Abstract
The purpose of this research is to clarity the methods students used to determine the validity of mathematical models. For investigative purposes, the data used was based on the ratio of the number of students and computers in an American school. Students had access to hand-held graphing calculators, capable of performing regression analyses. Students entered data and selected the regression command to best fit their data, then made predictions using their mathematical models. Having immediate access to this type of technology allowed students to quickly determine the validity of various proposed mathematical models and make revisions in their hypotheses to get more accurate results. The following results were obtained : (1) In the process of interpreting and evaluating models, students used two different representations, graphical and numerical, to determine the validity of the regression equation on the graphing calculator. (2) In the process of improving mathematical models, students selected the most suitable mathematical model based on their own hypotheses. (3) The authors conclude that the graphing calculator is an effective tool for determining the validity of various mathematical models and for choosing the most appropriate model.
