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Abandoning Algebra Is Not the Answer

The views expressed are those of the author and are not necessarily those of Scientific American.


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Source: www.ed.gov

In an opinion piece for the New York Times on Sunday, political science professor Andrew Hacker asks, “Is Algebra Necessary?” and answers, “No.” It’s not just algebra: geometry and calculus are on the chopping block, too. It’s not that he doesn’t think math is important; he wants the traditional sequence to be replaced by a general “quantitative skills” class, and perhaps some statistics.

Quite a few people have responded to Hacker’s column already. I highly recommend these posts by Rob Knop, Daniel Willingham, and RiShawn Biddle.

There are so many problems with Hacker’s essay that it’s hard to know where to start. Hacker’s first main point is that math is difficult, and the poor grades that result prevent too many people from graduating high school or college. His second is that the math we learn is not the math we need in our jobs.

Math certainly is incomprehensible to many students, but from where I sit, poor teaching is often the reason. Math education is failing many of our students. Few pre-college math teachers majored or even minored in math, and until more teachers do, improvements will be hard to come by. Ironically, it seems that people who have mastered “useless” algebra and other higher math topics tend to get jobs that pay more than middle school math teachers earn. I have the utmost respect for people with math degrees who choose to teach in spite of the poor pay and discipline problems, but few people make that choice. Math education needs help, but Hacker’s suggestions throw out the baby with the bathwater.

What is algebra anyway? It’s a huge subject, but at its heart, it’s about relationships. How does a change in one quantity affect another quantity when they are related in a certain way? Hacker suggests that we need arithmetic but don’t need algebra. But it’s really difficult to separate these two skills. Algebra and geometry, another subject Hacker could do without, help develop logical skills and abstract reasoning so we can understand why we are making less money than before if we get a 20 percent pay cut followed by a 20 percent raise (or a 20 percent raise followed by a 20 percent pay cut—hello, commutative law of multiplication!) or how much merchandise we can purchase if we have $100 and a 25 percent off coupon.

Hacker is probably right that very few people use high-level math directly in their work. My work never requires me to know anything about the themes of “The Old Man and the Sea,” but my life would not be as rich if I had never been exposed to great literature and the challenge of analyzing and understanding it, as difficult as it was, and still is, for me. When I was in high school, I didn’t (and couldn’t) know whether my future job would require math, chemistry, writing or music. If I had stopped taking every subject that I probably wouldn’t use in my career, I don’t know what classes would have been left.

Hacker says that math is required in many professions “just to look rigorous,” as “a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.” But what if it’s not just because it sounds good? What if medical schools know that calculus is not needed in a doctor’s day-to-day practice, but that the skills she learns when taking it, including perseverance in the face of a difficult subject, make her better at understanding and responding to the flood of information she encounters in her work?

Mathematicians are recruited by hedge funds, consulting firms, and technology companies not because they already know how to balance portfolios, what the best corporate strategies are, or how to optimize user interfaces, but because their mathematics degrees indicate experience and acuity at problem solving. It’s easier for companies to teach someone with a strong mathematics background how to do their specific work than to teach someone who knows the company business how to solve problems. And, like it or not, algebra is one of the first places students start to learn these problem solving skills.

Hacker acknowledges that math is important. It underlies technology and science that we use every day, and there is and will continue to be a need for mathematically able people in lots of professions. Eliminating abstract math education in the early school years, or allowing young students to opt out of rigorous math classes, will only serve to increase the disparity between those who “get it” and those who don’t. Those who have a grasp of mathematics will have many career paths open to them that will be closed to those who have avoided 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.

Evelyn Lamb About the Author: Evelyn Lamb is a postdoc at the University of Utah. She writes about mathematics and other cool stuff. Follow on Twitter @evelynjlamb.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. sapbucket 8:18 pm 07/30/2012

    I agree. In fact I think that Physics should be taught at an earlier age using the very same math Hacker wants to eliminate.

    A greater issue with math education, in my opinion, is that it is not applied. I am an engineer. Pure math, for math’s sake, I cannot fathom. But show me how it may be applied to turn on a light bulb, make a car engine operate, or take a chimpanzee in to orbit, and the math has a meaningful place in my toolkit of skills I learn in school.

    When I was 13 years old I had a better education than most of my teachers. How boring it is to be taught a subject from a sub-rate teacher. There is nothing wrong with our students, or our classical subjects, the burden of education falls squarely on the teachers. I would hope that people like Hacker understand this and instead write meaningful articles about the incentives teachers have to do well, or the disincentives they have that are causing their students not to learn effectively.

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  2. 2. QuipsTravails 8:38 pm 07/30/2012

    As a high school student, the one class I failed (well, besides P.E., but that was my lack of trying) was Algebra. As a food blogger and avid cook, I inwardly curse that failure regularly, because algebra is such an intrinsic part of cooking. Good cooks use algebra by feel – you know that grandmother whose biscuit recipe nobody knows because she “doesn’t measure?” Algebra. In her head.

    I had to teach myself how to balance equations just to scale a recipe from 8 servings to 10. Again to resize the photographs on my blog, knowing only one side length. Algebra is everywhere. All things have relationships to each other: there are constants, there are variables. One day, you and your F in Algebra are sipping a different-size latte, wondering why the flavor is off…and boom! Algebra comes knocking at your coffeeshop.

    Yes, I had an aptitude for English and Drama and got degrees in both of them: I liked them, I needed them…but I LOVE science. I wasn’t in the Drama club in high school, I was in the Science Club, going to fairs and doing projects, gettin’ dirty with tadpoles, crickets and shades of grey. I should have done more in college, gotten more degrees – but I feel like my science career ended in grade school with the mantra “I’m just not good at math.”

    That being said, it wasn’t really my teachers’ fault: back then, there were exactly zero strategies for helping kids who learn differently in math…I was raised in a time when dyslexia was just becoming known. Even today, dyscalculia is barely known and hardly studied – research now indicates that it exists, it’s real (I and kids like me are not just stupid or hopeless) but hasn’t provided much in the way of strategy.

    Rather than wringing our hands, saying “just not good at math” and giving up, shouldn’t we be actively searching for ways to help struggling students? After all, we wouldn’t stop at saying “you’re just not good at reading” to a student – we’d find a way, because READING IS FUNDAMENTAL. Why do we get away with different rules and attitudes for math?

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  3. 3. gypsi 8:49 pm 07/30/2012

    That is one of my main complaints in college…having to learn math without any application. I’ve complained about it to my physics professors and they just shake their heads.
    I disagree that this is all the teachers fault although they do share some of the blame, but I would blame the parents as well. It’s been passed down how difficult math and some sciences are that children go into the class already planning to fail and when they find it difficult they justify not trying because it is so hard and difficult.

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  4. 4. Unksoldr 8:57 pm 07/30/2012

    In high school and my first time in college I always barely past Algebra. My second stent in college I took a electrical engineering based Algebra class, I got an A!
    All those A,B and C’s became V,R and I. When taught in their proper contexts these subject are no longer abstractions and make perfect sense. If these subjects were combined with the activities they were developed for most students would find they finally and truly understand math.

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  5. 5. aj1350 9:03 pm 07/30/2012

    I believe that removing any math courses will be a terrible mistake. Even people that “don’t get it” still benefit from trying and failing. It opens the mind to other possibilities. The very act of putting your mind at work is a step in the right direction. Isn’t it bad enough this country has high school graduates that can barely read ? Would you trust an electrician who can wire a light to turn on without understanding how and why it works ? Maybe we should just train apes to do all our tasks and let computers do all the thinking so everyone could sit around to watch tv and eat icecream.Being brain dead is no way to go through life !

