I read HN, I assure I am not good at math. :P
Note that a) your sons are linked to you genetically; b) your sons' genetics likely differ. You can't actually derive any useful information from this anecdote alone.
I think it's a mixed issue. There most likely are differences in effectiveness of picking up math in people, and they may be significant, but the environment is making them too significant and creating unnecessary thresholds (i.e., if you can't do X math by age Y, there's a problem).
From what I've seen, most institutions want the most easily teachable students, which automatically selects for all ducks to be in the row, regardless of whether these factors are fatally influential. So if someone just has an easier time with math, for whatever reason, they'll have an easier time in general, because they require less work from institutions.
I think we have very little data of what good teaching can do because it largely doesn't exist, so mostly we're just looking at flat ability.
Understood. I think the information I feel I can derive is this : with sufficient effort you can turn a "can't do math" person into one that can, modulo your theory that there are some "untransformable" people.
>I think we have very little data of what good teaching can do because it largely doesn't exist
True, although in the case of my kids' teachers I can immediately tell which of them has any real appreciation for Mathematics and it seems to correlate strongly with outcome. For example our schools like to hire English teachers to teach math in middle school. That doesn't seem to work out so well.
Moreover, in my experience I see lots of people in the US say "I'm bad at math" if they are not good at algebra. Algebra is not math. Neither are fractions. Geometry is part of math. So are combinatorics, logic, numerical analysis, etc.
Since I'm reading HN of course I'm good at math. However, I don't really believe there is any such thing -- rather I had some good teachers, and father who knew math and who was willing to invest time explaining it to me, and something of a desire to "understand everything" which of course includes (starts with) Mathematics. Deep down I guess I think that perhaps when you get to Hilbert's problems _then_ you might be talking "hard math" but until then it really isn't that much to get your head around. You just need a decent teacher, time and effort.
So now I have two sons. Both I will say struggled somewhat with Math up to 7th grade when they hit a good teacher. By "struggled" I mean they got constant A/A+ but I had to put in significant work (as did they) to get them there. First son now in 9th grade gets continuous A+ without any help from me. Sometimes I ask him questions about what he's studying, and try to expand his horizons accordingly. The other son in 7th grade is still somewhat struggling but I can feel he is getting to a turning point.
Second son would often become disillusioned and say "I'm just not good at math". I can just imagine teachers and family members nodding in agreement. I didn't do that : I told him he just doesn't understand it yet but he will.
Anyway, my concern in this is : how many kids end up believing they're "not good at math" due to their teachers, family and environment? How many scientists and engineers (or just members of the public who understand statistics and interest rates...) are we losing because the idea that "math is hard" is so widely held and propagated like a virus?