Abstract
Visualization is a powerful tool for understanding and solving mathematical problems. The use of Venn diagrams to visualize set expressions, however, is problematic for many students and may actually hinder their problem-solving efforts. In this study, 92 university students construct visual representations of eight set expressions. Through the use of a production system model and detailed analyses of students' work and verbal protocols, it is discovered that (1) competent and error-prone students construct and use procedures to complete set translation tasks, and (2) two-thirds of the observed errors arise from the consistent implementation of ill-formed procedures. The procedural origins of students' errors are identified and conjectures are offered regarding the perceptions and experiences that lead to the development of erroneous translation procedures.
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This article is based on the author's doctoral dissertation completed in 1992 at Indiana University under the direction of Frank K. Lester.
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Hodgson, T. Students' ability to visualize set expressions: An initial investigation. Educ Stud Math 30, 159–178 (1996). https://doi.org/10.1007/BF00302628
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DOI: https://doi.org/10.1007/BF00302628