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  6. 6. mihondo 9:22 pm 07/30/2012

    Far from eliminating algebra, it should be taught earlier. Many “arithmetic” courses that precede algebra require the student to memorize a vast array of specific equations – something I call “gestalt mathematics” : you somehow are able to directly write down the solution.

    With a small number of algebraic rules and the ability to translate language into an equations, all those silly equations go away.

    Teach someone an equation and they know how to solve one problem.

    Teach someone algebra, and they can solve a lifetime of problems.

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  7. 7. MChilton 9:36 pm 07/30/2012

    I hear him on the point that we could stand to be more practical when it comes to math education, but as a Realtor, I use algebra and geometry in real life all the time. Many land subdivision and recombination problems can only be solved through Geometry – indeed that is precisely why Geometry was invented.

    I seldom use my calculus skills at work, but understanding the concepts behind integral calculus increases my understanding of all sorts of “real life” situations – from figuring loan payoff amounts (mortgage amortization) to calculating the net present value of a future stream of income. Yes, I mostly use the computer to do my dirty work, but knowing how to do it without the computer allows me to 1) more easily see when I have made a data entry error and therefore gotten the ‘wrong’ answer from the computer and 2) solve these sorts of problems even when a computer is not readily available (eg while showing a vacant house to a potential buyer).

    And there are many, many other occupations that rely on understanding high school level mathematics – especially many of the best paying jobs from Medicine to Law to Real Estate to Insurance to Finance. Can you be a Doctor or Lawyer without knowing Algebra? I suppose, but I wouldn’t hire you.

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  8. 8. Bearly Literate 9:40 pm 07/30/2012

    I read Hacker’s op/ed and can empathize with him because I flunked algebra in 9th grade and dropped out after 10th grade when I found out I would have to pass it before I could graduate.

    Fast forward 35 years and I entered college… and was faced with algebra again! Yes, I passed it and did remarkably well throughout my college years– for a high school dropout.

    I understand how hard algebra is and I wish that I had better math teachers when I was in high school, but belatedly, I learned that it does no good to drop algebra or drop out to avoid it. Throughout my construction career I used math extensively and I came to appreciate it.

    Keep algebra in school and hire exceptional math teachers (give them a good raise too, do the math!).

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  9. 9. Chuck Darwin 9:46 pm 07/30/2012

    Hacker has a point: algebra is not that useful in a variety of professions and occupations. A basic understanding of statistics, however, undeniably IS–statistics are used every day in a wide variety of settings, from ordinary news stories to business. And most people, including those who mastered algebra calculus, have little understanding of how statistics are used and misused. If I were going to construct a math curriculum that were more useful and relevant than the one we have, I would start with inserting a semester of statistics for everyone.

    The second point is one that most readers of Scientific American won’t personally identify with: a large percentage of students are either not mentally or emotionally equipped to learn algebra. Anyone that doesn’t believe this needs to spend some quality time in a typical remedial algebra course at a typical public high school. Most of these kids are never going to learn algebra, and forcing them to try to do so just because we require the same of kids who are going to go to college is worse than pointless–it forces failure on legions of young people who could be productively taught something more useful.

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  10. 10. tftillman 9:52 pm 07/30/2012

    Algebra and calculus is an absolute waste of time for 99% of all students. In everyday life, you need only the 4 functions of math and an understanding of percentage calculations. Unless you have a specific need for it, It is a stupid, condescending, pretentious, graduation-blocking area, promulgated only by academics. Why make everybody waste time trying to learn math they will NEVER use in everyday life. How many of life’s problems have you ACTUALLY solved with albebra? Get a clue, Mr. University boy.

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  11. 11. MChilton 9:56 pm 07/30/2012

    “What if medical schools know that calculus is not needed in a doctor’s day-to-day practice”

    Not needed in day to day practice? Doctors have to stay abreast of new developments in Epidemiology constantly. And you can’t understand much of anything in Epidemiology without (at least at-one-time) having learned Calculus (and Statistics and Algebra).

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  12. 12. babyunagi 10:43 pm 07/30/2012

    I wish to God I understood math. I would like to. I finally had to be tested–which revealed a disability & accompanying anxiety component (duh). All through school, I was the kid in tears at the blackboard in math class. That didn’t change in college (still crying at the board). I tried four times to pass the most basic of math courses (never did; they finally waived the requirement, but that doesn’t make me proud). People understand the word illiterate; few people understand dyscalculia. I feel nothing but shame, embarrassment, and guilt b/c I can’t understand this. I can’t argue with those who are saying math should be taught. It’s just so…frustrating.

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  13. 13. tftillman 10:49 pm 07/30/2012

    I said 99% of all students. My point is, only a very few really need it. And they should be allowed to choose to learn it, if that is their chosen direction. Forcing all to learn it is wrong, and a stop for many people, and a block to learning more useful skills, and maybe even graduating.
    I will add geometry and basic statistics to the basic skill set. Not so hard, and useful for many. Calculus, useful for a fraction of 1%
    So why make everyone wade through it?

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  14. 14. tftillman 10:54 pm 07/30/2012

    babyunagi,
    Thank you for making my point. My feelings exactly. Don’t force it on everybody.

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  15. 15. differentiablef 11:26 pm 07/30/2012

    Reading these comments, it is rather clear to me that almost none of the people commenting have any sort of real experience: 1) Teaching Mathematics; and 2) Using the full strength of Mathematics (in particular logic.)

    The confusion seems to be caused by a failure to understand the interesting position mathematics has relative the other fields of science. In particular the boundaries between the field of Mathematics and every other field studied are nebulous and ill-defined. This is because: All of them rely on, and are fundamentally shaped by the analysis of models, and these models live in the world of Mathematics proper.

    In particular, they are constructed, analyzed, and reasoned upon, within the boundaries of Mathematics (whether you accept this fact is a personal thing, and does not change its validity.)

    Moreover, for anyone to effectively use or work in this paradigm, a basic skill set is required (e.g. algebra, trig, basic calculus, and linear algebra.) And it is disturbing to me that anyone would argue against equipping every student (each of which has the potential to be a scientist later in life) with this tool set.

    That you might not have enjoyed a mathematics course is a mater of personal taste, and does not diminish the relevance of the material it covered. This is the fault of the current state of Mathematics education in this country, which is lagging about 100 years behind the field as it is practiced by Mathematicians (and this is not an exaggeration, modern mathematics education theory is still based on works written in the late 1800s.)

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  16. 16. frankblank 11:35 pm 07/30/2012

    I did NOT abandon algebra. Algebra abandoned me!

    That said, saying students should be spared algebra is like saying they should be spared critical reading.

    Oh. Sorry. Forgot. They are. American Education is geared to the intellect of the average consumer of advertising.

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  17. 17. truittjs 11:43 pm 07/30/2012

    Come on, what do we need math for when we have computers to do our thinking. Even our cells phones can do complex math now, it’s a useless skill in today’s world. I see people pull out their cells phones to calculate out a 20% tip for God’s sake. What on Earth do we need math skills for?

    The direction this country is going and with more science being cut, we’ll all be in service jobs anyway. What good will an engineering degree and math skills do you if you don’t have a job.

    Our education system is so far behind other countries and our universities have followed the down grade the hole may be too big to climb out of anyway, so come on eliminate math we don’t need it.

    We’re going down in flames and we’re too damn lazy, stupid or both to even know we’re on fire. I don’t know, maybe we just can’t pull ourselves away from the game console long enough to care.

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  18. 18. differentiablef 11:50 pm 07/30/2012

    @truittjs

    You only further the validity of my opening claim.

