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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."
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.
A decent statistics class isn't any less difficult than an algebra class.
My Other Computer Is A Data General Nova III.
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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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.
As soon as you replace a number it a calculation with a variable like cell A1, you have jumped into algebra.
http://thebestpageintheuniverse.net/c.cgi?u=math
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?
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."
There is no God, and Dirac is his prophet.
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.
Don't take life too seriously; it isn't permanent.
The only reason why maths is hard is adults keep telling children that it's hard.
Those who do not learn from commit history are doomed to regress it.
.
Why even bother having school at all. It would be a lot easier to just play throughout your childhood.
Apart from algebra being an intellectual hurdle to be jumped which may help separate people academically I have thought this for about the last 30 years, and no I didn't "flunk" maths. As a matter of course we don't teach people medicine or geology or Latin, these are specialisms which people with an interest study as they refine their possible future choices. So why algebra? I am an engineer in an advanced engineering company writing engineering software and I "do maths" about once a year at most. Yes there are people here who do a lot more than me but there are also people who do a lot less so why does the average Joe need to know about quadratic equations?
The suggestion to study statistics seems very sensible, it might help people understand when the politicians are lying...
Art is the mathematics of emotion
I picture Justin Long playing the doctor from the movie "Idiocracy"....
There is no God, and Dirac is his prophet.
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.
Good people go to bed earlier.
Idiocracy was not meant to be a documentary, nor a roadmap for the future.
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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advanced mathematics requirements, like algebra, trigonometry and calculus
That is not advanced mathematics.
That is just about basic mathematics.
However, the curriculum needs to be revised with modern tools. Computer algebra systems makes a lot of what is taught in these courses obsolete. Courses that use CAS then start pulling in advanced content to fill up the time.
This is analogous to what the calculator did. Nobody knows how to even calculate a square root by hand (ok a few people) and nobody does long division. There are so many things in math classes that simply need to just go away like long division.
What I wonder is how the dear professor intends to teach statistics without referring to the many statistical formulae which are written in - algebra.
Seven puppies were harmed during the making of this post.
It's not necessary to make all school math 'practical' but to explain it in terms that are observable in the world around us. Poisson distributions ('bell curves") are all around us if we care to look. And before getting bogged down in the fine points of l'Hôpital's Rule, explain derivatives as the rates of change that we see around us (resting object, moving object, falling object...).
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. :)
I've fallen off your lawn, and I can't get up.
There is a reason we expose young people to intellectual pusuits rather than just putting them where they'd be useful like in diamond mines or in chimney sweep jobs. There brains are particularly plastic and need stimulation to develop. Math is among the pursuits they need for their intellectual health. Leaving it out would be like leaving running out of physical development.
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.
I was going to use my mod points, but there are too many good comments (and plenty of modders anyway).
However, one point no one seems to have made yet: TFA seems to worry that, without Alg2, you won't get a college degree, and the world will be denied the next talented sports writer or EMT.
To me, a better question is: Why in the world would you expect a sports writer or an EMT to have a college degree? Those are both fields that require a certain amount of training, but a college degree seems to be the wrong kind. What is it with the US (this is very US oriented), that everyone is expected to go to college? The simple fact is that most people don't (or shouldn't) need a college degree for their careers. And by forcing everyone to go, you only water down the contents of a college education, so that everyone can pass.
Also: I agree with the Ms. Goldstein's husband: you require high school students to do math for the same reason you require them to read Shakespeare. High school is a generalist education that should expose students to an essential broad cross section of academic and cultural studies.
Finally, Ms. Goldstein hits on a key problem with math education in the USA: "American teachers, especially those in the elementary grades, have taken few math courses themselves, and often actively dislike the subject." Might just make it hard to learn...
Enjoy life! This is not a dress rehearsal.
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.
I think the problem that they are referring to is that Algebra 2 and Calculus are being required for most non-STEM degrees, such as an English or philosophy major and the average person seems to be wired for one or the other, few can do both well.
"Be particularly skeptical when presented with evidence confirming what you already believe." -
I would tend to agree with you here. While I do completely agree with removing those courses as hard requirements for all of the described reasons - particularly calculus...maybe not algebra 2 and trig...replacing one kind of complex math course with another semi-hard to graph math course that many people won't use isn't going to help much.
IMO - right idea, wrong solution. Replace that course with an intense personal finance class...that seems more like applied math that should be required.
"Don't teach a man to fish, feed yourself. He's a grown man. Fishing's not that hard." - Ron Swanson
I don't know. Several more Hunter S. Thompsons could be fun.
"Be particularly skeptical when presented with evidence confirming what you already believe." -
" the average person seems to be wired for one or the other, few can do both well."
True. I, by nature, am more into philosophy than math. Interesting I loved logic; and from logic I got into programming; and from programming I picked up math.
If you're scared of your govt then you need to further restrict its powers
Vote 3rd Party in 2016 and beyond
f(x)=ae^-( ((x-b)^2) / 2c^2)
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.
