It is named after Robert Lee Moore, a famous topologist who first used a stronger version of the method at the University of Pennsylvania when he began teaching there in 1911.
Instead of using a textbook, the students are given a list of definitions and, based on these, theorems which they are to prove and present in class, leading them through the subject material.
The Moore method typically limits the amount of material that a class is able to cover, but its advocates claim that it induces a depth of understanding that listening to lectures cannot give.
[…] Having selected the class he would tell them briefly his view of the axiomatic method: there were certain undefined terms (e.g., 'point' and 'region') which had meaning restricted (or controlled) by the axioms (e.g., a region is a point set).
After he became familiar with the abilities of the class members, he would call on them in reverse order and in this way give the more unsuccessful students first chance when they did get a proof.