Thinking Mathematically

Chapter 2 in the text provided us with an interesting way of examining problems in math. I feel that I was in fact following a format similar to the one presented, but not in such a formal way. The text book provided us with a three step technique in solving problems. The first step, is the Entry Phase, here the student is to carefully read the problem to try to grasp a better understanding for the problem. The text recomends three questions in order to facilitate the Entry Phase; (1) What do I KNOW? (2) What do I WANT? (3) What can I INTRODUCE? using these three questions should help lay the framework for the next step. The next step is the Attack Phase, this is the stage through which you feel that the problem has become your own, and the problem is either abandoned or resolved. The third stage is the Review Phase, here one should review their work. There are three aspects to the Review Phase: (1) CHECK the resolution (2) REFLECT on the key ideas and key moments (3) EXPAND to a wider context.

Chapter 3 refers to the responses to the state in which the individual has a feeling of being STUCK! This feeling in my opinion can act as both a positive and a negative depending on each individual. Some might interepret being STUCK! as a motivator while others may find it frustrating and give up. But just as stated in the text I believe that this phase should provide easch student with some sort of learning. There can also be the great sense of accomplishment from this phase which I would think is similar to the AHA! response.

There is one aspect of the two chapters that stood out to me which we need to be aware of. As much as me might believe that every child should love math or should enjoy math it is just not going to happen, just as not all students enyoy PE or English or Biology and so on. The textbook refers to taking math problems as a chef would take tasting food, in that a chef would savor the flavor. In this context yes a chef would savor that flavor but would a dentist or a math teacher, so it is difficult to ask everyone to look at math the same.