As someone alluded to earlier in this thread, an early decision to dismiss mathematics has a cumulative effect on your entire education. Start with refusing to learn algebra and soon enough you won’t be able to do probability theory, physics, statistics (and psychology), economics or accounting, programming, genetics, and so on. It cuts off what paths are open to you if you don’t learn math. Any of the jobs you might want that require some math are suddenly closed to you. And it’s only going to get worse as technology progresses.
@gouf78 it was infuriating, but in our school the gifted program is a pullout for math and language arts. The teachers do all sorts of creative things in that time and it would have been difficult for one of them to agree to teach math at the same time so that he could switch with a second grade teacher. (You have to have two teachers on board with the plan.) He probably didn’t belong in regular fourth grade math anyway. And the principal was also really, really against any kind of acceleration - she was sure their must be some other kid in his grade with whom he could have had an accelerated group. There wasn’t. In the end he did EPGY math outside of school and his various teachers provided various sorts of enrichment or solo activities. In third grade he did a lot of computer programming. He finally got some subject acceleration in middle school. Sometimes I regret not homeschooling him, but I think we would both have become hermits if we had. (And I do know about all the homeschooling groups - because I had friends who were homeschoolers.)
This is mathematical navel-gazing. All you learn is how pointless proofs can be and how math instruction focuses on the irrelevant. I personally don’t find anything elegant or beautiful about proving the sum of two even integers is even. It doesn’t result in my life being any more enriched, nor does it do anything to help me in my job.
I personally don’t find anything elegant or beautiful about certain pieces of art/literature/music, but that doesn’t mean they are not worthwhile or beautiful to others or important to study for one reason or another.
Sure, you could go without learning about proving the properties of odd/even numbers, or even the discipline around it (discrete math) that uses it merely as a straightforward example of logical reasoning from definitions. Start down that path, though, and you will quickly make many of the useful results of mathematics closed to you. Sure, discrete math or even real analysis might just look like obscure “mathematical navel-gazing” if you simply choose to treat those subjects as irrelevant or beyond the scope of your understanding. And yet, these theoretical classes open the door to understanding a lot of highly practical, highly useful results from mathematics - differential equations (and PDEs), linear algebra (at anything but the most basic level), stochastic probability, numerical analysis, algorithms and theoretical computer science, cryptography, quantum mechanics, and… pretty much everything else, including the subjects that depend on these mathematical results. That all starts with simple results like even + even = even.
The author says our main need is for more people to do low wage work. By that standard, maybe they don’t need more math. Indeed it might be better for some others if they don’t have it, so they don’t aspire to leave those boring jobs. If they don’t understand what the manager does, they’ll be satisfied with their very long days doing simple tasks.
That idea goes against the heartfelt desire of almost everyone in education, and everyone else too, that believes education is good. But I’ll give the author this. He has the chutzpah to promote it openly.
Indeed many jobs don’t require “advanced math” like Algebra 1. (I was wondering what this term meant, because I don’t consider any math taught in HS to be advanced, but then I have a warped mind. I think a bit of calculus is good for everyone to know, but I know that not everyone will get there.) Not everyone needs a HS diploma, especially if the goal is to make them “happy” in those low-skill jobs.
Educational credentials have a purpose in signalling what one achieved. If we dumb down the HS diploma any more, it will just mean that more people will need community college for what are now considered low end jobs. And whaddaya know, that’s Obama’s plan – to send everyone through 2 years of community college. It doesn’t mean they’ll learn more, just that they’ll be busy in school for longer before looking for a job, and we’ll sustain and expand the already bloated Education Industrial Complex.
Coding and math are indeed very separate skills. Coding should be taught to everyone, and we should get rid of the Algebra 1 requirement that is frequently a prerequisite for it. That’s one good idea the author has – but it’s far from original with him.
You do close off many future careers based in math (very good point all things being equal) IF that is what you want to pursue. If you aren’t able to do math and have no interest in it would that be a viable option? Probably not.
What if math is your “nemesis” but you have other talents? Are you to be left behind? Can’t go to college?
I know some very “lop-sided” talented kids. Very verbal–score exceedingly high, articulate and smart, great writers and artists. And can’t get beyond algebra (but smart enough to pick up what is needed for business purposes) so regular college admissions may be cut off despite their innate talents. Math career choices would never have been a choice
.I haven’t heard anyone extolling the virtues of writing because a Journalism major option has been derailed.
It works both ways–for a math geek essay writing may be like pulling teeth.
Mcafee (after offering to crack encryption on terrorist phone) was asked why the government doesn’t already have someone on staff who can crack code on a phone without having to go to Apple.
