In this section, we follow Neal's journey through the class. I chose Neal for the portfolio for two reasons. As a teacher, I saw the greatest growth in Neal throughout the term, so he shows what I think can happen in the course as a best case, but I also chose him because Neal represents an important type of student that we see in senior level mathematics education courses. A type I would refer to as a disillusioned, computational oriented, preservice teacher.
Early on in the term Neal told me he was a student that had been pretty good at mathematics until he hit “this proof stuff"” right after calculus. He also told me that he needed at least a 3.0 in the class or else he could not go on in his teacher education program, but unlike some students, he recognized that he had to do the work. I have seen many students like Neal in teaching the capstone class, although not all needed a good grade in the class. In studying Neal, we see him go through a transformation throughout the term. By the end of the term he is more confident about his mathematical abilities, many of his proofs are written in an acceptable style, and he has come to realize that a desire to learn mathematics is something that can in the best circumstances come from an internal motivation.