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

Ban math

[Anonymous Coward]

Math should be banned and replaced with something more practical in the USA... like watching reruns of Seinfeld, or learning on how to turn off the ceiling fan if the batteries in the remote die.

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."

Difficulty?

[JBMcB]

A decent statistics class isn't any less difficult than an algebra class.

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?

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?

[AmiMoJo]

It sounds like they only want to replace the higher level algebra stuff, so the base would still be there as a necessary foundation for studying statistics.

This sounds like a great idea. Statistics are regularly, routinely abused to mislead people. As a life skill for the general population, statistics is going to be much more useful than advanced algebra or 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:Difficulty?

[superdude72]

He suggests dropping Algebra II as a requirement. The first two statistics courses I took in college had only Algebra I as a prerequisite. This wasn't "statistics for poets," either, they were the same courses taken by math majors.

Re:Difficulty?

[digitig]

According to the description, he's advocating scrapping the teaching of logarithms. Will the kids be taught that everything has a rectangular distribution?

Re:Difficulty?

[AthanasiusKircher]

He suggests dropping Algebra II as a requirement. The first two statistics courses I took in college had only Algebra I as a prerequisite.

As someone who actually taught Algebra II in high school (years ago), and who taught it one year in a lower-class mostly minority school district, I'll offer a few observations:

(1) I think a stats course would be a great alternative for many students compared to a second year of algebra.

(2) Algebra II was in fact a barrier for many students. There was a high rate of students failing and dropping the course. (At that time, in the state I was teaching, it wasn't strictly required for graduation -- but it was strongly recommended.)

(3) However, the problems with algebra II often start with teaching in algebra I. The algebra I and "pre-algebra" classes tend to be the "dumping ground" in many school districts for less qualified teachers. Teachers with real math degrees often were required to take stuff a lot more complicated than high school, and they often find it barely interesting to teach calculus or pre-calculus. So, in most places the qualified teachers who understand math often teach those upper-level courses, and the random coaches and people who barely passed the math certification test end up teaching algebra I. (There are serious teacher shortages in many places in the US, particularly for secondary math and science.)

(4) As an algebra II teacher, I was confronted with many students who had had a substitute teacher in algebra I for a large portion of the year. The district simply couldn't find qualified teachers to fill those classrooms. The students knew nothing. The previous algebra II teacher (a really smart woman) quit in the middle of the year, because she recognized this and wanted to either (a) send the students back to algebra I since they shouldn't have passed in the first place or (b) require many of the students to come in for mandatory tutoring outside of school hours. She wanted to help the students and was willing to take her own personal time to fix this problem. But the administration said neither was possible under state law, since the students already "had credit" for algebra I. After fighting the battle for a while, she quit.

(5) In many states, algebra teachers are forced to make stupid curriculum choices due to state-mandated curricula. I haven't looked at the new Common Core approaches and what they require, but I can tell you from my experience that we often were required to spend a ridiculous time on stuff that might have been useful for scientists and engineers headed for college in the 1950s, but these skills were much less relevant with modern calculators and computers.

(6) In general, most state curricula have tended to emphasize symbolic manipulation over real-world application (which often comes with true understanding). I was forced to spend many weeks going over how to put conic section equations into standard form, but there was nothing in state guidelines asking teachers to spend time on much more relevant real-life stuff, like applications of basic exponential equations to calculating loan terms or mortgages, investments, etc. When at some point I realized that only 2 of the 140 students I was teaching that year knew what the term "compound interest" meant, I actually abandoned the state standards for a couple weeks because I thought it was my moral responsibility to teach these kids some actual skills that could be useful in personal finance -- this would likely be the last class that many of them would ever take in their lives.

(7) Given the poor teaching and introduction to basic abstractions like variables that students receive in pre-algebra and algebra I in many schools, the only way to "teach algebra II" is learning stupid abstract algorithms for symbolic manipulation, which are generally forgotten a few weeks later. The understanding of basic algebra is often so poor that you really can't teach algebra II on a deep level

Re:Difficulty?

[Cytotoxic]

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.

