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Teaching Background

I have taught calculus I MATH 115 (4 times) and calculus II MATH 116 (once) as a graduate student at the University of Michigan. At UofM the math graduate students are given the opportunity to teach our own sections (about thirty students) of calculus. We prepare our own lectures and are responsible for all in-class components of the class (quizzes, office hours, etc). A course coordinator is responsible for preparing the exams and the exam grading is done collectively so that we don't grade our own students exams.

This has been a great experience for me and I have learned an enormous amount in the process. Teaching as a graduate student provides a great opportunity for growth as a teacher as it is likely the last time you are both teaching and taking classes at the same time.

Lessons learned teaching as a graduate student

Here are some simple teaching tips I have picked up:

• No matter how well thought out your lecture is, if the students struggle to read your board work they will quickly lose heart.
• Nobody likes a moving target. Set clear expectations for assignments, grades, etc. Any level of uncertainty in the students minds about how they will be evaluated puts their focus on grades and not on the subject material.
• It is okay to have a personality, it is even encouraged. Nobody likes learning from a math robot.
• Know the students names and what they are interested in. This may sound obvious but in my experience the best way to get students listening is to give an example and say "Now lets see an example of exponential growth in a population of bacteria. First lets consult our resident biology majors Sarah and Tim...."
• If you don't have the time to do an example without skipping steps, then don't do it. Avoid ending the class with confused students.
• Provide an outline for the class at the start. Students are more forgiving when they know where you are going in the lecture.
• Having a class website to post announcements, grades, notes, etc will reduce confusion among the students on the adminstrative details of the class. It is also a better way to disseminate notes or solutions than email.
• Asking good questions of the class is difficult and should be part of your preparation for class. It is very difficult to tell the difference between silence because the question is to easy or because the question is unclear/difficult. Make questions into more of a discussion. A discussion implies that we are trying to solve the problem together instead of a pop quiz and encourages student participation.
• If something is important, write it down! In math we have a habit of copying the theorem on the blackboard and then turning around a giving our insight orally. The insight is what the students need from the teacher, they can get a list of theorems from the book.