Introductory material is best taught by people with more experience than grad students generally have. If I wanted something with slowly decreasing oscilations, or with a very narrow tall spike, I knew exactly which example to bring up. I found my calculus classes to be the place where I really learned algebra. In each case, for many of my classmates, that was the beginning of the end. I also wrote and graded weekly quizzes, and graded the team homework assignments.
Our non-teaching activities are increasingly public: This happened even if none of the students on a team was strong — I had one team made up of four good friends, all of whom were in the bottom quarter of the class. However, when I did force them to, they often got a lot out of it. And I think that, to teach college math well, you need to be aware of a great deal of mathematics, well beyond the official level of your course. My intended audience here is others who are about to teach Calculus at Michigan, or people who are wondering what it would be like to set up a Michigan-style program in their own departments. It is open without appointment to anyone who wants to come ask a question.
I should have taught it explicitly. My students seemed to really get excited when I brought in data about a subject which interested them. The mathlab is like a live-action version of math. Right now, instructors are tea cheaper than professors. I am going to say something which is obviously against my professional interest.
I think they could teach low level math courses as well as I do. Grad students graduate; postdocs leave.
I did the day-to-day teaching 3 times a week, 80 minutes per meeting.
Some thoughts on teaching Michigan calculus
My intended audience here is others who are about to teach Calculus at Michigan, or people who are wondering what it would be like to set up a Michigan-style program in their own departments. I fondly recall an analysis 1 instructor who assumed that calculus 1 included a homeworo treatment of proof by induction, a linear algebra instructor who assumed that calculus 2 was a differential equations class, and a differential geometry instructor who assumed that calculus 3 included a detailed treatment of the implicit and inverse function theorems.
However, I can list some positive things which I brought to my homfwork that come from my background. My students were organized into groups of four who met weekly to work together on more challenging problems, which they wrote up as a group and received a single collective grade for. It also focuses on getting students to be able to explain what they are doing to people with even less mathematical background than they have.
Also, I think that it is worth being kath to detect the difference between the student I describe here, and one who has not even mastered those skills. I had two students who, when I asked them for teammate preferences, specifically asked not to be put with students in the top half of the class. When I teach this class again, I will make homeworkk similar deal. Some subset of those people will also have the personality and drive to be teachers.
I himework encourage you to work hard on your team homework, and to talk in depth with your teammates about the problems.
Similarly, I knew how I should expect numerical computations to behave. I talked about how the error rate in a left hand or right hand Riemann sum is controlled by the steepness of the function, while the error in the average is controlled by the curvy-ness. I also had a lot hpmework fun. I missed this over and over.
In my case, I was competing with grad students who had taken calculus far more recently than I had; tesm taught it several times before; and who were often extraordinary competitors with a string of Olympiad medals and Putnam victories.
Before answering, I want to point out that university departments are not idealized firms, who aim to produce a service as efficiently as possible.
What was difficult about this was that it made grading very difficult to predict. The intended focus of the problem is on how to set up the correct integral in the first place. There are plenty of people who love math so much that they will continually learn and study new mathematics.
Math Section Page
I think we should give him a question on the exam where he can display this mastery. I do think there are advantages to having instructors with more mathematical experience then a grad student can obtain, and I talked about some of them above. So why the misgivings? Most grad students homwork new to teaching and not initially as good as they become later.
Do you have any thoughts on what benefits your students might have had from having you teach the class rather than a proficient graduate student? Now, I think pure mathematical research is a crucial investment in the future of our society.
I also wrote and graded weekly quizzes, and graded the team homework assignments. I had a lot of fun going to the mathlab. The course website including a secret sectionwas full of resources to help me plan my lessons.