This is undoubtedly true. I can completely get behind the author's notion that more people need to understand statistics. When I was in basic bio-medical research it was appalling how often statistics were not properly applied. Mostly it was "run a student T test and look for P values of .05 or less" with no further analysis. It was not at all uncommon to do a paper at journal club that had serious problems with their data, but had nice looking numbers supporting statistical significance.

I include myself, of course. I had enough statistics to know how to apply the formulas and to spot some basic issues, but until I collaborated with a real PhD statistician I had no idea just how bad it was. She basically showed me that I had no idea what I was doing, even though I was following the industry standard protocols. And she showed me just how awful the statistics were in most of the work I was reading. At least I think she did. I don't know. Most of what she was talking about I had to take on faith..... because, you know.... my knowledge of statistics isn't that advanced.

As long as....

[Rogue974]

I will agree to this as long as they remove foreign language requirement for engineers! The accountants and poets don't like high end math, I don't like foreign language requirement (and I am fluent in more then 1 language and an engineer)!

Re:As long as....

[CastrTroy]

The amount of a language you'd learn in a single class, or even taking a single course every year in high school isn't enough to get you be fluent, or even passable in a second language. There are millions of Canadians as hard data that show you can put students in plenty of classes in a second language without actually learning anything. Unless you have an immersion program where people are forced to use the language, then people aren't going to learn the language at all.

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.

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.

Logic?

[MindStalker]

How about a course in logic, particularly Boolean logic? I agree, very few people really need to understand logarithms or even polynomials. But learning how to think, and solve problems is important.

Re:Logic?

[pr0nbot]

I did the International Baccalaureate (a European curriculum for high schoolers), in which you got to choose the subjects you wanted to study, within some constraints. However, there was one mandatory class called Theory of Knowledge. This was a combination of logic, ethics and philosophy, and was by far the most interesting class I ever took at school.

Math doesn't suck, you do

[Anonymous Coward]

http://thebestpageintheuniverse.net/c.cgi?u=math

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.

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

[kwoff]

Meanwhile, apparently the number of American teens who excel at advanced math has surged... Not to mention, considering algebra and trigonometry "advanced" is just ludicrous.

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

[serviscope_minor]

You're going to have to do a lot of convincing to get anyone to believe that people do math because they enjoy it.

Indeed, the idea of maths has become so perverted that people don't even seem to believe that it is an enjoyable activity in its own right. It's so far perverted that despite a rich history of people doing maths for curiosity and fun, you still find it unbelievable even though evidence abounds.

Maths for its own sake dates back to the Babylonians, who pretty much invented maths.

Math is a means to an enjoyable end.

It is, and always has been also an enjoyable end in itself. Here are some quotes by Hardy:

"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."

"I am interested in mathematics only as a creative art."

"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics."

Robert Heinlein said it best...

[VAXcat]

Speaking as Lazarus Long "Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house."

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:School isn't job training

[jenningsthecat]

Granted, modern education is too expensive to devote solely to mind broadening educational pursuit for its own sake (for most).

I agree one hundred percent. And I would ask "Why is it so expensive?". The professors I know don't make all that much money. Yes, the facilities are costly, and so are up-to-date equipment, books, etc. But it still seems to me that higher education costs MUCH more than the mere cost of keeping the institutions running.

However, that is begging the question of the purpose of education all over again. Its only a "waste of time" because the cost has skyrocketed, and that is because it is being sold as an "investment" in future income.

Yes. And instead of being viewed as an investment in future income, it should be viewed as an investment in future society, and therefore should be more heavily subsidized by society. Perhaps in return for that societal investment, students fresh out of college of university could spend a year or two 'giving back' in some capacity that would both extend their education and ease their transition into real-world paying jobs.

The problem is that job-training focused education actually de-values education generally by de-emphasizing exploration and discovery and stampeding students from one supposedly lucrative field to the next.

This probably is the result of our skewed aspirational values. We either conflate 'standard of living' and 'quality of life', or we judge the former to be somehow superior and more desirable. I think the increasing corporatization of society, (and of education), is largely to blame for these attitudes.

No one needs algebra...

[NReitzel]

Nobody needs algebra. There are plenty of jobs at McDonald's and algebra is just a waste.

