Lesson One: You can and will work at a desk for seven hours straight, routinely. For several years, I have been teaching 18.30, differential equation, the largest mathematics course at MIT, with more than 300 students. The lectures have been good training in dealing with mass behavior. Every sentence must be perfectly enunciated, preferably twice. Examples on the board must be relevant, if not downright fascinating. Every 15 minutes or so, the lecturer is expected to come up with an interesting aside, joke, historical anecdote, or unusual application of the concept at hand. When a lecturer fails to conform to these inexorable requirements, the students will signify their displeasure by picking by their books and leaving the classroom.
Despite the lecturer’s best efforts, however, it becomes more difficult to hold the attention of the students as the term wears on, and they start falling asleep in class under those circumstances should be a source of satisfaction for a teacher, since it confirms that they have been doing their jobs. There students have been up half the night-maybe all night-finishing problem sets and preparing for their midterm exams.
Four courses in science and engineering each term is a heavy workload for anyone; very few students fail to learn, first and foremost, the discipline of intensive and constant work.
Lesson Two: You learn what you don’t know you are learning. The second lesson is demonstrated, among other places, in 18.313, a course I teach in advanced probability theory. It is a difficult course, one that compresses the material typically taught in a year into one term, and it includes weekly problem sets that are hard, even by the standards of professional mathematicians. (How hard is that? Well, every few years a student taking the course discovers a new solution to a probability problem that merits publication as a research paper in a refereed journal.)
Students join forces on the problem sets, and some students benefit more than others from these weekly collective efforts. The most brilliant students will invariably work out all the problems and let other students copy, and I pretend to be annoyed when I learn that this has happened. But I know that by making the effort to understand the solution of a truly difficult problem discovered by one of their peers, students learn more than they would by working out some less demanding exercise.