**Course:** Mathematical Sciences Department, Mellon College of Science

**Assessment:** Problem Seminar in Math Studies

## Purpose:

A group of instructors felt that they needed a way to assess how effectively majors in Mathematical Sciences can apply the abstract theories of algebra, metric spaces, and multi-dimensional calculus in 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 mathematical research. Finally, they perceived a need to stimulate majors’ interest and capabilities in mathematical research. The best way to meet these goals was to develop a course that combines lecture and seminar formats.

## Implementation:

This course is a meeting where the two lecturing professors give the students problems to solve and discuss. Students are not formally assessed during the seminars, but rather are allowed the freedom to explore mathematical proofs in a collaborative setting. What takes place in the problem seminars is not always directly related to the lecture material because students are encouraged to approach the proofs collaboratively.

## Results:

The professors have noticed that the problem seminar has encouraged students to approach and analyze problems mathematically by applying lecture concept to real mathematical proofs and that it has motivated students’ interest in mathematical research. The class has also grown in popularity.

## Comments:

When this course was first developed, the class size was small and all students could talk about their solutions during the 90-minute class period. However, the class size has increased and it has become more difficult for all students to participate. We have addressed this problem by placing students in groups of three to solve the mathematical proofs and having one person from each group present the solution to the class.

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