What-if-not

What-if-not? Yes, what is that?

It is a strategy to assist you in problem posing. It is a systematic approach that has five levels.

• Level 0 Choosing a Starting Point: ie. Pythagorean Theorem
• Level 1 Listing Attributes
• Level 2 What-If Not-ing: Take an attribute and ask yourself, 'what if that attribute was not true and was instead something else?' List as many alternatives as you can think of. ie. What if the Pythagorean Theorem was instead written as a^2 + b^2 <>
• Level 3 Question Asking or Problem Posing: What questions come to mind when you write down this alternative form? When is it true? Is it significant?
• Level 4 Analyzing the Problem

You can also combine your What-If-Not's to form even more possibilities.

How can I use this technique in preparation for my groups micro-teaching lesson next Wednesday on Logarithms and Exponentials? At the moment, I'm not really sure how it will be of use. However, I am sure we'll be able to use this problem posing strategy to think of some questions that could be useful for the presentation.

As a level 0, we could possibly begin with one of the rules for logarithms, such as the Power Law, or Multiplication/Devision Laws. From there, who knows where it will go?

The strengths of the What-if-not method is that it is a pretty direct way to formulate a lot of questions from a single starting point. It is a tree that keeps expanding and is interconnected with itself to create even more possibilities. Another positive aspect is that fact that it is a systematic approach to problem posing. It walks you through the steps making sure you really analyze the starting point, the topic you chose, by listing all the attributes you can see. For every question you get a what-if-not question and you are forced to analyze to prove/disprove (find out when true/false) each statement before continuing. You will really able to flesh out the topic you are looking at using this method.

The weaknesses of this method is that it can take a long time, and I mean a LONG time. And after putting a lot of hard work into the process, you may find yourself with nothing to show for it. For example, you may create a lot of what-if-not statements similar to Attribute 8 on page 50. Those arn't going anywhere and will prove to be a waste of time (If I'm wrong about that last sentence, please let me know). Nothing useful may come out of the process meaning I could have watched an episode of House instead of using the strategy.

I'll try using this method during the preparation for the micro teaching lesson. I'll see how it goes.