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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.

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fluoridation 4 days ago | parent [-]

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.

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margorczynski 4 days ago | parent [-]

> Where's the data backing up what you said?

What he is saying is the default hypothesis based on our understanding of biology and psychology. If you have variability in genes you'll get variability in characteristics that are connected to them - height, bone structure, mental capacity, etc.

It is on you to prove that there is an arbitrary cut-off when it comes to this variance from which point it doesn't matter in regards to e.g. cognitive and mathematical ability.

> 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.

No it doesn't if they do not have the abilities to comprehend it. I think you're living in a bubble of at least average-smart people and don't get that probably millions if not billions of people around the globe (based on average IQs) won't really get that concept.

	▲	fluoridation 4 days ago \| parent [-]
		>If you have variability in genes you'll get variability in characteristics that are connected to them - height, bone structure, mental capacity, etc. Then you're agreeing with me. The thing all of those have in common is that they follow normal distributions. The shortest recorded adult and the tallest recorded adult are quite far apart, yet the vast majority of adults are between 150-200 cm tall. That's precisely what I was saying; the outliers of mathematical skill are very very far apart, but most people are roughly equally capable. >I think you're living in a bubble of at least average-smart people and don't get that probably millions if not billions of people around the globe (based on average IQs) won't really get that concept. What I'm saying it that it even someone with below-average IQ could do it, if taught properly. Mathematics is less about being smart and more about being rigorous.