| This qualitative study describes how third-semester calculus students used visualization and technology in forming multivariable calculus concepts during Fall semester 1999. Four students were provided TI-89 graphing calculators giving them access to three-dimensional graphs. Data from four interviews with each student, copies of their written work, and the investigator's field notes (as a non-participating classroom observer) were analyzed by the method of constant comparison to provide answers to the research questions. Students used metaphors and prototypical examples, many adapted from single variable calculus, as mental pictures in forming their concept images. They used technology primarily as a drafting tool when assignments required its use. From these findings, models of the interactions between visualization, concept image formation, and technology usage in multivariable calculus were developed. Zimmerman and Cunningham's (1991) definition of mathematical visualization was extended to include mental images and three-dimensional models in addition to hand-drawn or computer-generated graphical representations. |
