I am feeling good about the progress I have made since our last class on the project. Namely, I have finished reading through all of the sources that I compiled so that I have a much better working understanding of my topic. This has led to a few other developments in the work.
First, my topic has shifted subtly. I began by focusing on designing complex problems, but I now believe based on the research that I have done that the more pedagogical, tactful skill is in facilitation of student problem-solving. A more refined version of my topic might be the question "What sort of scaffolding is appropriate when presenting students with challenging problems?" This is a subject with some debate in the literature, but the upshot of it is that there is extensive discussion to draw from.
In terms of connections to the real world of teaching, I had a number of conversations last Tuesday with teachers at my practicum school that were very helpful, both math teachers and teachers of other subjects. They generally employ a method of guided instruction, so I am glad I had the chance to speak to them about why that is - the consensus seemed to be that it was more replicable and less taxing on time than a more problem-based approach, although some teachers made clear efforts to work some problem-solving into each class by way of an "opener" that took the previous day's concept and extended it in a problem.
Something I am currently struggling with a bit is the creation of an interactive component. I am tempted to just provide a complex problem for students to investigate but doing so in the space of 15 minutes doesn't feel true to the spirit of the inquiry. It may have to be something that I leave the class with to investigate on their own, but then I have done exactly what the research warns against which is to provide minimal guidance! Tricky, tricky.
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