Mathematics is a unique field of study. A study that can only be explored through pure reasoning of logic, and a healthy dose of skepticism. Having dealt with mentality of what mathematics is by incoming freshmen, my first goal to a class to instill a notion of skepticism. To not simply repeat my lecture, but confront it. I explain to every class that I do not want them to believe me. But it is my job convince them to the that what I say is true through a well reasoned argument. I want them to question everything they have learned before, and be confident in what they know by the end of the course.

I always keep in mind that this is their first time seeing the material, so it is my job to help facilitate their exploration of a new mathematical concept. For in class computations, I dissuade students in checking with me for quick verification on a solution. Rather, I encourage students to look to each other, and work together on a problem. Not only does this push students to work together outside of class, they can learn that initially being wrong on a problem is part of the learning process. As Carl Sagan once said,
"There are many hypotheses in science which are wrong. That's perfectly all right: it's the aperture to finding out what's right."

Or as I would say to a class, "If you're willing to wrong, you can learn to be right."

Learning mathematics is fun as it is challenging for students. And, it is my personal aim to make sure that the environment of my class is one where a student looks forward to returning to---one where they enjoy learning math.