Why Algebra is Necessary: Rebutting Andrew Hacker July 31, 2012

Why Algebra is Necessary: Rebutting Andrew Hacker

I teach Geometry. I’ve taught it for years. I’ll have two sections of it this year. Probably 65 kids. Every year that I’ve taught the subject, kids have freaked out at the mere mention of the word “Proof.” Without actually knowing what they are or how to do them, they want to give up immediately. And they rationalize their fear by asking me when they’re ever going to use it in life.

My response has always been something like this:

You will probably never need to prove that two triangles are congruent to each other, but this unit isn’t really about that. What we’re doing is proving something that you only intuitively think is true. You’re using a logical, step-by-step approach, justifying every single argument you make. Furthermore, you’re only allowed to use a basic set of rules to justify your thinking. Can you explain your answers to me in a way that is easy to understand and impossible to refute?

And then, inevitably, the next day, they forget that speech and ask me when they’re ever going to use this in life. And then I slam my head on the desk.

The worst part is that a number of math departments that I know of are pushing to de-emphasize proofs, spend less time on them, make them less rigorous, or get rid of them altogether. Which is the worst possible way to deal with the issue since, in my mind, proofs are the most important part of the class.

So you can understand my rageface as I read Andrew Hacker‘s article in the New York Times asking, “Is Algebra Necessary?

(Quick note: Andrew Hacker wrote a *wonderful* book with Claudia Dreifus calling into question how colleges are run — I can’t recommend it enough. Awesome book.)

Back to Hacker’s article, which I’m not a fan of. Here’s what he writes:

A typical American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.

Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.

His argument can be boiled down to this: A lot of people suck at algebra and we hold them back because of it, but most students will never need to know the specifics of algebra to do their jobs later in life. So why put such a big emphasis on the subject?

My response is the same one I give my Geometry students: It’s not about specific calculations. It’s about being able to take a set of rules and apply them in different situations.

This idea of not teaching kids things that might be difficult and that they won’t directly use in life could justify getting rid of damn near every class. But we ought to approach them the same way as we do math. English shouldn’t be about the specific books we read — it should be about how we analyze them and what we take from them. History shouldn’t be about specific dates — it should be about the patterns and trends that emerge.

It’s hard to convey all that to students (and some teachers) and most of them will never pick up on that when they’re in school. But that doesn’t mean we should skip out on these subjects.

As Evelyn Lamb at Scientific American puts it, “Math education needs to improve, but if illiteracy were on the rise, I don’t think we’d be talking about eliminating reading from the curriculum.”

(Of course, there are also all the standard math teacher responses: Every career uses some form of math. You’re gonna have to know some basic algebra when you’re buying a house, or creating a budget, etc. Even if you don’t think you need math later in life right now, you may change careers.)

Hacker says later in the piece that requiring all students to take some form of statistics would be more worthwhile, and I agree with him, though not at the expense of ignoring core math subjects.

Art Benjamin actually gave a wonderful and really short TED talk on how schools ought to restructure their curriculums so that the pinnacle of math is Probability and Statistics instead of Calculus. I show it to my AP Stats kids the first day of school:

Benjamin is saying something not too far removed from Hacker — let’s make sure the math we’re teaching to students is relevant to our society. I agree — Statistics is far more relevant to the public discourse than Calculus — but even Benjamin is only suggesting a realignment of our priorities, not avoidance of a tough subject.

(Not to mention you really can’t do basic Prob/Stats without an understanding of basic algebra.)

One of the problems we have in the math world right now is that the standardized tests that are used to evaluate schools and teachers force students to focus on the wrong things. They focus rote calculations instead of critical thinking. Hell, there’s an entire test-prep industry built on helping students get high scores without necessarily knowing all the material.

But, again, the solution to all of this is not avoiding the subject. It’s teaching it better.

For example, one of the things my department is working on this coming year is getting away from spending all our time on skills that just require mindless work — plugging and chugging — and spending more time in class on one or two problems that require a lot more thought. Let’s see how far the students can get on their own (or with a group) and help them when they get stuck. That would force them to think in a much different way, which gets to the heart of why we teach math.

We also have to revise our teaching because we live in a world with graphing calculators and Wolfram Alpha — and we want students to use them. So let’s teach them when and how to use those tools. Again — less regurgitation of skills, more critical thinking.

Will it still be tough? Absolutely. But if we don’t challenge students, why should we expect them to work hard and push themselves? Math isn’t supposed to be easy. But it is logical. And the students who understand the rules tend to do pretty damn well.

A few more notes.

Hacker writes this:

What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey…

It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.

Riiight. Reading Jane Eyre and studying the periodic table doesn’t help with any of that either. Should we kick English and Chemistry to the curb, too?

Does anyone know what that formula is? Because it’s actually pretty amazing. It’s Euclid’s formula for generating Pythagorean triples (like 3,4,5 and 5,12,13) — it even resembles the Pythagorean Theorem, c² = a² + b² — and it can be very useful if you’re studying Geometry. But if you just think of it as a series of variables without any context, as Hacker does, it’s pretty meaningless.

Andy Soffer elaborates on that formula:

To be fair, I don’t think we should expect non-mathematicians to recognize this formula. It’s beyond what I think is necessary to be a well-rounded citizen. But I do think we should expect the average American to be able to do the basic algebraic manipulations to prove this identity. This is the sort of mathematical literacy I would deem the rough equivalent of being able read, or being able to write in complete sentences.

Hacker also says he thinks all students should be able to do things like “long division,” that they should know basic arithmetic skills. But the students who don’t do well in algebra usually struggle precisely because they don’t know basic arithmetic.

Show me a student who can’t find x and I’ll show you a student who needs an iPhone app to calculate a 20% tip.

I’ll leave you with a much more blunt take on the matter by Maddox, who believe Math doesn’t suck, you do:

Math is exactly like cooking: just follow the recipe. Symbols look confusing? Can’t figure out how to solve a problem? All I hear is, “Waaah! Boo-hoo! I didn’t read the introduction to the chapter that tells me exactly how to solve this generic category of problems!”

Math isn’t some voodoo that only smart people understand. It’s something that people understand on their path to enlightenment, and it’s about as straightforward as thinking gets.

… if you’re leading your life in such a way that you never have to do math, congratulations, you are a donkey.

Why is math the only discipline that has to put up with this bullshit? People gladly learn art, music, literature and geography. You’ll even nod like a happy idiot when you learn what a haiku is, and you never complain or whine about how you’ll never use this in your “life.” When is the last time you wrote a haiku, asshole?

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  • ACN

    As a physicist, anytime I hear someone pontificating about higher mathematics, and then say something like:

    “I say this as a writer and social scientist whose work relies heavily on the use of numbers.”

    I typically stop listening. It’s cute that they think it’s all about numbers.

  • If your concern is that students will lose out on the critical thinking portion of math, why not remove the “useless” algebra, replace it with something most people will use, say (for lack of a better term) “life math”, critical thinking or programming class?

  • Stev84

    I agree about statistics. I first had it in college and it was the first maths course in my life that I actually enjoyed. You need some calculus for the slightly more advanced things though. The other maths course that was great was cryptography.

    There are ways to make it interesting. In the general maths course the professor just read everything literally from her sheet. It was horrible and few people understood anything. She completely failed to include any practical examples to make the material relevant. She was teaching vectors to a group of computer engineers and didn’t think it may be interesting to make an excursion into 3D graphics for example.

  • TheExpatriate700

    Actually, I remember lots of students complaining about how they didn’t need to learn about poetry, history, and many other subjects. Claims that math is singled out don’t really hold water in my experience.

  • Tainda

    As someone who is HORRIBLE at math and dreaded going to classes (horrible to me was B’s and C’s lol), math is a must in school.  Children need to experience everything before they know what they can be good at.  Not only that, it DOES teach critical thinking skills.

  • Yukimi

    Yep, my boyfriend is an engineer and it’s always complaining about having had to study Literature and what would be your English. It makes me pretty mad and it’s not even my main field (Medicine student), specially because it plays on the stereotype that science people can’t enjoy, be interested in or understand anything outside their field (like literature, …) that’s pretty prevalent around here.

  • P. J. Reed

    My response is the same one I give my Geometry students: It’s not about specific calculations. It’s about being able to take a set of rules and apply them in different situations.

    On the other hand, if your real goal is to teach students how to solve problems logically, is Geometry the only way to do that?  Is it the best way?  If not, why push it as though it is?

    I’ve always seriously struggled in any math class that required I do proofs.  In high school I struggled through trigonometry  and calculus.  Being able to pass them at all was mostly a combination of luck and being so bullheaded about it that I’d eventually figure out the right answer.  Doing mathematical proofs is something that I just don’t get, and it takes me hours of staring at a page to figure things out that seem to just come intuitively  to some people.

    But then I learned about Boolean algebra in college and started taking classes in stuff like finite state automata and discrete mathematics, and I was amazed at how much more sense everything made.  That kind of stuff comes easily and naturally to me and did more to help me understand logic than my high school mathematics classes ever did.

    So I guess my point here is that logic is important, but I don’t think the traditional high school method of, “You must learn algebra then geometry then trigonometry!” is necessarily the best way for everybody.

  • Ellentann

    I would agree that it’s all about how subjects are taught – teachers who can make the classroom lessons relevant to the real world are what our schools need.  This can be in the specific details of a lesson and/or explaining how the skills translate into life skills. 

    I’ve always contended that being able to solve ‘word problems’ where you have to ferret out the pertinent details and determine how to put them together to reach an answer – first specifically encountered in math class –  is one of the most basic skills needed to succeed in life – since life throws word problems at us every day.

    I was fortunate to have great algebra & geometry teachers.  Statistics, on the other hand, pretty much left me cold & most of the details of any given section were immediately forgotten as soon as the test ended.  But I did at least learn the basics – questioning statistics & studying how a number was arrived at rather than just accepting them at face value, and the important differences between average, median & mean (though I still sometimes have to look it up).

  • NickDB

    As a kid I was one of those that didn’t understand why “Proof” was needed, I gave you the answer what more do you want? And blowing my own trumpet it a bit, I was good at maths, very good, the answer I gave was usually 95% of the time right. My teachers hated me because I coasted along at 1% above a pass.

    Now however that I’m an adult and working I understand exactly why proof is required.

    It’s not to prove you can do it, it’s to prove to others that you can do it.

    I use the following example to my god children.

    You’re a civil engineer in a huge court case because the building you helped design and build fell down, killing hundreds of people. You’re on the stand being grilled by a lawyer looking to blame you for the incident. IF you can’t explain step by step in a way that a jury can follow how you came up with the concrete formula or the design for the building, you’re going to jail for murder.

    This is what the proof is teaching you, not that (2 x 4 / 1 ) x 2 = 16. It’s about the process and a way of thinking.

    You can also swap engineer for doctor, accountant, lawyer, chef and just about anything.

    I really don’t get people who say they don’t use algebra or maths after school, do they not add up their grocery bills or do their budget every month?

  • icecreamassassin

    I blame poor mathematics education in the United States on crap like FOIL – it taught me the mentality of how to get an answer but NOT SOLVE A PROBLEM.

    Also, I just plain hate the whole damn FOIL thing…frankly, remembering “first, outer, inner, last” seems to take more effort than to simply understand order-of-operation.

  • Brian Westley

    “When is the last time you wrote a haiku, asshole?”

    When is the last time
    you wrote a haiku, asshole?
    So close, yet so far

  • solsticepixie

     Spanish teacher, here!  Each and every day I have to justify my subject  to my students.  I even have to justify it to their parents and some of my colleagues.  Every few years a former student stops by to tell me how something I taught  helped him/her with something in their studies or their life and it finally clicked for them that I was right.

  • NickDB

    Because “life math”,  critical thinking or programming are all based on algebra? Bit hard to teach those without the basics.

  •  I see this as an argument to push for the jury to know math, not just you. If they can’t think logically because they never took math and science in school, then you are screwed, no matter how well you prove your point.

