Date: Mon, 30 Oct 1995 14:20:09 -0500 From: dwh2@cornell.edu Message-Id: <199510301920.OAA03790@postoffice2.mail.cornell.edu> Mime-Version: 1.0 To: Curricom@math.cornell.edu Subject: Special sections of M112 Cc: Harelb@math.cornell.eduTo: Curricom

From: David Henderson

I have been asked to report on the "Special" sections of M112. These sections were conceived and intiated by graduate students (Harel Barzilai, Lisa Orlandi, Maria Gargova, and Bob Milnikel). They took a proposal to the chair (and also Curricom?) and were approved to organize special sections for last spring.

Harel and Lisa taught two special sections last spring under the "supervision" of Cliff Earle. Cliff reported to Curricom that the section "went well" but took too much of the grad student's time. Curricom voted to try the Special sections again this fall with a regular faculty member in charge.

I was asked in May to be that faculty member. I have in the past taught Calculus and other courses in non-traditional ways, but I had never used the types of activities and projects that Harel and Lisa selected. I was amased at how well it worked. Harel and Lisa should be strongly thanked and appreciated by the department for the development work they put in.

1. The special sections cover almost the same CONTENT MATERIAL as the regular sections -- so far this semester we have left out the formula for surface area and covered less of partial fractions then the regular sections but we have covered (in projects) more than the regular sections on the fundemental theorems (including when the upper limit of the integral is a function) and on the development of the exponential function and solutions of dy/dx = ky.

2. Class time is the same as the regular sections except that about once a week we devide the class into small groups that work together on "ACTIVITIES" mostly taken from the book "Calculus: An Active Approach with Projects", but some written by Harel and/or Lisa. These activities serve a variety of functions: introduce new topics, give the students an expereince of the ideas behind the theory, use calculs to solve 'real-world' problems. The activities are sometimes finished in 20 minutes in class and sometimes they are longer and are finished by the students outside of class as part of their homework.

3. There are 3-4 longer PROJECTS which are completed by students in small groups (3-5 per group) outside of class. Each project is in the context of a "real-world" problem and takes 3-4 weeks to complete and require putting together several different parts of the curriculm and writting a complete coherent report. This semster: Project 1 requires the students to combine volume by slices, fundemental theorem of Caculus, chain rule, and natural logs. Project 2 requires combing differential equations, infinite series, binomial theorem, and exponential function. Project 3 requires combining infinite series, error estimates, speed of convergence, and integral inequalities.

4. The special section have only two prelims (instead of three) and a final.

1. The students like the activities and projects -- there is no grumbling. They report that they learn and understand caluculus better in this way. The kind of mathematics that the studnets go through in a project is what we would expect honors students in M122 to be able to do but the Special sections ALL students (working in small groups) do it and understand it enough to write a conherent report. Most of them would not be able to do it on their own.

2. I am convinced that students in the special sections understand calculus better (on the average) than those in the regular sections. I do not mean by "better" that they would do better on a standard final -- I expect they will do about the same. What they understand better is the ideas of calculs and how these can be applied in concrete settings -- isn't this what we want?

3. I do NOT recommend that all section of M112 be changed to Special sections. THis would likely be a disaster. I do recommend that any grad student or intructor who wants to use activities and projects should be allowed (and encouraged) to do so. It does not have to be an all or nothing thing. It is perfectly feasible for an instructor to try only a few activities and only one project in order for them to experience what happens. We have two books full of tried and tested activities and projects to choose from.

4. My original proposal was an attempt to institute 3.

5. It would have been easier for me this semester to have had a paper grader but NOT to have had a TA who takes one of the sections. THis is because at best it saves me 1 hour but also takes time to coordinate with the TA and made the schedule of activities and what-is-covered-when more difficult to organize. Thus I propose we go back to the 4-meetings-a-week-no-TA format.

I have in my office a collection of activities and projects and the written reports of the students. Please stop by and look them over. Also, on Monday Nov 6, Harel and I will give a report on the special sections in the Ocasional Seminar -- please come.

David