alt Hacker NewsYour 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.