|
Richard Jernigan -> RE: Alan Bennett on Teaching (Aug. 16 2013 19:32:51)
|
The supposed dichotomy between depth of learning and professional preparation is not inevitable, in the hands of a talented teacher who is allowed to teach.
R. L. Moore was arguably the most successful teacher of professional research mathematicians of the 20th century. His 50 PhD students dominated the field of topology during the middle half of the century, and they themselves produced numerous able, productive, and even famous research mathematicians.
Besides his distinction as a teacher, Moore was an outstandingly productive and original research mathematician, President of the American Mathematical Society, Member of the National Academy of Sciences, and so on.
Every year Moore taught freshman calculus. His method was utterly radical. He lectured perhaps a total of fifteen minutes during the two-semester course. Teaching was done via a brilliantly conceived and carefully graduated sequence of problems. Only one problem was assigned at each class meeting. The students were expected to solve the problems on their own and present the solutions at the next class meeting. There was no text, and students were forbidden to read.
By the middle of the fall semester the assigned problems included the proof of theorems in basic mathematical analysis. These were the beginnings of an education in pure mathematics.
At every meeting, Moore would call upon the students for their solutions. Unerringly, he began by calling upon the student least likely to have solved the problem, and worked his way up the list until someone claimed to have a solution. At times he would call on 25 or 30 people before someone presented a solution. Those without a solution were expected to pay careful attention, and to question anything they didn't follow.
The course was notoriously rigorous. Moore would accept about 35 students in the fall. Seldom did more than 25 sign up for the spring semester. There were no exams. Any student who presented a valid solution in class got the highest marks. The rest got the next highest if they persisted in attendance and showed continued interest.
Other professors at the University of Texas taught calculus the usual way. Fifty-minute lectures, reading of a text, and numerous drill problems to be done as homework, graded by a student assistant. Three or four tests were given during each semester, and a final exam. These courses were meant to prepare students for engineering and science.
Every year there was a prize examination. The winner got $100. The deal was that all the other professors could submit problems for the exam. They would elect one of their number to choose the problems for the exam. Moore would contribute only one problem, with the unanimous consent of the other professors. Every single year without exception a Moore student won the prize, with a perfect score.
RNJ
|
|
|
|
