But how could some 7 year olds have vastly different ”pre-requisites” than others?
In my experience aptitude plays a far bigger role. Yes, you compensate for lack of aptitude with a lot of hard work, but that’s a different matter.
In my experience aptitude plays a far bigger role. Yes, you compensate for lack of aptitude with a lot of hard work, but that’s a different matter.
Often aptitude is not aptitude at all, but all of the above.
Then, during learning anything, the same thing also applies. How much support you get from teachers and parents. What sort of environment you have available to practice in. And a lot more.
Finally, when all other factors are equal, aptitude can play a certain role. But one that in an educational setting is largely irrelevant. Because if everything else is perfectly in place to teach something, including learning any prerequisites, aptitude is only something that matters in hindsight.
Which is extremely important as well. Labeling someone as lacking aptitude can be highly discouraging. Repeatedly hearing that they aren't “naturally” good at something can lead them to stop trying, even if it's not true.
Of course it’s not fair, life isn’t fair. But the good news is that you can quite easily compensate for lack of aptitude with more work, and that is most definitely the case for mathematics, up to and including undergraduate level.
I grew up in Sweden where everyone goes to the same kind of pre-school, that does very little math teaching. Still, the difference in aptitude when we started school was significant. But we all know this.
Your take is so black and white that it only holds up if you almost willfully ignore all other context. Obvious things like different kids having a different home experience, exposure to different things outside of school, exposure to different things in the years leading up to pre-school, etc. These are just a few factors that actually heavily influence where someone starts and how easily they pick up some subjects. Then there is the fact that following the same curriculum or even being in the same class doesn't mean getting the same attention from teachers. In fact, ironically those with "more aptitude" sometimes get more attention further increasing their headstart.
I honestly want to invite you to go back, read my other comment again, actually take the time to internalize it then reply back again.
Because you are very close to actually agreeing with me. Specifically because you mention the practice and extra work bit. You just don't realize it yet.
So even if we limit "aptitude" to a strictly genetic sense, it will still explain most of the difference in math ability at 7. All other factors related to growing up will add up to less than half of that.
Regarding practice compensating for genetics, I am not talking about having more supportive parents or more demanding pre-school, I am talking about Asian level hardcore drilling. That can certainly make up for most of the difference, at least when it comes to basic mathematics. But that means that the concepts that a child with math aptitude will pick up in 5 minutes will take 5 hours of drilling for another child.
That is again a simplification of reality, leaving out a lot of context and nuance.
1. You are right that research seems to indicate that intelligence is heritable, meaning that genetic factors play a role in individual differences in intelligence. Estimates of the heritability of intelligence typically range from 50% to 80%, depending on the study, age of the participants, and the methods used. I am guessing that this is where your "All other factors related to growing up will add up to less than half of that" remark comes from. However, that 50%-80% is in relation to the inheriting intelligence from the parents. It does not mean that it influence more than half of your intelligence. It also highly depends on the specific aspects of intelligence that is being measured.
2. If we are throwing in statements as borne out by science then you can't ignore that studies also show that factors such as education, nutrition, and socioeconomic status significantly impact cognitive development. In fact, some of the most critical periods for brain development occur in early childhood. Things like:
a) Prenatal environment: Factors such as maternal nutrition, stress levels, and exposure to toxins can affect fetal brain development.
b) Early childhood nutrition: Proper nutrition in the first few years of life is crucial for optimal brain development.
c) Stimulating environment: Exposure to a variety of experiences, toys, and learning opportunities in early childhood can enhance cognitive development.
d) Physical activity: Regular physical activity from an early age can promote brain health and cognitive function.
e) Parental interaction: The quality and quantity of interactions with caregivers, including talking, reading, and responsive care, significantly impact cognitive development from infancy.
f) I could go on for a while, but the picture should be clear enough.
And some people are just lucky to have the right environment. I happened to have had access to some more advanced books from older relatives as a kid and I noticed that it gave me an edge over my peers in some areas.
(I mean, that's not my opinion, that's just how modern society has been running for... a century or two?)