Pages 33-66 The Art of Problem Posing Reading

I thought that the reading from The Art of Problem Posing was quite interesting and a bit difficult.

Firstly, language was a bit difficult to read through and the details was a bit hard to grapple on. But in general, I really enjoyed the authors use of analyzing how we could approach theorems and "truths".

I can see a few strengths and limitations in the what-if-not approach and using it in a classroom setting. Firstly, by using this technique, it would help students to think on their own and to try to formulate their own thoughts. By using this concept in class and modeling it, the students will be able to perhaps develop this technique and approach the questions in this method. By doing so, they could perhaps make their own discovers, understand concepts much more deeply and gain further insight. Another strength to this method would be that students would not be taking facts at point blank, and coinciding with Brent Davis' lecture, it would promote growth-minded thinking. By questioning what is true, one can figure out and perhaps even make new discovery! As teachers, I believe that using the what-if-not technique and incorporating it into the lesson is very important if it is possible.

One limitation from using this technique is that at the high school level, most students are already familiar with taking theorems as facts. They may not appreciate questioning everything and become more confused in the class setting. As well, due to class and time constraints, using this approach may take much longer than expected and one simple "fact" may take a whole lesson to help students test out their "hypothesis". Furthermore, there is no real end to using what-if-not and if there is poor classroom and time management, this could pretty much go on forever. As well, I believe that the mindset of the students is really important to have them engaged with this approach. Otherwise, they would not take much out of it and only want the "fact" and not want to think too much over the concepts.

But all in all, I believe as teacher candidates, we should try to incorporate this form of problem posing into the classroom. The method is a great way for students to start thinking and questioning and probing into mathematics. By using this technique, some students may find that math isn't as boring as expected and that there is much to discover and much to probe. Furthermore, by using this form of probing questions there are a variety ways of approaching the theorem (for example, with Pythagorean theorem, the students were able to look at it geometrically as well as numerically).

Though the what-if-not approach is an interesting one and it sounds appealing, I would like to test it out in the classroom setting to see if I can apply it in reality.