Reflection from "The Art of Problem Posing"

Pg.33-65

I agree with the idea that we often 'take the given for granted'. With a given problem, we usually focus on the given information. It is important that we can use whatever information we can get from the problem to help us to solve the problem. But as the author has demonstrated, by doing that we often limit ourselves in problem solving.

I understand that if we could teach our students to think independently, they would be able to have a better understanding of the taught concepts. In the context of Mathematics teaching, many students would prefer the traditional lecturing style due to academic performance pressure. Are we teaching our students the learning as memorizing and getting good grades?

I do like the author's approach of 3 levels of problem posing: attributes listing, asking "What if not attribtes", and problem asking. I can see that I incorporate even one or two levels in my lesson.

It is a good idea to first ask students to brainstorm all they know about a topic. This can help in making connections of ideas learned. Then we can ask the "What if not attributes" questions. This would definitely encourage/trigger for different thinking about a concept/problem. I also think this can help in extending the concepts.

However, not all lesson plans can be taught using the WIN approach. If for example the lesson is to teach algebraic manipulation, WIN strategies wouldn't be effective. In addition, students can be overwhelmed by the cylcing of new questions making them more confused with the extra problems. We also have to keep in mind that there's the time and curriculum constrains and it can be easily off topics with the WIN method.