    I teach physical sciences to undergraduates, mostly in humanities majors. I have had girls hyperventilate and cry when I ask them to use a very simple formula to rearrange and plug things into. The word “variable” seems to be terrifying. It’s baffling. But I come from a catholic girls school abroad, not the American school system. Those nuns did two things right: make me an atheist, and teach math.

  • solsticepixie

     Studying statistics in college and grad school changed my attitude about math.  Like you, I hadn’t enjoyed math until then.

  • Rrpostal

     Did this guy just suggest we will do better on global aptitudes if we make the test a lot easier for us? Let’s hope the rest of the world continues real education so that they can continue making all the stuff we use. I used to like science fiction and dystopian stories until I saw I was living in one.

  • Cash registers were down at the local CVS 3 weeks ago. The woman working there at the register had to pull out a calculator to figure out the change. I gave her $20, what I was buying cost $18.56. I think math classes need to work on more *figure this out in your head* since most people today are so reliant on technology to figure out their problems for them that they lack the basic math skills to get by. 

  • Rrpostal

     (sorry that wasn’t meant as a direct response to Stev84)

  • Ronlawhouston

    I still haven’t figured out why Americans generally suck at math.  I was good at math and loved to solve problems; however, as I look back I wonder “why in the hell did I need to learn that?”

    It reminds me of Paul Simon’s “Kodachrome” (I date myself with that one) “When I think back on all the crap I learned in high school, it’s a wonder I can think at all.”

  • Gunstargreen

    First we take away math, then we take away literature, pretty soon school just becomes a place for parents to get rid of their kids for the day.

    The country grows dumber every day.

  • NickDB

     It would help if the jury also knew maths, but if you
    can been seen understanding it and are able to explain it clearly and
    professionally, then the jury will feel more comfortable in trusting you.

    No matter what the maths levels are of the jury, going “That’s the right
    formula, because it just is” is not going to do you any favours.

    Have to laugh, I also went to a non American catholic co-ed school, and you’re
    right, nuns (and priests) do make good atheists and mathematicians. I wonder if
    the critical thinking they instil by teaching maths has anything to
    do with the atheist part.

  • mswool

    when I get asked the inevitable “when are we ever going to use this in real life???” by my students, my stock response is to say “did you do jumping jacks in PE this morning?” “yes” “When are you ever going to use jumping jacks in real life?” “probably never!! but they are exercise and make us healthy!!” and I respond with “the math we are doing today is exercise for your brain, makes your brain healthy and helps you learn how to think and solve problems… not just math problems.”

    They huff and puff a bit more, but tend to get down to it.

    As far as using what we learn in school… for crying out loud, I have never used osmosis in my real life! but it’s still cool to know about it. We learned LOTS of things at school that we never use in real life. But it’s important to exercise your brain and teach it to take different pathways.

  • mswool

    a not insignificant number of my middle school students will simply not do hte story problems. They will do the equations, etc. and skip the story problems, preferring to take whatever grade they get for not completing all the problems rather than figuring out how to do them.

  • Andrew S

    I have to say that I’m partially concerned with the desire that everything we need to learn be “useful.”  I’m a high school English teacher, and I do try to make sure students see the connections between “Romeo and Juliet” and their life (and human life in general), but I think it’s pernicious that everything around us, and everything we learn, must have a specific use. I think that’s part of the reason we have a country so invested in religion:  if we debase everything that doesn’t have a specific use for us, there’s very little importance in a life that is a cosmic blink of an eye, let alone a beautiful poem without a concrete meaning (say Mallarmé) or a fun mathematic concept like Kaprekar’s Constant that has little to no practical import.

  • Tyrrlin Flamestrike

    “When is the last time you wrote a haiku, asshole?”
    *laughs*   On July 7th, for a writing/art/photo contest that ends tonight, actually.  I wrote three of them.

    Just becuase someone might not *use* the information given in school does not make knowing that infomation (or especially the drive behnd it) useless.  The more one reads, researches, learns, travels, discusses, debates, listens, etc, the more well-rounded one becomes.  Someone who dismisses an entire subject of learning because “it’s hard and I won’t use it” is someone with whom I don’t wish to associate.  High School Honors-level Physics was an incredibly difficult class for me (especially since my math class was six months behind), yet I took extra tutoring and worked very hard to learn the basics.  I’ll tell you, it was a *wonderful* class!  We got to do some amazing real-world experiments and tests.  If I had given up, I never would have had those experiences.  

    Maybe I don’t use vectoring in everyday life, but I’ll never forget our test of placing a target so that the catapult shot would hit the bullseye.  Each ring had a point value.  You fired ten shots at three different (random) angles, the closer to the bullseye, the higher your grade for the test.  It was fantastic!

  • Alan E.

    I love that TED talk about statistics. I reference it in nearly every conversation I have about mathematics (been having a lot more on Facebook after this article came out)

  • I was more interested in languages than maths at school, and one of my childhood dreams was to study linguistics. Not only did I continue to learn new languages as I grew older, but I also did a PhD in linguistics and I’m currently employed to do research in the same field. While I don’t regret for one moment learning all those languages (it’s still my main hobby) I’m not sure I could put my finger on any point where that knowledge has been directly relevant to my research. Maths and programming, on the other hand, have been vital. I didn’t expect that.

    (I realise this doesn’t speak directly to your point about the general skills that maths give you, but I thought it was worth adding.)

  • Gus Snarp

    I too think that we should focus on statistics more. It is absurd that we graduate high school students who have never had any education in basic probability and statistics, even if they’ve had advanced calculus.

    I also agree that we should not do away with algebra. I think what should happen is some introductory algebra, followed by some probability and statistics, more algebra, more statistics, eventually into calculus. In a perfect world, there wouldn’t have to be strict breakdowns where one year is algebra, the next year is statistics, etc. Algebra and statistics should be blended seamlessly. Why is it that we teach kids how to graph the slope of an equation without explaining what that line equation is commonly used for? How many kids graduate and go on in life thinking the equation of a line was useless, never understanding that it’s used all the time in calculating those trend lines we see all the time? Then they move on to more advanced polynomial equations, never knowing that calculating probabilities is a powerful use of those tools.

    Honestly, this killed me in math. We had Algebra, Geometry, Algebra II, Trigonometry, and then Calculus. I never made it through Algebra II, and a big reason was not that algebra is too hard, but that I was simply told that the solution to a certain equation was a certain curve and that was it. Not why the equation described that curve, not what it meant in the real world. Of course people think there’s no real world use for algebra, they have teachers and books that can’t seem to communicate the very obvious real world uses.

    Then I went on to take two years of probability and statistics in college and it was like somebody turned on a light bulb. Why had no class ever linked this stuff before? I was playing catch up, but I had just enough algebra to get by and I learned so much, did well, and discovered that I’m not actually “bad at math” and that I could love and be fascinated by it. But I was too far behind. I didn’t have the fundamentals to go any further and would have to spend countless class hours catching up on Algebra II, Trig, and Calculus to advance my math education. Some of my computer science courses were made more difficult as well. So this is one more reason we need to teach algebra, on top of all your good ones: because we shouldn’t close the door on students. Algebra is a door to a wider world of knowledge, and you never know when a student will discover in their junior year of college, or even years later that they want to see where it leads. We shouldn’t take that away from them.

    The answer is not to get rid of algebra, but to teach it better, and it seems to me that most of higher math is inextricably linked with statistics, separating it makes things that should be deeply meaningful seem utterly meaningless, and it is a huge mistake. What I don’t understand is how we’ve gotten here, how people who know far more about math than me didn’t work to link statistics and algebra from day one, and why more aren’t trying to reconnect them in curricula now.

  • Well, Hemant, here’s how I figure it goes. I’m a scientist, doing primary research. I’m good at math, I speak a couple of foreign languages. I’m an Alpha. You’re smart and good at math, and are serving society by teaching. You’re a Beta. Most of the people on this forum are Alphas or Betas. Just about everybody else is walking around in the fog of soma, often delivered in the form of political dogma, religious dogma, or magic crackers. Those Gammas, Deltas, and Epsilons are useful for keeping the gears of society oiled, but they don’t need any algebra, or know how to logically prove anything. Indeed, it’s better if they don’t know these things, because otherwise they might get ideas about invading our more elite strata, right?

  • John Small Berries

    I was one of the kids who said, “Pfffft, when am I ever going to use this in real life?” So I learned for the test, and promptly forgot it afterwards.

    Then, a few years after I was out of college, I discovered 3D graphics; as the renderer I was using didn’t have a GUI modeller, but required the user to describe the geometry of all the models in text files, I ended up having to relearn all the geometry, algebra, and trig I had dismissed as something I’d never need.

    Ironically, one of the few things that did stick in my memory – “FOIL” – I still haven’t found a use for. But I’m remembering it just in case.

  • Stev84

    It’s true that not everything taught has to be relevant or practical to be justified. That’s not really the point most non-students make I think. But if it’s possible to make something relevant it’s a good way to motivate students to pay attention. You can teach some maths subjects very abstract and risk people just tuning out, or you can find something practical and 1.) increase the chance of people paying attention 2.) make it easier for them to understand

  • Nicely done, Hemant.  

    You’re right that Benjamin’s position is not too far from Hacker’s. In fact Hacker would say that some form of applied statistics (what he clumsily calls “citizens’ statistics”) should be required.  He doesn’t suggest that algebra should be eliminated, only that it is elective.  I think he’s wrong to think that one can understand statistical analysis deeply without some basic algebra, but that’s another story.

    Re chemistry and Jane Eyre:  I think I disagree with you here.  A working knowledge of the periodic table and Bronte’s yawner really can facilitate ” more credible political opinions or social analysis. ”   For periodic table, one would have a deeper understanding of climate change, ozone depletion, and a jillion other things that should be informed by science.  Jane E. is chock-full of themes on morality, gender and class issues, and so on — what every child needs to be adept at social analysis! (And anyway, unlike Algebra, Chemistry is usually an elective–which is what Hacker advocates.)

    But seriously, nice post…

  • Alan E.

    Another major problem with mathematics is the general mentality that “math is hard.” You also have parents who tell their children that they were not that good at math when they were in school (and look at them now). This gives  pass to the children to not push themselves or feel like they don’t have to try.

  • Carolyn

     When I moved to Ontario, I heard a lot of people proudly state that they’d studied french for 5+ years and can’t speak a bit of it. In the next breath half of them claimed that everyone in Quebec speaks perfect english and they just don’t to make a political point.

    (This is usually where I usually switch to french while explaining exactly why they’re idiots)

  • While I have to say, I’ve never really used much of the higher level math that I learned in high school and my first go at college (and have since forgotten much of), it certainly reinforced the lower level stuff that I learned before that. And I do use that stuff. A lot. And I think it reinforced my intuitive ability to figure out how to figure out math I need to solve, even if I didn’t remember the actual stuff I learned. 

    So yeah. Math. 

    Maybe everybody should be required to learn a bit more physics, chemistry, finance, computers (especially spreadsheets) statistics, home ec, industrial arts, phys ed, and other subjects that actually apply the math learned in math.

  • Gus Snarp

    Yeah, this is absolutely huge. Do you want your life in the hands of a jury someday who don’t have the skills to work through a problem in a logical manner? (Well, maybe if you’re guilty you do). 

  • susanrubinsky

    There actually is a skill where you don’t even need to calculate it out in your head — I was taught this years ago by a cashier in a store I worked at. You count out the change first, then any bills. For example, look at 56 then add 4 pennies to make 60 then add a nickle and a dime to make 75 then add a quarter to make 1 then add the 1 to the 18 to make 19 then add another 1 to make 20. It takes longer to write this than to do it. It’s not even about numbers really, it’s about following a process. 

  • Vend Tana

     Too long didn’t read.

    And what’s with all the foreign words in that post anyway? I speak English. I don’t need to know any other language. Try using Google Translate next time kthx.

  • Roxane

    I suck at math, but I loved geometry.  Doing proofs made me a much better writer.

