{"id":667,"date":"2010-02-24T22:15:42","date_gmt":"2010-02-25T03:15:42","guid":{"rendered":"http:\/\/mathgradblog.williams.edu\/?p=667"},"modified":"2017-02-07T14:22:35","modified_gmt":"2017-02-07T19:22:35","slug":"motivating-calculus-students","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2010\/02\/24\/motivating-calculus-students\/","title":{"rendered":"Motivating Calculus Students"},"content":{"rendered":"

by Brian Katz<\/a><\/p>\n

I’ve been struggling with motivating calculus students this term, so this issue has been in my mind constantly. I’ve found two different techniques for improving student engagement in the course, and I wanted to share. Also, I sincerely hope that you will post other ideas that have worked for you.<\/p>\n

<\/p>\n

Application Project:<\/strong> I have asked my precalculus and calculus I students of the last few years to seek out an expert in their field of interest (which is almost never mathematics), articulate the skills learned in our course, and find an application in their field that could not be understood without calculus. Almost every one who has done this assignment has realized why they are being asked to take calculus, and a few of them even caused faculty in their field to discover why they were asking their students to take calculus. In my experience, you need to ask student to write 2-3 pages about their interview or they will not get as much out of the experience. (Be prepared to ask for a rewritten version.) I also think this works better as an extra credit project than as an assignment, but both have worked for me. (For the record, I got the idea for this from Adriana Salerno, now at Bates College.)<\/p>\n

Challenge Problems:<\/strong> I give a lot of quizzes in my calc courses, and I like to write a challenge problem on the board during the longer quizzes that the faster students can think about when they’ve finished. These work best with the students who could be math majors if they only knew the true beauty of mathematics. Here is one of my favorites:<\/p>\n

Consider the integers, {…,-2,-1,0,1,2,…}. Notice that:
\n(i) The integers come with an operation, addition, that takes two integers and produces a new integer, and that operation is associative. This means that (a+b)+c = a+(b+c) for any integers a, b, and c.
\n(ii) There is an integer, 0, so that a+0 = a = 0+a for any integer a.
\n(iii) For each integer, a, there is another integer, -a, so that a + (-a) = 0 = (-a) + a.<\/p>\n

Now consider the set of strictly increasing, differentiable functions, with the operation of composition. Translate each of the sentences above into this parallel case and then try to argue that they are true. (You are proving that these sets are “groups”; look this term up on Wikipedia after class.)<\/p>\n

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by Brian Katz I’ve been struggling with motivating calculus students this term, so this issue has been in my mind constantly. I’ve found two different techniques for improving student engagement in the course, and I wanted to share. Also, I … Continue reading →<\/span><\/a><\/p>\n

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