How has this course changed or not changed your perceptions of teaching math?

I originally thought that math was as basic as introducing a basic formula to students and building on that. I never thought much about using manipulatives past the younger ages of students. I liked how the class forced me to look at problems the way my students would and break them down in order to be able to teach them to my students. This class frustrated me several times because it took me so long to understand the importance of breaking problems down the way Dr. Rein's did. Students need to be challenged and given opportunities to approach problems in different styles. Each student learns a different way and at a different rate, which means that my instruction should cater to the differences of my students. In order to teach a problem, it is important to start with the basics and work my way up.