  • Gus Snarp

    You can get very far in computer programming without algebra. You may be able to code up a simple web page, but as soon as you want to say, assign unique colors in a gradient based on some numeric property, you’ll need to figure out the algebra to create the code. You can forget writing anything like a decent video game without some algebra. Computer code expresses equations differently from an algebra text book, but it’s all about variables and algebra. I’d be all for folding some programming in with the algebra teaching, so kids learn something practical and get to approach the problems from a different direction, but you’d still be teaching algebra.

  • susanrubinsky

    Sometimes what we learn may seem irrelevant in the moment but become meaningful later. 

  • This goes along with the question of whether we should we have a one-tier or two-tier society.  The “one tier” argument would say to minimally educate everyone to at least a “basic education” where some people will be over-educated with skills they will never use in certain subjects.  This argument says that it is better to have a society where everybody is at least minimally educated to a certain level in a whole variety of subjects.   The two-tier argument says to only educate people for what they will actually use in life.     This argument says that we waste a lot of time and energy educating people for skills they will never use and everybody should be free to opt out of any education they don’t want.  This argument would say it is OK to have illiterate uneducated people walking around as long as they are able to do their job.

    I’m for the one-tier approach.

  • NickDB


    (Joking, in the same way I hope you are)

  • rhodent

    I used to work in tech support, and when filling out tickets we had to use the “PAR” structure (state Problem, Action taken, and Result).  We made a game of being able to write our tickets in poetic forms — haiku, limerick, etc.  Usually we needed one haiku for Problem, one for Action, and one for Result, but I did manage to write an entire ticket (a simple password reset) as one Haiku:

    P: User can’t login
    A: Reset password in AD
    R: Login now working.

    (AD is Active Directory, the program we used to control user accounts.)

  • eonL5

    Exactly. I learned that at my very first job, age 16 or 17. It’s not hard at all and takes all of 5 minutes to understand.

  • Stev84

    It actually takes more time to become fluent in French than it does to become fluent in English. French is a lot more complicated.

    Though it’s really no excuse when you live somewhere where it’s spoken. The reason I forgot most of my French is because I never had a chance to use it.

  • Where does the savage fit in?

  • vexorian

    What? Long division? If anything, it is silly long arithmetic that has
    become completely useless in life, ever since calculators were invented.
    Although you can treat it as a good mental exercise.

    Being against proving things sounds to me like the typical trend of
    wanting to remove science from class rooms. You just learn your
    divisions, you will never learn to doubt on a lemma until you know a
    proof. Our modern world is built on algorithms like long division, but I
    wonder if so much people have bothered proving why it is correct to
    split the problem like that.

    That Hacker’s article, it boils my blood and comments are now closed. Just about all of school’s subjects are not going to be used by the majority of people in their lives.  Historians won’t get to use calculus. Engineers won’t get to use History. But that’s the whole point. For starters, how are kids ever going to find out they like Maths, or they like Calculus if they don’t get to it?

    And Americans supposedly struggle with Algebra. Isn’t it a reason to make it a more important subject rather than to delete it? If such a basic skill is not as easy to learn, then we need more education for it.

    Statistics replacing other things baffles me. How are you going to learn statistics without calculus or algebra?

    I think there has to be made more game theory and optimization and the such. The moment you start seeing that with some math and creativity, you can really get better results. Spend less money, spend less time. Win more often than lose. It tells you, the reason you are not using math knowledge to improve your life, is because you never learned it well enough.

  • Stev84

    Aldous Huxley’s Brave New World

    Great idea, but the story turned into complete nonsense when they reached the Indian reservation. It would have made a lot more sense to have the people live there like today IMO

  • Where does the savage fit in?

  • Vivian

    It is very sad! It’s also sad that it is taught vigorously in other countries and students can answer it coherently. I use to work in the kitchen and it’s amazing how often I have to use math. Constantly. Even knowing geometry helps you cut the cake correctly for odd numbers of people. But that isn’t the point, you are right about that. We constantly talk about teaching critical thinking and people don’t get what that means. It’s the same thing as English class. I saw a meme some sad high school kid made about reading the subtext of novels and how it’s just made up by the teacher. In this case, we aren’t solving a specific problem, but building skills to develop our understanding of people and clues to who they are and how they think. Do these kids just want to go to school and learn manual labor? See how they’d like that. 

  • susanrubinsky

    Thanks for this post. I totally agree with you and was completely offended when I read this article in the NYT this past weekend. I am so sick of the dumbing down of America. As someone for whom math was always a struggle, I am grateful for that fact that I retained some geometry and algebra because I use it almost every day. In the business world I often find myself shocked when people can’t even create a simple formula in Excel.

    The U.S. would be absolutely stupid to remove Algebra from the curriculum. Not only would it increase the general dumbing down of our population, it would decrease our ability to create and be innovative. Another issue is jobs and people capable of doing them. Yeah, we’re still recovering from the recession and unemployment is high but just look at some of the professions in which we don’t have enough skilled workers: Medical doctors (The same issue of the NYT included an article noting the the U.S. will face a shortage of 5,000 medical doctors by the year 2014) and software/computer engineers. Both of these professions require mathematical skills far beyond Algebra. We might as well just hand over our economy to Asia because Algebra still matters there.

    I’m appalled at how short sighted the Hacker article was.

  • Michael

    I recently completed my doctorate in a hard science and can confidently state that I would never have made it if I didn’t know that little bit of Latin.

    I got surprised by jargon in an exam at undergraduate level and if I’d missed that grade I’d probably never have got a good enough undergrad degree to do a doctorate in the first place.

    As for geometry, you use it to complain that your parking spot is too small, hang a door without drafts and write a best-selling computer game.

  • RebeccaSparks

    Alpha children wear grey. They work much harder than we do, because they’re so frightfully clever. I’m really awfully glad I’m a Beta, because I don’t work so hard. And then we are much better than the Gammas and Deltas. Gammas are stupid. They all wear green, and Delta children wear khaki. Oh no, I don’t want to play with Delta children. And Epsilons are still worse. They’re too stupid to be able to read or write. Besides they wear black, which is such a beastly colour. I’m so glad I’m a Beta.

  • Nankay

    Maybe it’s because I come from a background where the large portion of kids never went to college,   I have always thought a very basic consumer math class should be required before graduation.   How to figure out which is better: a 1000 dollar rebate or a lower interest rate. How much does the suit cost at 20% off?  How long will it take to pay off a debt at 6.5 % interest?   How much will gas cost you every week driving that SUV back and forth to work?   Even those few college bound kids in the advanced classes could use such a class.

  • vexorian

     Pretty sure that’s not Italian, I bet it is French or Spanish.

  • Em

     Speaking as someone who’s taught both FSL and ESL, I find that my francophone students have a lot harder time learning English than the other way around. French’s grammatical rules and pronounciation are a lot more consistent than English, and it has fewer irregular verbs.

  • Em

    One of the things I try to explain to my students (I tutor all subjects through elementary school, and math/physics/literature through high school) is that every subject – every one, from mathematics to fine arts – is the same subject. Knowing more about one thing helps to understand everything else. The artist and the theoretical physicist both do the same thing – they observe the universe, grok it, and demonstrate why and how it is or is not amazing.

  • Miko

    You’ve missed the point of the article (and your assertion that his main argument that people shouldn’t do math because it’s hard is entirely wrong).  I’ll highlight it for you:

    Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required.

    It’s a good point.  For many people, algebra is worthless.  Forcing them to take it just means that they have less time to take something more useful.  And if your goal is to teach people how to make structured arguments, a geometry class (or, indeed, a math class at the high school level, period) is a pretty poor choice of place to do that.  If that’s the goal, why not cut geometry entirely and replace it with a class on how to make structured arguments?  (To answer the inevitable question of why we shouldn’t try to shoehorn critical thinking into high school math: if you try to do too much, you end up doing it all badly.  Consider the fact that Hemant is a high school math teacher, yet still has critical thinking skills at a level that allowed him to conclude that Hacker’s main argument was that math is hard.)

  • The Other Weirdo

     I’m not convinced that lack of programmers is due to the dumbing down of America(or Canada, for that matter). In fact, I view it as a smartening up of the population. Kids growing up over the past 20 years or so have witnessed the absurd upheavals of this industry and decided, en masse, to forgo it. That’s actually smart. Why enter professions that the corporate world values so little and has no problem with simply shipping wholesale overseas, and in fact searches day and night for the slightest reason to do so?

  • The Other Weirdo

     The irony is that religion itself has no actual specific use. It’s not even entertainment.

  • The Other Weirdo

     Ah, Kodachrome 25. Now there was a slide film.

  • Carolyn

     Actually, having learned both as a native language, I found French easier to learn to read than English (well, write correctly)  The sound-letter encoding/decoding is more consistent. Sure, you have to memorize verb conjugations, but for the most commonly used tenses, most verbs fit in a few categories.

  • The four blondes go to Starbucks and the bill comes to $28.
    They can’t work out how much that is each so they call the cute waitron guy
    over to help them.


    He decides that they are as blonde as they look, and says “That’ll be
    $25 each.”


    The one blonde who’s a bit sharper than the others says, “How
    did you get that number?”


    He says, “Easy if you know long division.” He takes pen
    and paper and writes:



    4 | 28


    “Now 4 doesn’t go into 2, but 4 goes into 8 twice, so we
    write it like this:”




    4 | 28


    “2 times 4 is 8, so we have to subtract it from 28, and that
    leaves us with 20.”




    4 | 28





    “But 4 goes into 20 five times, so we write it like this:”




    4 | 28








    “And so $28 divided by 4 is $25.”


    Well all the blondes think that he’s not only seriously
    cute, he’s really clever too, so they happily give him $25 each.


    But after he’s gone, the one blonde who’s a bit sharper than
    the others says, “Something doesn’t seem right. I wanna check that.”


    So she writes down,








    “Right, so 2 plus 2 plus 2 plus 2 is 8.”









    “Then 5 plus 5 plus 5 plus 5 is 20.”











    “And 8 plus 20 is 28. He was right.”


  • Hestia

    When I read all these comments (and many on other threads) I can’t help but think that the issue is some kids not wanting to do the work. Because when they say, “When will I use this in the real world,” it’s really just code for “this is going to take work and concentration, and I don’t want to do it!”

    I’m not slamming “kids” here. Plenty of kids work hard and get it done: witness more college applications/Ivy League applications than ever before. But the thing that would make the most difference is motivating more kids to work harder. It’s something that I discuss often with my own kids: “Work hard to start with, or you’ll just end up working harder to fix/avoid the problem” and “go above and beyond the assignment when you can.”

    Oh, and for every commenter (most of you) here who didn’t slam teachers, or say that they’re “teaching it wrong” or say something about how in America teachers are the mediocre students who can’t find anything that pays better and that’s why American education “fails”: thank you, thank you, thank you! It gives me some small measure of hope in the future.

  • On a point of note: Required reading for anyone old enough to masturbate is Simon Singh’s “Fermat’s Last Theorem” (USA title: “Fermat’s Enigma”) which is an awesomely brilliantly written book which will keep you riveted for each of its 300  odd pages.

    Read the reviews here: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622/ref=sr_1_1?ie=UTF8&qid=1343752001&sr=8-1&keywords=fermat%27s+last+theorem

    I’ve read his “The Code Book” and “The Big Bang” and both are real examples of science writing at its most gregarious… I’d even score him a half a point above Dawkins!

  • Neverenoughrain

    It’s really too bad the Maddox’s bit is so full of misogyny. It was otherwise pretty much perfect.

  • Stev84

    There were times when I learned French that most of our time seemed to be taken up with memorizing irregular verbs. For months on end. English has maybe 300 irregular verbs that you actually need, but they only have three forms. In French it’s more tenses (for English it’s only two past forms) and of course more genders. So although there may be less irregular verbs in French, a lot more time needs to be spent learning them.

    Yeah French grammar is consistent, but it’s also a lot more extensive than English. English has one of the most simple grammars.

