How to prepare for an exam, the paper chase method.

The lecture scene in which Kingsfield explains the Socratic method is quite
a universal and can apply about teaching in general. It could equally well
be applied to mathematics. The Socratic method is a
teaching method which goes through questioning and answers.
In college, this method had been used only by a few teachers, like Ernst Specker
while most other plenary lectures were mostly lecture.
In high school, the Socratic method had been the primary method for my
teachers. It is usually done the `soft way" by asking questions, and getting answers by volunteers.
The `hard way" is to randomly select students and force them to answer. The ``hard way"
can lead to confrontations as the second scene illustrates. The movie paper chase
has been mentioned in a talk of Larry Summers who gave as the President a plenary
Bok Center Teaching conference lecture sometime around 2001 or 2002. It had been
a brilliant lecture itself papered with personal anecdotes from his own teaching
like describing a situation where he had to stop a lecture, say, "time out.
What I told you is not quite correct. I start again". The Socratic teaching
method is hard because the line of questioning can depend on the answers so that the
teacher has to master a wide array of possible cases and also know how to deal with
unexpected turns. It requires from the teacher to listen and understand the answers and to
lead the way. It is much more difficult than a straight lecture. When using as a
``soft method", it requires an active audience.