Students' ability to visualize set expressions: An initial investigation |
| |
| Authors: | Ted Hodgson |
| |
| Institution: | (1) Department of Mathematical Sciences, Montana State University, 59717 Bozeman, MT, USA |
| |
| 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.NotesThis article is based on the author's doctoral dissertation completed in 1992 at Indiana University under the direction of Frank K. Lester. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
