That's quite surprising, given how different the methods are. What about a control group that received no schooling?
Genuine question, just curious how anyone firmly on the "schooler" or "unschooler" side of the fence can know without some kind of external reference, particularly one which they themselves didn't choose in case of bias.
Which is perfectly fine as long as you know what that "it" is, which assumes a base-level familiarity with subject X.
The problem cases I can imagine are ones where you don't have the base familiarity, or in other words the cases where you don't know what you don't know (as opposed to knowing what you don't know and where to look for the answers).
This is the case that I see leading towards the so-called "expert beginner" stage of understanding.
That's the value school has. It teaches you how to learn about things you might not be interested in, but will be useful later in life.
I found it useful as a foundation to understand rationalising algebraic fractions; but outside that I've probably only used it a few times, none of which would have been essential.
What was her degree? Demanding maths when it's not needed by practitioners in a degree subject area seems perverse to me [I love maths FWIW].
Degree is inconsequential. I'd say "if she is a human, she will do better by learning math rather than not doing it."
How so?
Maths is more about "thinking creatively, clearly and critically about things that are complex and abstract" rather than about doing "arithmetic". And I guess, "thinking creatively, clearly and critically about things that are complex and abstract" is a very essential thing in human life. The entire human progress depended upon this skill and in fact, the very survival of humans depended upon this skill in the earlier world which was very hostile for humans.
Now coming back to the issue of having to do long division in early childhood: yes, it may be the case that you don't need to do long division (later) in your life even for once. Long division may not be that important but the concept of division (and remainder) is very important in our life.
Why is it important to learn division along many other complex (boring) topics in math? It's to hone your skills to "think creatively, clearly and critically about things that are complex and abstract".
Proofs in geometry and algebra help you more in this conquest. Sadly, most mainstream schools these days take out the creative challenges and motivational aspects from the math education and stuff it with mundane procedures to be followed like rituals. Sadly again, the much-tauted non-standard schools (like Waldorf, Sudbury etc) do away with the math almost entirely and which is very detrimental to academic progress of the kids.
edit: corrected some grammatical errors.
What I am trying to say is that at degree level, if you're mastering a field that has no intrinsic core mathematical content that you should be able to get certified in those abilities separate to maths ability. If an employer needs/desires a student to have mathematics abilities then they can request a certificate to demonstrate that.
Suppose things worked the other way and science majors had to produce a paper on Chaucer and Puritanism in order to graduate? Whilst IMO that wouldn't be a wasted educational experience, would be mind expanding, it's pretty orthogonal to the skills one needs as, say, an astrogeologist.
TL;DR more carrot, less stick.
When you say value, are you talking about the economic type? Because Susie here is probably better off focusing on her music career than learning long division.
I don't see how you can analyze value without quantifying cost and benefit. Even if a better method existed you'd have no way of knowing - especially without more experiments and bigger data sets.
I have addressed this issue in a comment in a thread here [1].
People are getting hung up on the fact that I said "long division" but it was basically anything beyond addition and subtraction.
Still. You would think that there would be a correlation between music proficiency and maths.
"Because I absolutely had to", is a pretty good motivator. I've lost a lot in life, and had little support:
"Why did you start a business at 20?"
"Because I absolutely had to."
https://mic.com/articles/94992/the-scientific-reasons-we-sho...
"Mathematics, especially, are aided by music education because it targets a very specific set of brain activity: the development of spatial-temporal reasoning. Highly developed spatial-temporal faculties are imperative for working through solutions to the complex problems in fields such as architecture, engineering, science and, obviously, mathematics — fields that our country desperately needs more children to pursue if we're to remain competitive in a globalized economy."
This is something that I recently was amazed by. I had a friend play 140 [1] and found that he struggled with many of the advanced puzzles even after being instructed to count the beats of the music. For some reason, it was very hard for him to multitask the movement of his character with the counting of the beats.
Now that I think about it, it's quite obvious that this would come to me easily, since I played the piano for over 10 years.
[1] A platformer game where you have to time your movements to the background music. It's really cool and polished and you should check it out; it's on Steam for a few bucks.
As a musician, I disagree with this rather strongly. Math underpins music in pretty much every aspect. Even a beginner musician will end up needing to know basic fractional arithmetic (since note lengths are represented as fractions or multiples of a "beat" length, and said "beat" is in turn usually notated as a fraction of a minute). So if you can read music even at a basic level, you're using math constantly, even if it's notated using dots and stems instead of (or in addition to) numbers.
This isn't even going into some more advanced topics of music theory, like the wavelength ratios between notes in a scale/chord, the difference between "just" and "tempered" tuning, how resonance works and why some notes on some instruments resonate differently than other notes on other instruments, etc.
Besides, it's not like many of the people who did manage to pass their math classes actually learned it all that well. I bet if you took random adults and asked them to solve long division problems, a sizable fraction wouldn't be able to do it. They just figured out how to put in enough work to jump through the right hoops and get out of the school system.
Personally I'd much rather have an education system flexible enough to motivate and engage students like her (even if that means skimping on basic math) than systems which try to force everyone down the same path regardless of how well it fits them.
To be clear, I absolutely think math is important. If anything, I think mathematical thinking is one of the most important skills you can learn. (Not that high school math is any good at actually imparting it.) And I even think I presented a false dichotomy above: you don't have to skimp on math to motivate students not interested in it, you could also just do a better job teaching. (But that's hard, of course!) If that was the choice, though, I'd rather not worry about a minimum amount of math, especially for students who clearly have lots of other things going for them.