Problem Seminar in Math Studies

Instructor: Multiple (Example submitted by Bob Prego)
Scope: Course - Problem Seminar in Math Studies, MCS
Assessment Tool: The Problem Seminar in Math Studies

Motivation:

A group of instructors felt that they needed ways to assess the extent to which students are able to apply the abstract theories of algebra, metric spaces, and multi-dimensional calculus learned in the lecture to the kind of collaborative problem-solving required in mathematical research. They also wanted students to learn to solve and present mathematic proofs in a collaborative setting that mirrors the environment of the research mathematical profession. And finally, they perceived a need to further stimulate students’ interests and capabilities in mathematical research.

Goal:

To assess how well students are able to apply the abstract theories of algebra, metrics spaces, and multidimensional calculus to solve mathematical proofs and to assess how well students are able to present and defend solutions to mathematical proofs to their peers.

Method/Tools:

The key method to address our goals was the development of the “problem-seminar. ” The seminar is a complement to the lecture. The lecture is intended to give students techniques while the problem seminar is intended to allow them to direct these techniques to the intellectual pursuit of coming up with mathematical proofs. The seminar provides students with problem solving opportunities and provides us with a means to assess whether students are able apply the techniques and concepts learned in the lecture to mathematical proofs.

Implementation:

The problem seminar is a meeting of the students outside the regular lecture time where the professors who teach the class give them problems that they solve and discuss during this time. The focus of the class is to develop students’ interest and capabilities in math as a research discipline and to encourage camaraderie and collaboration among students in the class. So what takes place in the problem seminars is not always directly related to the subject matter that is covered in the lecture.

Participants:

This is a high-powered class targeted at the best undergraduates in Mathematics.

What is the nature of the data, how was it analyzed/interpreted?

Students are not formally assessed during the seminars but rather are allowed the freedom to explore mathematical proofs in a collaborative setting that is facilitated by the two professors who co-teach the class. Students are divided up into small groups and each group works on a problem and then presents the solutions to their peers and professors.

Impact/Results:

The instructors have noticed that the problem seminar has encouraged students to approach and analyze problems mathematically by applying lecture concept to real mathematical proofs, and motivates students’ interests in mathematics as a research discipline. The class has also grown in popularity.

Comments:

When the problems seminar was first developed, the size of the class was quite small, allowing for all students to talk about their solutions in the ninety-minute class period. However, since the class-size has increased, it has become more difficult to open up the floor to everyone. We have addressed this problem by dividing students into groups of three to solve the mathematical proofs and then having one person from the group present the solution to the class.