Everyone is capable of, and can benefit from, mathematical thinking

A nice sentiment but clearly a large % of people never do learn even basic mathematical thinking and seem very confused by it. So is there some scientific study backing up the claim that all these people could easily learn it or are we just making it up because its a nice egalitarian thesis for a math popularization book?

That certain countries both now and in the past have had significantly higher mathematical ability among the general population and much higher proportions going on to further study suggests that ability isn’t innate but that people don’t choose it. In the Soviet Union more time was spent teaching mathematics and a whole culture developed around mathematics being fun.

Why would ability not be innate just because some people with the ability don't use it?

Or more specifically, two of my friends teach special needs children in the 50 to 70 IQ band. Who are we going to blame for them not becoming mathematicians? The teachers, for not unlocking their hidden potential? The kids, for not trying hard enough? Claiming that the only thing holding them back is choice seems as cruel as it is wrong, to me.

Yeah, we're probably not cultivating anywhere near the potential that we could, but I personally guarantee you I am not Ramanujan or Terence Tao.

Well, I guess what I mean is that most people have some level of general intelligence that when applied correctly can generally give good results in most subjects. In general the people who do well in school do well in everything, even if they have a preference, and as such could do well in most of those subjects if they went on to further study. The evidence tends to be that in lower income countries people push towards subjects more likely to bring financial stability than those they prefer which bears this out somewhat.

There are some extreme cases of course but I’m not sure the general public needs to worry too much about those, most of us aren’t an Einstein nor do we have learning disabilities.

The extreme case does not imply a binary scenario ie that there are those that can those that cannot.

Rather, learning ability is a continuum. people have varying degrees of ability to learn mathematics. Couple this with environmental factors and society generates a huge variability in mathematical ability that crosses income levels and other demographics.

This view is rejected by many because it is against the push for equality.

You get a huge variability if you consider the absolute extreme outliers. Most people should be able to reach a level of competence where they can understand mathematical concepts abstractly and apply that same reasoning to other areas, and not feel a visceral rejection at the mere idea. I think that's a modest enough standard that a good portion of any given population should be able to reach, and yet education is failing at achieving that.

Your statement is not backed up by data and simply wishing it should happen isn’t a strong argument.

You probably have a narrow definition of “most people” (probably some motivated high school or undergraduate student) and too loose with what it means to “understand mathematical concepts abstractly”.

Take an analogy: imagine professional musicians saying that most people should be able to take a piece of music and understand its harmonic structure, then apply it to a new setting to generate a new piece. Most people will reject this idea as absurd.

Where's the data backing up what you said?

>You probably have a narrow definition of “most people” (probably some motivated high school or undergraduate student)

I was thinking "3-4 out of 5 people you pick on the street at random".

>too loose with what it means to “understand mathematical concepts abstractly”.

Enough that they could recognize whether a mathematical concept is applied correctly (e.g. if I have a 2% monthly interest, should I multiply it by 12 to get the annual interest? Why, or why not?) and conversely to correctly apply concepts they already understand to new situations, as well as to leverage those concepts to potentially learn new ones that depend on them.

>imagine professional musicians saying that most people should be able to take a piece of music and understand its harmonic structure, then apply it to a new setting to generate a new piece. Most people will reject this idea as absurd.

Okay, but we're arguing about what is the case, not about which idea has more popular support. Since most people don't understand thing 1 about composition, why should their opinion matter? A skilled composer's opinion on the matter should have more bearing than a million laymen's.