Stop passing on the hate

[The Evil Atheist]

The only reason why maths is hard is adults keep telling children that it's hard.

While we're at it...

[QuietLagoon]

... let's remove history and literature classes as well. As an Engineer, I found those humanities-oriented subjects to be too difficult to master and I have no use for them in my engineering career now.

.
Why even bother having school at all. It would be a lot easier to just play throughout your childhood.

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.

Solving the problem by ignoring the results.

[lorinc]

You don't solve a problem by simply ignoring the results or breaking the measuring tool.

Basic algebra, trigonometry and calculus are not difficult. If the students can't handle it, they are dumb, even if that doesn't please you. End of the story.

They are dumb, and that's a problem. You're not going to solve the problem by bending reality and saying basic abstract maths are difficult and that they are not dumb. You are just ignoring the problem, which may (will) have unintended consequences in the future. Actually, if you want to solve the problem, you should invest more energy in the process that is failing. That could be more hours, less student per teacher, or researching a new pedagogy that makes the acquisition of such simple and fundamental concepts more successful. Or anything else that doesn't imply lowering the expected outcome.

It has nothing to do with the jobs they will do in 30 years, simply because nobody can predict that. You are just promoting the race to the bottom.

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

[Flavianoep]

I wonder how can one develop the proper reasoning need for a philosopher without the formal Logic training that is algebra.

Re:I actually found this funny

[Falconnan]

Algebra 1 is sufficient for formal logic, though. He isn't saying to eliminate all algebra. Frankly, stats would not be my choice as a follow-up, but rather a combination of critical thinking courses and civics. Society would likely benefit greatly from more people being involved and more capable of separating their emotions from their important decisions.

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:I see the argument, but its deeper than just ma

[swb]

Very well said. There is a tremendous bias against jobs that involve working with your hands and far too many people are encouraged to "go to college" in order to obtain some apocryphal "white collar" career. I would say that a lot of the IT problems many companies have originate with this blue collar bias, with the belief that IT employees are somehow not quite white collar.

I had a conversation with the maintenance supervisor at a client who told me about his son. In the top 10% of his class in high school, he told the school counselor he didn't want to go to college. The counselor requested a meeting with his dad and basically beat him up for not making him go to college (the kid ended up getting some kind of 2 year drafting education, and works for a kitchen equipment maker travelling to job sites to review kitchen construction plans to make sure the planned designs and installations will work -- the guy said he makes close to 100k).

As far as I can tell, all the "go to college" rhetoric has done is build college administration empires, make oodles of money for the student loan industry and probably dumb down traditional academic courses that vocationally-minded students have no interest in.

And what's the end game, exactly? $100k in a debt so you can make coffee? We've flooded the market with half-educated college graduates aspiring to a mythical middle class lifestyle that's becoming increasingly unobtainable even by well educated graduates.

One thing that kind of counts against a lot of skilled trades is the abysmal, old-school hostile management-labor relationship. I worked closely with journeyman electricians as my last job and while the benefits they had seemed great, the work environment seemed really unpleasant. Draconian, authoritarian management schemes, forced overtime and work rules that make a $20k a year cubical job seem pleasant.

Calculus not needed for intro level stats

[sjbe]

Forget algebra, how can you teach stats to someone with zero exposure to calculus?

You can do a basic stats class for people who haven't had calculus. I know because I have taught and tutored people in stats who haven't had calculus. You will find very few stats classes that will require you to actually have a deep understanding of calculus. Sure, if you do know calc you can go deeper into stats but it isn't vital to start with. You can teach Bayes theorem, conditional probability, and lots more without ever doing a derivative or integral. I made my living doing statistical simulations and none of it required me to actually do any calculus to get useful answers.

Probability theory can't be described without limits and infinite summations, i.e. you can't comprehend it without calculus.

Not true, at least at the introductory level. Most people can understand a bell curve just fine without ever having taken a calculus class. Just because they can't derive the formula for the curve doesn't mean they can't understand the concept it represents. It's no different than intro physics in that regard. Plenty of people take intro physics prior to or concurrently with calculus. It's when you want to go deeper that you might need to understand some calculus but most people will never get there.