Proof :: Math Education Papers

Proof Proof. What is it and why does this simple term cause such a stir among mathematics educators and mathematics students? If you were to ask a young child to prove a mathematical fact, they would be happy to show you many examples of how it works. This does not constitute a proof but it is a step in the right direction. If you were to ask a high school student or first year college student to do a proof, you will most likely be met with groans and feelings of disgust. Students at this age have probably encountered proof in a geometry class where they were expected to follow a strict format without much freedom to express proofs on their own. However, if you were to ask a mathematician about proof they would begin to tell you about how beautiful proof in mathematics can be. Proof has always been a topic of interest for me. In high school geometry and my first year of college, I too did not understand proof. I felt like many other students, frustrated by the fact that we were asked to prove theorems that the book had already told us were true. It was as though the instructor was playing magical games on the chalkboard and all of the sudden we had a proof. However, as time progressed, I began to see the beauty of proof. Then, mathematical induction introduced me to the power of proof. In this paper I hope to address the concept of proof, how it relates to understanding and the implications for mathematics education. BACKGROUND In the 1950’s and 60’s proof played a significant role in mathematics education. Then in 1989, the National Council of Teachers of Mathematics (NCTM) deemphasized proof and replaced it with reasoning. Following this, mathematics educators began to see that students had difficulty with proof because they had little contact with it. In response, NCTM in the 2000 standards, elevated proof to a standard, emphasizing that it should be part of all students mathematical experiences (Knuth). Schoenfeld states proof is inseparable from mathematics. It is essential in communicating, doing, and recording mathematics (153). Throughout most of the history of mathematics education, proof has been more of a topic of study instead of a way to understand mathematics (Knuth 73). In addition, proof has only been limited to the college bound student or the student enrolled in geometry.