> For example, an average observation, my father on his late 70s beat people in their 20s in doing mental math not because he is a genius because his generation had a better general education in math than the people at 20s.

You don't need a 'better general education in math' to be good at mental arithmetic. In fact general education in math' is pretty much irrelevant to mental arithmetic.

To be better at mental arithmetic, you need to learn and practice mental arithmetic.

I am willing to bet your father did exactly that when he was younger, compared to today's 20 year olds?

Your father might or might not also have had a great general math education. But that's pretty much irrelevant for the topic at hand.

(I'm a mathematician by training, so I have a pretty good 'general education in math'. But how good my mental arithmetic is depends very heavily on whether I've recently had reason to practice.

I was my best at mental arithmetic in about 7th and 8th grade. 7th grade is when calculators are first allowed in schools where and when I grew up. If, like me, you keep forgetting your calculator at home, that means all of a sudden your mental arithmetic gets a lot more of a workout than before.)

I think we are saying the same thing: based on IQ tests my father, on average, could easily beat people on their 20s and this is not related to any advanced math or language education. He has a better education and, probably, better epoch for learning than, in average, young people now.

I don't want to focus on his math mental skills but his overall education was better. He can also beat people in language/words associations.

> I don't want to focus on his math mental skills but his overall education was better. He can also beat people in language/words associations.

Well, _different_, possibly. Neither word associations nor mental arithmetic are the be-all-and-end-all; mental arithmetic in particular has been more a party trick than anything else since the advent of the pocket calculator.

You cannot use pocket calculators in IQ tests though.

I mean, sure, but the purpose of education is not to train people to be good at IQ tests.

Indeed, based on current scientific studies, you cannot greatly modify your IQ. I will not talk here about spaced repetition.

It's trivial to modify your IQ. Keep bonking your head hard or drinking too much or sleeping too little, and your IQ is sure to go down.

What's hard is not _modifying_ your IQ, but increasing it.

Depends entirely on your IQ test.

> You don't need a 'better general education in math' to be good at mental arithmetic. In fact general education in math' is pretty much irrelevant to mental arithmetic. > To be better at mental arithmetic, you need to learn and practice mental arithmetic.

Is mental arithmetic practice not part of a general math education curriculum?

Yes, but it is a tiny fraction of "general education in math", and there is no causal connection between performance in those two.

You'll be able to improve your mental arithmetic performance by orders of magnitude from pure memorization + practice alone, but this is not how people typically learn math in general, and rote memorization will not make you a good mathematician in the long run (it's probably not even good enough to get you past university-level exams).

Not really.

I too am a maths graduate.

My peak mental arithmetic was about age 11 by then I had learned times tables etc by rote and could deal with money - being the UK this was LSD so had to convert between 20 and 12s as well as decimal. Then in the next few years we want decimal so no need for that daily task of converting and we got calculators if we needed figures so little practice - I could still keep track of what the total amount I would pay in a supermarket and calculate change quicker than the assistant using the till but even that has gone as you just pay by card.

Nowadays do you need to be good at mental arithmetic, probably for doing quick estimates but I don't know if educators think that getting mental arithmetic working well is needed.

IQ tests itself are age relative. The tests already take this into account, that's why your IQ is relative to people in the same age bracket. Basically, when you say "my IQ is 100", it's means that you are in the 50th percentile of the peers of the same age. It doesn't have any "absolue" value, and it shifts with the years (100 IQ 50 years ago is not the same as 100 IQ now)

The core problem is if IQ tests are context sensitive. IQ tests are relatively new in human history so we don't know how do they operate (without much changes) in a 400 year timespan.

Yes, though details depend on the exact test and how it's normalised.

Nobody asks you for your age when you are doing IQ test befire giving you your result.

Originally IQ was defined as "mental age" divided by actual age and it was for testing development of children. The actual age was capped at 16. So it was expected for any person 16 and over to have the same result in the test to have the same IQ.

> because his generation had a better general education in math than the people at 20s.

Which we hear a lot these days but which is extremely difficult to prove. Formal education only helps you so far and only for some small percentage of students.

I had access to what you mean by good math education through school and University, had private tutors at school and so on. I can say that with my peers there is a huge spectrum of innate math abilities. Only about 5% probably absorbed naturally everything we've been tutored through the school (1-2 persons in a class of 30).

I am not gifted with math, so I have OK formal knowledge, however few of my friends who worked in humanities all their life are much better at "head math" than I ever was.

Also, I live in a country which have aggressive math curriculum from young age. Looking how my kid goes through it I can say for sure, that it is massive waste of kids energy to be pushed for general population.

> Which we hear a lot these days but which is extremely difficult to prove.

I would say that is extremely easy to prove but writing a solid paper on that consumes a lot of resources. That is why conjectures are part of the scientific method: we can discuss about things that we think are true or not before making a multi-year effort to prove the point in a scientific way.

The problem is when people confuse scientific publications with truth. In math that would be easier for the practitioners but in social sciences we know that we can publish ala Sokal affair.

You're describing the difference between fluid and crystallized intelligence. the first one peaks at age ~20, the second one peaks at age ~50:

https://en.wikipedia.org/wiki/Fluid_and_crystallized_intelli...