Solution Fluency: Expert Method & Action Research
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.