Problem Posing Strategy , "What_If_Not"

Problem Posing using “What-If-Not” strategy

Problem posing is one of the essential elements in teaching mathematics. As teacher candidates, we must be able to pose valuable problems that lead our students’ attitude toward exploring and discovering math. One of the great problem posing strategies that I just learned is “What-If-Not.” The strength of this problem posing strategy is that it makes many questions available for the teacher to use. In addition, posing problems using “What-If-Not” strategy leads to having more valuable questions that are ambiguous rather than very “clear” and “easily understandable” ones. However, sometimes dealing with such problem posing strategy is difficult since it is time consuming and it may get confusing in some cases.
Our microteaching project is about determining the nth term in a sequence, or its sum. The way that I related this problem posing strategy, “What-If-Not”, to our project was really simple. First, I started from a “concrete material”, level (0), and thought about infinite random numbers; then, I moved to level (I) and listed some its attributes such as: they are infinite, they are random, they start from 1, and so on. Next, I thought about negating each attributes, or in the other words “What-If-Not [ing]” them (level II). For instance, what if these numbers are not infinite, then they are finite, and what if they are not random, then they are non-random numbers and the difference between the two consecutive ones is d. After doing so, I used these new alternatives as a basis for my new questions (level III). For example, ‘what is the sum, or nth term of this finite sequence?’ After selecting some of my new questions I tried to analyze them (level IV) and come up with a logic answer which finally I did. Overall, posing problems by using “What-If-Not” strategy helped me a lot in posing my micro-teaching questions and provided me with more questions than I ever thought.