As an addendum to my last post, regardless of what’s been posted in the meanwhile:
(And it may be useful to force everyone to be exposed to the beginnings of an algebra class, to see if they might discover they have some interest in it. But they must have the opportunity to decide not to continue if they have no interest in it. Forcing them to actually suffer through and be yelled at for that lack of interest and likely corresponding poor grades, etc., just seems wasted effort.
In general, I don’t think people, even young ones, should have to take classes on things they don’t want to (exposure is good; let everyone be made to audit a few weeks of whatever key subjects. But continued forced labor is bad). Let them decide how to spend their precious lives. If they later on change their minds, let them take classes then. Trying to cram in everything scattershot up-front that they may, potentially, find useful down the line, even if they have no interest in it now, is a fool’s errand. I don’t think universal math (or chemistry or literature or what have you) knowledge is an important goal, and I don’t think universal math (or…) instruction even nearly accomplishes that goal.)
Algebra on it’s basic level is critical for many fields of work (manipulating Ohm’s Law for electricians, for example). If you can’t manipulate across the = sign, you’re going to really suck at trig functions, which are used in even the building trades, let alone anything more elegant. Even grocery shopping can be an exercise in ratio/proportion.
Again, it is true in a way but the ones you listed are just very simple Algebra that could be covered in a week instead of the two years required for most high school students. I don’t think anyone is advocating the abolition of all Algebra concepts in high school. It is just that its importance is vastly overstated and taught the wrong way. The best approach would be to teach the appropriate Algebra concepts where they are actually applicable and that could be spread across multiple classes from Physics to Home Economics to shop class to use your examples. More integration among disciplines is the most effective strategy in education.
Is there any real evidence for that however? I honestly don’t know. Did Steve Jobs get his inspiration from high school algebra or even Picasso for that matter? All I know is that I have never heard any successful person give credit to high school algebra for arming them with the critical thinking skills to achieve what they did. It is usually just presented as a slog and hurdle that you have to go through just because that is the way it has always been done.
It is unusual among subjects in that regard. Statistics are a real eye opener for most people for example and computer programming teaches strict logic very quickly but algebra is just something to endure.
What a bizarre statement. I took 4 quarters of calculus as well as some linear algebra, differential equations, and stats. And yet I still feel absurdly limited by my math skills. Doubling the amount still wouldn’t be enough.
Sure, in some weird limited way you don’t need math to program. But the point of programming is to actually accomplish something, and all too often that something requires math.
The fundamental mistake the writer makes is viewing math as a form of training, not as system for thinking abstractly. It’s also a language, and like other languages it sticks better the earlier you teach it. Delaying non-trivial math until college would be disastrous for those fields that depend on it.
Er, you are framing this as a disagreement, but in the quote you are responding to, ultrafilter was making the same point about formal logic courses that you are making here; it would be overkill and unnecessary for most people’s needs.
It’s not a question of whether it’s necessary; it’s a question of how hard it is for an early teenager to handle that level of abstraction. I’m claiming that geometry and algebra are easier than logic in that sense because they relate to things that the kids already know.
I suspect this is overstated as well. At least, I recall an awful lot of pain in my history classes which still seems to me unnecessary… memorizing names and order of Civil War battles and such. You could say that’s just poor teaching of history, not a problem with teaching history, and I agree… but I’ve also been able to get by fine in life without better teaching of history. I have some interest in history now, but it’s not clear that learning it in detail makes any practical difference to my life.
History lessons are, for the most part, more about cultural literacy then life competence. (And cultural literacy can be valuable, but let’s not pretend it’s something it isn’t.)
How is programming useful to anyone these days except computer scientists and people needing to do spreadsheet programming? Most of the stuff people needed to write programs for 20 or 30 years ago are done by applications today. My daughter’s computer 101 class did not cover programming at all, unless you count copying one line Javascript statements, but covered rlogin, ftp, and simple html.
I suspect your average person would use algebra far more than programming - or need it so infrequently that they’d forget how to do it.
Statistics, though, definitely.
Linear algebra, yes, but graph theory is even more useful, at least in the stuff I do. Lots of things are most naturally described as graphs, and being able to deal with them efficiently is important.
I took calculus, and differential equations, but am terrible at them, and it never has bothered me during a CS career. There are some fields I stayed away from, but nothing I regret.
I program computers for a living and even I don’t think programming computers is a widely needed life skill. If you aren’t trained in quantitative reasoning, learning progamming is easy, but if you don’t, then it is useless. Quantitative reasoning is based on Algebra.
You are making false dichotomy. No one, including the other of the original linked article, advocated innumeracy. What we are saying is that anything above basic Algebra is unnecessary for most people in general and could be incorporated into other classes where it is actually applicable.
If you went to high school in the U.S., you likely had to take two years of Algebra that went way beyond the basics and were quickly forgotten after you left the class because they were never applicable again even if you became a doctor or scientist. The same thing is true for calculus, advanced trigonometry, and geometry proofs
Can you articulate well how this as helped you today outside of using catch-phrases like ‘mental muscle’ that others have used? Studies and cites would be good too. Any fields that require those skills should be able to teach them on their own without resorting to a scattershot approach outside of them hoping that something sticks without any context.
As an aside, I have found that most advanced math is fairy simple to understand as long as it is described in plain language and real problems rather than being presented as abstract symbols in a textbook with no context. Not everyone learns the same way but I found out I am really good at applied and even theoretical math but it was never presented that way until college.
There’s little difference. One might as well claim that we should be teaching how to read emails and Twitter feeds instead of books, since that’s all anyone does anymore. It misses the point.
And not true of English, history, foreign languages, chemistry, biology, and so on?
No one has a proof that having a broad education makes for better individuals. It’s just something that we have to take for granted when designing an education system. However, it is obvious that many Americans would avoid certain poor decisions if they had better math skills. It is less obvious with other topics.