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  19. 19. QuipsTravails 12:19 am 07/31/2012

    @tftillman So, I take it you have never had to figure out how to make an eight-person recipe feed only two people with no leftovers? How to figure out how many party guests you can invite to a party if 1/3 of them have guests, but half won’t come? How to figure out how much food you can afford on a $100 budget, including tax and your 20% off coupon? How to split a dinner check with the tip, when not everyone had drinks with dinner?

    Are you saying that teaching kids the skill to answer these questions is an effete exercise for academics only? I think these are necessary life skills that you can’t get by just memorizing your arithmetic and learning decimals and percentages (which, BTW, are simple algebra.)

    Is it currently taught in an overly academic way? Yes. Does that make it unnecessary? No.

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  20. 20. priddseren 12:45 am 07/31/2012

    This Hacker character merely confirms political science is probably not needed at all or at least he is proving political scientists are not the people to be asking these kinds of questions about.

    Algebra is one of the most basic forms of manipulating numbers, he could not do his statistics without learning algebra.

    We probably should be teaching algebra, physics earlier and subjects like geography or basic engineering concepts as well.

    People like him already removed classes like machine shop from schools, now he wants to remove math and science? to be replaced by what sort of indoctrination? I would guess he would call it classes in critical thinking which is another word for think like him and his political class of people.

    If we want to continue the trend in america already resulting in 48.5% of the population living off the government dole, having no job and paying no taxes, in other words living of the other half of the population, by all means, lets remove math, science and every other “difficult” class subject so we can have even more people with useless degrees in political science, sociology and basket weaving.

    While we are at it, lets remove math and science from school so the Chinese, Japanese and Europeans continue to surpass America by taking the lead in Space, particle Physics, robotics and whatever else.

    At least all of these future useless freeloaders will have the quantitative skills needed to vote for politicians to keep increasing their handouts.

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  21. 21. nygizak@gmail.com 12:52 am 07/31/2012

    @babyunagi My son has the opposite problem. He is 13 and plays with math like it’s a toy. Writing a paragraph, however, is a nightmare. I can sympathize with your experience.

    I also appreciate all of the rest of the comments in this stream. In my experience, educational standards have been dumbed down. Also, in my experience, technology has afforded my son the ability to advance years beyond his peers in the academic fields of math and science.

    I can’t wait for public school systems to catch up1

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  22. 22. SteveO 1:38 am 07/31/2012

    Algebra is certainly necessary, but elementary to high school should be geared to cap student’s math experience with statistics (including the scientific method), not calculus.

    Calculus is probably the easiest of the maths to get the concept of – just adding up a bunch of rectangular areas – but most people don’t need this concepts to be good citizens or do their jobs.

    The *DO* need statistics to be good citizens though. Understanding confirmation bias, that expected variation is quantifiable, and that the plural of anecdote is not data, are all central to navigating modern life and politics, regardless of what you do.

    I’d say keep calculus as required for math, science, and engineering, obviously, as it is an amazing tool for understanding those disciplines, even if you don’t actually use it day-to-day.

    But focus sub-college education on a statistics capstone for a better citizenry.

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  23. 23. Timmy 5:07 am 07/31/2012

    really interesting issue. When I studied in primary school I had my best grades in arithmetic and geometry but later when it comes to algebra my grades fell down may be because I did not understand why I need to know those super formulas. Pythagorean theorem is needed to find unknown side of triangle but why I need to know integrals, functions etc.? This time I’m preparing for GMAT, exam to enter business school and mathematic part of it is really practical and not too algebraic

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  24. 24. macgupta 6:14 am 07/31/2012

    In his NYT op-ed piece, Hacker quotes a City University of New York Report: “The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.”

    That report is available online. It also says:

    ” “Killer Courses”—Mathematics, Science and English:

    According to data from the Office of Institutional Research, all the colleges have “killer courses,” or high fail-rate courses, 2 particularly in math (including algebra, pre-calculus, calculus, and quantitative analysis). Accounting and economics also appear to be high-risk subjects. At many colleges, chemistry poses the largest threat among the sciences, but biology and physics also enter into the equation. Our math initiative will be further informed by a study on math preparation being conducted by Dean David Crook and Professor Geoffrey Askt at Borough of Manhattan Community College.

    At many community colleges, failure rates in developmental reading and writing courses surpass those in math and science courses, especially in those colleges with the highest ESL populations. Nearly all community and comprehensive colleges exhibit high failure rates in composition courses.

    Of the 86 courses with the highest fail rates at the senior colleges, 36 of them are math courses (nearly 42%), with the highest numbers in calculus and algebra. Roughly 34% of the “killer courses” at comprehensive colleges are in mathematics (20 out of 59, with the highest number in algebra), and at the community colleges that number is 30% (most of them algebra as well). Out of the 265 “killer courses” identified University-wide, 92 of them are in mathematics, representing 34.71% overall. ”

    (ESL = English as a Second Language).

    Would Hacker advocate removal of the other 65% of “killer courses” covering accounting, economics, chemistry, physics, biology? And how about removing composition requirements as well?

    My point of view is that perhaps algebra is the canary in the coalmine; it provides an early symptom of failure in acquiring the ability to learn.

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  25. 25. stargene 6:54 am 07/31/2012

    The very fact that a supposed beacon of academic intellect is today proposing that we further hack
    away at our already blighted educational standards, standards which look quite tattered when compared
    with those of most other western industrial democracies, not to mention many nations in the far east, sums
    up an accelerating theme in the cultural decline
    of the USA.

    This follows inexorably from the insouciant and glib announcement in the early 1980s, by Wall Street and
    the beltway, that we were going to change over from
    an industrial oriented economy to (be still, my heart)
    a “service” oriented economy, and how wonderful that
    was going to be. It hardly needs mentioning that
    this was accompanied by the beginning of outsourcing
    of manufacturing to other, mainly third world,
    countries.

    Scientists, scholars, educators and even a few brave economists immediately pointed out that this was
    going to devastate educational standards and lead
    to high school graduates who were by and large
    woefully unprepared for college. They understood
    that arts and sciences, including math, would fall
    by the wayside… because, while an advanced industrial based economy requires an at least minimally literate, numerate and logical labor force, having some minimal critical ability in abstract thinking and problem-solving, a “service” oriented economy does not value
    that at all. The truth is, an ‘ideal’ service
    employee (which hopefully does not exist yet) is
    a kind of decerebrated module, whose potentially higher level thinking and independent critical mental faculties have been either completely outsourced, or reduced
    to a vegetative state which barely tolerates any
    higher norms of reason and creativity demanded of it. With this in mind and…

    …considering the current political and media fashion of fawning on God’s beloved (but so humble) super-rich,
    it’s worth noting that a national public which is increasingly illiterate, innumerate and therefore increasingly provincial and insular, is easier to
    control and manipulate.

    Easier to divide against itself. More prone to
    buy into the schemes of the nearest political/
    corporate snake-oil salesman. America is failing
    itself and its precious children.

    It’s not just you who are thus at risk. It’s your beautiful children… and their beautiful children.

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  26. 26. Quantum Ghost 6:58 am 07/31/2012

    I’m still in high school, I love math and although some topics really annoy me i begin to do well at them when i understand their use and applications. The applications don’t have to be current- trigonometry has lost most of its importance with the invention of the protractor- knowing the applications the older generations use math topics for is amazing when you think how relatively limited they were. I agree that some teachers are to blame, but my opinion is that the students themselves are the real problem. Most of my class doesn’t want to learn and only go to school because they are forced to. They don’t appreciate education the way it does and quite frankly don’t have enough of a futuristic look to know the benefits of an education.

