be taught to 140 high school students from Uruguay and the United States from June 2011 to October 2011. Four institutions and seven groups of students participated in the experiment. A mixed-methods methodology was developed with five sources of data: pretest, posttest, interviews, questionnaires, and video recording. The research questions were as follows: 1. What could high school students learn about Geometry (both 3D and 2D) in a two-week experimentation, using iMAT engineering? 2. How did that learning occur? 3. Can indicators be found that the teaching-learning iMAT approach could overcome the main epistemological and didactical obstacles for learning 3D Geometry? A six-item pretest was administered during the first class of the unit. The researcher taught each class for 2 weeks and then administered the six-item posttest. Each class lesson was videotaped and the lesson reviewed each day by the researcher. All students were interviewed in focus groups and completed questionnaires after the posttest. Analyses of these qualitative data indicate that students learned important concepts in 3D and 2D geometry during the two-week experiment, thus suggesting that iMAT is effective for tackling the study of 3D geometry. The quantitative data were analyzed using ANOVA and multiple regression tests on the pre- and post-test results. These quantitative analyses support the qualitative conclusions. Moreover, these analyses indicated that the iMAT approach was robust with respect to different factors such as country, pretest knowledge, and gender..