When Support Hides Progress: Insights from a Physics Tutorial on Solving Laplace’s Equation Using Separation of Variables in Cartesian Coordinates

The electrostatic potential in certain types of boundary value problems can be found by solving Laplace’s Equation (LE). It is important for students to develop the ability to recognize the utility of LE and apply the method to solve physics problems. To develop students’ problem-solving skills for solving problems that can be solved effectively using Laplace’s equation in an upper-level electricity and magnetism course, we developed and validated a tutorial focused on finding electrostatic potential in a Cartesian coordinate system. The tutorial was implemented across three instructors’ classes, accompanied by scaffolded pretest (after traditional lecture) and posttest (after the tutorial). We also conducted think-aloud interviews with advanced students using both unscaffolded and scaffolded versions of the pretest and posttest. Findings reveal common student difficulties that were included in the tutorial as a guide to help address them. The difference in the performance of students from the pretest after lecture to the posttest after the tutorial was similar on the scaffolded version of the tests (in which the problems posed were broken into sub-problems) for all three instructors’ classes and interviewed students. Equally importantly, interviewed students demonstrated greater differences in scores from the pretest and posttest on the unscaffolded versions in which the problems were not broken into sub-problems, suggesting that the scaffolded version of the tests may have obscured evidence of actual learning from the tutorial. While a scaffolded test is typically intended to guide students through complex reasoning by breaking a problem into sub-problems and offering structured support, it can limit opportunities to demonstrate independent problem-solving and evidence of learning from the tutorial. Additionally, one instructor’s class underperformed relative to others even on the pretest. This instructor had mentioned that the tests and tutorial were not relevant to their current course syllabus and offered a small amount of extra credit for attempting to help education researchers, highlighting how this type of instructor framing of instructional tasks can negatively impact student engagement and performance. Overall, in addition to identifying student difficulties and demonstrating how the tutorial addresses them, this study reveals two unanticipated but critical insights: first, breaking problems into sub-parts can obscure evidence of students’ ability to independently solve problems, and second, instructor framing can significantly influence student engagement and performance.