Before answering, I want to point out that university departments are not idealized firms, who aim to produce a service as efficiently as possible. Partly, I think this is important for maintaining student motivation. 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! SE and, while the questions are less exciting, the challenge of being face to face with the questioner makes up for it. When I teach this class again, I will make a similar deal. 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.
The coordinators also held weekly meetings to brief us on where the course was going. Next time, I should make sure that they spend a lot more time interacting outside their teams from the start of class. What was difficult about this was that it made grading very difficult to predict. Now, I think pure mathematical research is a crucial investment in the future of our society. If you are thinking of importing MI calculus into your school, you should think about how to take care of your teachers. Because, if I were a student in this class, I would have highly resented being forced to work with students not at my level.
mat This has two consequences. Our non-teaching activities are increasingly public: I also had a lot of fun. This student has not learned nearly as much as we want him to.
Michigan is a very competitive school and everyone who gets in here is excellent.
I should have taught it explicitly. You can see the exams here: There are a lot of problems in the webhomework mainly sections tram. The course coordinators were really hardworking and insightful people. 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.
Some thoughts on teaching Michigan calculus | Secret Blogging Seminar
I think we should give him a question on the exam where he can display this mastery. I just finished teaching two sections of first semester calculus at the University of Michigan. I homeworj just one item to add to your lists: He should do poorly on the exam — a C minus or a D.
I found my calculus classes to be the place where I really learned algebra. For example, one question asked students to numerically approximate at. I spent a lot of time in high school and college helping my fellow students, and I matn a lot by doing so. Because, if I were a student in taem class, I would have highly resented being forced to work with students not at my level.
Grad students graduate; postdocs leave.
I could look at a table of values which one of my students had computed and guess pretty quickly whether they had entered them into the calculator correctly. The exams You can see the exams here: The exams, especially the last two, were almost all challenging conceptual problems.
Once they started working together, their performance on quizzes and in class improved dramatically. So this advice really did turn out to work, despite my skepticism.
For example, when counting boxes under a curve, they pointed at the squares in a ujich order, rather than sweeping from left to right, top to bottom. The mathlab is like a live-action version of math. 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.
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Team homework My students were organized into groups of four homeework met weekly to work together on more challenging problems, which they wrote up as a group and received a single collective grade for. It builds personal connections within a department. 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. After all, you cost the department significantly more than a graduate student!
The athletes really got a kick out of table 1 from this papershowing how world class runners accelerate second by second; a lot of students enjoyed figuring out how long a runway a Ford Mustang needs to accelerate to mph using the data here.
I think these are very appropriate goals in theory.
Some thoughts on teaching Michigan calculus
From a more practical perspective, almost none of my students naturally grasped this idea. Introductory material is best hmework by people with more experience than grad students generally have. By continuing to use this website, you agree to their use. 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!