The Language God Talks -- Richard Feynman
A quote from the book with the same name, both in print and in audio, by Herman Wouk about his conversations with Feynman while doing research for his two volume magnum opus on WWII. According to Feynman the language is Calculus
"But it's not easy to see why potential poets and philosophers face a lofty mathematics bar. "
I was a Philosophy major in college and I did Calculus... I do agree that I hardly use more than basic algebra. Perhaps a real life math class and statistics are more useful. I find doing stuff like figuring out a mortgage and 'how long will it take me to pay off my credit card' is pretty useful.
Peace, or Not?
When did algebra become advanced math? I was 11 when I took my first algebra course.
In any case, by definition, competitive colleges have "barriers" to entry, and requiring all their students to know basic math and science (and that's what algebra and calculus are) is a reasonable barrier for them to have. If anything, colleges should be requiring more science and math literacy, not less.
Let's dumb down the general level ?
No thank you.
Instead of making knowledge easier students should be pushed to learn to learn, train their brain, the most they can.
Irrelevant news and morons using moderation to mod down what they disagree on. 2018 resolution: so long.
Learning to use chopsticks might not be useful every day to the average Anglo-Saxon diner, but the dexterity acquired by proficiency in their use might help a surgeon or EMT have a better success rate. I don't care if my doctor consumes Asian food or not but I care that his skills be the best possible for very obvious reasons. There are many tools available to improve mental acuity - mathematics is one such tool. Algebra helps develop, among other things, the ability to think in the abstract and develop or hone logical thinking and problem solving. At the same time, I do believe that certain curricula are loaded with irrelevant requirements that extend the duration of study for graduation solely to support greater revenues for the institution.
If we were really looking out for the next generation, we would be teaching them all Post-Apocalyptic Maths, along with how to knap flint and distill alcohol for fuel.
Because 99% of them are fucked already.
Another shite post from this douchebag.
http://www.acetonestudio.com
This guy is a political scientist I don't think he knows how much math is really used or in what fields. I would hate to think a Doctor or EMT wouldn't know how to figure out how much of a medication they could give over an amount of time vs body weight.
What gets me is this:
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."
Err... We educate to a certain standard because of societal needs. We, as a society, do not need (nor can we afford) more poets and philosophers. They're both noble and worthy things and great to have but you should probably have a day job. Unless, of course, you're going to be a "Philosopher of Mathematics."
Having said that, I'm sort of inclined to agree with the guy. The average person will never need Algebra II. They might need Algebra I and I think that's a fine point to stop - as mandatory goes. Obviously, Algebra II should be an option. One might even say that it should be a mandatory option, if such a thing exists.
So, what to fill that space with? How about a real Computer Science course but an entry level one? No, I do not mean programming. I do not mean learning to use an office suite. I don't even think computers should be a part of this course, at least not in the initial, basic, mandatory level(s). It should include things like safe hex, basic principles, history, vocabulary, and things like that. A high school graduate should understand the concepts of a firewall well enough to configure one, know what TCP/IP is, understand what an ACK is, know who Knuth is, know about Colossus, know about Babbage, know what binary is - and how it is used, understand protocols such as HTTP and FTP, understand the concepts of data storage and manipulation, what an OS is - and the choices between them, as well as having an understanding of the actual function of the hardware components that comprise the average desktop.
There's a lot more to add to that list, it should have a basic and advanced option, it should keep going into further levels, and it should be vendor agnostic. I'm reasonably sure that there are people here who are smarter than I and are able to refine the list of requirements. In this day and age, the concepts of things like data and computer security are essential knowledge, safe hex is important. Hell, we could go so far as to include some concepts on netiquette and privacy - again, not pressuring but to ensure that the options are known as well as the risks and rewards are known.
There's no reason for a graduate to not know how to configure a router from *any* vendor and be able to find and use the security settings. There's no reason for them to not know how their computer works. There's no reason for them to not understand the concepts of networking and the terminology associated with it. There's no reason for them to not know the typical file-types and what they're referencing. There's no reason for them to not know the history of computing and to understand the concepts of data processing, from CPU to RAM to storage. None... These are essential knowledge in today's world and we'll be better for it as a society.
Again, it shouldn't be programming nor should it be learning how to use a browser. Office shouldn't enter into it, nor should LibreOffice or OpenOffice. It should have jack squat to do with making a web page - but they should understand what (really) a page is - and how to go learn how to make one, as well as why they work and what markup (for example) means. No, they shouldn't be learning about how to use JavaScript libraries, but they should be learning what one is. They should be able to use something like uMatrix and know what the connections are, what they're doing, what risks are associated, and how to make an informed decision about what code they allow to run on their system.
I hate to use the word because of the connotations with the verbiage but they should be, in every sense, empowered. They should be empowered to utilize the freedoms associated with informed consent. They should be enabled to underst
"So long and thanks for all the fish."