“No one could figure out what a math lab was. Doesn’t a laboratory have Erlenmeyer flasks and things? Where are the flasks? Where’s the equipment in mathematics?” So observes Professor Haynes Miller in the introductory video to 18.821 Project Laboratory in Mathematics.
OCW had wanted to publish 18.821 for a number of years, but the course did not meet OCW’s standard criteria for a publishable course. Unlike most courses taught at MIT, this course has no set body of knowledge that the instructor hopes the students will retain and use after the course ends. The course has no textbook and no exams, for example. Instead, students are made to confront mathematics in the way it appears to a working mathematician. That is, they are offered the opportunity to experience the frustration and excitement of doing mathematical research. They work in teams on projects that are open-ended and may change every time the course is offered. They write papers in a style appropriate to journals in the field.
Happily, 18.821 was perfectly suited to an innovative treatment through OCW’s new Educator initiative, which enhances the OCW publication for educators. On the 18.821 OCW course site, Professor Miller and his teaching colleagues describe the structure and logistics of the course, the process of teambuilding, the selection of projects, the trickiness of guiding students without overdirecting them, and much more.
This is an innovative course model that fosters student creativity and shows mathematics as a dynamic and ever expanding field. Professor Miller hopes that the model will be adopted by other mathematics departments in the United States.