  • Business-type here. In the last 15 or 20 years, expanding computerization has transformed the business landscape. If you want a job in marketing, supply, purchasing, whatever, you had better be up on your algebra and statistics. If you work with a lot of graphs, which people in operations and production and analysis have since forever, you’ll need a little calculus.

    When you’re dealing with organizations that rely on optimization to compete, you’ll be surrounded by math. You’d better get good at it unless you’re okay with a career entirely at the departmental assistant level.

    Having said that, I read an article in a Psych journal a while back that explained why math is hard (or at least harder than many subjects): people are not naturally numerate. We are apparently wired for language and a degree of literacy, but numeracy only comes after much training, excepting of course those people who are born gifted at mathematics.

  • RebeccaSparks

    HS math class probably taught me the most “real-world” lesson in school.

      I was great at understanding math and did well on tests, but I was disorganized and lazy.  The math teachers at my school formed some sort of cabal where they all required that we keep a “math folder” with sections for our notes, turned in assignments, a running total grade, etc.  This stupid thing made up like half our grade, and I was always trying to put it together right before grading, and getting upset that they marked down my notes because I wrote down what I needed to remember, not exactly what they wrote down on the board.  I was furious and frustrated that so much of my grade had nothing to do with my actual ability to do math (at which I was very good at) but my organization (which I sucked at), and consequently my grades suffered.

    I have found this is the most work–like experience I had in school.  People don’t care so much that you can do the job, but that you do the job the way they want it done-including things that you don’t think are important and aren’t a part of your job title.  

  • Great rant, Hemant… 

    I’d have to agree with you that it’s not the subject matter but the teaching methods that count. If only my interest in history and biology was greater in school. Two immensely irksome subjects which required rote regurgitation of syllabi with, apparently, no real-world application other than to annoy types like myself.

    Surprise! These are two areas which I now pursue with avid interest… That’s not to say physics, chemistry or geography have become less interesting to me but rather to suggest that they were subjects that had consequence. Biology and History, on the other hand were just a memory game and never involved cause-and-effect problems.

    PS:Sorry to have to point this out but the plural of curriculum is actually curricula.

  • RebeccaSparks

    While people balk at learning math at the high school level, at the university level STEM  (science, technology, engineering & math) classes are the least threatened to but cut due to budget cuts.

  • This method sucks, only for the reason of those assholes who wait until you are halfway through counting out the change to decide to start digging through their pocket or purse for the smaller denominations needed to minimize the number of coins or notes they will get back. 

    If you simply do the subtraction initially, it’s much easier to adjust on the fly.

  • guest

    My wife was someone that was scared of math. She could calculate a 20% tip but did it the hard way. I showed her that dividing by 10 and multiplying by 2 was quick and easy. I also showed her how Algebra can help in daily life by showing how to check her speedometer. I showed her the math involved in rate x time = distance came to simply dividing whatever number of seconds it took to go a mile into 3600. She still doesn’t quite grasp that and thinks that I am some sort of savant but I believe that anyone can learn simple algebra and apply it to things in everyday life.

  • You’ve hit the nail on the head… I’m guessing, then, that dumbing down mathematics is a right-wing conspiracy to (over)populate the USA with serfs and luddites who will gleefully support the oil industry and buy lots of fast food.

    Stupid people are easier to control than smart people.

    USA… USA… USA…! 

    Number one in the developed world! (at least as far as ignorance and idiocy are concerned).

  • Why would an educational establishment that gets a lot of it’s funding from lotteries want a public that understands math?

  • Ignatius Antioch

    Yea, but what do you really need from the periodic table? 15, maybe 20 elements? And even there, you don’t need the atomic weight, number of protons, or the relative position in the chart.

  • Thegoodman

    Clearly LESS MATH is the solution to our country’s personal credit debt crisis.


    Every high school in the US should have 4 years of Math, 4 years of science, 4 years of Econ, and 4 years of Social Studies (not effing history, i mean social issues like white privilege, civil rights, etc..).

    Maddox makes a terrific point. Every dumb ass in my class was ecstatic to read Shakespeare but cringed at the thought of doing Trig.

  • Parse

    When I haiku’d last?  I really don’t remember – Not that long ago.

  • Gus Snarp

    Or, on the other hand, consider the fact that Hacker is a professional writer, and still can’t manage to express his argument without making a lot of the people who he most needs to reach if he wants to seriously implement his ideas think that his main argument is that math is hard. Maybe it’s the fact that he essentially says as much in the very opening of his piece.

  • RebeccaSparks

    Making a structured argument is something that should be taught across curriculum in school.  In math you learn proofs, in science you learn the scientific method, in English you’ll learn how write and argumentative essay, etc.  This is because a) critical thinking is germane to every aspect of learning and b) repetition is key to learning something well. 

  • If it wasn’t for the genders, I think I could have continued with German. I was always excellent at grammar and decent at remembering new words. The genders were just impossible for me to learn though because there was no logical reason why some words were male, female, or neutral. It was very inconsistent which words were which.

  • You cannot outsource everything. True Story!

    The work we (here in the EU) farm out to IT companies in India/Bangladesh/Malaysia/Philippines is a fraction of the total job. There is still a large demand for professionals

    We, rightly, regard outsourcing as another form of hiring temp workers to help stabilise a large project. Our home-grown talent is still heavily engaged in translating the clients needs and implementing the project.

    What, then, will happen to the deficit of IT professionals in the USA? They’ll be imported from Asia while the American luddites will end up moving to Mexico to work in GM plants assembling cars.

    Unfortunately I wont live long enough to have a hearty laugh at that situation!

  • cutting a cake correctly for an odd number of people?

    bollocks! then there’d be no extra slice left over for me!

  • I hate, hate, hate those people!!! If you want to get rid of your change, get rid of it when you first pay me, not after I’ve already entered it into the register and am counting it out.

  • The Captain

    “Show me a student who can’t find x and I’ll show you a student who needs an iPhone app to calculate a 20% tip.” Wonderfully summed up Hemant!

  • RebeccaSparks

    At the risk of being a wet blanket on an inside joke, those are Greek letters–like A (Alpha), π (Pi) or 
    Ω (Omega).   People are mostly familiar with them in terms of fraternities/sororities, or possibly math equations.

  • In Singh’s book (to which I linked above) you can read how elliptic curves are related to modular forms via the Taniyama–Shimura conjecture.

    Two totally different areas of mathematics that were found to be inextricably linked! 

    The beauty of this discovery is that problems (of elliptical curves, for example) could be solved using the techniques of other mathematical disciplines (modular forms).

    Sexy stuff. 


  • In her defense, a job like that is a little different than it looks. People hand you money and all they do is wait for you to give the correct change back. Meanwhile she has to make sure she’s friendly, fast, efficient, and has done everything correctly. I’m good at math and of course I can calculate change and stuff, but it’s a job that involves multitasking and it’s very easy to get confused. She’s more likely to do everything correctly and quickly if she can make it routine and just punch it in.

    If there’s anything that changes or is distracting, it’s very easy to get flustered and forget what exactly you’re supposed to do. I’ll enter everything in the register and then the customer will hand me a different amount of change and then they look at me like I’m stupid when I don’t immediately know what I’m supposed to do. They’re just waiting for their change but I’m trying to make sense of the numbers on the receipt plus the new numbers they just threw at me.
    It’s hard to explain…I’m good at math, but it’s just different when you have to do math in your head on the spot while someone’s looking at you like an idiot.

  • digitalatheist

    I didn’t take Spanish in school, but after working for 9 years with a group that was mostly Hispanic, yeah,… Spanish is a handy thing to know. What some people don’t understand is that it never hurts to know things, just for the sake of knowing it… never mind there comes that time when ya DO wish you really had paid attention in class.

  • Hemant: Something just struck me here and I think you already know what I’m on about.

    When there are posts on equality, plenty of drive-by’s pop in to tell you that this is an “Atheist Blog” so lets stick to atheism and leave the feminism out of it.

    But it seems that a post on mathematics (although popular) has not garnered the same reactions.

    Why is this? Is this because mathematics is not activism so it can also be categorised as mundane? Like cooking or sport or gardening.

    Maybe the USA is not yet ready for equality, just like they are not yet ready for a black president.

    But, hey, guess what?

  • Guest

    so I sucked at math when I started high-school. my elementary teacher told my parents I would never ever make it to university. (my parents laughed and gave me the freedom I needed.I really want to see her again and show her the PhD I got last year) My first year in high school, we had a math teacher who told us that some of the stuff was hard but he was teaching us in small steps because small steps are easy, only the big leap is “hard”. I don’t remember anyone complaining and the class average was a B+ . in high school. in math.  I still remember that. It has helped me through a lot of statistics in university. Maybe this anecdote helps. I tell my student that a lot of statistics problems are fear, not that it’s really hard.

  • raerants

    Reminds me of the Texas GOP’s platform taking a strong stance against teaching critical thinking skills in school. Because at the end of the day, that’s what mathematical proofs are really all about: being able to think and analyze.

  • Generally I agree with you here, so I’m just gonna jump in on one point you made.

    “We also have to revise our teaching because we live in a world with graphing calculators and Wolfram Alpha — and we want students to use them. So let’s teach them when and how to use those tools. Again — less regurgitation of skills, more critical thinking.”

    Back in my Junior year of high school, I argued (successfully, in the end) that I should be allowed to use TI-BASIC programs during tests, provided I had written all the code for them. By writing the software, I was giving myself a much stronger understanding of the methods of solving complex equations. If I didn’t fully understand an equation while writing the code, I’d end up with wrong answers on the test day, and it would be my fault.

    As it turned out, I ended up falling in love with programming after being able to use it in such a practical way, and it has driven my course through life from that point onward. I use math every single day, even though I work with numbers very rarely. Math is simply the logic underneath the flow of information.

    And I really wish that was what we’d been taught in class.

  • Baby_Raptor

    Speaking as someone who failed Algebra 1 three times and Geometry twice, sometimes it isn’t “They didn’t read the beginning of the chapter.” I simply could not make what I was reading make sense. The school eventually gave up and just passed me, because my grades were so high everywhere else. 

    That said, I don’t agree with just stopping teaching math. 

  • vexorian

     I speak Spanish, so you can find out what was my post about :).

  • Onamission5

    I can’t figure out x in most simple equations, but I don’t need a tip calculator to find 20%. In fact, that’s the one simple equation that stuck from all my years of mathematics, probably because I’ve used it weekly since 7th grade! Was always in the slightly advanced math classes, and did well until I got to my second year of high school. Took math through Trig in high school and passed with a D- after months of bawling because I was always two to three weeks behind the rest of the class in understanding what was going on. Gave up eventually and just copied the back of the book. Only got through Geometry the prior year because my eldest sister baby stepped me through it, and when she moved out I was lost, lost, not to mention being completely incapable of memorizing the theorems and proofs needed to complete tests. Wasn’t until I took Finite Probabilities in college that I actually understood most of what I was learning while I was learning it instead of weeks after, and that was only because it was a summer course geared toward non traditional students with little to no successful math background. The prof gave us a sheet with all the formulas on it, we just had to figure out which applied to each equation and use it appropriately. It was like Rocks for Jocks, but instead was Probabilities for Art and English Majors. The lowest level math required for graduation besides statsistics, which scared me silly.

    Something happened in high school, and looking back I really do think it was a matter of outdated methods of rote teaching combined with hostility toward any student who asked questions or became confused. It is my hope that the way my kids are learning math now will help what they’re learning stick. My eldest learned about the Venn Diagram in 4th grade, and that’s something I wasn’t aware of until college, ffs. The way they are taught is so different from the way I was 25-30 years ago, it’s more about process and concepts and less about memorization. The way my second child’s 5th grade teacher explained it, roughly paraphrased, “We’re trying to build mathematical minds for life.”

    Maybe by the time they’re my age, my kids will be able to do better than triple a recipe in their heads and work out 22% on a napkin (me) or calculate square yardage for landscape mulch (their dad). One can hope!

