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Drawing appropriate diagrams is a useful problem solving heuristic that cantransform a problem into a representation that is easier to exploit for solvingthe problem. A major focus while helping introductory physics students learnproblem solving is to help them appreciate that drawing diagrams facilitatesproblem solution. We conducted an investigation in which 118 students in analgebra-based introductory physics course were subjected to two differentinterventions during the problem solving in recitation quizzes throughout thesemester. Here, we discuss the problem solving performance of students indifferent intervention groups for two problems involving standing waves intubes, one which was given in a quiz and the other in a midterm exam. Theseproblems can be solved using two different methods, one involving adiagrammatic representation and the other involving mostly mathematicalmanipulation of equations. In the quiz, students were either (1) asked to solvethe problem in which a partial diagram was provided or (2) explicitly asked todraw a diagram. A comparison group was not given any instruction regardingdiagrams. Students in group (1), who were given the partial diagram, could notuse that partial diagram by itself to solve the problem. The partial diagramwas simply intended as a hint for students to complete the diagram and followthe diagrammatic approach. However, we find an opposite effect, namely, thatstudents given this diagram were less likely to draw productive diagrams andperformed worse than students in the other groups. Moreover, we find thatstudents who drew a productive diagram performed better than those who did notdraw a productive diagram even if they primarily used a mathematical approach.Interviews with individual students who were asked to solve the problemprovided further insight.

A good diagram is valuable despite the choice of a mathematical approach to problem solving