For the past year, three other physics teachers and I have been investigating how explicitly teaching an expert-like approach in problem solving affects students in a modeling based physics classroom. We presented our findings Friday July 20th at Arizona State University and our report is, at last, complete!
We didn’t find anything groundbreaking. Unlike many larger/more popular educational innovations, our conclusions are conservative. Although we believe what we did has the potential to be beneficial to some students, we don’t claim it’s a silver bullet. In fact, we found that for students who didn’t build a strong conceptual understanding in physics, our explicit emphasis on problem solving was not beneficial.
Few people will likely be interested in reading our entire paper (it’s quite long!), but some may be interested in selected parts. I’ve posted our paper, Effects of Emphasizing Intentional Problems Solving here.
Here is our abstract:
Students begin their education in physics as novice problems solvers. Instead of carefully defining a problem, using qualitative models, and planning a method of solution, students often immediately attempt to find the answer to the problem. The result of this lack of methodical approach is that students are not only unable to solve problems, they are unsure of even the basic steps that lead toward solutions. Previous research has shown that intentionally teaching expert-like strategies increases students’ problem solving ability. Other studies have found that Modeling Instruction improves students’ expert-like problem solving ability. This study was initiated to evaluate the impact on students’ problem solving skills through teaching explicit problem solving strategies in addition to Modeling Instruction. There was no conclusive evidence that the gains from the two methods were additive; however, this approach was reported to be beneficial by study participants. There was substantial evidence that without a solid conceptual understanding, expert-like problem solving ability was limited.
Application: Expert Method
As a physics teacher, solution fluency is a skill always on my mind. All too often students respond to a physics puzzle with “I don’t know,” as if the solution was a bit of forgotten trivia. Instead of taking small steps that build toward solution, students attempt a single giant leap towards the answer. When this strategy fails – as it inevitably does for challenging problems – they are left with nothing.
As a part of a master’s degree I am pursuing with three other physics teachers, we are conducting action research into problem solving in physics. Although all four of us had already attempted to teach problem solving in our classes, our instruction was mostly ineffective (see psudoteaching). To be sure, our students could tackle problems relying on algorithmic like procedures. It’s hardly solution fluency to blindly follow memorized instructions though.
From the research we read, we discovered that the common types of “example problems” are grossly ineffective at improving student’s problem solving abilities. In hindsight, this is almost embarrassingly obvious since it is the teacher who builds up the problem, the teacher who supplies the logic and the teacher who evaluates the result. Problem solving, and physics in general, are not spectator sports. You can’t learn by watching experts any more then you could basketball.
There seems to be general consensus that experts effectively solve problems by systematically working from general to specific using the following steps:
- Translate the problem into their own words/pictures (i.e. understand the problem)
- Qualitatively describe the problem (i.e. what major ideas are relevant to the problems solution?)
- Quantitatively describe the problem (i.e. apply specific pieces of major ideas to understand the problem in more depth – in physics this often takes the form of a series of equations).
- Execute a solution (i.e. calculate/solve equations or graphs etc.)
- Evaluate the solution (i.e. use multiple independent checks to determine a solution’s validity)
We took this general problem solving strategy, applied it specifically to physics and then printed out papers for students to solve problems on called the “expert method.” (a picture is below)
Although our research is very much ongoing, there are promising signs. Completely on their own, one of my classes asked if they could have expert method sheets on the final (Yes!!!!!). Additionally, since I require students use the expert method on problems they get stuck on, and most of the steps can be completed even without getting the right answer, it is very easy for me to distinguish between those who didn’t get the homework because they didn’t understand vs. those who didn’t get the homework because of a lack of effort.
Overall, I think this expert problem solving method has potential far beyond its obvious applications in math and science. Just like we have powerful reading strategies, I think we should empower students with specific problem solving strategies. Hopefully students will internalize these strategies with practice.