Dan Meyer presented at the TEDxNYED conference recently and delivered this talk on teaching problem solving in US schools:
Let me say I couldn’t agree with him more!
His approach to developing problem solving is simple. Let students focus on figuring out what the relationships are, let them work through the details themselves and create their own understanding, instead of handing them the answer masked in a couple of simple computations.
I agree with everything that he espouses here and am glad that he is saying it because he says it so much more eloquently than I am able to.
My agreement means a lot to me but I understand others may be less swayed by my position, so I looked to research to back up these simple ideas. I found several pieces of research that add to this discussion. Notably John Sweller wrote in Cognitive Science
, 1998, about the difference between novice and experts when they are problem solving. Novices tend to work backwards from the answer to identify relationships they understand that they use to work their way back to the information provided. Interestingly, an expert tends to work forward from the information provided to direct themselves toward the target answer.
These two divergent perspectives become enlightening when compared to Dan’s approach. Instead of falsely providing novice learners an expert approach (by asking them questions that guide them from the information provided toward the solution) Dan espouses to let them progress through the novice stage, and let them build their cognitive understanding themselves. I would like to add that making this process a point of reflection for students may hasten their transition to the expert approach.
Sweller goes on to write that students who are asked to just determine as many relationships as they can are more likely to take an expert approach to a problem solving situation because there isn’t that focus on the one correct answer. This ‘brainstorming’ approach also more closely mirrors real life research in many ways in that direction is often established by observing relationships that can be determined rather than already knowing a direction to go.
This focus on process is critical to Schoenfeld (1987), and Garofola and Lester (1985) have suggested that students are largely unaware of the processes involved in problem solving and that addressing this issue within problem solving instruction is an important step in helping students progress through the different stages of learning.
All of the research is predicated on the fact that we allow students to work their way through problems, struggle with outcomes, and learn from the process. How can students take on this challenge if we as teachers continue to ask them simple problems and guide them through the process like an expert when they aren’t?
Garfola, J. & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163-176.
Schoenfeld, A. H. (1987). Cognitive science and mathematics education: An overview. In A. H. Schoenfeld, Cognitive science and mathematics education. Hillsdale, NJ: Lawrence Erlbaum.
Sweller, J. (1988). Cognitive load during problem solving: effects on Learning. Cognitive Science, 12, 257-285.