“And why do the best hackers on the planet not work for the FBI? "
" Because the FBI will not hire anyone with a 24-inch purple mohawk, 10-gauge ear piercings, and a tattooed face who demands to smoke weed while working and won’t work for less than a half-million dollars a year. But you bet your ass that the Chinese and Russians are hiring similar people with similar demands and have been for many years. It’s why we are decades behind in the cyber race.”
Maybe they all passed algebra and studied Brit Lit. and had a million volunteer hours. Or not. But maybe they would be even better at what they do with more instruction in what they wanted to actually focus on.
University education is in part focused on providing a more broad education to give students a more complete perspective of the world. That means that beyond their specialty, they should be expected to cover some universally useful topics - literature, writing, philosophy, humanities, history, language, science, and mathematics. In the same sense that a mathematician isn’t expected to be a brilliant historian, a historian isn’t expected to be a brilliant mathematician. But it’s far from unreasonable to expect that each is at least competent in the cross-discipline. The same way no one says that a programmer can’t be expected to be a competent writer, no one should be able to say that a journalist shouldn’t be expected to be able to do mid-tier math. I would personally draw the line at or around calculus, because I have found that with a reasonably supportive environment, just about any competent student (the kind that belongs in a university) can do algebra 2 and trigonometry. Calculus, maybe not, as it is a whole deeper level of what math is and how you use it.
The FBI issue isn’t about terrorism - if the contents of the phone are valuable then they already have what they need - it’s about control. But regardless, the point about “spiky” specialists who are highly talented at one topic but not very adept at others is an interesting one to explore. Personally I’d say that while those spiky people do exist and are productive, they are not an example to be encouraged. For every spiky genius, there are maybe 10000 losers who can do very little but are still extremely confident in themselves. And given how inherently political the ability to do work is, perhaps all that other irrelevant stuff actually matters.
Also, I wouldn’t quote or listen to McAfee. Not only is he a crackpot but he’s also wrong about his assertions about Eastern “hackers.” Russian/Soviet education focused far more on breadth in subjects considered “core” than American education does, and someone who didn’t take school seriously would not do so great. The overwhelming majority of those “spiky hackers” are a product of the formal education system.
While true, they like many international societies tracked students much more aggressively and expected students to have dealt with gen eds at an earlier stage in their education than their US counterparts.
A few classmates in HS and college along with some engineering/CS colleagues from the former Soviet Union/Russia all recounted they finished covering algebra and geometry by the end of elementary or early middle school(before 8th grade) though to be fair…tracking seems to have existed even as early as elementary school there.
A couple of Russian colleagues who attended K-12 in Soviet Union/Russia were taking advanced mathematics such as discrete math/number theory not only in academic-prep high schools specializing in STEM, but even more vocational oriented ones such as a couple who attended a vocational high school geared towards preparing graduates to enter the Soviet/Russian armed forces officer training schools*.
- Their equivalent of the FSAs or OCS/OTS were not regarded as equivalent to an undergrad university degree in their society. One of the colleagues emigrated with his family to the US to escape the requirements to go into officer training after HS graduation as required by his officer prep vocational HS in the aftermath of the Soviet collapse and the rapid deterioration* of the conditions of service even as a commissioned officer in the post-Soviet Russian armed forces in the '90s.
** Not only in terms of extreme fiscal constraints, but also skyrocketing violent bullying and crime in the post-Soviet Russian armed forces far beyond what existed before the Soviet collapse and rapid deterioration of the armed forces.
Algebra 1 is a pretty low hurdle for math competency. It’s reasonable for that to be implied by a HS “diploma”. Perhaps there could be a different sort of certificate or diploma for those who don’t complete that, but it’s fair to allow the market to know whether someone succeeded or failed at completing Algebra 1. If one is hiring a journalist, you don’t need it – apparently, from what I see many journalists say. Or, maybe the employer wants to ensure they hire journalists who are less clueless about math. We should enable that.
The FBI / Apple thing is about having more than one try to GUESS the code. Nobody could do that no matter how smart or knowledgeable about general cryptology methods. And to be honest, most of the good nerds look pretty boring and may not shower often enough or iron their clothes. But still they command more $$ than the FBI can pay, and so the FBI may need to pay up for that skill.
indeed “equity” (including non-tracking) puts a very heavy burden on our best students, those who will be competing head to head with the best from around the world in grad school and technical work. It’s almost like the current system is designed to ensure that our smart kids have the most limited future that can be constructed for them.
Well, an important aspect of Soviet education to note is that high school is not a generally expected requirement the way it is on this side of the world. There were three basic paths of education:
- Trade school after middle school, where you learn a working trade like welding or plumbing.
