A Problem-Solving Approach Aimed at Helping Calculus I Students Solve Related Rates Problems

After analyzing our Calculus I students’ performance on a related rates problem from a final exam, we designed a teaching experiment aimed at improving our students’ performance at problem solving. For our analysis, we used two frameworks – one specific to related rates problems and Polya’s general framework for problem solving. The analysis of student work on a final exam problem (N = 57) and interviews with 10 students revealed difficulties understanding the problem and making connections between data and unknowns. The results informed a teaching experiment the following semester when a different group of students (N = 13) used Polya’s approach to problem solving. The students solved and discussed related rates problems in geometric contexts, wrote their algorithms, and were assessed by a related rates problem on the final exam. All 13 students understood the problem, used diagrams, and all but one, established a meaningful relation with quantities from the problem. Having students create their algorithms seems to be a promising strategy in the teaching and learning of related rates problems.