    The beauty in maths, for people of my age, is solving a problem that takes time. The joy it brings is amazing. “You know what, I solved this. I wanna try another one.”

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  27. 27. Lowndes 7:07 am 07/31/2012

    So, if it’s “hard”, don’t make the little darlins take it because “it’s hard”, or they might flunk it, or they might not ever use it anyway. Sounds like a plan. Let’s serve them some cupcakes and tell them entertaining stories with happy endings.

    Better enroll them in a foreign language class, like Mandarin, Cantonese, or Putonghua. I hear those are real easy.

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  28. 28. lamorpa 8:21 am 07/31/2012

    With no formulaic feel, a typing error could tell you that the 20% tip on a $90 meal is $32. A 2 hour trip at 60MPH is 338 miles. A The price per pound of $4, 5 lb bag of potatoes is $0.13 per pound. You would believe that a $8 item at the store plus 5% sales tax is $8.98.

    The dimensions of a 7 inch diagonal screen tablet screen with a 2:3 aspect ratio are:

    2x^2 + 3x^2 = 7^2
    4x*x + 9x*x = 49
    13x*x = 49
    x*x = 3.77
    x = 1.94
    Screen H=3.9″, V=5.8″

    Everyone is subject to algebra every day. It’s just that some people don’t know it and suffer the consequences.

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  29. 29. sparcboy 8:40 am 07/31/2012

    Ones mathematical abilities are generally determined by genetics. I think everyone should be encouraged to reach as high as a level as they reasonably can. Expecting the average student to do as well in math as Einstein is like asking the average mathematician, or Lowndes, to play basketball like Lebron James.

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  30. 30. geojellyroll 11:13 am 07/31/2012

    I’ve thought about this for years.

    The litmus test for me is how many people when browsing through library shelves think: ‘it’d be fun to take out a book on math and flip through it tonight’…almost zero.

    I did well in math but, as a geologist for over 35 years, can count on my fingers I’ve needed anything deeper than what I learned in grade 6…basic division,a few fractions, etc. The calculator rarely gets taken out of the case.

    My thought is that this discussion is largely academic. If I had only had the resources found on the internet when I learned calculus!!!! This is the future of learning. What needs to be emphasized is the discipline to learn on one’s own. The teacher and the school, beyond the formative elementary years, need not teach specifics.

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  31. 31. wmnwmn 11:35 am 07/31/2012

    Although I majored in math at Yale and went on to get a doctorate in physics, I kind of agree with the author that the school-level treatment of algebra is, at best, very inefficient. Students spend months on things like factoring polynomials, solving quadratic equations, and solving artificial word problems. All of this work doesn’t really seem to help students develop their ability to manipulate numbers or solve any problems that seem remotely interesting. I would think most people could skip a lot of that and go straight into precalculus, where one learns about useful things like trigonometry and probability which provide motivation for actually doing math. The truth is that most of algebra is brain-dead simple, and the only reason that it gives students such a hard time is because it is taught in a conceptual vacuum where there’s no apparent reason for doing any of the manipulations other than to pass a test.

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  32. 32. kylemac 3:17 pm 07/31/2012

    I hate when people complain they learned Math “without application”

    I learned it with application so, unless the several schools I went to were crazy anomalies, so did nearly everyone else.

    The “application” part? Those word problems that everyone seems to hate. I never hated them at all – to me this was the application of the math. 2+2 = 4, that’s practice… but now if you have Mary and Sue coming for brunch and Gary and Stu coming for dinner, how many clean forks will you need – that’s application.

    Teachers cannot give you an application for everything you want to do ever. I never got any application problems for my eventual field, but I knew the word problems were the application part.

    I’ll admit it wasn’t great at Math unless it was visual (geometry and trig were fantastic) but I don’t think it has as much to do with how it’s taught as people are claiming. I think it has more to do with how it’s approached. How many kids want to learn math? How many parents tell their kids that math is important (versus “you will never use that stuff anyway – I don’t!”)? When students come in with this attitude, the best teacher in the world wouldn’t be able to turn them around. I’ve had some really, really great teachers that have been shot down by students…because the students were simply uninterested in what they had to say, no matter how they said it.

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  33. 33. keelyellenmarie 4:17 pm 07/31/2012

    I’m entirely willing to have a conversation about whether we should expect the majority of people to pass calculus. (We don’t, currently, but it is becoming a requirement for most colleges). I think Calc is great, but it is tricky and I’d agree that it’s probably not a priority for most non-STEM students.

    But basic algebra? That is not a high bar to clear. People are talking about this as if we’re asking everyone to master particle physics. Unless a student has a profound learning/developmental disability, a good teacher should be perfectly capable of teaching them algebra. I’ve yet to meet a child of average intelligence who can’t be persuaded to memorize math facts and apply basic formulas with the proper motivation, and if you can do those things you can learn basic algebra.

    As for identifying the problem with math education now, I think the biggest issues are a) cultural attitudes about math/math education and b) letting kids move on to higher math without mastering previous lessons.

    For a, if kids who struggle with math are told “that’s okay, not everyone is a math person”… that is giving them permission to give up, as well as giving them reason to believe that their ability to learn math isn’t under their control.

    For b… a passing grade most places is 60-70%, and often we don’t even really require ‘passing’ to advance a child to the next grade. (hoorah social promotion!) But math builds on itself, and if you only got 60-70% of say, pre-algebra, OF COURSE you’re going to struggle with algebra. What we SHOULD do is require a reasonable level of mastery of a list of important skills and concepts before passing anyone on to the next level of math. This is MUCH more work than the standard way of grading and determining who advances, which is one of many reasons why we should pay math teachers more than we do. But the current system will simply NEVER be able to teach the “not-a-math-person” kids adequately without working on a more skills-based system of advancement. I tutored remedial math students in college for several years, and by the time kids got to me, they’d been failed in their math education(by having poor teachers and by being allowed to advance without learning anything) for YEARS. Some of them couldn’t do basic algebra. It’s hard enough to teach a student who has a few holes in their knowledge of the background material, but catching up a student whose entire foundation in the subject is rotten? It’s virtually impossible.

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  34. 34. gmperkins 12:33 am 08/1/2012

    It is about more than math application because the effort to turn intrinsic logic that resides in everyone into extrinsic logic a person can use in all sorts of applications (beyond math) is EXTREMELY important.

    Bottom line, it isn’t the teachers. Students who struggle with math don’t get the proper outside support from parents because their parents are also poor at math and have convinced themselves it isn’t all that important or tell them useless stuff like ‘try harder’. You have to sit down and explain it EVERY night for an hour+ until your child gets it. Once they start getting it, it snowballs quickly.

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  35. 35. anisbenh@gmail.com 3:03 am 08/1/2012

    Maybe we’ll not directly need Algebra in our daily professional life, but trying to learn it establishes a way of thinking, an abstraction process and even self-confidence that will be surely helpful in other contexts.

    It’s precisely these mental exercises and abilities that are established and reinforced throw maths.

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  36. 36. ironjustice 10:59 am 08/1/2012

    This could be compared to the recent article in which they state ‘texting’ is the reason behind the fact people cannot spell , as opposed to the real reason. Lack of instruction in reading and writing in elementary school. Teachers who refuse or simply cannot teach are the reason behind ‘stupidity’ . Teachers should be hired on ability to teach as opposed to the ‘highest marks’ which should be determined by testing.

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  37. 37. ironjustice 11:34 am 08/1/2012

    Quote: At least all of these future useless freeloaders will have the quantitative skills needed to vote for politicians to keep increasing their handouts.

