In the old days, lecturing was easy, but this new pedagogy is difficult, challenging, time-consuming and very, very rewarding. It s rewarding for both the teacher and the student, Repsher said. Her innovative techniques expose undergraduates to aspects of math they usually don t see. Today, we have the opportunity to free young students to visualize mathematics, to think mathematically, and to experience mathematics as a tool for describing the world. We can integrate technology, not as a crutch for sloppy thinking and computation, but as a tool for constructing mathematical concepts.
Students can ask what if questions.
They can make and test conjectures. They can do real mathematics, even at the freshman level. In Repsher s courses, she starts with specific examples and practical applications, only later bringing the students to confront the abstract so they can build the concepts from their own experience. And she makes sure they do just that by insisting written reports accompany mathematical solutions papers she expects to be written in clean, simple terms that can be easily understood by a variety of audiences. This comprehensive teaching approach combined with her overwhelming enthusiasm about math in general, has Repsher s students writing more than quality reports, it has them writing rave reviews about her.