In order to bring our arguments to a common frame of reference, I think that I can reword my point as follows: to do the sort of abstract reasoning that is required for what is commonly (so not like the OP, who redefines calculus as 'abstract(ish) concepts that will be useful in real math later on') considered 'calculus', one needs a part of the brain that is not just 'grown' by training, but that actually needs to grow to a certain baseline before it can function at all - after which it can be further developed by training/practice.
So in other words, some brain functions just do not physically 'exist' (the matter needed for those functions) at very early ages. You can't take any 2 year old, or 3 or 5 year old, and practice until they get it. You have to wait until that part grows naturally. And growing (or maybe just 'activating') that part earlier doesn't say anything about overall intelligence, either.
And yes, it's different from emotion control, but not dissimilar - the mechanisms is the same.
All of this, of course, for the general population. I can't deny there are child prodigies who understand these things years before their peers; they exist, it's a simple observation. My point is: some things you cannot train in children. You have to wait for the brain to get there; and children not being there yet is not (necessarily) because of lack of training.
Hopefully this clears up my position, and contrasts it with yours. If it does in the way I think it does, it becomes a matter of the state of the art in neurology and neural development. My information comes from having read some popular literature (books, not the 'parenting' section of Marie Claire, but still...) on child development; not a very authoritative position, I'll freely admit. I never got the impression anywhere that this position is controversial or even just not universally accepted, but if it is, then our (apparent) disagreement can be reframed in these terms. (to preempt - at that point I don't have anything to add except the tried and proven 'trawl google scholar until I find something that I can bend into supporting my position, to make it appear that I have Science(TM) on my side although I don't really know anything about it'; but maybe I'm getting ahead of myself here :) )
oh that's fine. :)
I'll disagree on outlook though. I believe that at least neural-net-wise a brain develops according to what one practices the most. If that's reasoning then its reasoning.
I think its a bit frivolous to just assume that abstract concepts are beyond children of that age, I think if anything its more a failing of our means of explaining them correctly.
Of course its ultimately possible when the three year old I chat to claims to understand that they are lying to me or are just seeing their response as a hoop to jump through, however I would posit that the vast majority of the required components are formed by this point. The remainder just being a process of dispelling the various foggy bits through practice and exploration.
TL;DR; I fancy the brain to be more a thing that just improves over time. Even if incorrect I certainly doubt that "reasoning" or "abstraction" are just modules that are either IN or OUT of the developing brain. I feel like these sorts of distinctions are unproductive and too coarse to make.
Like I get that there are bits that are somewhat nonfunctional. She struggles to remember but she can if she really tries or events had impact, she can process-of-elimination to find the location of one of our tribe, she can understand that a word has double or triple meaning and double checks with us when we give her an old label with new meaning.
I feel like there is plenty of stuff going on there that could be fashioned into "reasoning" and "abstraction", hence my issue with your assertion.
So in other words, some brain functions just do not physically 'exist' (the matter needed for those functions) at very early ages. You can't take any 2 year old, or 3 or 5 year old, and practice until they get it. You have to wait until that part grows naturally. And growing (or maybe just 'activating') that part earlier doesn't say anything about overall intelligence, either.
And yes, it's different from emotion control, but not dissimilar - the mechanisms is the same.
All of this, of course, for the general population. I can't deny there are child prodigies who understand these things years before their peers; they exist, it's a simple observation. My point is: some things you cannot train in children. You have to wait for the brain to get there; and children not being there yet is not (necessarily) because of lack of training.
Hopefully this clears up my position, and contrasts it with yours. If it does in the way I think it does, it becomes a matter of the state of the art in neurology and neural development. My information comes from having read some popular literature (books, not the 'parenting' section of Marie Claire, but still...) on child development; not a very authoritative position, I'll freely admit. I never got the impression anywhere that this position is controversial or even just not universally accepted, but if it is, then our (apparent) disagreement can be reframed in these terms. (to preempt - at that point I don't have anything to add except the tried and proven 'trawl google scholar until I find something that I can bend into supporting my position, to make it appear that I have Science(TM) on my side although I don't really know anything about it'; but maybe I'm getting ahead of myself here :) )