High school students' understandings of geometric transformations in the context of a technological environment

This study sought to understand the nature of students' understandings of mathematical concepts within a technological context. A mathematical concept of particular importance is geometric transformations because it may provide students a context from which they can view mathematics as an interconnected discipline. Viewing mathematics as an interconnected discipline may allow students opportunities to develop more robust understandings of mathematics. The purpose of this study was to examine high school students' understandings of geometric transformations, which included translations, rotations, reflections, and dilations, when instruction capitalized on the use of technological tools such as the Geometer's Sketchpad and the TI-92 calculator.; The design of the study and the analysis of the data were guided by the following research questions: (1) What is the nature of students' understandings of geometric transformations when instruction capitalizes on the technological tool, Geometer's Sketchpad? and (2) In what ways does the computer mediate students' learning of transformational geometry?; The researcher conducted a seven-week instructional unit on geometric transformations within an honors geometry class. Six students within this class served as participants in the study. Four were selected for case studies. For each participant, their verbatim transcripts of the three in-depth clinical interviews, small group and whole group discussions, and their written work were analyzed. The analysis consisted of two case study and cross-case study analyses. The first analysis focused on students' understandings of geometric transformations and the second analysis focused on the ways in which students made use of and interpreted the computer and calculator.; The researcher found that there were key understandings that seemed to reflect deeper understandings of transformations. These included: understandings of domain, a focus on theoretical objects rather than concrete objects, and understandings of how to interpret and make use of multiple representations. The ways in which the computer mediated students' understandings of transformations seemed related to their understandings of the tool and understandings of mathematics. While the computer environment may have encouraged a concrete approach, students' reasoning appeared to move along a continuum between the concrete and the theoretical, which often included an interaction between theoretical and concrete.