Source: Gowers website, Jun 2012
What I emphatically would notlike to see is teachers learning “the right answer” and giving a mini-lecture about it to their classes. Instead, the entire discussion should be far more Socratic.
The idea is that the teacher would go into a discussion about a question like this with a good grasp of the issues involved, but would begin by simply asking the question. An initial danger is that nobody would have anything to say, but one way of guarding against that is to discuss questions that people are likely to care about.
For example, the question above about whether girls are better than boys at a certain subject is far more likely to encourage people to think critically about statistics than a mathematically equivalent question about a less contentious topic. If the discussion stalled, the teacher’s job would be to give it a little nudge in the right direction.
The main point is one I’ve basically made already: the discussions should start from the real-life problem rather than starting from the mathematics. Pupils should not feel that the question is an excuse to force some mathematics on them: they should be interested in the question and should feel the need for the mathematics, the need arising because one can give much better answers if one models the situation mathematically and analyses the model.
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