Most days I must resign myself to doing mathematics whether I want to or not. That is my job description. However, we each choose our tasking with a purpose, or we should. For me, a mathematics Ph.D. is a means to an end, of sorts. The fact is I need this degree to obtain a tenure track position at a school in order to have some job security. It is teaching that inspires me.

Each day I spend time planning lectures, teaching, considering successes or failures of prior lectures, grading papers, helping students in office hours, or writing tests and quizzes. To be sure, it takes an incredible amount of time. All the same, a good student makes it all worth it. Prissy O’keeffe and Elizabeth Jackson were two of my best students and are two of the yardsticks each new student is measured against.

I bring these two students up, in particular, because there have certainly been students who absorbed calculus more readily, but I never saw their metal tested. The marks of a great student are attendance, interaction, reflection and application.

If a student isn’t in class they are showing how much they respect the teacher and how important success in the class is to them. A students understanding is tied to curiosity. A wallflower spends the term of most courses with questions that father confusion and despair. To master a subject it is not enough to produce. A great student reviews their work and pursues their faults with an eye on their eradication. Finally, every student gets lost and becomes unmotivated and frustrated at times. To succeed in the classroom and in life you must dig down deep in those times and soldier on. These are the traits of great students, great employees, great managers and great leaders. These are the traits both Prissy and Elizabeth exhibited everyday.

The reward a teacher receives without any words is seeing these students succeed in his or her class. This reward grows with each chance meeting or interaction. These interactions can be a comment at the end of the course, a passing on campus, a request to write a recommendation letter or an email, or social networking blurb, telling about the job or internship they secured or that they needed something they learned in your course.

I am fortunate, in that, I encourage former students to seek out my assistance when they need it. From time to time I see a student in town. Today I saw Prissy at Barnes and Noble studying as diligently as ever. Each time this happens I’m reminded that even when I’m frustrated with the progress I may be making with my current class, it is always worth the effort.