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  • What you should also instruct is thinking about the spirit of the statement and less aboout technical correctness. "Actually,...." is rarely helpful. Commented Nov 18 at 8:56
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    @pyrochlor That is very field dependent. Mathematics for example is all about finding the edge cases (usually ridiculously pathological ones ), because they inform you about how to formulate a water tight proof. Commented Nov 18 at 10:09
  • @TimRias: Yes....Also there it depends on the situation. Even in university maths it is not always necessary, it is even detrimental to state to the student learning a conept all the exceptions and pathologies. Commented Nov 18 at 10:41
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    @pyrochlor The point I was making is that, when training professional mathematicians (which I agree is only a subset of university maths ), it is actually very important to get them to adopt the mindset of going "Where is the exception?" whenever they hear any statement. The "Actually, ..." mentality is at the core of how they need to learn to think. Commented Nov 18 at 10:50
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    @pyrochlor in university maths you might not need to tell a student what the exceptions are, but you should at least mention there are exceptions. It's really detrimental not to do so. At the start of university maths, we have to spend a fair amount of time overcoming misconceptions that arose because previous teachers weren't so careful. Let's not create any more. Commented Nov 18 at 10:52