Every department has three distinct curricula: If some of my readers were among those who did, can you tell me how you stayed motivated? Our non-teaching activities are increasingly public: Next time, I should make sure that they spend a lot more time interacting outside their teams from the start of class. 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. 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. However, I can list some positive things which I brought to my teaching that come from my background.
It builds personal connections within a department. The course maintains a problem bank of suggested questions to use on quizzes and in class. Most grad students are new to teaching and not initially as good as they become later. I can help my students put their struggles in perspective by authentically saying that there are math problems that have no procedure for their solution, take months to solve, and result in dense, barely readable, 50 page papers. Just emphasize how crucial it was to pass the Gateway a computer administered exam testing this skill , and the students would teach themselves. If not for your students specifically, are there benefits for the calculus teaching program as a whole from having you teach the class?
I was very concerned about this going into the course.
In my case, I was competing with grad students who had taken calculus far more recently than I had; had taught it several times before; and who were often extraordinary competitors with a string hkmework Olympiad medals and Putnam victories.
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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To find out more, including how to homeworj cookies, see here: Just emphasize how crucial it was to pass the Gateway a computer administered exam testing this skilland the students would teach themselves.
But I think a lot of it comes from continuously thinking about a wide umicu of mathematics over the last twelve years. The course website including a secret sectionwas full of resources to help me plan my lessons.
Next time, I should make sure that they spend a lot more time interacting outside their teams from the start of class. 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. The intended focus of the problem is on how to set up the correct integral in the first place.
Once they started working together, their performance on quizzes and in class improved dramatically. 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!
Some thoughts on teaching Michigan calculus | Secret Blogging Seminar
It builds personal connections within a department. Ohmework I teach this class again, I will make a similar deal. This has two consequences. Partly for the technological breakthroughs it creates, and partly for its own aesthetic value. But he also has mastered a nontrivial skill. Working with people, no matter what, will be a source of tension.
I am curious — the median score on the Putnam exam is a zero. New instructors can get the gist by talking to older faculty, but without close supervision, they feam have to guess a lot.
None of this comes directly from anything that I learned in grad school or in research. Do you have any thoughts on what teaj your students might have had from having you teach the class rather than a proficient graduate student?
Some thoughts on teaching Michigan calculus
I fondly recall an analysis 1 instructor who assumed that calculus 1 included a detailed 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 homewokr inverse function theorems.
Feel free to read, and feel free to call me David rather than Professor Speyer.
People who teach introductory classes generally do better at teaching advanced classes. I did the day-to-day teaching 3 times a week, 80 minutes per meeting. I talked about how the average of a teaam hand and right hand Riemann sum will converge much faster than either side alone.
Calculus at Michigan focuses very heavily on working with data and on understanding what computation to do, rather than how to do it. I had a lot of fun going to the mathlab.
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!
I think they could teach low level math courses as well as I do.
I drifted from the given schedule by a day at times, but I basically followed it and found that it worked well. I think I really did stand out from other instructors in these regards.
I do think there are advantages to having instructors with more mathematical experience then a grad student can obtain, and I talked homwwork some umichh them above. 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.
If you are thinking of importing MI calculus into your school, you should think about how to take care of your teachers.