  • I was one of those kids that struggled with math. The first time I took Algebra I, well, I barely passed. Know what I discovered? The teacher wasn’t teaching very well (he was there 20+ years and really didn’t care anymore). Most students barely got a C in his class. A few of us got a student teacher as a tutor that summer, came back with new skills (our tutor is now a math teacher at my old school, the kids are lucky because he knows how to teach well) and most of us ended Agebra II with Bs and As. We even helped other students understand things.

    I think it’s less to do with the subject and more with how it’s taught. Teacher taught it in vague abstracts and told us to read the book, tutor taught us the same abstracts and how they may apply in our lives later. I know which method worked best for me and many others.

    Good teachers and relatable lesson plans. It can be done.

    And sorry, Hemant, I still don’t care for geometry. ;D

  • NeedingMoreFacts

    “Children need to experience everything before they know what they can be good at.”

    Eehh, I don’t think so.  I think they should experience lots of things before they know what they do best, not what they can be good at.  If you only complete one task your whole life, you can be *good* at it, but you might be better at something else. 

  • Laura

    “Show me a student who can’t find x and I’ll show you a student who needs an iPhone app to calculate a 20% tip.”

    Really, Hemant? Really?

    You are so very wrong. I’m sure you wouldn’t make a similarly sweeping generalization about, oh, let’s say,
    atheists. So I’ll make one for you, even though I am an atheist myself:
    “Show me someone who doesn’t believe in gods, and I’ll show you someone
    who’s incapable of feeling love, expressing joy, and creating great art .”

    Ever heard that one? I have.

    Here’s the thing: I have zero aptitude for math, and zero interest. But I’m
    very good at foreign languages. Nevertheless, I was forced to take
    Algebra I twice in high school, but couldn’t take French III or IV as a result because my schedule was full. I can
    make an extremely strong argument that, as a writer, I would have gotten far
    more value out of French than I have ever gotten out of Algebra. The idea that you can’t learn critical thinking skills anywhere but in a math classroom
    won’t wash, either. I learned them — far better than my own father, a mechanical engineer who tithes 20% to
    his megachurch every single week.

    Do I use math everyday? Of course. We all do. Is it math I learned in 4 semesters of basic Algebra? No. I learned how to make change, figure a tip, do my taxes, figure
    out how much paint I need to cover my walls, and all those other “life
    math” skills you need to function in society, by seventh grade. I can’t
    “find X” to save my butt. Nor do I care to. Believe me, I’d love to
    be good at everything, just like all of you clearly are. But I’m not, and I
    never will be.

    So how about we drop the whole “STEM careers are the only ones that smart
    people go into” and “Algebra was easy for me and you’re just a lazy thinker” crap, and realize that people are different. That doesn’t mean that
    the non-mathematical among us are stupid. Let’s meet our students where
    they are, help them find their aptitudes, nurture their interests, and send
    them out into the world armed with the practical skills they need to function every
    day and the passion to excel in their chosen fields, whatever those may be.

    Finally, this whole discussion reminds me why I have cut down dramatically on my reading of atheist blogs and websites. Most of them display a bias towards STEM readers and professionals that goes completely unquestioned. I would remind you all that it is very possible to be an atheist, a skeptic, and a critical thinker without knowing how to solve for X. It saddens me that, as an artist, there is clearly still no place for me here.

  • NeedingMoreFacts

    I think it’s funny that everyone (not just here, but everywhere) thinks they have the solution for teaching mathematics.

    There will always be people who understand it, and there will always be people who do not understand it – no matter how you teach it, assuming you’re correctly teaching it.  Given that few students ever build up to “doing proofs” – meaning, the first time they ever really see or experience it is in high school geometry, I can understand *why* they automatically run from it.

    Parents also prolong the idea that geometry is difficult, with phrases like, “I could never do that in high school.”  Having been a math teacher, I’ve seen this time and time again.

    However, ridding students of supposed  obstacles doesn’t help everyone. 

    I make a killing as a high school math tutor.  I don’t charge an enormous amount, there are just that many kids that “need” a tutor.  Most of them just do not apply themselves, they don’t need me – but their parents think they do.


    Try manufacturing just about anything without a good working knowledge of math.  It won’t happen.

  • MariaO

    The perfect answer by the professor who got the “when will we need this”-question one time too many:
    You will probably never use this – so just sit back, relax and enjoy the beauty of it!

    He was right: Math is the most beautiful artform humans have ever invented – and should be taught like music and art and literature, nat as something necessarily useful. The ephiphany of finally understanding the open cover-theorem will never leave me! But what a disappointment at university that Riemann had invented the complex Riemann sphere long before I did the same in high school…

  • Laura

    Yes, yes, and yes! Your experience of math is almost identical to mine — although I never made it to Trig. I had to take Algebra I twice in order to take Geometry I, which was ridiculously easy for me. But because I could never have passed Algebra II, I wasn’t allowed to take Trig. Which was probably just as well. I took one math class in college — Finite Probabilities, same as you — and passed with a C- only because my then-boyfriend was a Physics major and coached me through it.

    The problem in high school wasn’t my teachers, either. They were, by and large, good teachers who did the best they could with me. No one could understand why someone as bright and inquisitive as I was simply couldn’t cut it in that one subject. When I look back on my high school math classes, I still get the feeling I had then: This teacher is speaking a foreign language, and NOT one of the ones I know!

    I have a teenage daughter who also struggles with math now, and I hate it that I can’t help her. My husband is a bit better, but not much. At 13, though, my kid already knows how to do just about every “real-life” equation she will ever need. She’s also a great critical thinker and a skeptic. It kills me that she will have to continue to struggle through useless math classes for the next 5-9 years in high school and college, when all she really wants to do is study Linguistics. What a waste of time for her, and for her future math teachers.

  • unclemike

     Except that he wrote it in 1931, so “like today” was kinda relative.

  • Laura

    I don’t think we should stop teaching math, either. But I also don’t think we should equate achievement in math with overall school success and intelligence. My husband the accountant is completely tone-deaf. Should his school have forced him to stay in choir throughout school anyway? Of course not. Once you get past the point of basic life skills and music appreciation, there’s no reason for non-musicians to take music if they don’t wish to. But that’s exactly what happened to me. I was forced to take and re-take a math class that bewildered me. My constant questions and requests to go more slowly were a nuisance to teacher and students alike. I knew by age 12 that I wanted to be a writer. Advanced math was and is useless to me. I had acquired all the math skills I will ever need by 7th or 8th grade, from figuring a tip to reviewing a freelance contract for fairness. But I was forced to take more math classes anyway, because of some misguided “value” placed on those classes and applied uniformly to all students, regardless of aptitude and interest.

  • TCC

    I was seriously about to make a snarky reply along those lines, but you totally stole my thunder. I’m in total agreement.

    I would suppose that any such “drive-by” would give Hemant a pass on this because he’s a math teacher, though, just like the same people ask Hemant if he’s gay because he’s bringing up gay rights. Some people just don’t get it.

  • Neil

    Good point, Rebecca.  My high school introduction to critical thinking and making structured arguments was presented mainly in honors English and history courses, and never touched in math.  The idea was barely touched in non-honors courses of any kind. 
    I don’t think Miko’s suggestion is in any way helpful.  In my experience, taking related subjects completely separately only makes it seem like more work, and makes later integration of skills more difficult.  What good is a whole class on making a structured argument if you’re not going to apply it to subjects where stuctured arguments are actually used?  Sure, we could take out more classes to make room for every high school student to take the equivalent of college level philosophy and Intro to Logic classes, or we could fold more general subjects into more specific subjects and help learning actually be interesting.      

    Although I never had a very hard time with math, it was presented in the most boring and dry ways possible in high school, hard to absorb and impossible to remember or any length of time.  I would have loved to have had math classes that were more integrated with other related subjects.  I barely passed Algebra 2 because I could barely keep my eyes open and my brain focused, yet I flew through chemistry and college level astronomy because the math was applied to interesting and more concrete subjects instead of just being page after page of numbers with no obvious context.  I know that students should be able to appy math skills generally, and we don’t want to tie them down to  few applications, but a I think more students would learn to enjoy math if we at least tried to make it relevant to something else that interests them.   

  • I saw a great comment on this somewhere Hemant, can’t remember where now. A math teacher said that when a kid asks him when he’s going to use that in the future, he responds with something like “I don’t know. Tell me exactly what your future holds, and I’ll teach you only the math that you will need. Given that that is impossible, I’m trying to give you the basic tools to solve any problems you might come across.”

  • TCC

    You’re making sweeping generalizations that simply aren’t warranted. Hemant’s point is correct: you need an understanding of how to solve for x (at least to a degree) to be able to do your own calculation of a tip. He’s also suggesting that knowing how to do such a calculation is a good thing for any person to know, not just a “mathematical” person. That’s not unusual; we generally have lots of things that we think are standard in a well-rounded education.

    You just strike me as taking these things too personally. Maybe it’s the fact that I have long had an interest in science and math, despite pursuing careers in the arts and humanities, but I don’t find that there is any such bias against non-STEM people, of which I am one (I teach high school English). I have never gotten the impression on any of the atheist blogs I read (and I read a lot of them) that I’m not intelligent because I didn’t become a scientist or engineer. Loosen up a bit, would you?

  • Neil

    This sounds a lot like my experience.  High school chemistry gave me a slight hint, and college astronomy showed me clearly that math was much, much more intreresting and frankly much easier than I had ever thought in high school.  Almost two years into an English major, I dropped out because(among a few lesser reasons) I had figured out that I didn’t want to be an English teacher at all, an English lit degree was otherwise nearly worthless, yet it was just too late and too expensive for me to switch it up and start over, even though my abilities in math and science were growing (top of every course I took). 

    Twenty years later, I don’t really have any regrets- but if I ever become wealthy enough to not have to work every day, I would probably try to go back and take some more math and higher level astronomy classes just for the pure fun of it.  Maybe someday in the far future, decades or centuries from now, if the human joy of learning ever surpasses our species’ neediness and greediness,  such a thing will actually be an option for non-rich, non-young people who can’t spend tens of thousands of dollars, or work 100-hour weeks for years on end, or sacrifice good jobs for flexible but lower-paying ones, which is what our current system pretty much requires of any older adult who wants to take some classes and not starve while doing it. 

    Ok, I’m done whining.  Learn your math, kids- it’s the key to the universe.      

  • Windsngr

    I struggled with math throughout primary and secondary school; while I could usually eke out a B, it took constant work, and a great deal of relearning basics that I had forgotten. By basic I mean multiplication, adding large numbers: BASIC. I also had a hard time distinguishing left from right, selecting between greater and lesser amounts, and telling time. The only exception was geometry, which I somehow breezed through.
    It wasn’t until I applied to college that I learned that I had acalculia. The admissions office saw my ACT scores (12 in math, upper 30s in everything else), and called to ask if I had ever been tested for a learning disability. I was floored. Even the teachers who realized that I was struggling never suggested that such a thing was possible. I have since learned to work around my problems, although this entails NEVER using cash, using my iPhone for calculating tips, and forcing all financial decisions on my already-overworked engineer husband who, having bullied me through college algebra (the last required math I had to take), is very supportive. Luckily, I chose my major according to my strengths rather than job prospects, and am currently rocking the perpetual English grad student lifestyle.
    I still am grateful that I took all those years of math classes, although at the time I hated every second of them. I may not have learned math, but I learned humility and the importance of hard work. I only wish that there was more awareness that such a learning disability exists, especially among educators in primary school. I always wonder whether there might be strategies I could have learned as a child, before I internalized my not-very-efficient work-arounds, which would have made it easier to do the things I need to use.

    tl;dr – Math is useful, even for people who can’t do it. Learning disabilities suck.

  • Onamission5

    Have you any idea if you are affected with dyscalculia? I am not, but I do wonder if many people who painfully struggled with math as children have this learning disability and don’t know it, much like children with dyslexia struggled before it was widely understood.

