The Importance of Conceptual Knowledge of Solving Physics Problems

Using Qualitative Problem-Solving Strategies to Highlight the Role of Conceptual Knowledge in Solving Problems - William Leonard et al. 1996

Presenter: Anna Boehle

By focusing on problem-solving strategies, are we forgetting/compromising the conceptual knowledge we want students to have?

We know that even efficient problem solvers are not taking away the conceptual knowledge that they should at the end of undergraduate physics courses. You can be an efficient problem-solver if you know how to "plug-and-chug" without really understanding why you are using the equations. We want scientists to be able to explain what they've done, and that takes conceptual knowledge.

When TAs and professors model problem-solving, we usually don't explicitly write-down the explanations; we just write the relevant equations on the board. Are we doing our students a disservice?

Suggested way of teaching problem solving:

  1. highlight the major principles and/or concepts (WHAT)
  2. justify the use of those principles/concepts (WHY)
  3. write the procedure down (HOW)

Take the time to write out the strategy before attempting to solve the problem. This method can be lengthy and time-consuming. You might only have time to present/model one problem during class time. Homework solutions should include strategies as well as the quantitative solution (equations). Grading is based on strategies as well as the computation.

Challenge at UCLA: How would we grade strategy writing? We don't have enough TAs to handle that kind of in-depth homework analysis. Is there a way we can automate it by looking for keywords (that's what the Blackboard app does).  Maybe we could use peer graders - they grade each others' homework sets and are, in turn, graded on their evaluation. Alternatively, the TA can spot-grade the homework sets (though students might not like it). Maybe TA's could give feedback during discussion sections.

Posting homework solutions on the Internet

One the one hand, students expect the solutions to be posted. On the other hand, once you post the solutions, you can never use those problems again. What do we do to combat that? TAs and faculty do NOT want to re-write their problems every year. Is there a more secure way to deliver homework solutions? What about giving weekly quizzes that are similar to homework problems; don't grade the homework, but if the students work through the homework problems, they will do better on the quiz.

Group work could also be a solution; students working in groups need to justify their solutions to each other. Plus, if you have groups submitting a single solution, you cut down on the number of problem sets your TA has to grade.

Most importantly, stress the importance of practice problems to the students; be explicit about your expectations. Would it help students to have a separate required course on study skills for all freshmen? Maybe the problems given should be tougher ("challenge problems") to encourage students to work together and be explicit about their strategies.

Evaluating the effectiveness of this approach

Can you teach two courses - one traditional, and one using a strategic-approach? The IRB (Institutional Review Board) will not let you "experiment" on undergrads by providing a "sub-par" class, but where do they draw the line? Can we do this sort of experiment at UCLA to make sure that we have the data we need to back up the claims we're making? If you don't publish your results, you don't need to go through IRB. But wouldn't you want to publish the results at some point (or at least have it as an option)?

What is the effect on television programs and/or outreach on the education of the general public?

We don't want our physics classes to be like Cosmos - we need to focus on real content besides just getting students excited. How important is it to sacrifice excitement for content? Hype does a lot for the students, and will get you very good evaluations. But how much are they actually learning? If students are very excited about the topic, but under-prepared for future courses, have you helped them or hurt them? Is there some excitement to be gained (for first-time scientists) from the successful completion of a problem?

The key is to encourage the students to develop critical thinking skills. Those usually lie between the initial excitement and the quantitative evaluation of the physics. This is the crux of "thinking like a scientist" which is important for students even if they are in "Physics for Poets" type of schools.