    Answer: We had blackouts in India , one tenth of the world without electricity in one second. Can you even imagine what will happen when every single person in the world WANTS what YOU seem to think is important ?? Big screen tv , SUV , air conditioning for a huge home , swimming pool ? Just the simple things ? THE ‘goal’ in life IS sitting on your arse doing very little to pollute the world , low carbon footprint , and the sooner you understand that , the better the world will be. It is people who figure they deserve to be able to pollute the world with their ever increasing need to have , stuff , and do , stuff. Smoke a cigarette , it is much less harmful to the world , generally. Imho.

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  38. 38. ironjustice 11:58 am 08/1/2012

    “This time element is essential. The investigator may be made to dwell in a garret , he may be forced to live on crusts and wear dilapidated clothes , he may be deprived of social recognition , but if he has time , he can steadfastly devote himself to research. Take away his free time and he is utterly destroyed as a contributor to knowledge.”

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  39. 39. dadster 2:23 pm 08/1/2012

    its the teaching of maths that needs uplift. the subject is a veritable tool kit applicable in every human activity .the way you use the tool is up to the user. whats the use of a screwdriver if you have no clue how to use it ? arithmetic questions in classes are mainly regarding its application in banking ( money transactions )and in the purchase of consumerables and at best in cooking various recipes .not in how to hit a ball , or throw a stone or cricket ball or calculate population growth or in betting , gambling,or the probability of you being born . the market place themes are repeated over again ad nauseum. its application in physics and chemistry is taught only in physics and chemistry classes and hardly in maths classes , the students getting the impression that physics is entirely different from maths . in other words maths is taught as if its an abstract subject as it was thought to be by Greek philosophers . not only algebra , but Euclid’s geometry calculus , trigonometry et al must begin with their interesting applications even from year four onward ( when a child is 8 year old ),to display the splendor of maths .Teaching maths as an abstract subject at lower classes is like teaching language beginning with its grammar before even reading or speaking or writing . Grammar syntax ,idioms,they all come later.maths should also start with real life challenges and in the working it out only different ways of doing it and thinking must in their natural course appear . formal teaching the abstract principles involved (Algieba)should come out as a language of maths out of the situation presented . the syllabus and text books should be developed accordingly .then maths use and power would reveal itself to the young minds and passed on to the generations before that too, who now are blind to the power,rhythm , harmony and music and practical use of maths . Parents also need to be taught maths to change their attitude towards the subject which they are used to consider as an abstract and hence obtuse subject of study . Empower the people with the use and application of the weapon and they will invent newer ways of using it in everyday life knowingly that they are using the principles of maths for their daily breathing and living.in today’s “information” age once the curiosity of young imaginative minds are truly kindled many of them would get smitten by maths and find their own way through it striking newer paths never traveled before by man to enrich humankind .

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  40. 40. DrSteveA 5:08 pm 08/1/2012

    Hacker is mostly correct that our current junior high through high school math curriculum spends too much time on algebra (often the same material repeatedly over and over again over multiple years), leading to calculus or at least pre-calculus. Our current math curriculum is a relic of a bygone era, based on 19th Century ideal of the education a landed gentleman should have, notably algebra and trig in order to do land surveying and architecture. A modern, rigourous, scientific and nationally useful curriculum would spend much more time on logic, probabilty and statisics, which are not universally (or even often) taught as part of the mandatory universal curriculum. And insofar as something has to be reduced to make room, then advanced algebra should proably be it. This is not dumbing down. It is moving from 19th century to 21st century.

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  41. 41. VietVetforObama 6:25 pm 08/1/2012

    Re those supercillious mandarins who insist on algebra-for-all…

    these are the people responsible for the financial illiteracy of the American people, the sub-prime debacle and subsequent ascendancy of the extreme right wing Republicanism.

    These are geniuses whose narrow minds now doom our children to a life of third world enslavement.

    The reason this country bankrupt is because of the financial illiteracy of the average voter.

    The average voter is financially illiterate because the high priests of mathematics have deemed that algebra and calculus are prerequisites to Econ 101 and introductory courses in Finance and Accounting.

    I dare these ivory-towered panjandrums to cite a single instance in which algebra would be essential — much less practical — in consumer finance, corporate banking, real estate, or financial planning.

    When I took algebra in the 60′s it was taught by a chain-smoking megalomanic who dashed through equations, riduculed those of us who struggled to keep up, and made my life miserable.

    Years later, with an MBA in finance and accounting, I worked for twenty-five years in corporate banking — in mid town Manhattan, one of the most competitive financial markets in the world — as well as 10 years in residential real estate — and never, ever needed a polynomial to make an informed decision.

    With an Excel spread sheet, I have prepared my own taxes, as well as budgets and financial plans — with nary a quadratic equation.

    I may regret the bad grades in math that kept me out of the college of my choice.

    I may regret the time wasted on an arcane and virtually useless subject.

    But my ignorance of algebra and calculus has been no more a hindrance than that of Latin, Sanskrit, home economics or shop.

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  42. 42. chairthrower 11:15 pm 08/1/2012

    In fact, universities like mine are doubling down on writing skills, having requirements for “writing across the curriculum” such that you’re doing writing assignments in math and science classes. I have no problem with this. I would, however, like do see “math across the curriculum” or “algorithms across the curriculum” or “science across the curriculum” in similar fashion. Scientific illiteracy and innumeracy are ultimately contributing to countless social ills, from climate change denial to thinking that you can cut taxes, increase government services, and balance a budget simultaneously.

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  43. 43. patnclaire 11:27 am 08/2/2012

    I had to repeat 8th grade math (Pre-Algebra) in summer school. Got an A. I did great in Algebra 1. Was trying to solve equations with 2 or 3 unknowns. I borrowed my neighbor’s Algebra 2 book. I was intrinsicly motivated. I was constrained by the school system and the teachers. Good job Vara.:-)
    I had to retake Geometry in summer school and got an A. Could not understand proofs but I could do constructions. The teacher was great. Now I love Geometry.
    I had nightmares about my Algebra 2 teacher. My best friend could attest to me waking up in the middle of the night screaming that Nelson was coming to get me. I re-took it in summer school and got an A.
    As a Senior, I took Trig and Analytic Geometry with dismal results. Coach Dunleavy taught me how to look at math problems even as I was floundering. I still remember, Coach. Thanks!:-)
    As a senior in college, I dropped College Algebra (more proofs again) before failing. But, I would not quit.
    After a year of working in the steel mills, I could feel my mind going. I enrolled in a community college and got an A in Algebra/Trig, and in Calculus/Analytic Geo. They were taught by good, caring teachers. I was more Mature. Thank you Dr. Arthur Conn!:-)
    10 years after Vietnam, I majored in Math/Econ and got A’s and B’s all the way up to Differential Equations. Thank you Drs. Kiel & Yost.:-)
    A year after Desert Storm I majored in Quality Engineering which was heavy with statistics and accounting and graduated Cum Laude. Thank you Dr. Gitlow.:-)
    The math enabled me to understand Econ. I avoided the Dot-com melt-down and the housing melt-down because I could see the burst coming. I almost did not make it out of the Housing burst because of the time it takes to move 401k accounts around.
    Start Algebra earlier, and teach statistics by Senior year in HS. I sorely miss having taken Calculus with proofs instead of with applications. With the proof, I could have understood where it came from, how to derive it, and how to apply it to something new.
    Math saved my life in the Army. Math enabled me to remain employed during the depression. It enabled me to keep my 401k’s without significant loss.
    Teaching-Learning anything is a 2 way street. The teacher has to be good, with good methods like JUMP and good lesson plans. The student has to be, at least, partially motivated and receptive. The parents have to reinforce the learning and home work. I have great empathy for those people like myself who struggled. I wish that I had the capabilities of Good Will Hunting.