  • Laura

    For you math is the key to the universe. For me, it’s not even close. And my English degree is far, far, FAR from worthless.

  • vexorian

    Learn numbers not algebra!

    Except… what we know as numbers are cute, lovely polynomials.

    362 = 3*x^2 + 6*x^1 + 2
    560 = 5*x^2 + 6*x^1 + 0

    So, if you wish to find out what 362 x 560 is, you would have to solve a very cool polynomial problem. And we do that all the time. The whole base 10 arithmetic would not have been possible without algebra. We would still be using Abacus for that stuff.


  • Neil

    No offense, but I hope you are better at art than logic, because your analogies aren’t that great.  You take great offense yet don’t even realize that you ARE using math and “finding X”, and to be honest it couldn’t hurt you or your art to know a little more. Or AT LEAST appreciate it, and all the wonderful ideas that make what you do in this life possible.

     I too have spent much more time in the arts than the sciences, but really- what are we supposed to do, just say that nothing matters except personal taste?  We encourge literacy in math and science because it’s important and necessary for survival and almost everything beyond survival.  Because circumstances change,  knowledge can fade, and a time could come where your own life, health, or ability to make a living are at stake, and how many people knw useful thiongs could become very important.  How much better would the world be if we just encouraged everyone who isn’t a math genius to ignore math and science, and to be proud of that ignorance, as too may already are?  It might be a world with some stunning art, but only because art can sometimes make great beauty out of suffering and misery.  I doubt there would be many enthusiastic fans though.  Most people who have lived without the many modern benefits of math and science didn’t have a lot of spare time, resources, or motivation to go around appreciating other people’s art, except maybe at church.

    I’m a guy who learned critical thinking and basic logic in English and history courses, not math or science.  I’m a guy who depends more on visual artists, writers, musicians, and comedians than scientists (or preachers, of course) for keeping me humble, moral, and open-minded.  But your rant here, quite frankly, comes off as hyper-sensitive and missing the point.  If you think you knew everything you needed to know by the seventh grade in ANY area, AND were capable of deciding that fact for yourself in the seventh grade, you’re self-aggrandizing and dramaticizing to the point of delusion. 

    Als0-I don’t know what kind of high school you went to or when, but how did repeating ONE math class make you miss out on TWO electives?  By my senior year, I had at least three electives, half of my class day.  If you couldn’t come up with another elective to cut out to make room, is the school just supposed to give you a pass on basic requirements?  There is no art our language class in high school that you can’t get privately or in college- but innumeracy, unfortunately, is often forever.  For a school to say “Oh, it’s okay, she’s wanted to be an artist since she was 13!” would just be stupid and negligent. 



  • Laura

    I appreciate your insight, and yes, I will try to loosen up. I do know how to do basic calculations, which, of course, is a form of finding X. And that’s a good thing for everyone to know.

    But on various atheist blogs I have seen my skills and profession dismissed as worthless. So I apologize for the sweeping generalization…but I’ve seen it firsthand. I’m possibly more sensitive to it because I am not interested in math at all, and am only interested in science as a spectator. There doesn’t seem to be a ton of arts and humanities coverage on the atheist blogs I read. Maybe I’m reading the wrong ones!

  • Laura

    You know, that would explain a lot.

  • smrnda

    As a mathematician, and a person who has worked in engineering, it has been fairly rare for me to meet a person who doesn’t know calculus. I’d agree that statistics is probably more necessary than advanced calculus, but I did take statistics and you *sort of* need to know calculus to actually do statistics; you can do the calculus free version, but it’s not like this is an either/or thing.

    As for algebra, I have run into adults with vague memories of sitting through it without any idea of what it’s all about. I think what’s missing for these people is a concrete link to the real world, because a lot of the time, the notion of what an equation is and what it does and how to solve for an unknown is something they understand when it’s applied to a specific, concrete situation.

    people who teach math tend to get it better than average, and they tend to see its relevance more than most people. The trick is to figure out the mind of  a person who isn’t like that, and try to get through.

  • Laura

    “Every dumb ass in my class was ecstatic to read Shakespeare but cringed at the thought of doing Trig.”

    And there’s the very questioning of intelligence that I was anticipating when I started reading these comments.

    Trig is no more the answer to our debt crisis than Shakespeare, by the way. Although…a close reading of “The Merchant of Venice” might be illustrative.

    Really good Economics and Consumer Math classes? Absolutely. Trig. Nope.

  • RebeccaSparks

    I learned how to make change, figure a tip, do my taxes, figure
    out how much paint I need to cover my walls, and all those other “life
    math” skills you need to function in society, by seventh grade.

    These are basic algebra & geometry skills.  If you can figure out how many cans of paint you’d need to paint the walls of a 8’x10’x’6 room, where your paint can cover 20 square feet and you’ll need 2 coats, than you’ve solved for x (the number of paint cans).  Your math is more advanced than you’re giving yourself credit for.

    I can understand that there is a strong science/math vibe to many atheist meetings, but I don’t think that Hemant was trying to devalue art.  I bet this struck a nerve, but please, feel welcome 😀

  • Beef

     Much like when the kids get rid of their parents in a retirement home!

  • Prick4u51

    … if you’re leading your life in such a way that you never have to do math, congratulations, you are a donkey.

    Fuck you

  • I did the same thing way back in High School but in my case, I programed my HP reverse-Polish calculator.

    I wrote a program that used numerical methods to home in on a solution through iteration to a problem and used it on a test. While it was cranking way, I went on and solved the problem analytically by hand in parallel just to have something to do while the program was running. We both got the same answer.   The teacher was impressed.  I got a good appreciation of the two different ways to solve such problems.

  • Ken

    My issue with this article is that its missing the point.  At 60 years old, I can categorically affirm that algebra, as taught in school, has never been of use to me.  When I went back to college in my 50s, I had to take algebra all over, and I did very well in it, but still could never see the use in it for me, and have promptly flushed it out of my brain.  Now the arguments for teaching logic and proofs are actually quite good, and I admire them a lot, but the algebra connection is just a non-starter.  It has nothing to do with basic math skills (which are woefully poor at the local Home Depot).  I don’t argue against its existence or usefulness, but I would no more force algebra on anyone than I would force them to learn how to disassemble and reassemble a helicopter because they might need to do it some day.

    There is a real problem with math being the stumbling block that discourages and holds so many students back, but that’s because it is presented so abstractly and dryly.  Also, what is the purpose of pushing algebra onto students who can’t make change from a dollar, then punishing them for it?  

    And for the comment: “As Evelyn Lamb at Scientific American puts it, ‘Math education needs to improve, but if illiteracy were on the rise, I don’t think we’d be talking about eliminating reading from the curriculum.’”  Hate to burst anyone’s bubble, but reading IS becoming less of an issue every day as feature magazine articles shrink to 300 word essays, and bestsellers bear no resemblance to Shakespeare, Dickens, Hugo or even Hemingway.  Been to a movie lately — call that writing?  Too many college grads and their professors can neither read nor write coherently, let alone at length or in depth.  Windows and Apple have made using a computer a visual experience thanks to their graphical user interface, and instant response technology has destroyed the capacity to use abstract symbols like letters and words for complex thoughts (except for programmers).

    The issue is essentially relevancy vs “the way we’ve done things before.”  Change is inevitable, and algebra is boring.  Boring is no longer acceptable, so it must adapt to become more relevant or it will be dropped from the curriculum, just like band, art, typing and home economics.  Justify it or lose it, particularly when money is tight and grades get stuck over nonsense like where two planes meet flying from opposite side of the country.  (Though I know such info is important, I’d just Google it.)

  • raerants

    There was an Abbot and Costello routine that played with numbers like that.
    Someone else did a variation of it, too.

  • I stopped teaching FOIL. Hate it, too.

  • Ken

    Not a programmer, so not applicable.  I am an artist, and learning to draw involves a great deal of very pragmatic information about perspective, color and volumetric space.  The craft aspect of art is very learn-able, and used to be considered essential for gentlemen and their ladies (like penmanship).  But nobody expects everyone to draw, even though it is a useful skill involving logic, spatial and critical application problems.  It is really applied geometry, but seldom taught as such.  “I can’t draw” is considered a valid excuse (by many artists, as well), but I don’t get math is some kind of crime or deficiency?  I know how to find the information I need on the internet, and I have never needed algebra for anything but a grade in a class.  And I do make change instantaneously because I leaned the multiplication tables by rote up to 15×15 — now that has been useful.

  • My favorite excuse in the “Why I Will Never Have to Use This in Real Life” are the kids who tell me that they won’t have to do math because they will be rich and pay someone else to do it.  How someone becomes wealthy without resorting to the use of mathematics, other than by inheritance, never seems to be an important question to them.

    In my first year in a classroom, I had a young lady tell me that she would never need to read or write after she graduated from high school, for the same reason.  It was adorable and frightening all at once.

  • Like like like like! x 1000!  🙂  Señora Friedman dice: Most of you aren’t learning Spanish to become Spanish speakers or to use Spanish in your job.  Some of you are.  That’s awesome!  For the “most” of us, we’re learning Spanish to get our minds to think about things differently, to express things from more than one point of view, to understand our *own* language better, to understand other people and cultures, and to give us a leg up when we start studying that *other* language that we really wish were offered in high school.  I don’t care if you never say more than “Hola” after graduating.  

  • Stev84

    It would still be more modern than being primitive savages

  • Stev84

    If you want computer scientists to understand long division, make them write a program that is able to divide arbitrarily long numbers (or add them for simplicity). There are some algorithms that are more efficient than literally replicating the way you do it per hand, but hardly anyone will bother to look those up.

  • Stev84

    I’ve found that many people are either very good at languages or maths, but rarely both. At least that’s how it was in my class. All the maths geniuses were bad to mediocre at languages, while the ones who were good at foreign languages didn’t excel at maths

  •  …In basic Spanish you write basic logic by the end of 1st semester “Él es artístico porque le gusta cantar, dibujar, y pintar” (He is artistic because he likes to sing, draw, and paint).  In advanced Spanish you do the same expository writing essays that you do in language arts and have debates in the target language. 

    …In art you defend your media and color choices based on precedence and artistic purpose

    …In science you write lab reports that provide evidence for or against a hypothesis

    Structured argumentation and critical thinking exists across the curriculum 🙂

  • We must be twins! I also had to take Algebra I twice in high school. And I barely scraped by with a D in Algebra II, which I’m sure was the teacher’s way of taking pity on me. I had many different teachers and a heck of a lot of individual and remedial instruction, and I still can’t understand algebra.

    My math skills are worse than the average middle schooler’s, but I get by with calculators. I find the original post disheartening because it divides people into pro-math and anti-math camps. People have different aptitudes for different subjects. Those of us who can’t do math or who don’t have an interest in math aren’t stupid. We may have other strengths. For me personally, nothing positive came of being forced to sit through three years of algebra. The only thing I got out of that was feeling ashamed and frustrated.

  • Wow, what a nasty piece of work Maddox’s comment is.

    Math is exactly like cooking: just follow the recipe. Symbols look confusing? Can’t figure out how to solve a problem? All I hear is, “Waaah! Boo-hoo! I didn’t read the introduction to the chapter that tells me exactly how to solve this generic category of problems!” Math isn’t some voodoo that only smart people understand. It’s something that people understand on their path to enlightenment, and it’s about as straightforward as thinking gets. … if you’re leading your life in such a way that you never have to do math, congratulations, you are a donkey.

    A donkey? Seriously? This is a great way to make people who can’t do math feel even more inferior. Like I didn’t get enough of that in every single math class from second to twelfth grade. Being insulted certainly doesn’t give me warm-fuzzy feelings about the subject he’s trying to promote.

  • My experience is a lot like yours, except I was tested for learning disabilities and they couldn’t find anything wrong. So I ended up feeling even more frustrated and ashamed about the whole thing.

  • Maddox’s whole schtick is to say offensive things. I still think it’s hilarious. (My personal favorite is when he graded children’s drawings.)

