Tensions and trade-offs in instructional goals for physics courses aimed at engineers

In planning and teaching courses for engineering majors, physics instructors grapple with multiple instructional goals: extensive content coverage, quantitative problem solving, conceptual understanding, motivation, and more. The temptation is to treat these goals as mutually reinforcing or at least as not in conflict. We argue, however, that at least for novice instructors, these goals can be in tension. In our study, one instructor was experienced and emphasized traditional quantitative problem solving. A second instructor teaching another lecture section of the same course was a novice who chose to emphasize a goal suggested by physics education research and studies of practicing engineers, namely mathematical sense-making-translating and seeking coherence between mathematical formalism and physical reasoning. A common final exam, containing standard traditional problems and also opportunities for mathematical sense-making, enabled us to document the following trade-off: the novice instructor outperformed the experienced traditional instructor at fostering mathematical sense-making but underperformed at fostering traditional problem solving. In other words, the novice instructor's success at teaching mathematical sense-making came at a cost. A third instructor, expert in emphasizing mathematical sense-making, showed that it is possible to succeed at teaching mathematical sense-making without a significant trade-off in teaching traditional problem-solving. However, for instructors considering the adoption of physics/engineering education research-based instructional strategies, trade-offs must be acknowledged and tough choices must be made.