Middle-school students' concept images of geometric translations

Abstract

This study explored sixth grade students' concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students' concept images and their concept definitions. However, most of the students' concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students' concept images of geometric translations.