The Use of Modeling and Inquiry Problems in a Single Variable Calculus Course

David Smith and Mike Huber

United States Military Academy

Here at the United States Military Academy, we try to provide courses to make our cadets expert problem solvers. Although they need to learn the basic calculus fundamentals, we stress using these fundamental tools to solve problems. To emphasis this, we recently changed the way that we assess our cadet’s performance in the Single-Variable Calculus course. We used to use a series of mid-term exams that tested basic concepts as the primary assessment tool. This year though, we have changed to what we call Modeling and Inquiry Problems (MIP). The MIP’s emphasis is on modeling and discussion and not on finding an answer and double underlining that answer. We want the cadets to use the various resources to solve the model, but finding a solution is not the ultimate goal. The cadet must also be able to communicate and discuss the relevance of the solution in the context of the problem. Does the answer make sense? How could assumptions change the model? This is inquiry and it is just as important as modeling. The MIP presents a single problem scenario. Cadets are graded on how well they set up the model, the solution to the model, and the discussion of their solution. They must complete this is the 55 minute class period. We hope these MIP will make solving difficult problems second nature to the cadets. We also hope it will reinforce the idea, that the solution is not merely a number answer, but a discussion of all factors relative to the problem.