Natalie Smith

EMAT4680/Sheehy

Reaction to proof

I never feared proofs until I entered college. In high school, I delighted in geometry proofs and my ability to understand them. Now ninth grade is a memory, and my classes and these readings challenged me to really understand not only the proof’s content, but also to understand why we prove things in general. Particularly, this reading opened my mind to new ideas about proofs that I never before thought of entertaining. It took a few times for me to grasp the chapter from Rethinking Proof, but reading those ideas compared to the NCTM’s application standards solidified some realities of proof.

It was an interesting exploration for me to see the defined functions of proof and how those functions show the use of proof beyond mathematics. Each function related a way of thinking and a way of processing new information. Proof takes defining things beyond locating the mental schema and really challenges us to know "why". From NCTM’s example it was interesting to see how each function of proof was manifested into the classroom’s thoughts without specific instruction. The functions of proof are logical and subconscious, yet it’s important to recognize them so that we can really understand the importance of proof.

These readings about proof further supported my own ideas about a mathematics classroom. I see a math class not as a mere lecture on numbers, but more importantly as an opportunity to grow as logical and abstract thinkers. I have always been encouraged by a thought once shared by one of my high school teachers: "it’s not always what you learn in math that counts, but how you learn." Proof validates our old ideas and acts as a vehicle for new discovery.