How aspects of a modified Moore method in an upper-level, proof-intensive, collegiate mathematics course impact confidence among students

Abstract

In pursuing a degree in the field of mathematics, there comes a point when a student is no longer solving problems, but rather constructing mathematical proofs. It is through these proofs that we are able to verify the validity of different mathematical concepts and formulas. One must understand and be able to prove his work if he hopes to make his mark on the field. Further, the kind of thinking developed in this process is necessary for successful performance in a number of fields, especially science, technology, engineering and math (STEM). However, how does one learn the art of proof writing? A proof cannot be memorized and reproduced like the quadratic formula. A proof requires deep thought and planning in order to make the reader understand the logistics behind the argument. This process cannot be taught like a traditional algebra or calculus class. The best method for thoroughly and effectively teaching these classes is where research and opinions begin to differ among educators and mathematicians.