"What-If-Not" Approach

After reading pages 33 to 65 of "The Art of Problem Posing" by Stephen Brown and Marion Walter, I have a better idea of how to plan questions. The authors describe a 5 level process to posing problems.

• Level 0: Choosing a starting point
• Level I: Listing attributes
• Level II: What-If-Not-ing
• Level III: Question asking or problem posing
• Level IV: Analyzing the problem

This process of posing problems can be used by my group for next week's micro-teaching lesson. Our group chose a starting point: we will be talking about graphs, data points, and sets. More specifically, we decided to describe a linear relation. In being more specific, the linear equation will have a non-zero y-intercept and there will be a scenario setting up this word problem. The next step of "What-If-Not" set us up to develop two other graphs. In thinking about how the graph might look like if it wasn't linear, we formulated ideas of problems involving quadratic relations and reciprocal graphs. New questions could be asked in describing these new data points. Of course, analyzing the problems simply is a matter of graphing the data set and looking at the pattern.

I believe some strengths of the "What-If-Not" approach are that you are forced to think about alternatives (e.g. ways your question could go wrong) and you look at all sides of the problem. I believe a weakness of the "What-If-Not" approach is that it can be time-consuming, creating all the attributes and "What-If-Not"s for the situation.