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On designing cognitively appropriate computer learning environments: Software for geometric thinking
Abstract
In this study a model for the design of mathematical software was developed and tested. The model, which is based upon current cognitive theories of learning, was used to design Transformer, a computer learning environment (CLE) for exploring transformational geometry. In a pilot study, the software was used in middle-school classrooms and in in-service workshops, and then refined for use in the current study which tested the design model qualitatively. Two cycles of in-depth interviews were conducted with each of twelve high-school students, who used the CLE to solve geometric problems. Transcripts from videotapes of student work on two problems were extracted and subjected to a protocol analysis. Analysis revealed patterns of misconceptions and patterns of problem-solving approaches by the students, which led to suggested improvements in software design model and in the CLE. The most common misconceptions, confusions regarding reflections and rotations, led to redesigning display features including placement of mirrors and animation of rotation. Many participants found the use of both physical manipulatives and transparent screen overlays a significant problem-solving aid. It was concluded that CLEs which incorporate the use of such manipulatives would be easier to understand for many students. The model was expanded to include design principles of making the CLE accessible to a greater number of students. Implications of the research for mathematics education and for software design are discussed and suggestions for further testing of the model presented. Appendices include a typical protocol analysis of one student's work on a selected problem.
Subject Area
Mathematics education|Educational software
Recommended Citation
Lipp, Alan, "On designing cognitively appropriate computer learning environments: Software for geometric thinking" (1989). Doctoral Dissertations Available from Proquest. AAI9011760.
https://scholarworks.umass.edu/dissertations/AAI9011760