The What-If-Not approach of problem posing interests me. It takes a commonly viewed notion and turns it upside down. It takes something true, and asks how we can change these attributes. This would lead to a great many questions that need to be asked, of varying significance. I think that this strength is also its weakness.
Asking what-if-not, as said earlier, leads to many new questions asked. In asking these questions, these lead us to new and profound ways of mathematical thinking. It sparks our curiosity because we ask questions that, in some cases, have nothing to do with the original idea. It is, however, bad as well in a sense. The depth of these questions relies significantly on how the problem poser thinks. Things might be left out. Even deep questions that let us form a new mathematical perspective may be missed because the problem poser didn’t see an attribute and change it accordingly. Also, changing an attribute a certain way could lead to a similar problem like this.
Given that, it would be very difficult to put this sort of thinking into factoring quadratics. But that wouldn’t stop me. I could ask questions like what if it wasn’t a quadratic? What if the exponent wasn’t an integer? What if it wasn’t just one variable?
These thoughts would all lead to very open ended discussions revolving the subject matter. I like the WIN approach. It challenges both the problem poser and the problem solver. These what if not questions can lead to deep and profound mathematical ideas that could very well reach outside of the mathematics curriculum and I think that would be totally awesome.
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