# Moore method - Wikipedia (Teaching method based on finding proofs by oneself)

the content of the course is usually presented in whole or in part by
the students themselves. Instead of using a textbook, the students are
given a list of definitions and theorems which they are to prove and
present in class, leading them through the subject material If a student
had already studied topology elsewhere or had read too much, he would
exclude him. He would usually caution the group not to read topology but
simply to use their own ability. Plainly he wanted the competition to be
as fair as possible, **for competition was one of the driving forces**.
[…] After stating the axioms and giving motivating examples to
illustrate their meaning he would then state some definitions and
theorems. He simply read them from his book as **the students copied
them down. He would then instruct the class to find proofs of their own
and also to construct examples to show that the hypotheses of the
theorems could not be weakened, omitted, or partially omitted**. When
the class returned for the next meeting he would call on some student to
prove Theorem 1. 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**. When a student stated that he could prove Theorem x, he was
asked to go to the blackboard and present his proof. Then the other
students, especially those who had not been able to discover a proof,
would make sure that the proof presented was correct and convincing.
When a flaw appeared in a ‘proof’ everyone would patiently wait for the
student at the board to ‘patch it up.’ If he could not, he would sit
down. Moore would then ask the next student to try The students were
forbidden to read any book or article about the subject. They were even
forbidden to talk about it outside of class. Hersh and John-Steiner
claim that, “this method is reminiscent of a well-known, old method of
teaching swimming called ‘sink or swim’ “.