A genetic decomposition of geometric transformations
This study tried to find out how the concepts of translation, reflection, and rotation were developed and how they were learned. The study is based on a system of approaches proposed by Dubinsky which consisted of three components: (1) a general theory of advanced mathematical concept construction, (2) the investigator's understanding of mathematical concept, and (3) observations of students as they try to construct mathematical concepts. The van Hiele Levels were used to develop the questions. Eighteen preserve elementary school teachers were interviewed. Each entire interview was recorded and transcribed. Four levels were distinguished by the results of the interviews. A description of a construction process for developing schemas of the transformations was obtained. Based on the description, a practical instructional treatment was outlined. It consisted of computer experiences designed to stimulate the students to move along the cognitive constructions for developing schemas for the geometric transformations.
Dubinsky, Purdue University.
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