I sat down to grade the second midterm for our Introductory Algebra-based Physics course. Exam grading can be simultaneously rewarding and punishing; you get to see exactly how much your students have improved (or not) in their abilities to solve physics problems. It was during this grading session that I had an epiphany about story problems and the ways many students struggle with them.
The problem in question states:
A box slides up a rough, wooden ramp and comes to a stop. Below is the free-body diagram for the box while it slides up the ramp. Does the free-body diagram match the description of the situation? Explain your reasoning.
Many students correctly identified that the acceleration (net force) along the ramp is wrong as it needs to be pointing down the ramp in order for the block to come to a stop. Some students also correctly identified that the normal force drawn on the FBD is longer than it should be (forces must balance perpendicular to the ramp where acceleration is zero).
All but a small handful, however, missed the fact that the FBD included a force pushing the block up the ramp even though no other objects or forces are mentioned in the story problem. Many students say something like “the force pushing the block up the ramp” or “the tension force pulling the block up the ramp” even though neither pushing nor pulling were described in the problem statement. The bigger issue is that another common statement associated this force with the velocity: “the force pushing the block up the ramp is correct, because without it, the block would not be moving.” At first glance this statement makes me think students are (incorrectly) associating force with velocity. On the other hand, the statement is fundamentally true: the block would not be moving up the ramp if there had never been a force acting on it. The issue is that we wrote the problem assuming that force had already gone away and that the block had some velocity up the ramp. The students know intuitively that blocks don’t just move spontaneously up ramps; did they just assume the force was still there? Hence my epiphany:
Story problems are hard because physicists are excellent problem solvers, but not always excellent storytellers.
These students needed the backstory behind this situation. What is the block’s motivation? Why is it moving up the ramp? Without that information, they are perfectly comfortable including a force that should (in our minds) not be there. In the literary sense, that force was implied by the fact that the block is moving up the ramp. As we emphasize in the liberal arts, every discipline relies on the others. For this very reason it is important that we recognize students will answer questions incorrectly for a variety of reasons: sometimes the reason is that they haven’t mastered physics… but, at least occasionally, it is also because we haven’t mastered storytelling.
Andrew Dawes 