I think I have told this story before, but it fits here because I think it is an example of how the interplay between student and a good teacher can really work well, and even though strictly speaking "off syllabus" gave insights that probably embedded the syllabus more deeply as a result. I was, I guess, thirteen and my maths teacher remarked in passing that any right angle triangle with integer sides had one of them divisible by 5. I realised when he said it I didn't know how to begin to prove something like that. So I puzzled it over while the rest of the class went on. Then, when we were all doing some exercise or other he was wandering amongst us and I asked him how you would go about proving it. He then stopped the exercises and explained to the whole class how to do it. And in the course of that he tied in some of the stuff we had been learning so we saw how those ideas tied in together.

Factual? Well yes, but much more about skills than facts.