The Case Against Algebra

HughPickens.com writes: Dana Goldstein writes at Slate that political scientist Andrew Hacker proposes replacing algebra II and calculus in the high school and college with a practical course in statistics for citizenship. According to Hacker, only mathematicians and some engineers actually use advanced math in their day-to-day work and even the doctors, accountants, and coders of the future shouldn't have to master abstract math that they'll never need. For many math is often an impenetrable barrier to academic success. Algebra II, which includes polynomials and logarithms, and is required by the new Common Core curriculum standards used by 47 states and territories, drives dropouts at both the high school and college levels. Hacker's central argument is that advanced mathematics requirements, like algebra, trigonometry and calculus, are "a harsh and senseless hurdle" keeping far too many Americans from completing their educations and leading productive lives. "We are really destroying a tremendous amount of talent—people who could be talented in sports writing or being an emergency medical technician, but can't even get a community college degree," says Hacker. "I regard this math requirement as highly irrational." According to Hacker many of those who struggled through a traditional math regimen feel that doing so annealed their character while critics says that mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession's status. "It's not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it's not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better."

Comments

Same goes for all other skills

[mwvdlee]

There are plenty of good arguments to be made for moving the math curiculum to statistics, combinatorics and other areas, but "making more people pass the exam" isn't one of them.

Okay, so it makes some Americans feel bad...

[ausekilis]

So many here get their underwear riding up because they have to solve an abstract math problem?

Okay, say we do drop Algebra and higher from the common curriculum. Then we're going to go even lower in the list of math rankings by country. Perhaps it's because of the way it's taught, not because of the material. I distinctly remember hating word problems because they were always so inane. "If the flag pole is 10 feet tall and the sun is at a 30 degree angle, how long is the shadow?". I also remember having the teacher assign 50 problems in one night (2 through 100, evens only since the answers to odds were in the back of the book). Now, with this common core nonsense (no idiot left behind), we are just cramming more of this crap down kids throats.

What was lacking for me was the true application. I hated math growing up, and ended up being an engineer. It wasn't until I started to realize the cool things I could do that required math, such as tinkering in OpenGL, that I really started to latch on to it.

I'm curious, how is it taught in other countries that routinely get higher rankings in math/science? Is it a matter of teaching? a matter of culture? How do the Japanese view math? The Germans? Chinese?

Re:Okay, so it makes some Americans feel bad...

[arth1]

distinctly remember hating word problems because they were always so inane. "If the flag pole is 10 feet tall and the sun is at a 30 degree angle, how long is the shadow?"

Those are the best kind of problems, because they test understanding. Using those instead of rote formulas is what other countries do and is one reason why they score so well.

In your example case, it's not about whether you use the "right" formula, but whether you apply your knowledge to get a correct answer.

The thought process could go something like:
The flag pole, ground shadow and line from the end of the ground shadow to the top of the pole forms a triangle. The pole is 10', and the angle at the end of the shadow is 30 degrees.
sine(30) is 0.5[*], so the flag pole height is half of the hypotenuse (distance between end of shadow and top of pole). So the hypotenuse is 20'. The cosine of 30 degrees is about 0.866[*], so the ground shadow will be about 0.866 times 20, or about 17.3'
(Or alternatively, if not remembering what a cosine is, deduce that the opposite angle must be 60 degrees, and use sine(60) instead)
Then the litmus test - does the answer seem reasonable? 30 degrees is the sun being rather low, so shadows are long. It seems reasonable that the shadow is almost twice as long as the height of the pole.
No x, y, z needed. By all means, use them, but you should be able to calculate stuff like this in your head, at least to get an approximate answer.
That's where we fail - our students memorize, they don't *understand*, so they can't apply the knowledge to real life. So you end up with ramps that are too steep for a wheelchair, or extend into the street, because someone didn't understand simple trig.

[*] At least the 30/45/60 degree sines should be memorized, because they crop up so often. Much like pi and the square root of two, knowing the first couple of decimals comes in very handy. But even if you don't, there are sine tables, slide rules, calculators and computers.

School isn't job training

[jbmartin6]

It only works if one assumes that this level of school is merely job training. Some could argue that education is about broadening knowledge and exercising the brain, not just 'how am I going to use this in real life?'

Re:Difficulty?

[digitig]

More to the point, how on Earth are people going to be able to do statistics without a good grasp of algebra?

