Chapter 9 Developing Mathematical Thinking

Summary:
By provoking your mathematical thinking you can see other peoples mathematical thinking and therefore better teach Math. The chapter looks at the processes of inquiry and your emotional state for developing your thinking. To develop your math mathematical thinking it is very important to review and reflect on the problems you have done and be aware of your emotional state. The problems you do must challenge your thinking.  Mathematical thinking is not just used in math problems but everywhere.


What surprised me:
The first thing that surprised me was how right the book was that the understanding of the content overshadows your inquiry into math and your mindset towards math. I think this speaks to what we are trying to do in this course but just presents it in different words.   The book separates understanding of mathematical concepts and inquiry, I do not agree that they need to be separated. I argue that to fully understand a concept you first need to inquire around the concept. When learning how to implement the concept one does not need to inquire about how the concept came to be, why it works that way, or when it should or should not be applied. These question can be answered by a teacher or a book but to practice these questions, to really learn the answer to these questions one must inquire about the concept. ( I hope this makes some sense I could not come up with a better way of explaining my thoughts.)

The second thing that surprised me was the addition of emotional state in mathematical thinking as this is an older book. I think with would have been a very progressive thought when the book was published, but it definitely speaks to where some troubles with math start. Having the right mindset going into a problem can dictate how the problem is solved as well as how the review of the problem goes.


Patrick McManus