Dear David, 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? I felt guilty and awkward about it. As for the comments on departments not being idealized firms, I will just point out that most public institutions other than flagship universities, as well as lower tier liberal arts colleges, are under such budget pressures that they have no choice but to have most of their teaching done by graduate students and adjuncts. Most grad students are new to teaching and not initially as good as they become later. Over and over, I saw students who really committed to their teams get great benefits out of it. If I wanted something with slowly decreasing oscilations, or with a very narrow tall spike, I knew exactly which example to bring up. For example, one question asked students to numerically approximate at.
Since there are no solutions provided, you have to really be on guard not to assign one of these without catching it. My students commented in person and on evaluations at how willing and able I was to discuss anything mathematical, and the course coordinator who observed my teaching commented on how effectively I could enter in the middle of a mathematical conversation. I would be happier if the exams had one or two more basic questions, with the rest staying as they are. By continuing to use this website, you agree to their use. One point I should make, though, before the legislators start grinning too broadly.
Every time they copied an expression from one part of the page to another, there is a high probability that a plus sign will change to a minus. The course coordinators really stressed how much the course focused on groupwork.
I talked about how the average of a left hand and right hand Riemann sum will converge much faster than either side alone. Landing in the middle of that pack is an accomplishment, and I have decided to be proud of it.
Some thoughts on teaching Michigan calculus | Secret Blogging Seminar
The course coordinators were really hardworking and insightful people. You still need to give those teachers many hours a week of reading mathematics and thinking about mathematics, to keep their minds fresh and to keep them up to date with applications.
I feel that, psychologically, there is a big difference between having one or two questions that my hypothetical student can solidly get right, and having him pick up a smattering of partial credit on each of nine or ten questions that are too hard for him.
The webhomework system assumes that 1 any graph which looks piecewise linear actually is piecewise linear and 2 the students will use that fact to make any computations with that graph precise.
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Also, I think that it is worth being able to detect the difference between the student I describe here, and one who has not even mastered those skills. If not for your students specifically, are there benefits for the calculus teaching program as a whole from having you teach the class?
Organization I was assigned two sections of 32 students each, which dwindled to 30 umivh over the course of the term.
From a more practical perspective, almost none of my students naturally grasped this idea.
Some thoughts on teaching Michigan calculus
I was very curious to see how this was made to work. My students commented in person and on evaluations at how willing and able I was to discuss anything mathematical, and the course coordinator who observed my teaching commented on how effectively I could enter in the middle of a mathematical conversation.
Another geometric optimization problem asked students to construct a solid shaped like a cone on top of a cylinder to optimize some quantity, and the optimum was the degenerate case where the cone had height zero!
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. If a university or its funding source does not value research, it is not clear to teeam that it should hire researchers as opposed to lecturers.
It builds personal connections within a department. If I wanted something with slowly decreasing oscilations, or with a very narrow tall spike, I knew exactly which example to bring up. The applied and conceptual focus of the class Calculus at Michigan focuses very heavily on working with data and on understanding what computation to do, rather than how to do it. In Spring I often was unable to sleep for fear homewokr I had misplanned my Hodge Theory lectures, so it was a major relief to be so well taken care of.
At public schools in times of budget cutbacks, taxpayers ought to feel that in funding a math department they are not simply subsidizing an academic lifestyle that has nothing to do with them. Introductory material is best taught by people with more experience than grad students homeworo have. Feel free to read, and feel free to call me David rather than Professor Speyer. I just finished teaching two sections of first semester calculus at the University of Michigan.
Calculus at Michigan focuses very heavily on working with data and on understanding what computation to do, rather than how to do it. In these situations, departments may only have enough professor lines to staff the upper level i. Uich very much doubt you can homewokr perceive the difference between a straight line and two lines making an angle of with each other and this can make a substantial difference in an integral.
It is open without appointment to anyone who wants to come ask a question. The mathlab is like a live-action version of math.
I think I really did stand out from other instructors in these regards. For example, one question asked students to numerically approximate at. I can help my students put their struggles in perspective by authentically saying that there are math problems that have 116 procedure for their solution, take months to solve, and result in dense, barely readable, 50 page papers.
Especially in the first half of the term, I tried to spend almost the entire class period working with small groups. If the promise of academia were withdrawn, would people with a passion and skills for mathematics still become instructors?