What if Not?

The Strengths of this method are seemingly quite obvious, despite being seldom used in ‘real world’ problem solving. This strategy enables the problem poser to consider a great many alternative situations to the current problem, in order to see the current problem in the clearest possible light. As with any tangible object, if one can pick it up and rotate and flip it and hold it in different shades of light, one is going to know much more about what it looks like than if it were simply stared at from across the room.

There are unfortunately limitations to this strategy. Time constraints can become a factor if a multitude of other situations are considered instead of focussing on the job at hand. Confusion and loss of focus can result for many people if they delve too deeply into other explorations. Some ‘what if not’ questions, as can be seen with some of the examples in the book, are simply a waste of time and do not help with the solving of a problem at all. Another limitation to consider is that many problem solvers may be thrown off their ‘rhythm’ by allowing their minds to wander around a problem.

In our microteaching assignment for Wednesday, we have been asked to incorporate the ‘what if not’ strategy. I think this will be a fun a way to ‘teach’ the concept of Arithmetic Series, especially considering the students will already know the concept. Questions come to mind such as “what does it mean for a series to be arithmetic and what would it look like if it were not arithmetic?”, “what if we could not generalize an arithmetic series?”, “what would a series look like that had no sum?” It should be a fun and thought provoking way to introduce a concept.