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  44. 44. rkansky 8:02 pm 08/2/2012

    I wonder where Ms. Lamb got the data to support her assertion: “Math certainly is incomprehensible to many students, but from where I sit, poor teaching is often the reason. Math education is failing many of our students. Few pre-college math teachers majored or even minored in math, and until more teachers do, improvements will be hard to come by.”

    According to the 2012 National Center for Educational Statistics (NCES) report “Education and Certification of Departmentalized Public High School-Level Teachers of Core Subjects,” 82.8% of 143,600 high school mathematics teachers had a major in mathematics. That data is for the year 2007-08. [There was no data on how many of the remainder of that 143,600 had a minor in mathematics, but we can be certain it was more than 0%.]

    On the other hand, of 676,900 mathematics classes taught in 2007-08, the NCES report states that 29.6% were taught by teachers who did not have major in mathematics. That practice of schools is referred to as an “out of field teaching assignment.” Now why might such assignments be made, and who is allowing those teaching assignments to be made?

    The assertion that content-unprepared teachers are the problem has become fact by repetition. It has been echoed repeatedly by the uninformed media, policy makers, and general public so often that it has taken on the aura of research-based evidence. Such ignorance supports the arguments of mathematician Lynn Steen and colleagues in “Mathematics and Democracy”:
    http://www.maa.org/ql/mathanddemocracy.html
    for the development of mathematical literacy as a public school alternative for many students — future business, political, social science, and media leaders. As it is — that is, from where such informed persons “sit” — opinions are likely to be based upon others opinions because those all of those opinions are generated by persons who are unable to understand the NCES data reports.

    An exploratory study conducted in 1994 looked into the mathematical literacy of policy makers and educators regarding understand of executive summaries of NAEP results. (Are NAEP Executive Summary Reports Understandable to Policy Makers and Educators?, Ronald K. Hambleton and Sharon C. Slater, University of Massachusetts at Amherst, Draft report, 1994. ) The results of the study indicated a need to improve the understandability of so-called public reports (e.g., NAEP, the National Assessment of Educational Progress ) if they are to achieve desired communication with the target audiences. That communication problem is two-fold: (1) the bulk of the target audiences is mathematically illiterate and (2) the researchers employ language (e.g., statistically significant, standard error of measurement) and graphics that ignore the limitations of their audiences.

    Conclusions of the Hambleton-Slater study are consistent with observations later made by attendees of the 1997 National Science Foundation (NSF) meeting of the Project Directors of its Statewide Systemic Initiative (SSI) program. In the SSI Conference Summary of the Spring 1997 Meeting, panel members reflected on the problem of communicating assessment results to the public. Manuel Gomez (Puerto Rico SSI), having tried to use a press conference to report results, found that “The reporters on hand, however, did not know how to read or interpret the data. ‘They didn’t have numeracy.’” [NOTE: The Hambleton-Slater study was to have included members of the media. However, the experimenters reported that "several newspaper writers who we did contact declined our invitations to participate. They said that they preferred asking questions to answering them and would not participate in the study."] Frank Watson (Vermont SSI), whose SSI held a session for television reports to describe the reform effort and report student performance scores, asserted “We must educate these people on what we’re trying to do and how much progress we’re making.” Kenneth Shepherd of the Chattanooga Comprehensive Program for Mathematics and Science Achievement added “We try to educate the press, and it takes hours to explain such terms as criterion-referenced and norm-referenced. But we have the same problem with our teachers. They’re not well-versed, and we must do better here, too.”

    Ms. Lamb’s blaming of teachers is pitifully misplaced.

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  45. 45. cstewart456 10:19 am 08/3/2012

    I could not agree more with sapbucket. I used to be rubbish at maths because of bad teaching (even here in the UK we have the same problem). I now have a degree in mathematics because I was lucky, we moved house and I went to a school with a brilliant teacher (a PhD no less) who loved his subject. Untill 10 years ago I myself taught at a voluntary saturday morning school and I taught mathematics by teaching pratical electronics. We designed and built amplifiers and radio from surplus components. We designed the circuits from the ground up and getting the students to understand electronics from simple r-c networks to class A and class A/B amplifiers meant they learnt a lot of algebra right through calculus and differential equations because the subjects had a context and the students had goals to their understanding (one simply wanted to understand why the amplifier he built sounded horrible). Taught this way the students did not know they were learning mathematics just as you might look up and learn the compoud interest formula to determine how much your bank loan is going to cost you. From the classes I taight I know of 8 people who went on to do degrees in either physics or maths. One of my ex-students is now working in the same organisation i’m working in. He has A-Level mathematics himself and an engineering degree.

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  46. 46. bethyself49 10:29 am 08/3/2012

    I have three grown children. Two did well at math, one of whom achieved a degree in engineering. The third child asked me one day when she was in high school why she couldn’t do as well in math as the other two. Having been good at math myself and knowing how I loved numbers (a love which I had full-fledged at the age of six), I told her quite confidently that it was difficult for her because she didn’t love math. She was satisfied with that and went on to get a masters in music. I personally believe it is pointless to expect people who don’t have an underlying love of numbers and figuring to get very far in math. I think everyone should be able get through algebra, however, but anything beyond that would be simple cruelty. I still cringe at how painful my one year of biology was.

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  47. 47. docclay 12:43 pm 08/3/2012

    Hmmmm. What an interesting discussion. To algebra or not to algebra, that seems to be the question. To be honest, I’m pretty surprised that on a Scientific American discussion board that we’re even getting as many anti-algebra opinions as we are. Let me see if my own close encounters of the math kind might ring true with some of you.

    To start with, I did D and C work in Algebra I and Geometry and Algebra II in High School. I even got an F one quarter in Geometry. You have to admit that I was persistent if nothing else. I kept taking these classes because I really liked the teacher. She let me cut up in class to my heart’s content. I now see the situation for what it was. I was very immature for my age, and this teacher was, in all likelihood massively burned out. She would let the kids like me have a good time in her class, and she would spend all her time teaching to the kids who were already good at math. I suppose I couldn’t really complain except for the fact that when she wasn’t helping the “brains” in the class, she was egging me on. I’ve always had a knack for being entertaining.

    When I got to college all of a sudden all this math that evaded me in High School, just clicked for me. I was majoring in Chemistry and going into it I thought the math would be my downfall. Funny enough, it was my chem classes I had the trouble with and I was doing great with math.

    As it turns out, I’ve encountered many, many, many people with this very same story. They were bad at math in High School and good at math in College. I spent quite a bit of time since trying to figure why that was. The conclusion I’ve arrived at is that my experience is fairly typical. I was too immature to buckle down on my own and I didn’t have teachers awfully interested in teaching to students who weren’t good at math already. Maybe it was job burn out, maybe it wasn’t. All I know is that of the two different math teachers I had in High School, both of them quit within three years of my graduation to pursue other areas of employment.

    And the only reason I’m telling you this story is that you may know somebody in a similar situation. Or you your self might be in a similar situation. And if you’re in a similar situation there’s just one thing that you can do. You hafta walk up to the man. You gotta walk right up to the man with the 27 8X10 color glossy picture with circles and arrows and paragraph on the back of each one explaining what each one was to be used in evidence against us, you gotta walk right up to the man and say…Opps, I just devolved into a 70′s flashback. College was very fun for me back then. (And if you don’t understand that last rant try googling Alice’s Restaurant, lyrics and see what you get.)

