Reflection to Art of Problem Solving – “What if Not”

How can you use some of these ideas in microteaching:
To be frankly honest, I am not too sure how I can apply the “what if not” approach in teaching all math topics. I think I can use some parts of the approach to help my students gain a better understanding in my microteaching lesson-arithmetic series. For example, given arithmetic series, I can first ask the students to predict terms in the series and calculate the sum of the series in any method they would like to use. Then engage the students in a class discussion and hopefully the students will have different methods of solving these problems. For each method, I can ask the students “what if we were not to use this method are there other ways of solving the problems?” This would be level 2a of the “What if Not” approach and the alternative methods would be level 2b. For each method, I can also pose the question (level 3) “can we apply this method and be able to calculate the sum of arithmetic series or predict terms in the series in a minute or two?” Then in the final level, together as a class we can analyze how applicable is this particular method to every arithmetic series.

Strengths and weaknesses of “What if Not” approach:
Strengths:
- Useful in facilitating thoughts and helpful to developing a more in-depth understanding a mathematical topic
- It may help to (re)connect to other mathematical topics
- It can help us to come up with creative ideas and ways of looking at a mathematical topic and perhaps, can be used as a way to engage students

Weaknesses:
- This “what if not” strategy is REALLY time-consuming
- It is challenging to implement the strategy in a classroom setting
- The list of attributes and “what if not questions” may add to students’ confusion and frustration, especially for those students who only have a basic understanding of a mathematical subject
- This strategy in the end might have a negative effect on students – for example, students may end up hating the math topic they have exhaustively examined