Style of teaching/learning mathematics: by proofs of theorems only?

[Mark44]

The very idea of the method. Moor (sic) puts a statement on the board and waits for the students to prove it. He does not move on until it is done, and he only shows what is wrong with their attempts but doesn't give hints.

Seems to me that showing that some work is wrong is a pretty powerful hint.

 

[Stephen Tashi]

The very idea of the method. Moor puts a statement on the board and waits for the students to prove it. He does not move on until it is done, and he only shows what is wrong with their attempts but doesn't give hints.

As I experienced the Moore method (as used by one of Moore's students), the class is asked to prove or disprove statements. They don't know in advance whether a statement should be proven or disproven. They get experience in giving counterexamples.

In my opinion, the Moore method places a great demand on the instructor's ability to organize the subject matter so the class proceeds at an appropriate pace. It doesn't suit instructors who may have an encyclopedic knowledge of their field but don't have a vision of it as a sequence of inquiries and deductions. Perhaps there are fields of study where nobody has such a vision. And there may be mathematical results created by some genius that nobody else can understand as a step-by-step sequence of inquiries performed by mere mortals.

In addition to the general objections that have been raised against the method in this thread, there are some mundane ones. I think Moore (R. L. Moore) applied the method to teaching point set topology ,which is not everyone's favorite mathematics and did not use terminology completely matching that used by modern texts. Also (the web says) that R. L. Moore supported segregation and refused to admit black students to his classes. So a method associated with his name is tarnished by that.

 

[WWGD]

Yes, " Moore Spaces" , in Topology, are named after him :

And , as per Stephen Tashi's post, we have the issue of whether we separate the artist's/author's work from their personal lives.