  • Be that as it may, I can’t find it funny. Math was traumatic for me, and I have too many bad memories of feeling worthless because I couldn’t understand what I was supposed to do.

  • TCC

    Saying that atheist blogs don’t often focus on the arts and humanities is perhaps a fair point, but I think that just reflects the general interests of the community (so to speak) more than a bias against artsy people. I would recommend searching out arts blogs rather than atheist blogs for that kind of thing, and you might be more likely to find atheists writing about the arts than if you search for atheist blogs that are covering the material (if that makes any sense).

  • Thegoodman

    “And there’s the very questioning of intelligence that I was anticipating when I started reading these comments.”  Stop with your anti-snobbery B.S. I was using the words “dumb ass” as an insult, not to imply that I am of a higher intelligence.

    Your implication that Trig has no use in everyday life is just as silly as the implication that Algebra is worthless. Neither are worthless. Econ and Consumer Math may be valuable, but so are all of the other “difficult” high level math courses.

    I have not read “The Merchant of Venice” but I am very much impressed by  your reference. I am however doing a terrific job of managing my financials despite crushing student loan debt. The math courses of algebra and beyond expand and reinforce simple math skills which we all use every day, you choosing to deny the utility of Trig does not make it so, it just makes you look like the author of the article in question, stupid.

  • vexorian

     To be fair, Maddox is an equal opportunity misanthrope.

  • Deltabob

    I was working as a sign designer. A customer came in with a photo of a real estate agent’s sign and wanted me to make an exact duplicate of it. I sat for a long time, playing around with guessing at the size of the fonts and trying to manipulate the images to match the photo. Then I realized if I measured the size of the letters and other components in the size, I could figure out how big they should be based on the entire size of the sign in the photo with the size it should be.

    Then, I realized, “holy cow – I just used algebra in real life.”

    As regards proofs – I found them the most important part of geometry – and that led to a lifetime love of logic.

  • Pollo Diablo

    I think even if kids don’t immediately grasp it, it doesn’t mean they never will. I really didn’t like math in high school and college, but I gained a new appreciation of it when I was already working. If I didn’t have at least some knowledge of it, I never would have had even that to refer back to. 
    Re-learning math (and science, but its more difficult to understand that without math) was really important to me because it kind of shaped my worldview. I found it comforting and amazing that some things in the world could be expressed, explained and predicted using math.  It helped me have a deeper understanding of the world and be happier as a result.

  •  This is indicative of a need for literacy across the curriculum (equally essential as numeracy and critical thinking).  And if a math teacher writes off a confused student by shaming them for having not read the chapter intro, my first question to that math teacher is “did you ever *teach* your students how to *read* a math textbook”?  

    Too many high school teachers resent being reading teachers.  We should remember that the last time our students had reading teachers was in 5th or 6th grade, and they certainly didn’t go over things like academic literacy (required to easily comprehend science and math texts). 

    I’m willing and excited to incorporate numeracy, rhetoric, and science into my curriculum.  I appreciate colleagues whose curriculum incorporates literacy.  We teachers should be able to do at least the level of work that we expect of our 10th graders. 

  • I find it more problematic that he seems to think being able to do math is a matter of reading the chapter intro. It’s not that simple. Some of us read the instructions, and we still couldn’t figure out what to do because we couldn’t understand the symbols or the memorize the formulas. To me, it’s like looking at Japanese characters. No amount of poring over my textbook helped because I couldn’t understand what any of it meant and couldn’t remember what to do without copying directly from my notes.

  • Windsngr

    Silly me, of course I meant dyscalculia: no brain damage, just math/spatial dumb. What kind of testing did you undergo, Anna, and how old were you? They had me give directions from a map, pick different groups of things (which group is larger? Which is on the left?), and do some basic math functions. I was ok at the map, but everything else I did terribly on. I remember thinking the entire time, “They could have done this when I was five”.

    I grew up in a rural area, and high school was long ago. I’m just wondering if there’s more awareness of the existence of this disability now.

  • Dr. Stat

    I am always saddened by my own experience with math in school (no programming/computer science programs to have fun in because “it wasn’t in the budget” or “the students are mostly girls, so they aren’t interested, obviously”). Add to that teachers who would use sarcasm/insults/ignoring (plenty of rolling eyes and ignoring questions) to silence students who needed help, and I eventually gave up trying to enjoy math. The only exception to this rule was my Stats class, which I loved and did very well in. Even today, I enjoy pointing stuff about Stats on the news to my friends, and even correcting the news’ interpretation of graphs!

    Despite my bad time with math in school, though, I agree that it is necessary. Especially proofs (which funnily enough, I enjoyed heavily because I was having to prove something), which lead to me being good in history debates in terms of organization of thought. 

  •  Funny, I studied Latin in high school, German in college and had slight contact with learning Spanish and French before visiting Spain and France (so I could read menus and street signs; ask directions, etc).  I found that the three genders of Latin and German were vastly more logical than the two genders of French and Spanish.   When you have three, the few exceptions from the a) logically male, b) logically female and c) all others are neuter were very easy to deal with.

  • I’m sorry, but it takes me a little longer to dig out the change due to being disabled. (I do indicate, however, that I have the change, and am digging it out, so please hold on just a moment, thank you.)

  • I think I was 13. I don’t remember much about the math testing, but I think spatial reasoning was involved. The results came back that my math skills were extremely poor, but they couldn’t determine that I had any kind of learning disability that would explain my performance.

    I’ve read about dyscalculia since then. Perhaps I do have it, although according to the list on Wikipedia, I only have 7 of the 15 symptoms.

  • I loved “story problems” because they made more sense to me.

    My brain just… locks up when you throw a bunch of numbers at it. I do understand that there are a lot of maths that we use on a near-daily basis, yes, even bits of algebra and geometry. I only question the necessity of the higher maths (calculus, trigonometry, advanced algebra, and the like) — we’re not all going to be engineers or programmers, and aren’t going to actually need those things. I think, in some respects, education should be tailored to the student, and for those not going into maths-intensive careers, the requirements should be lessened. I honestly cringe when I think of all the time I wasted struggling with concepts and equations I did not (and still don’t) comprehend, when I could have been furthering my education in other areas.

    (Yeah, I’m a word nerd, and I really do wish I could have spent that time and effort on delving more into the forms and functions of language.)

  • Eh, the Japanese characters actually make MORE sense to me.

  • Aramisgm

    BTW, I have friends who are practicing linguists. They program and use a lot of math beyond the high school level, so I can say this is incorrect. Those classes in math are quite likely to be necessary if your daughter wants to do linguistics at some point.

  • Pseudonym

     This is not haiku:
    A season is not mentioned.
    No, neither is this.

  • NickDB

     When mixing colours for your paint, you do things like X amount of white tint added to the red gives you = Y, right?

    Xwhite + Yred = Zpink.

  • I see a lot of replies to this comment to the effect of “What? That isn’t true. Your feelings are wrong”. Fuck that. Nobody can tell you how or what you should feel, and nobody with a sense of decorum would just say “You’re wrong, don’t take things so personally”.

    It does seem that there are a lot of scientists and science focus in this movement – I think there’s two reasons for that.

    1- Several of the most revered people in the movement are scientists, or feature science and science-based arguments in their work

    2- This is a very internet-centric movement, and nerdy types seem to appear disproportionately there. (Seriously, if you don’t like pro-STEM self-aggrandizement, don’t go to the XKCD forums – there’s a whole lot of “Engineers are the best people ever” sentiment over there. What a shock that there are a lot of tech folks in that community, who value their own talents over talents they don’t have)

    And if you do find some great arts blogs, please share – I’d love to read some. All I read is Fuck Yeah Art Student Owl, which can be quite insightful at times.

  •  Didn’t she get by, though? She figured out the change (with some technological help)

  • Fabien

    Algebra is basically: calculate an unknown quantity based on what you know.
    Calculus is basically: calculate how something changes.

    Both are pretty fundamental in our technologically advanced world. While you might never solve one of those odd, abstract problems, that thinking you develop (if you develop it) really comes in handy for understanding how technology works. For instance, if you play a stringed instrument, someone had to calculate how long the string had to be such that, if it was under so much tension, it would produce a certain note. FM radio: someone had to develop the concept of frequency modulation, which requires algebra, trigonometry, and calculus. Math is a gateway for understanding and having a bigger appreciation for the technology that is used everyday.

    I don’t blame people for getting turned off from K-12 math though. I honestly didn’t start liking math till my 2nd-3rd year of double majoring in physics and electrical engineering, and I really started liking it more when I skipped classes and freely studied on my own. Math was actually my weakest subject, but I realized that you don’t have to understand math to succeed – you just gotta be good at memorizing procedures and regurgitating them. So I managed to get As and Bs without understanding what I was doing. The current lecturing system is pretty weak, and it’s no surprise that many of the smartest minds in those fields (Einstein, Newton, Ampere, Feynman, Leibniz, etc) had a mostly self studied education.

  • Well that’s different. Plenty of people say they have change before they hand me their money and that’s fine. But here are lots of people who hand me their money, watch me enter it in and start to count out their change, and *then* say, “Wait, I’ll make this easier for you!” and hand me their change and they don’t realize that it actually makes things much more complicated.

  • Vend Tana

     Exactly…I almost signed my post “Omega”. GMTA.

  • Vend Tana

     Yeah but like all the Greeks are extinct.

    p.s. I Pie.

  • justabil

    How much will that cheaper house in the suburbs cost you in gas and insurance and wear/tear on the car/time driving every day?

  • justabil

    You wrote way too little for an English major.

  • Ladycopper5

     I’m a lifelong (higher) mathophobe and one of those who struggled and cried a lot over proofs. The most difficult part of algebra for me was looking at a problem and being expected to somehow know WHICH formula to use to solve it. If I knew which formula and had the steps in front of me I had no trouble solving it, so I know I’m capable of the calculations,  but honestly the word algebra still inspires fear.

  • Heidi

    Tell them that they can get paid more money at any job if they’re bilingual. That might help. I wish I remembered more of my high school Spanish.

  • RebeccaSparks

    You can always make an atheist tumbler–just make sure to post it back here somewhere so that we can all follow along 😀

  • RebeccaSparks

    I r
    ² a pie heart-er. 😀

  • Alex

    1. Spend thousands upon thousands of dollars on college tuition.
    2. Complain and whine that none of the stuff you are learning is useful in life.
    3. ????
    4. PROFIT!

  • I’m not sure about Japanese. While I was always excellent at languages, anything involving symbols throws me for a loop. It took me forever to decipher Roman numerals and learn how to read an analog clock. Impossible as a child, and even as an adult I still have to spend a lot of time working it out. I also can’t read music. I nearly failed my college music class because we had to learn to read music and compose a simple song, and I absolutely could not do it.

  • There’s just something about symbols that… I dunno, they “click” with me. They make more sense, somehow.

    Letters? Letters are awesome, too… until they start blurring together into an odd squiggle.

    Numbers? Just don’t make sense to me beyond a certain point.

  • Abra

    I absolutely agree that basic probability and statistics should be a standard part of the K-12 math curriculum in order to prepare people to be functioning citizens. I don’t know about “pinnacle” though. I took basic probability/statistics in 8th grade as an elective at my rural public school. It wasn’t the most rigorous class but that was mainly because I was the only nerd who signed up voluntarily and one of few who were grade-level proficient at math in the first place. Even so, it covered about the same content at the first couple of weeks of grad-level intro stats.

    I am not a math educator but I am a fan of lumping all of the subbranches together and teaching them together. I was taught (7th-10th grade) with a series that included algebra, geometry, and trigonometry in each book and taught it very cumulatively so that we had problems on each topic for weeks and then off-and-on for the whole year. You had to figure something out or you got it wrong every set for weeks. To this day I still think of it all as “algebra” and I am glad that I do because I think if I had had to do trigonometry separately I would have developed a bad attitude about it. We switched for pre-calc, calc, and college algebra and even at the time I thought it was a poor choice. 

