This project had three major goals: (1) investigate the extent to which introductory physics students misuse or misunderstand formulas; (2) catalogue the typical ways in which they do this; and (3) begin the larger task of identifying key types of knowledge that successful problem solvers use to give formulas meaning. Exploratory interviews and group sampling studies were conducted. The interviews were conducted with approximately 25 freshmen and sophomore engineering students. As a result, the project was able to discover new misconceptions about qualitative concepts in physics, develop and refine more simple and elegant problems which would expose and isolate those misconceptions with a minimum of distraction from other possible difficulties, and form hypotheses about four levels of knowledge being used in successful problem solving. A series of three different 45-minute diagnostic tests were conducted with entering freshman engineering majors, using sample sizes of 150, 34, and 38 respectively. These each involved approximately 18 of the questions which had been pilot tested in interviews, including both algebra and physics questions. A parallel test was given to an older group of 24 engineering majors who had just completed a course in introductory mechanics. These tests allowed for the comparison of students before and after taking introductory physics to determine whether the students' learning had been formula-centered. Findings and comments on the research methodology are presented in this final report. (Author)