Teacher Resources

Math Lesson Plans

• Middleweb

The Discovery Method
Professor R. L. Moore of the University of Texas (Austin) pioneered this method in the 1920's. This method works best in a class that is homogeneous in terms of ability. School Geometry and university freshman Group Theory courses are particularly suited to this method. The main idea here is to establish competition between students, but not between teacher and students. Here is how to accomplish this.
1. At the beginning of the course, tell students they are responsible for finding errors in proofs presented on the board.
2. After an error occurs and no one sees the error, tell the presenter "I don't understand," and ask her if she could go over the step again.
3. When the presenter looks to you for approval, look at students for approval.
4. When a student asks you a question about the proof by the presenter, ask the presenter.
5. After a student has presented a valid proof, do not present a more elegant proof.
6. when you are presenting a new theorem whose proof is best presented by yourself, ask for ideas first to the students who were least successful in their presentations.
7. If a student presented only part of the proof, name it a lemma - Gregory's Third Lemma, for instance - and then ask someone else to continue with the proof using the lemma.
8. If a student is too shy to come to the board, offer to be his writer on the board.
9. You should not point out the obvious.
10. If a student is not successful at the board, ask another student to take it up from the step where the presenter was wrong.
11. If no student could present a valid proof, take valid portions collectively presented and incorporate in to a proof you present.
12. When a student is presenting, go and sit in the student's empty chair.
13. Be patient and respectful - you are dealing with the nation's most precious resource - the young minds.

CAUTION! Clearly, not every topic is amenable to this activity. This is actually a merit - the students also get to see the teacher do some lecturing the usual boring way. This is slow-going, and you may end up covering only a part of the syllabus, so pick representative topics that would sparingly cover the syllabus. However, the ability and knowledge the students would acquire through the "activity" would enable them to think mathematically far more than the math sermon we can preach to them. The activity approach might "rescue a potentially creative mathematician from oblivion [1]."