In these situations, departments may only have enough professor lines to staff the upper level i. So why the misgivings? I would be happier if the exams had one or two more basic questions, with the rest staying as they are. Michigan is a very competitive school and everyone who gets in here is excellent. The mathlab is like a live-action version of math. I think they could teach low level math courses as well as I do.

I think I took these messages too strongly to heart. Grad students graduate; postdocs leave. So why the misgivings? A word to any of my students who find this post. 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 think I really did stand out from other instructors in these regards.

There are a lot of trick questions in there!

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. By continuing to use this website, you agree to their use. Every time they copied an expression homeowrk one part of the page to another, there is a high probability that a plus sign will change to a minus.

My students seemed to really get excited when I brought in data about a subject which interested them.

I had a CS student who, for a final project, was making a winamp-like program and was trying to figure out how you take an audio signal and extract a sequence of musical pitches, so I got to tell him about Fourier windowing, and he really did get it to work! Even if the math dept got to keep the money, I suspect there is nothing we would like to do with it more than hire a top researcher!

I highly encourage you to work hard on your team homework, and to talk in depth with your teammates about the problems. A word to any of my students who find this post. Michigan is a very competitive school and everyone who gets in here is excellent. So this advice really did turn out to work, despite my skepticism.

However, I can list some positive things which I brought to my teaching that come from my background. Michigan has a large room called the mathlab it could probably hold people or so filled with round tables and staffed 8 hours a day by tutors who can provide help with mathematics courses.

There are very few people who will enjoy an activity at which they regularly have no small successes. Also, I think that it is worth being umch to detect the difference between the student I describe here, and one who has not even mastered those skills. Mat example, one question asked students to numerically approximate at.

But I think a lot of it comes from continuously thinking about a wide range of mathematics over the last twelve years. 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.

It is open without appointment to anyone who wants to come ask a question. Dear David, Do you have any thoughts on what benefits homeeork students might have had from having you teach the class rather than a proficient graduate student?

I think I really did stand out from other instructors in these regards.

# Some thoughts on teaching Michigan calculus | Secret Blogging Seminar

This happened even if none of the students on a team was strong — I had one team made up umicb four good friends, all of whom were in the bottom quarter of the class. I did the day-to-day teaching 3 times a week, 80 minutes per meeting. Team homework 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.

If I wanted something with slowly decreasing oscilations, or with homewirk very narrow tall spike, I knew exactly which example to bring up. The exams, especially the last two, were almost all challenging conceptual problems.

## Some thoughts on teaching Michigan calculus

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. Because, if I were a student in this class, I would have highly resented being forced to work with students not at my level.

And, while skilled instructors with an excellent command of the mathematical field may be more common than skilled researchers, they are going to be rare as well. Next time, I should make sure that they spend a lot more time interacting outside their teams from the start of class. It also focuses on getting students to be able to explain umidh they are doing to people with even less mathematical background homewirk they have. I can help umixh students put their struggles in perspective by authentically saying that there are math problems that ohmework no procedure for their solution, take months to solve, and result in dense, barely readable, 50 page papers.

If a university or its funding source does not value research, it is not clear to me that it should hire researchers as opposed to lecturers.

I talked about how the average of a left hand 1116 right hand Riemann sum will converge much faster than either side alone. Consider a student who has learned the basic mechanical skills of numerically approximating a derivative from data, or of differentiating some complex expression.