Ten highly motivated and above-average intermediate algebra students were selected to complete a ten-week schedule of activities involving the mathematizing of some physical representation of a phenomena and the studying of that model. Ten activity-based exercises, most adapted from LABORATORY MANUAL FOR ELEMENTARY MATHEMATICS by Fitzgerald, et al., were the source of techniques and procedures. All sessions were recorded on audio tapes as the students worked in small groups or individually. The results of the study were reported using the case study procedure. The investigator felt that the results demonstrated that within the constraints of normal classroom conditions, high school students can achieve a higher level of understanding the entire nature of model building both physical and abstract, of the axiomatic process, and of the process by which propositions are logically deduced from other assumptions and proved. (Author/DT)