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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."
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)!
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.
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As soon as you replace a number it a calculation with a variable like cell A1, you have jumped into algebra.
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?
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?'
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Nobody needs algebra. There are plenty of jobs at McDonald's and algebra is just a waste.
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Why even bother having school at all. It would be a lot easier to just play throughout your childhood.
More to the point, how on Earth are people going to be able to do statistics without a good grasp of algebra?
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The reasoning is kind of weird. Even at the college level, statistics is extremely abstract. Statistics did not start making sense until I took it as part of my masters degree. The same is true about almost everyone I know. What you learn in the bachelor's level course is just theory, with no partial applications. What is the Poisson distribution for? When to use the Xi-squared curve?
It's not until you get into more advanced statistics classes that things start to come together, which is the same situation as algebra and calculus. I'm a mechanical engineer and, to me, calculus is like second nature because I went through all the advanced practical courses in college. Won't the same be true for stats?
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.
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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.
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What I wonder is how the dear professor intends to teach statistics without referring to the many statistical formulae which are written in - algebra.
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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. :)
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Maybe the problem is with how it is taught? Back in the day, high school math teachers tended to have a degree in mathematics (and biology in biology and chemistry in chemistry, etc.). Then in the 1970s this notion of certifying teachers came into being. With certification you were taught many things, like classroom management, child psychology, etc., but no longer was being a math or science teacher based on a demonstrated knowledge of the subject matter.
For anecdotal evidence, I had an excellent organic chemistry teacher in high school. When my state passed new teacher certification rules, she was grandfathered in (or would that be grandmothered?). She often quipped that since she didn't have a certificate, it made no sense that she could teach us as freshman in college, but not seniors in high school. BTW, she finished her dissertation the year after I graduated and continued teaching in high school, without a certificate for an additional 20 years.
Anecdote #2. I have a very good friend who is now a retired teacher. Math was her worst subject. However, the school system needed somebody to teach junior high math and she had a teaching certificate, so that is what she was hired to do. She would often say how grateful she was for the instructor's guide for the lesson plans, because without it she would be lost.
In short, if you want kids to learn math and science, they need teachers that know math and science. My wife is a teacher, so I type this with some trepidation, but maybe instead of dumbing down the subject matter taught to students, we should quit dumbing down the requirements to teach them in the first place. If you want kids to learn, then need teachers who have mastered the subject matter.
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.
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.
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Your understanding of daily life is no doubt better, though. You understand, probably intuitively, how things relate to one another better than you would without having been walked through these windows on the world.
I won't go as far as the offered snippet does, but I am pretty confident that the more math you know, the more likely you are to gain an improved understanding of the world around you. I think that's entirely a good thing.
Same thing for the scientific method. I'm not too worried about how much data you know about any one area of scientific endeavor, but if you actually have been taught and have understood the scientific method, the world is much more of an open book to you -- because you then have an open window on objective reality. You can draw the appropriate distinction between a baseless assertion and experimentally validated results; you're a lot less likely to be taken in by various scams, religions, and superstitions.
Same thing for history. It isn't about preparing to repeat the battle of Hastings. It is about developing an overview of human nature. If you have a good overview, you can be more effective for yourself, for your family, as a positive force within your society, etc. If you don't, as the old saw says, you're probably going to just be repeating mistakes, or supporting others who are repeating mistakes.
Learning isn't just about collecting facts and learning procedures. It's about building a big picture that actually represents the world you live in. The closer you can get to that, the more effective you can be, the more your choices can actually bring you closer to your goals, the better you get at winnowing the wheat from the chaff at every level.
Finally, learning does not have to come from schooling. You can pursue it yourself. The autodidact can easily become better informed than the person who has been through a rote process designed to fit the average student. Most people aren't really comfortable in that role, but for those who are, the world can be a truly open book.
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It's also useful to detect how someone's data is misrepresented. Can anyone lie with statistics to a statistician?
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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.
I don't know. Several more Hunter S. Thompsons could be fun.
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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."
Where are those mathematicians who wear shoes, bathe and keep a tidy house? This hasn't been my observation.
> But learning how to think, and solve problems is important.
Concur 100% as does Paul Lockhart's A Mathematician's Lament agree with you: (I've included an exert)