- Vocational technical school, a 3-year program after high school that is just about the equivalent of a Bachelors degree.
- University, which is the equivalent of Masters or higher depending on the specialty. Also after high school, but graduates from vocational school can do this option later if they want.
So the fact that they are even in high school suggests that they already have an academic bend, and they are taught subjects in the depth that you would expect to teach students who, say, take all AP courses in the US. Middle school is also a lot more serious than in the US and not too far from the depth of lower achieving high schoolers in the US.
It’s safe to say that everything was pretty bad in the 90s in the former Soviet Union. Privatization was a horribly botched affair and much important infrastructure, including the military, was left to rot in disrepair while people tried to seize their share of it.
That’s structurally similar to the German system which the Imperial Russian/Soviet/post-Soviet Russian educational system is modeled on.
Also, high schools are technically regarded as optional and not the default path in Mainland China and Taiwan. Academic high schools and many higher vocational high schools are quite selective and not treated as the “inertial path” as is the case here in the US.
One cannot just automatically attend high school from middle school by merely graduating from middle school or in some cases…being socially promoted despite failing too many classes as is the case in some US public school districts.
From the way those colleagues and their families described it, the deterioration in status and conditions of service between the time they entered those military vocational high schools for aspiring military officer trainees and when they opted to emigrate to the US was very dramatic in only a span of 2-3 years.
I liked math, I felt I sharpened my skills doing the work. It can be overwhelming, and the math in some degrees stop people that enjoy the field of study because they are not the best at math. I believe it should not make or break someones dream as long as they are understanding the concepts. College is also becoming a monopoly with no end to the debt in site. More students are becoming home college schooled with upper level degrees and even bachelors degrees because of price gauging at Universities, and unrealistic goals for some.
Well, in fields that are actually mathematically inclined, I think people who “enjoy the field but aren’t the greatest at math” should learn to get better at it, because it expands what you can do with it. I’d say that a few fields where advanced math is very useful but not strictly necessary are economics, psychology, biology (especially genetics), and education. In all of them, you can still be somewhat productive without math, but a rudimentary understanding of algebra, calculus, and probability/statistics would do a lot to expand what you can do with the field. It’s a good thing to learn.
Part of the point of the breadth requirement of a university is to expand the scope of what you can accomplish with what you learned. Math is one of the most universal skills that benefit in just about every field in one way or another, and I think that it is a bit under-emphasized as a breadth course (often, breadth is only one-sided in that science/engineering learn humanities but humanities barely touch math/physics/science). While I fully understand that calculus and beyond are not meant for everyone, I fully believe that anyone who has any place being a university student should know up to algebra 2, and perhaps be introduced in a very basic way to calculus (just what a derivative and integral are and how to apply them to simple problems, without real analysis or Taylor series or any of the other nasty stuff).
Really? I find discrete math more engaging than calculus and on par with probability and stats for usefulness at work. I had one entry-level engineer cleverly differentiate herself in an interview by unexpectedly transforming her initially convoluted solution to an elegant one by applying DeMorgan’s laws. Her explanation concisely and definitively convinced me her change was correct. In any case, even if it’s navel-gazing, what’s wrong with that? I’d suggest navel-gazing is what’s missing from math instruction as struggling for and reveling in the AH! or AHA! moment is intrinsically motivating. Quoting Pascal, “all of humanity’s problems stem from man’s inability to sit quietly in a room alone.”
As an aside, my previous “even + even = even” example could lead to a memorable interview moment if someone used Boolean algebra to show the zero-ith bit will never be set.
Thank goodness that art and music aren’t required (any more). This discussion would look a lot different if the requirements were “paint a portrait” and “write a fugue”…
Post 156–".As an aside, my previous “even + even = even” example could lead to a memorable interview moment if someone used Boolean algebra to show the zero-ith bit will never be set".
LOL–It could be very memorable depending on what job you’re applying for. A lot of employers might just consider you too nutty for words and move on to the next applicant…
But there is nothing wrong with navel-gazing. It helps solidify theory and hopefully lead to new insights in all sorts of subjects.
Promoting negative stereotypes is wrong and hurtful.
Furthermore, commenting on people’s looks is very superficial. Not everyone can be the good looking. well-groomed person who wears ironed clothes all the time… like your typical philosophy PhD student.
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Exactly! Agreed! Please, tell YOUR children to stop learning harsh and senseless math. Tell them to stop at the elementary school (diluted by Common Core). My DDs take Algebra 1 in the 6th grade - thus, according to Mr Hacker (political science guru) elementary school is enough.
In the meantime, colleges are recruiting undergrads from Asia, most graduate STEM students at top universities are foreigners, Microsoft is relocating lots of R&D into India …