    I suppose the point is, don’t give up on algebra. You may never have to solve quadratic equations or factor polynomials but you sure the hell will have the opportunity to need to manipulate simple formulas, and if you have the ability to factor that polynomial you can figure out how to find what three squared, squared is. Or what will happens by way of Charles’s law if you set an oxygen tank on top of a radiator in the winter.

    As for the tftillman’s in the world I say, the country needs busboys and dish washers too. Although I said that with a little tongue in cheek I don’t intend any disrespect. But, if you do want to take the easy way out every time there are still jobs out there for you. And as for sparcboy, you don’t have to have a genetically altered brain to do well in algebra. You may need superior genetics to have the altered brain anatomy to do math with unsurpassed ease such as Einstein did. Everyone else, unfortunately, has to work at it. Often you have to work pretty damn hard, I did. I can still remember trigonometric identities. I just learned to enjoy it. Look at them like little puzzles.

    Finally, the one thing I know we don’t need is to continue to dumb down this countries already abysmal academic standards. You don’t see Sweden or Japan or China advocating eliminating algebra. I worked for a short period of time with an Electrical Engineer who worked on the Apollo Moon project in NASA. I asked him once why someone needed to know how to find the value of a volumetric solid derived by the rotation of a two dimensional function about a third axis, and he told me, “you never will”. “So,” asks I, “why do they make you learn it”. He in turn told me, “It teaches your brain how to think. And if you can pass these sorts of classes it lets a potential employer know that you’ve got experience at problem solving. That you can think”. So I guess there’s your practical application. Well, I guess not if you plan to explore an exciting and rewarding career in the fast food service industry. But then again…

    Political science?!?!? Are you F***king kidding me??? This guy is a political science professor and he thinks he’s qualified to have a valid opinion about Algebra or anything else he considers an educational time waster. Pa-leese!!! He’s a Political Science major for God’s sake!!!

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  48. 48. ssa-ed 2:25 pm 08/3/2012

    What, no math? We’d all have to become either political scientists or environmental scientists. What fun would that be?

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  49. 49. russian_tomcat@yahoo.com 2:47 pm 08/3/2012

    Algebra made absolutely no sense to me in high school as a subject in and of itself. However, when I took physics the next year there was that Aha moment where it clicked. Algebra made sense because there was a reason for it besides just figuring out what x was. So I found out that algebra did have a purpose and a use. Maybe if I had been taught that along with the algebra initially it wouldn’t have been so hard.

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  50. 50. GeorgeA 3:07 pm 08/3/2012

    @sparcboy:

    I know this wasn’t your point, but the example of Einstein is more relevant than you think!

    It seems that Einstein was not as mathematically gifted as most of us imagine — certainly, many who have made important contributions to theoretical physics were much more mathematically fluent than Einstein.

    And his own struggles with math probably made him a better physicist — his main approach to problems wasn’t mathematical, but rather a kind of visual and physical intuition and imagination. He asked questions, and saw relationships, that a more mathematical person would have missed.

    He began the theory of General Relativity (usually considered his most important work) with such an intuition. It took him many long months of mathematical study to learn enough “higher math” to express his ideas in mathematical form.

    Years before Einstein, Michael Faraday looked at the strange ways magnets and electric currents interacted with each other, and had a startling insight into their relationship which he visualized in terms of gears and axles — but which he didn’t know how to express it as a coherent physical law. Luckily, his associate James Clerk Maxwell had the mathematical talent to transform Faraday’s intuition into the field equations now seen as a cornerstone of physics.

    At least two of the great aerodynamicists — people who revealed the mysteries needed to solve practical problems of aviation and civil engineering — also struggled with math, and like Einstein, approached questions first by “physical imagination,” and only then worked out mathematical expressions.

    Yes, there are a few who absorb math like a sponge, without seeming effort. But the struggle with the hardness of learning math can be enormously worthwhile to those who lack such a gift … and to all of humanity.

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  51. 51. Calvinist 9:39 pm 08/3/2012

    I am no mathematician. I do technical work on a daily basis. All of that is no matter to my comment.
    When I was in 4th grade my teacher kept me after school (I’m dating myself here) until I had my multiplication tables down to 12. To this day I express my appreciation for a great teacher who demanded excellence. Twila Willman at John Muir Elementary school,in Parma Ohio, I thank you for your diligence and your commitment to this student. Memory reminds me she had grey hair and was likely just a few years from retirement back then, and she was still determined for her students to move up with the skills they needed. Though I hated it at the time I learned later what a great gift this lady gave me. Math in my head for the rest of my life (“Priceless”). Students today do not get this level of commitment from ‘teachers’, they just learn how to pass a test which dumbs us down.

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  52. 52. DAK 12:03 am 08/4/2012

    Since when are ALL high school students required to take algebra? Are ALL high school students now enrolled in a “college prep” curriculum?

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  53. 53. Heteromeles 10:43 am 08/4/2012

    @48: speaking as someone who majored in environmental sciences, bite me. The science part of environmental science requires algebra, calculus, stats, trigonometry, and differential equations, all in one undergraduate course. (There’s a book called Consider a Spherical Cow that you might want to check out, if you don’t believe me).

    I don’t know what you think environmental science is, but when you’re dealing with things like the rudiments of climate science or how pollution plumes spread, the math gets very hairy, very fast.

    There’s a similar issue with ecology. The learning curve is a sigmoid, just like so many of the phenomena we study: there’s a low flat part, then the curve goes vertical (because everything is connected after all, and you have to understand all of those connections), then it flattens out high in specialist territory. Often teachers err and teach ecology at *too basic* a level (in fluffy-bunny courses) because they know that, if they made it just a bit too realistic, they’d fail all but a few students.

    I was going to make the point about replacing calculus with stats for the general math curriculum (because everyone uses and remembers stats. The only math I’ve forgotten is calculus), but I see that’s been made already.

    Instead, I’d like to point out a bigger problem: students forget what they’re taught, because it is rarely used after the test. In a general ecology class at a major university, one teacher gives the students a math test on the first day of class. In general, these highly intelligent kids test out cold at an 8th grade math level. Here are some things they can’t do:
    –understand logarithms or exponents beyond 2
    –read and interpret graphs
    –Turn an equation into a graph
    –Understand stats beyond a trivial level (averages, possibly standard deviations)
    –Understand derivatives (in the sense of acceleration), although calculus is listed as a pre-requisite for this course.

    This is devastating, because it means that the students will struggle to understand things like population growth (which accelerates), or tries to read a graph that involves curves, not straight lines.

    The students response was “Of course, what do you expect? You always forget stuff after you’ve been tested on it. The grade is all that matters, you know.”

    That, more than anything else, is the problem with our educational system. So much of it is about the damn grades. From a perspective of keeping society running, the grades are irrelevant, but from a student’s view, they are all that matters. Given that we no longer teach memorization (because computers always remember, why should we?), I fear this problem will only accelerate. We teach kids to forget, long before we teach them things they might want to remember.

    The only place I’ve seen this attitude starting to break down is in work-study students working in college labs. When they actually see classroom subjects put to a real world, science use, they don’t forget what they’ve learned. I don’t know how you can give middle school students similar work experiences, but we do need to do something.

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  54. 54. ssa-ed 2:22 pm 08/4/2012

    @53: Perhaps you’re young and haven’t yet gotten around to researching the history of “environmental science”. But if you are correct and some math is now required, then I agree, your discipline is improving and sorely needed to. Over the last 50 or so years, I’ve been extremely cynical, because I am a mathematician and was weary enough to investigate warming data and conclusions. Which I’d like you to do also.

