Apologies for not writing in so long. Transitions can be hard and making my way through a new school, new place to live and way too many other changes in my life have caused me to put this blog lowest on the priority list. However, in preparing for my course at the PEA conference next week, I came across a wonderful article in the Interdisciplinary Journal for Problem-Based Learning by David Jonassen at the Univesity of Missouri. I have meant to write about this for quite a while because he write about “Supporting Problem Solving in PBL” and has created this great structure that describes the components and scaffolds for PBL environments. It kind of shows the different parts of a PBL environment and the cognitive ways in which students move through the environment focused on the problem, but how they navigate learning. One of the pieces that he talks about that was in this environment was “worked examples.” When I first read this, I was aghast and totally taken aback. How could this be? Why would someone propose that worked examples are part of PBL and isn’t this totally against everything that PBL stands for? I mean, why not just go back to direct instruction and have the teacher standing up at the board working examples for the whole class? OK, that’s a little extreme. I think I over-reacted and went to Jonassen’s part of the article where talks about this.

He states “The most common method for supporting schema construction is the worked example” which I believe is him stating that from a cognitive standpoint the “most common” way for a student to build a schema of seeing how to do something is for someone to show them how to do it. I do believe there is research that shows this. However, I do not believe that there is research that shows that this is the best way for the to construct a schema for understanding. In fact, Jonassen goes on to say that “worked examples should break down complex solutions into smaller meaningful solution elements, present multiple examples in multiple modalities for each kind of problem, emphasize the conceptual structure of the problem vary formats within problem types, and signal the deep structure of the problem…It is doubtful that worked examples are effectively applicable to very ill-structured problems. How can you model a solution that is unknown?” So if teachers did what he says here, they would work examples in many modalities – all representations so that the conceptual connections could be made and not just the procedural ones. Students would be able to see the bigger picture of mathematics more often because they would realize that in the real world they are not given problems that are repetitive and exactly like one that has already been worked out for them. They would be prepared for the fact that they could be given a problem that may have a solution that is unknown. We have a responsibility as teachers to prepare them for that possibility.

So I believe that what Jonassen is saying here is, don’t be afraid to, if necessary, stand up and work out a problem for a student if they are confused and ask you to show them something. That is part of your job to clarify a question or a process for them. However, it should not be part of the plan. Be open to different modalities of representing the work – not all students think the same and they need to see the differences in order to understand the full concept to big picture overall anyway. Limiting yourself to one way of working out an example is not helping them in anyway. So allowing yourself to be open to helping them “work it out” is really the best way to handle it for everyone.