I sat in on a class taught by a colleague of mine at Northern Virginia Community College for my teaching observation. The class was Differential Equations taught by Joe Agnich. Joe and I have discussed teaching philosophies, syllabi, etc. in the past, so I knew going in that he and I had similar outlooks with respect to teaching mathematics. I found his class to be interesting, well organized, appropriate to the capabilities of his students. I thoroughly enjoyed it.
Joe began his class by writing a short schedule of upcoming events on the left side of the board, talking about each before beginning in earnest. He then passed out corrected take-home quizzes along with photocopied handwritten solutions for their later perusal. He highlighted portions of the solutions, emphasizing how important it is to read carefully and to stay neat, organized, and not to skip steps. He also singled out two students who had impressed him with particular components of their solutions. Joe, like myself, cultivates a casual attitude in the classroom. He makes use of dry wit and, where appropriate, self-effacing humor. He is methodical in his approach to the subject, making sure that the students understood what they were doing and why. He made sure that they understood both the techniques involved in the lecture at hand, but also where this lesson fit in to the rest of the chapter.
Even when demonstrating how to solve the example problems, he always kept a conversational tone. He kept a running commentary while working, tying everything back to content the students should (at that point in the semester) understand, and explaining how to move from one case to another. At every transition he made sure to ask for questions. He did not pause as long as I normally do when checking for comprehension, but when students spoke up, they received his full attention.
I learned, to my great pleasure, that Joe and I are similar not only in our philosophical approach to teaching, but in our implementation of those philosophies as well. His handwriting is significantly crisper than mine, and he writes fifty to seventy-five percent larger than I do, but the way he approached the material felt very “right” to me. I told him afterward, in all honesty, that he is exactly what I look for in a mathematics professor and that I thought I would enjoy taking a class from him.