I see the argument, but its deeper than just math

[nimbius]

disclosure: Im a systems engineer, and have never had trouble with basic algebra.

in the US at least, we seem to have this fever-dream mentality when it comes to education and employment. Namely, that we presume so long as everyone can "code" and learn maths, that they can one day successfully achieve gainful employment and become a productive member of the workforce to lead a meaningful life. We assume little johnny needs to code because thats what his employers want, but it couldnt be further from the truth. Most businesses want a few engineers, but they dont want to spend a lot of money on them. They want the nuts-and-bolts sorted out so that reproduceability obsoletes them and permits them to hire cheaper workers because truthfully business is a job-creator as a last resort.

the issue we need to sort out as a nation is how we value work in general, whichs seems to have gone off the rails since the early nineties and NAFTA/CAFTA. Cooks, carpenters, welders, EMT's, and auto mechanics are all incredibly important --and in some cases in high demand -- professions for people to consider. However the pay and hours in these fields is a form of misery not seen since the old testament. You cant raise a family on any of these careers, and for some of them retirement isnt really an option. we use education as a whipping stick for these careers to insist theyre worth "less" than they really are, or at least so we can justify it to ourselves. If you want to see this self-fulfilling prophecy of underemployment in the real world, just look at the trucking industry. Perpetually understaffed, underpaid long-haul tractor-trailer drivers that get no vacation, sick leave, or retirement fund yet are in such ridiculous demand that most trucking companies like Dart or Swift will pay the driver to finish their CDL education. The demand is so high, drivers with a good record can quit a job and be hired at another in the same day.

So, If you want to obsolete maths like algebra, I propose we obsolete the puritanical tradition of shitting on trades that dont always rely on it. And while we're at it, lets take a sobering step back and realize that not everyone needs to code to lead a fulfilling life.

Re: Burn those algebras ladies

[Dunbal]

What I wonder is how the dear professor intends to teach statistics without referring to the many statistical formulae which are written in - algebra.

I actually found this funny

[fyngyrz]

If imposing math reduces the number of philosophers, sports figures, and poets... I unconditionally support us becoming a lot more focused on adding math requirements.

Sadly, I don't think it will do anything of the kind.

But it was still amusing to read. :)

Re:I actually found this funny

[AntronArgaiv]

"Few people realize that the % symbol indicates an exponential function."

It does not. The % symbol indicates that the number preceding it is the numerator of a fraction whose denominator is 100.
Percentages are often used in situations involving compound interest, which IS an exponential function with time,
but that's not what the % symbol represents.

Re:As long as....

[jellomizer]

The problem is the focus on grades, which is preventing us from learning.

I had an argument a while back about this.
Me: College Requirements for graduation should have more Advanced Math classes, as Math teaches you valuable problem solving skills.
Education Major: Not everyone is good at Math, so they shouldn't be forced to take the classes and hurt their GPA
Me: Well I am not good at English classes and they are hurting my GPA so I shouldn't have to take them?
Education Major: No you need to take these classes, They offer valuable skills for understanding people and society.
Me: But Math offers valuable problem solving skills.
Education Major: But not everyone is good at Math. ...

The problem is with our grading system, we reward people who already know the answers, and not on what is learned. For Liberal Arts, you many can BS their way a good grade on a paper. Approaches include a war of attrition where you give so much words that it is impossible for the grader to really grade correctly. Play to the graders ideology You can twist the topic around to support what ever cause the grader feels strongly at. It is difficult to BS in math. If the answer is correct or not, that is where the hatred of math is.

Math isn't about working hard, it is more about doing it right. So people make mistakes and they can't make it up by just doing more. So they feel like they suck at math because where they may be an A+ student they get Cs in Math. Because Math Grading is normally very mechanical.

However from my experience classes I got a C in are the classes I have learned the most in, the ones I got in A in was because it covered topics I already knew a lot about.

Re:Difficulty?

[Anonymous Coward]

Forget algebra, how can you teach stats to someone with zero exposure to calculus? Probability theory can't be described without limits and infinite summations, i.e. you can't comprehend it without calculus.

Re:Difficulty?

[vtcodger]

AFAICS, most people who think they understand statistics don't. What they understand is how to apply some rote rules to data that all too often shouldn't have those particular rules used on it. If we're going teach anything in that domain a survey of probability would likely be a lot more useful.

It's been half a century and perhaps I misremember, but I think a course built around Darrell Huff's "How To Lie With Statistics" might be a lot more useful to most High School Students than a standard mathematical treatment. And it'd certainly be a lot less mind-numbing.

Re:Difficulty?

[Flavianoep]

It's also useful to detect how someone's data is misrepresented. Can anyone lie with statistics to a statistician?

Re:Ban math

[Pseudonymous Powers]

We could ask the Chinese. They likely designed and built the thing.

Great idea. In fact, I think you've hit upon a workable solution for this whole issue:

"Thanks, Mr. Chin, you're a lifesaver. That thing was shining in my eyes all night and keeping me cold all winter. Hey, while I've got you on the phone, can you help us a little with our space program? It's like, all "polly-nomials" and stuff. It's so stupid, I don't see why we have to learn this shit. I'm like, I just want to go to Mars--I don't need to hear about, like, Pythagoras or Edison or whatever. I mean, I've got plenty of street-smarts. And I've got people skills. That's what's really important."