What-If-Not-Approach

The What If Not Approach is a powerful way of thinking about mathematics concepts. Instead of just focusing on one certain "thing" about a topic, it looks at other concepts around the topic. This is where I have a problem. I am not that creative at looking at things a different way. To me, the What If Not Approach is a question one poses to start the exploration on a topic. I am not used to asking the question, “What if not?” I find that I get stumped when I ask myself that question and draw a blank. It's like a stumbling a block. To quote Erwin, “students might not have the mathematical ability to grapple with "cycling" two negated statements and combining them into an alternate statement because it doesn't seem natural.” This was basically my problem. For example, in the geometric board, I was not able to see anything about the amount of pins there would be if the board was a different shape. It didn't even occur to me that is what would happen. I was thinking maybe the same square but the diagonal of the square would be the diameter of the circle.
In our micro-lesson, we sort of have a “what if not approach”. We are not simply, having the students graph some points and fit it to a straight line. We are exploring the possibility of what if the relation and graph were not linear. Students will either explore a y=1/x, y=x^2 or y=mx+b relationship and report back to the class their findings. That way, the students will see that graphing is a technique suitable for all type of relationships between variables.