Unschooler here. I am the only unschooler from my 12 person cohort of hippie parents who did not go to University. And I am doing okay. So I think school basically has no effect. Mostly just daycare. It is good at that, though.
Sounds like your cohort was great. There was an "unschooled" girl in my college friend group who was failing remedial math and science classes in her third year. She never wanted to learn basic mathematics (we're talking long division here), so she never did, and she did not understand how to motivate herself to learn about something she wasn't already interested in. She didn't end up graduating despite the small, private school bending over backwards to try to accommodate her with personal tutoring and endlessly lengthening deadlines. She was first chair violin and had an almost full ride scholarship because of it, so she didn't lack motivation in general she just could not bring herself to care about math or science even when her degree was on the line.
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.
Hope many times do you think the subject of your comment needed to use long division "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].
>>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.
I agree with the thrust of your comment, I'm not arguing that maths isn't worthwhile, that it doesn't develop critical thinking skills, push the capabilities of the brain. Neither am I arguing that you should hold back on teaching younger children basic skills, even if it's outside their core competencies and outside their natural area of focus (all that changes quite fluidly when you're young).
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.
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 would agree if she didn't want to learn calculus or linear algebra, but I think long division is a pretty fundamental skill in today's world. How much is my monthly car payment going to be if I take this loan? What is my share of the rent in this house? What are the consequences of running up a credit card balance?
No, sorry it's not a fundamental skill in the least. It's a method for dividing on paper. In 37 years I've never used it outside of school as I have calculator in my pocket as does everyone else (smartphone obviously). Furthermore, "In the United States, long division has been especially targeted for de-emphasis, or even elimination from the school curriculum..." according to Wikipedia: https://en.wikipedia.org/wiki/Long_division
To clarify even though it's probably too late. She couldn't do division or multiplication of any size in her head, and was fuzzy on what occasions to use them in. For example, if you said "pay me back over 3 years for this $30,000 car", she might first multiply it by 3, get a very large number and then try dividing it and decide that's the right answer.
People are getting hung up on the fact that I said "long division" but it was basically anything beyond addition and subtraction.
The flipped perspective is that she's clearly a talented, competent person who can succeed—the fact that she didn't says more about how the school system defines success than it does about her. Hell, who's more likely to end up doing something great: her or somebody who fills out the minimum requirements exactly but nothing more? Even if they manage to learn long division and she doesn't?
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.
She works at Trader Joes and has for four years now and is in severe credit card debt. Not to say that being bad at math makes you more likely to get into debt but not understanding compound interest or even percentages certainly makes it harder to understand the ramifications of it.
Why on Earth would there be a correlation between music proficiency and maths? Math involves no musical skill, and music only involves mathematics because mathematics is abstract enough to apply to literally every human discipline. Music is probably one of the places where math is used the least.
"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.
You can't do anything without counting. And I've met plenty of mathematically incompetent musicians. Enough so that I'd say the more accomplished of a musician you are, the less accomplished of a mathematician you'll probably be.
Lots of genres involve math compositionally, and some for performance - mathrock, jazz, some classical compositions, even pop music, it's definitely necessary to properly comprehend a piece. Let alone if you're going to try anything with polyrhythms, tackle anything beyond basic harmonic theory, or have an interest in understanding the physics behind sound..
Those are some vague claims that I don't see any evidence for. I have not seen any part of music theory that requires anything more than basic fractions, and the vast majority of music that people write doesn't even require much of that.
> Music is probably one of the places where math is used the least.
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.
Sounds like a failure of research and planning on her part and on the part of her parents. There are universities which have no core curriculum nor any general education/breadth requirements. I believe Olin college fits the bill.
How would you know what you don't know, though? Or what you never experienced or could have experienced?
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.
The assumption is that if there is something you need to know and you encounter a situation that requires it, you can learn it. And if it turns out you do not need it, you saved the time. Further, formal instruction only works for some types of people, albeit probably most. Synthesis from learning when you are interested tends to be more useful than memorization. The experienced part is the scary one, although in terms of spending time with peers, doing sports, art, etc. we did not really miss out on that.
> and you encounter a situation that requires it, you can learn it
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.
I'd imagine that if you can describe a problem, Googling can give you a name for the problem, with which you can google for more formal introductions to the topic (articles, papers, texts, etc). Recursive Googling is a solution to an awful lot of problems in 2016.
