The Problem Solving Framework
Man I could talk about problem solving all the live long day. I think it is such a central theme to what math teachers do, and we talk about it and we sense it's importance but I think we do such a bad job of teaching it.
How do you solve problems - how do you talk about it generally? When I do talk about it, I frustrate the hell out of my students because I am very reluctant to provide recipes to solve certain kinds of problems which is
exactly the opposite of what students want. Students want to know how to solve the problem involving distance and time - they want a framework to solve that distance time problem that you find in the rational algebra section of introductory algebra textbooks, or the solution mixture problems. And hey, those recipes exist, but my question, my point is, what the hell good is that? When in real life are you going to solve those problems?
Ok, fine, I concede that they will be helpful to you in a math class in which you will be asked to solve one of those problems. But then we are doing something that only has one limited and, honestly, fairly ridiculous use. And, please see my philosophy if you haven't already,
but I believe my job is to provide you with meaningful work. So to me, the point is about critical thinking and problem solving. How do you learn how to connect the dots between the information provided and the end result desired - regardless of the context. Well, I tell you, if I had the answer I would be rich and famous - at least in math teaching circles.
So I have some ideas - hell I have lots of ideas. One is the problem solving framework (PSF). Another is more for teachers because it has to do with the kinds of problems we provide, how we scaffold the experience of facing harder and harder problems and eventually teach students something about modeling - the act of turning information (words, drawings, data) into equations.
Those two tasks overlap so much that they are confused. Stand by for more information about thoughts on what we can do as instructors.
Here is the most recent version of the PSF.
