R. L. Moore was an influential mathematician at the University of Texas who developed a distinctive way of teaching.
The standard way that mathematics is taught is that the lecturer presents definitions, theorems and their proofs, and examples, and the students either copy this down or are provided with printed lecture notes. Moore decided that he did want to do this, and instead used a more discovery-based system.
He would give axioms, definitions, and theorems and then students were expected to find proofs independently, and present these to the class. The class was expected to look for flaws in these proofs, and these would be discussed and the proof changed and improved as necessary.
The role of the lecturer in this is to give some guidance to students, and to moderate the student discussions to keep them civil and constructive.
Supporters of the ``Moore Method'' cite the increased student involvement as a great advantage. They also note that it will probably mean the same amount of work for the lecturer - it is not an easy way to lecture without doing any work.
