NCTM's Reasoning and Proof Standard lists four goals for all students to achieve, describes how reasoning and proof should occur in the classroom, and discusses the teacher's role in developing reasoning and proof. This broad Standard focuses on the need to integrate reasoning and proof into everyday classroom activities, the variety of proof techniques that should be used, and the importance of reasoning and proof in providing a deeper understanding of mathematics. The more specific Functions of Proof article takes a deeper approach by examining students' disposition toward proof and classifying various functions of proof for the express purpose of making it more meaningful in the classroom.

The perspectives and purposes of the two articles complement each other nicely. As an accompaniment to a mathematical software package, the Functions of Proof article fleshes out some of the points made in the necessarily terse Standard. The Standard opens with the assertion that "[m]athematics should make sense to students." Addressing this concern more specifically, the Functions of Proof article identifies the "problems that students have with perceiving a need for proof… as a major problem in its teaching." It responds to this critical question with a very insightful analysis of the problem as well as practical suggestions for solving it. Conversely, the Reasoning and Proof Standard illustrates the role of proof as part of the reasoning aspect of curriculum and instruction. Motivating the use of proof with its different functions as the Functions of Proof article suggests can serve as one component in the teacher's overarching quest "[t]o help students develop productive habits of thinking and reasoning" called for by the Standard.

While I support the ideas in the Standard, I particularly enjoyed and agreed with the Functions of Proof article. I liked the fact that it was written from an unashamedly mathematical perspective yet it still emphasized high school mathematics and pedagogical concerns. This balance was evidenced by frequent references both to the practices of mathematicians and the needs of students. I especially identified with the article because it formalized and clarified the radical changes in my attitudes toward proof as I moved from high school mathematics classes to rigorous upper level mathematics courses. My high school offered only Informal Geometry (geometry without proof) and my infrequent exposures to proof lead me to dread proof as a mysterious, impossible hoop to jump through only to "prove" something that was already intuitively obvious. In calculus, I develop a greater appreciation for proof as means of explaining why something worked or deriving a formula or rule. In my major classes at UGA, I began to desire proofs for convincing myself of difficult results, for solidifying the relationships within a series of axioms, theorems, and corollaries, and for satisfying my personal desire for a sense of mastery of a concept. The article summarized what I "accidentally" learned about proof over the last few years and outlined a progression of the uses for proof that loosely fit my own experiences.