Geometric Translations: An Interactive Approach Based on Students' Concept Images

Abstract

We present activities are based on the nature of middle-school students' concept images of geometric translations. We propose the use of interactive GeoGebra files, prototypical examples, and nonexamples. These are chosen to help students develop their thinking through the natural stages of thinking about translation as a motion. We discuss the importance of geometric transformations in the learning of geometry, and the central role of examples and nonexamples in the learning of mathematical concepts. We describe three stages in middle-school students' thinking about geometric translations as motion translations; and some misconceptions found in research studies. Twelve activities constitute the main body of the article. We discuss more advanced stages in the understanding of geometric translations that will need to be addressed beyond the middle-school.

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