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David Epstein: Innovative Teaching Techniques

Article: 97 of geometry.college
Newsgroups: geometry.college
From: sander@geom.umn.edu (sander)
Subject: David Epstein: Innovative Teaching Methods
Sender: news@news.cis.umn.edu (Usenet News Administration)
Organization: Geometry Center, University of Minnesota
Date: Mon, 20 Sep 1993 14:57:13 GMT
Lines: 72
"I have been interested in teaching for a long time. For many years I was worried about the ineffectiveness of my teaching. My sister was a primary school teacher and is now a lecturer in sociology. She has always complained to me about the quality of mathematics teaching at university. The problem was I never knew what to do about it," says David Epstein, professor of mathematics at Warwick University in England. "I first saw how I could improve my teaching at a summer course two years ago at the Geometry Center."

"The course instructors were all famous mathematicians: John Conway, Bill Thurston, Peter Doyle, and Jane Gilman. The students ranged in age from 15 to 65. Many of them were high school students. Some of them were famous research mathematicians. However, despite their diverse backgrounds, everyone learned something.

"The class consisted of discussion and problem solving; there were no formal lectures. Through unusual presentation techniques, the instructors managed to present some quite advanced mathematics usually first encountered at the graduate level. For example, to describe curvature of a torus, they made use of peelings from potatos. We often made models and cut objects out of paper."

"The Geometry Center summer course inspired me to try to improve my own teaching. I have been trying some new techniques with a course on metric spaces at Warwick. The students are polarized on whether they like the outcome. The unusual format of the class means they have to work harder. Some of them do not like this, but others have told members of the department to make their classes as hard as mine. In general I think it is good for the students. The course is in its third year, and it improves each time."

Here are some of the teaching techniques in Epstein's class: Despite having approximately 160 students, Epstein uses a discussion format rather than a formal lecture style. In addition, Epstein attempts to concentrate on understanding rather than tests. To this end, in past years he has tried giving a variety of extra credit questions, with monetary awards for those who have answered the most extra questions correctly. Epstein plans to continue his tradition of giving out examples of all the standard errors made on past tests and making the students work out flaws in the reasoning.

This year, the most important change in Epstein's class is the syllabus; "I like to annoy my collegues by pointing out that our syllabus design is based on a never ending process; we always design a course as a fundamental building block for more advanced courses. We never reach a goal. Using a technique explained to me by Regine Douady, an expert in elementary education, this year my class has a syllabus different from any book on metric spaces. The students start with a list of problems which they can understand and attempt before the class begins. However, solving these questions is quite difficult without some powerful theory. The object of the class is to design the tools necessary to answer these problems. This means that there is motivation for the material. When they see the key to solving one of the problems, it is a relief and often a surprize."

Click on the icons below to see the problems for Epstein's class. Though some problems involve quite advanced material, they are definitely worth trying. If anyone has further questions about the course, email to David Epstein at dbae@geom.umn.edu

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Created: May 15 1994 --- Last modified: Jun 18 1996