With this in mind, to what do you attribute your success?
Well, looking back I have to attribute a lot of my perception of success with blindness, in the sense that 5-6 year old me thought he was a hot math talent because he knew about integers when the teacher was teaching the class about natural numbers. (I still remember raging against the claim that the right answer was “you can’t subtract 3 from 2!” instead of “negative 1!”) From what I can tell from looking at curriculum online, that’s ~5 years ahead of schedule but I’d interpret that as the curriculum putting it late (though, on reflection, that could be Dunning-Kruger).
I remember jumping ahead of (well, deeper than- below?) the curriculum frequently, and suspect that it had different causes in different circumstances. Rapid calculation is probably just high g, but rapid perception of concepts and connections probably has something to do with intuition or vision that I find difficult to articulate.
I’ve also never been particularly good at explaining why I know what I know with regards to math- from refusing the step through the algebra when I could solve a problem in my head, to avoiding college classes which were primarily about proving that methods worked (i.e. calculus the second time around) rather than introducing new methods. I have, through deliberate practice, gotten better at writing proofs in the last year or two, but still regularly come across simple theorems where I say “I know X is true, but don’t know how to show X is true.”
I do think I would have been more successful in a Moore method environment which is designed to teach a deep understanding of mathematics- it seems likely to me_now that me_past would have learned/wanted to care about rigor much earlier in that sort of environment, and would have kept pushing my math boundaries much more uniformly.
Well, looking back I have to attribute a lot of my perception of success with blindness, in the sense that 5-6 year old me thought he was a hot math talent because he knew about integers when the teacher was teaching the class about natural numbers. (I still remember raging against the claim that the right answer was “you can’t subtract 3 from 2!” instead of “negative 1!”) From what I can tell from looking at curriculum online, that’s ~5 years ahead of schedule but I’d interpret that as the curriculum putting it late (though, on reflection, that could be Dunning-Kruger).
I remember jumping ahead of (well, deeper than- below?) the curriculum frequently, and suspect that it had different causes in different circumstances. Rapid calculation is probably just high g, but rapid perception of concepts and connections probably has something to do with intuition or vision that I find difficult to articulate.
I’ve also never been particularly good at explaining why I know what I know with regards to math- from refusing the step through the algebra when I could solve a problem in my head, to avoiding college classes which were primarily about proving that methods worked (i.e. calculus the second time around) rather than introducing new methods. I have, through deliberate practice, gotten better at writing proofs in the last year or two, but still regularly come across simple theorems where I say “I know X is true, but don’t know how to show X is true.”
I do think I would have been more successful in a Moore method environment which is designed to teach a deep understanding of mathematics- it seems likely to me_now that me_past would have learned/wanted to care about rigor much earlier in that sort of environment, and would have kept pushing my math boundaries much more uniformly.