    During the 60′s and 70′s, the environmental sciences were led by the likes of Norman Myers [here's a great quote by him on his academic background]:
    “My first degree was in French and German, and nothing at all to do with the environment. When I became a professional photographer I learned pretty quickly that getting a picture of an elephant just standing there wouldn’t get me any money. I had to get an elephant tearing up a tree. Or I had to get a lion jumping on board a zebra. And getting shots like that is very difficult. I used to go out just before dawn every day and go to a water hole where I’d find a lion waiting in ambush for zebras to come down and drink. And I’d wait and wait for hours until the zebras would arrive and the lion would attack. And stupid thing, it would miss 29 times out of 30. And I’d have to sit there for five days before I’d finally get this work in action. But all the rest of the time I’d just be sitting in my safari truck. So to pass the time I started reading popular articles about wildlife, and then scientific articles. What makes the lion tick? What makes the zebra tick? How do they tick better together? And during five years I put myself though an undergraduate course in biology without realizing what I was doing.
    Then I came on a lecture tour here to Berkeley and a professor said, “Have you ever thought of coming to grad school and putting all this knowledge and understanding into some shape?” I hadn’t thought of that but it didn’t take me long to decide that that was what I really wanted to do. It took me to age thirty-five to know what I wanted to do with my life.”

    So you see 53, it was a PHd who seeded the idea that environmental scientists need no math.

    Or how about a threesome, Paul Ehrlich, Lester Brown and Stuart Pimm who have predicted one calamity after another.

    Who said “London will be under water by the year 2000″.
    Was it a mathematician or environmental scientist? By the way, did you know that the earth accumulates water from space. As a planet, we were born bone dry, Thankfully, our orbit puts us in a path where we can accumulate 8 or 9 cubic meters every second of every day. So when an environmentalist tells me that the oceans are rising, I say of course they are – a cm or two every century – it can’t be stopped. But to claim it’s caused by AGW . . . I’m skeptical.

    From more recently from the climate-gate emails:
    Three themes are emerging from hacked emails: (1) prominent scientists central to the global warming debate are taking measures to conceal rather than disseminate underlying data and discussions; (2) these scientists view global warming as a political “cause” rather than a balanced scientific inquiry and (3) many of these scientists frankly admit to each other that much of the science is weak and dependent on deliberate manipulation of facts and data.

    About scientific transparency: A defining characteristic of science is the open sharing of scientific data, theories and procedures so that independent parties, and especially skeptics of a particular theory or hypothesis, can replicate and validate asserted experiments or observations. Emails between Climategate scientists, however, show a concerted effort to hide rather than disseminate underlying evidence and procedures.

    “I’ve been told that IPCC is above national FOI [Freedom of Information] Acts. One way to cover yourself and all those working in AR5 would be to delete all emails at the end of the process,” wrote Phil Jones (EAU), a scientist working with the United Nations Intergovernmental Panel on Climate Change (IPCC).

    Michael Mann (Penn State) and Phil Jones (East Anglia) aren’t exactly environmental light weights but their practices warrant doubts about their credentials, their “science” and their universities. I like to know who awarded them PhDs.

    Don’t get me wrong, I’m not a denier, I’m a don’t know-er because environmentalists refuse to turn over global temperature data to those most capable of analyzing it.

    Link to this
  55. 55. cgervasi 11:05 am 08/6/2012

    I had a negative reaction to foreign language in high school, and now I’m fully proficient in Spanish and have a broader view of the world. Moreover, unlike Spanish literature which I don’t use on the job, most good-paying jobs requires some algebra. If you consider only jobs that require no more than a 4-yr degree, jobs that require math pay much more than other jobs. http://bit.ly/Mathcl

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  56. 56. logicalnot 11:06 pm 08/6/2012

    My math experience in school was horrific. I consider myself self taught in the awesomely wonderful language called Mathematics. To those who say math is not needed in most jobs, I say BS. It is perhaps thee most useful skill in any occupation.

    How it is taught, is the problem, I think. Anyone can do it with right instruction and I mean anyone.

    Take the Kahn Academy approach for example. It is the exact opposite of traditional math class. Instead of a teacher giving a lecture then assigning homework to practise. The lecture is the homework. Watching a video lecture on the math subject to be learned(which can be paused and replayed at the students pace until they get it). Then when students come to class they do their ‘assignment’ with the teacher who is there to guide them through the practical. The chances for success/understanding with this approach are extremely good.

    I think this approach is the future of education.

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  57. 57. Tractorthoughts 1:08 am 08/7/2012

    As someone who has taught math for over fifty years, I have met only a handful of students who were not capable of learning algebra. However, the number of students who BELIEVE that they are incapable is huge. Almost a third of my students report that at least one of their teachers admitted math was their worst subject. How these teachers expect that their students would think themselves as capable of learning math is beyond me. Our standards for elementary teachers must be raised. But we can’t do that by demonizing teachers as seems to be a popular sport. Decent pay for competent teachers would be a start.

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  58. 58. rmberkman 12:19 pm 08/7/2012

    I’ve taught mathematics from pre-k through college and agree with Hacker’s assertion; however, this does not abdicate our need to teach algebraic thinking, which is a lot different than the textbook algebra which is taught is most schools. You can read an extended text of my opinion at http://bltm.com/blog/?p=139

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  59. 59. oldtimer 2:45 pm 01/10/2013

    This is one of the most serious issues in our society today. There is a movement to tie all learning in with job placement, even to the point that students are being asked to defer college diplomas to get a ‘special’ placement.

    Asymptotically this is just suicide.

    Unless you intend the next generation (your children) to be serfs to their employers you better think this one through!

    Many people, including Evelyn are “Math Sleepers” that could be lost to society with a short sighted knowledge transfer model from this generation to the next.

    The problem of deeper math understanding impacting future progress of students due to poor grades is a different problem that needs to be addressed with sensible levels of math education structuring to insure that a reasonable founding in math fundamentals is presented to everyone with those with ability and interest referred to more advance programs.

    Poor education policy and miss directed funding is no excuse to dumb down an entire generation of Americans to solve short term generational political/social/economic issues based on the short sighted views of a self interested generation.

    Of course arithmetic is just Group Theory applied to decimal polynomial (using Rational numbers) representations of approximations of real numbers, so it is very important that we expose everyone to some degree of abstraction of these concepts at a level that does not penalize them in future endeavors regardless of where they end up in the knowledge based society and work force (note: the meaning of ‘endeavors’ in this reply is considered archaic so Evelyn’s comment on understanding literature applies!) .

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  60. 60. obscurantist 7:50 am 01/12/2013

    Although I like math, arguments such as the old “It’s exercise for the brain” or “It enriches your life,” need some refining. For many years those were precisely the arguments used to keep Latin and Greek at the heart of education.

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  61. 61. TylerVo 10:35 pm 02/8/2013

    It is nonsensical to compare the practicality of reading to the miniscule benefits that algebra offers.

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  62. 62. emmarq 3:51 am 02/28/2013

    GAH! I majored in Environmental Science and Political Science in undergrad, and now am grad student researching water policy (who wudda thunk?) As someone who considers herself a budding political scientist, I am embarrassed by Hacker’s statement and would just like to mention on here that not all political scientists are, well, politicians. I have worked advocating for environmental issues and have had to deal with politicians denouncing every subject/topic they don’t understand.

    Link to this
  63. 63. JulianaClark 9:12 am 08/27/2014

    “math we learn is not the math we need in our jobs”, I’m agreed with it. Students usually ask when and how they can use Algebra in their daily life. Sometimes their questions shocked me. You remind me those moments.

    Link to this

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