  • Chuckles

     Ah, joy, another wonderful individual who thinks the youth of today are stupid compared to the youth of way back when. Tell me, when were movies written better than today? Because they weren’t great in the nineties. They were dreadful in the eighties. In the seventies they were made of racism and bad haircuts. 

    The movies of the last decade and a bit are better than the movies of any time previously in history. The kids today write more and see it as a more necessary skill than any preceding generation, unless you’re going to claim that the kids of the sixties had much better composition skills in all those emails, IMs and statuses they didn’t write.  We’re just better in every way, and it’s hilarious watching old fools scramble to find any possible way to scorn us.

  • EAH

    I was completely with you right up to the last paragraph of the Maddox quote. If you think students don’t complain that they’ll never need to know the stuff taught in high school English, sciences, etc., I can only conclude that you don’t teach those subjects. I work as a private tutor for kids in Grades 5–12, and they all make that complaint whenever they encounter something they find difficult. If anything, I find English gets the worst of it—kids complain about having to read poetry and Shakespeare and write essays long before they get to anything in math they’re convinced they’ll never need.

    Your post is spot on about why math is so important and why the arguments for scrapping it are ridiculous

  • Paul_Robertson

    A little while back I grew frustrated with a particular homeopath who would continue to post the same lies even after they had been shown to be false. So I started framing my replies to her as haikus. She tried to respond in kind but was unable to even count syllables. There must be a homeopathic remedy for that…

  • I’ve used geometry extensively to do things as prosaic as building a picnic table.  In fact I’ve used trigonometry, because I needed to work out such things as how far I needed the table off the ground, and how far out I wanted the feet to go, and how long to cut the legs.  In fact, I’ve used calculus (Taylor-series expansions of the trigonometric functions) because I didn’t have a calculator with me.

  • As an engineer, I don’t get where this idea comes from that engineers don’t need strong communications and language skills.  In my experience, it simply isn’t true.  Let’s imagine you’re working at a nuclear power plant and this e-mail crosses your desktop:

    “Jus want 2 let evry1 no that wer’e gonna be shuttin down #3 reactr for feul swap dont worry cause it’s not dangerus lol.”

  • Bravo!  My first thought upon reading Hacker’s piece was what difficult subjects should be given the axe next. Writing? Critical thinking?

    Algebra is often taught when kids are 13 and 14, far before they know WHAT they’ll be doing in college and beyond. Education is about giving people choices down the road — we help children develop a toolbox of skills that allow them to choose from the wide array of options of study and work. Omitting algebra eliminates options down the road.

    Elementary math in this country is poor. It’s largely taught by people uncomfortable with math. Change needs to happen there, at the start. Poor mathematics education early turns kids off to math as well as poorly preparing them for higher math. Fix that, and more will find algebra enjoyable and interesting while keeping their options open.  Here’s my longer take on it: http://quarksandquirks.wordpress.com/2012/07/31/math-matters-a-response-to-is-algebra-necessary/

  • prisnerich

    To all those who proudly declare “I never used any Algebra in my whole life. Nothing except arithmetic”.
    I have a neighbor who proudly declares he never reads, never read anything in his whole life (although he learned to read), nothing except street signs. How do you react? Do you think: “Wow, this guy is right, you can lead a successful and satisfying life without reading. Get rid of reading.” Or do you pity this guy, do you suspect that he is leading a very limited and sad life?

    Well, the same is my reaction about these proud “never used Algebra/Math” guys. Of course you can live a life without. Even a financially successful one, that’s not the point. Just excel in sports, for instance. But how much richer is your life if you do read, and if you apply mathematical/logical reasoning in your life. And also, all these poor decisions you can avoid with a little mathematical thinking.

    And—Math is far more than quantities, also more than just quantitative reasoning. Higher Math is the logical study of structure. 

  • I don’t think math has a “pinnacle”.  In my experience, by the time you’re halfway through a decent undergraduate understanding of math, it just starts branching out like mad.  Then those branches start cross-connecting.

  • Paul A. Foerster

    A “Foersterism,” and Cecelia
    When students ask me, “When will I ever use this stuff,” (starting in  my Algebra  I and going through BC Calculus classes), I use the following (coined a Foersterism by students in a Houston  high school):

    “What you know, you may never use.
    But what you don’t know, you’ll definitely never use.”

    And then there was Cecelia, my Algebra II students about 40 years ago. She used to be bored and sleepy in my early-morning  class until I suggested,  and she moved, into my late afternoon class. There she blossomed. She majored  in computer science in  college, eventually becoming Tax Assessor-Collector for Travis County, Texas, where the capital  city, Austin, is located. At my retirement ceremony last year (after 50 years of teaching high school mathematics),  Cecelia, testimonial was that as a result of  learning algebra, she had shed her fear of numbers. Her career involved very large numbers!

    Next posting I shall mention Dee,  a nationally  know choreographer, who heard that the Fibonacci sequence generates interesting patterns, and so choreographed dances where  the numbers of steps in a particular direction are Fibonacci  numbers.

  • prisnerich

    Sorry. Not true. 5+5=10, but 5 +5 is not equal to 1*x^1 + 0. 
    It’s irrelevant, I know, but I just couldn’t resist the urge. 

  • Patriciahkahn

    Is algebra Nec?   is insulting to people who actually have an interst in learning and teaching …….a nec mental exercise……the objective is to learn to think

  • TruFru

    In my view, mathematics should be studied for its aesthetic beauty. The fact that it has real-world applications is only a by-product.

    I suggest you to read “A Mathematician’s Lament” by a school teacher, Paul Lockhart.

  • vexorian

     do not get.

  • Weirdlaugh

    It’s not that students don’t complain about them, but that it is socially acceptable to complain loudly about math and not so much about literature (being illiterate is connoted with being stupid, but not doing math is connoted with being normal) or a few other subjects.  It is true that certain aspects of each subject is allowed to be viewed as something for the elite only (some poetry, history, non-English languages in North America), but watching Jeopardy you’re more likely to see a trivia question based on any of those than you are about math.

    That’s why the “math is singled out” argument is even stated.  In fact, my girlfriend was an academic advisor at a community college for a while and she came across more math-phobia than anything else.  

  • Weirdlaugh

    If only there were formulas for that so I could come up with a quick answer … oh wait, that requires Algebra.

  • That’s great, really, it is. It’s just that some of us simply don’t (and in some cases can’t) grok the higher maths.

  • Dfmcmahon1

    I work on a help desk–underemployed due to going back to school at a late age and then having to leave my grad math program due to a very ill spouse and a child with a disability. There is a smattering of hardware and software knowledge I have to use, but sadly the underlying software information is inaccessible or horribly documented (so much for verbal skills). At the end of every month we get frantic calls from managers for whom a certain report has an awful number in it they will get yelled about. The quantity is very derivative. Our documentation has a formula involving derived quantities itself–well, the documentation *says* it is the formula, I have my doubts about that even aside from the really perplexing thing about the formula. I will use just letters instead of the abbreviations they use in the documentation, but it’s something like X = Y + Z + Q + S + X.  Assuming Y,Z,Q,S are what they purport to be, I doubt they had up to 0 (for one thing, none of them should be negative–but that’s relying on the documentation, which cannot be relied on). And the only quantity I’ve found a way to tweak at the source will just make the X (the number they are freaking out about) worse. I have submitted “feedback” pointing out that there is a problem with the formula, but have the uneasy suspicion (based on similar experiences) the gatekeeper for the feedback will not comprehend the problem I see. Said gatekeeper is also one of the key people in the organization for managing the information we have access to. Not only that, due to contractual obligations I am required to confirm with the caller that the problem has been resolved by the end of the call. Either that, or stay on the line . . . forever . . . or get someone higher up the food chain to accept the issue never happen, part of their job is fending off such submissions, and they have a copout which is to go back and research a zillion production cost items and “find the item that is causing the problem” (remember, I don’t have access to the source calculations. . . plus I have been told there is some calculation that gets frozen into the program when the function is first run for the month, not that I have ever been told what that something is. . . plus every time I find a way to correct components on that side, the final number–the X–gets worse). I have a low-level management person who has even less access to the underlying information who has to report to upperlings who could care less about the underlying information–they just know that according to the number, somebody must be stealing the cheese (so to speak). So, the call goes on and on and on, my scheduled lunch break oozes by, my brain is becoming fatigued, and all I can do is hope that the caller gets worn out faster than I do. 

    Something like this has occurred in most of the jobs I have had. Basic problem-solving (a la Descartes’ Discourse on Method) is to figure out what you do know and proceed from it to the unknown (I’m not keen on applying the method to the question of whether I exist, but elsewhere it comes in awfully handy). Is there perhaps an algebra Superhero who might swoop in to save me and the poor low-level manager sweating bullets in Oswego?

  • Call me weird, but I
    use algebra in real life

  • Gotta love that Fibonacci sequence! It crops up every so often in knitting (and crochet) design. You’d be surprised to see how many of my fellow yarn freaks are math geeks – just Google math knitting or math crochet!

    Then there’s the work of the late great Elizabeth Zimmermann, especially her universal sweater formula and her “pi shawl” formula for knitting in the round…I wonder how many gazillions of kntters have used her algebra without realizing OMG! THAT’S ALGEBRA! I CAN’T DO THIS! RUN AWAY! RUN AWAY!

    ‘Nuff for now…back to the pi shawl I’m designing…got the prototype half done…got a Fibonacci round thing on the drawing board too… =^..^=

  • Jill

    First you say, “For example, one of the things my department is working on this coming year is getting away from spending all our time on skills that just require mindless work — plugging and chugging — and spending more time in class on one or two problems that require a lot more thought.” and then you say, “But the students who don’t do well in algebra usually struggle precisely because they don’t know basic arithmetic.” Correct me if I’m wrong, but it sounds as if you are planning to try and teach skills through problem solving, and that methodology already has been proven to be ineffective. How do you expect students to be successful without the drill? They DON’T know the basics, and cutting them out of the curriculum is setting your kids up for failure. I have been teaching for 22 years and am an educational consultant, presenting workshops to teachers, so I have “been there and done that,” so to speak. This is not a good plan – there has to be a balance between drill and problem solving.

    In regards to the article, the thinking skills you are talking about can be taught outside the parameters of algebra and geometry. I have been teaching since before the time that students could graduate without ever having taken Algebra I. Back then, Algebra I curriculum is what we teach in Algebra II today. Why? Because we have had to water stuff down so much so that everyone can pass and be successful, even though everyone doesn’t belong there. I agree that Algebra and Geometry teach problem solving skills that kids need no matter what field they go into, but do the really need college prep Algebra and Geometry, dragging the true college prep kids down to their level? No, I think there is a better way, and Statistics may be the answer. I have met Art Benjamin, and he may be on to something…

  • Jane Shevtsov

     OK, that’s not a knowledge issue (at least, not just a knowledge issue). That’s a math anxiety issue. You might want to look at some of the literature on the subject.

  • Jane Shevtsov

    FOIL is just an easy way to make sure you’ve done all the necessary multiplications. What’s the problem?

  • When the problem gets even a bit more complicated (with, say, three terms instead of two), students don’t know what to do because FOIL no longer applies.

  • Brian Sherson

     Maddox is known for his inflammatory writing. He doesn’t tiptoe around anybody’s emotions. He bulldozes right through them.

  • Brian Sherson

     Laura, as a graduate student who also is a TA in math classes, make sure your daughter understands that office hours are available to her to get help from her professors and TAs outside of class. Of the students I have who struggle with math, the ones that pass are usually the ones who come to my office hours on a regular basis.

  • Jaymolstad

    Algebra is just a technique for  understanding the relationships between numbers.   Things like:

    When people drive more, what happens to gas used, and to gas prices.

     How much faster do you have to drive, if you need to get somewhere by 5 and you don’t want to drive fast over the 20 miles near the speed trap?

    Calculus is just a technique for tracking how quantities change, and how those changes add up.

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