When Stupid Ideas Go Mainstream: Algebra on the Chopping Block

A picture of a burger and fries.  http://morguefile.com/archive/display/685158#

The Only Subject We All Still Use: Lunch!

When you own a website, sometimes you need to type out an article and complain culture.  Usually, this coincides with hitting a certain age and believing “that wasn’t the case when I was a kid”.  I don’t have any excuse like that; my cynicism is a reaction to a perfect storm of articles over the last few months which, far from moving the Overton Window, broke the window and ripped out all the framing leaving a gaping hole in the side of the house.

Idiots With Megaphones

My initial annoyance came a bit more than a month back with an article on the New York Times Opinion page entitled, “Is Algebra Necessary?“.  In that article, Andrew Hacker, an Emeritus Professor of Political Science argues that making algebra mandatory leads to unacceptable dropout rates, prevents us from developing young talent, and yes, prevents students from gaining entry into college.  The article, of course, also notes that other countries are better (Finland and Canada anybody?) at mathematics, but writes them off by claiming it’s simply perseverance.

Of course, the article also advanced the most ridiculous non sequiturs you can imagine:

  • Picture of an equation.

    Greek? What is this?

    … a definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above.“  Right, so we should cancel physical education because most people sit at their desks.  Let’s cancel literature since most of us don’t read classics at work.  In fact, let’s cancel everything except lunch – at least a majority of us still eat lunch at work!

  • Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” ‘ – The same thing is true for any ostensibly hard subject.  So, for Ms. Bagwell, I propose we eliminate grades.  Grades are the major impediment to kids graduation and going to college, so if we stop ranking children, more will graduate.  Too extreme?  Let’s just eliminate all the subjects kids fail.  History?  Too hard.  English class?  Useless – kids can just use emoticons to get their points across.  Political Science?  Too easy.  Gone.  Biology?  Chemistry?  Useless!  When all we’ve got left is lunch, everyone will pass!
  • Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math.” – Obviously, why stop in High School?  Let’s allow unlimited Mulligans in college too.  If you fail a class?  Let’s automatically drop it from transcripts.  Obviously, the only important thing is to have the degree, the knowledge that degree is supposed to represent is a joke.  Right?  Anyone?

Poe’s Law?

Of course, I could just be falling victim to Poe’s Law.

For the uninitiated, Poe’s Law states that without an indication of intent, it’s impossible to know if a piece is a parody or satire (see this recent article about Paul Ryan), or just an extreme idea.  In this case, if I’m being dense, it’s because I’m ignoring that Mr. Hacker is a Professor of Political Science.  It’s possible the New York Times just published a trolling article to pump page views and discussion.  DQYDJ has been known to publish satirical pieces from time to time, and the comments generally take the articles as serious (try to find them – and watch out for future posts!).

Of course, as you can tell by the tone of this article, I think that the author was serious.  I wasn’t the only one – after he penned it, articles agreeing with him started to roll in… here’s a representative piece from Jacob Vigdor at the American Enterprise Institute (and a Professor of Public Policy and Economics at Duke).  He makes the argument for curricular specialization – the idea we should be testing the potential (capacity?) of our 8 year olds to determine their future schooling prospects.  Maybe he’s right – but do we have any tests which are at all predictive at 8 years old?  I mean, you’d have a hard time convincing me college kids have any clue what they want to do with their lives, let alone pre-teens.  If we only have a subset of our kids learning algebra, what do we do with 18 year olds who suddenly want to work in a technical field?  Seriously, I’d like to know the answer.

Defining Standards Down

Here’s what I think: our culture of defining standards down has gone to far.  If there is a pendulum that determines whether we are being too strict or too light on our kids, it’s approaching the top of the ‘too light’ path.  For years now (especially to kids born in the mid to late 90s and beyond), we’ve been teaching children that self-esteem is the most important thing they can have – whether or not they’ve actually done anything to deserve it.  Participation awards?  Sports without scores?  Pass/no pass?  All of these are symptoms of the same drive to never have to deal with loss and failure.

From youth sports and kindergarten, it has traveled up the chain.  If there are no losers in youth soccer anymore, it’s tempting to believe we should do the same thing in all of our classes.  Because, let’s face it, if your child never loses at anything and gets all As (or ‘P’s) all the way through college, gets into an Elite University, then takes home a C, how do we expect them to act?  We have no clue – it could be anything from quiet contemplation to thoughts of suicide.  Learning to lose and to fail is an important thing to learn.

We all know that when faced with a problem, such as only 4% of students qualifying for elite colleges due to their Math SAT scores, or a bunch of kids failing a subject, there are two ways to ‘fix’ that problem.  The first, of course, is to devote more time to that problem – for example, fixing how we teach algebra.  The second and easier way?  Change the standard.  By defining passing down, we’ll also have more people pass and more students qualifying for elite universities.  It still doesn’t fix certain ironies – soon after publishing an article disparaging Math, the New York Times editors proved they slept through English class.  To wit?  There is a major difference between “C.E.O.’s” and “C.E.O.s”.  Yep, one is possessive, the other plural.

What’s next, should we protect self-esteem in dating?  Perhaps we should force kids to marry their first boyfriends and girlfriends to avoid hurt feelings during the break-up?

How did you do in Algebra class?  Would you prefer your children didn’t have to take Algebra?  Was the NYT article trolling, or was it completely serious?  What other subjects would you love to eliminate?

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Comments

  1. greg says

    I agree with your point of view, and had a similar reaction to the NYT article.

    What I find ironic is that we just had a massive financial crash partially due to unbridled human impulsivity that was helped along by *complete ignorance of mathematics*. How can people function in today’s world without understanding the real impacts of a simple loan, much less an adjustable-rate mortgage?!

    Second, I feel people are being especially lenient in terms of effort considering pretty much all math in this country up to college Calculus involves no real reasoning aside from following simple rules. I got burned later because math was too easy and I never had to really think while following orders … but still finished engineering school with some real work =P

    • says

      Greg,

      If you’re down for some cursing, check out Maddox’s article about math. Good stuff.

      I can’t even see people understanding purchasing things without a rudimentary understanding of math – but like my co-writer commented, it’s okay to be “highly educated” yet to tell people “I’m not very good at math”. Where’s the stigma?

    • sullivanb3 says

      I think Greg is right. Most math classes can be passed with eyes closed. Just follow the rules. There are some that can blindly follow those rules and get by. I also think that things involving math are different from other subjects because logic is a main governing factor. On the other end of the “pendulum”, there are some that get by with just logic. It appears that there are many in the middle that are trying to apply logic but apply it incorrectly. They are trying to grasp but cannot reach.

      Are these people in the middle trying to build with no foundation? Can logic be taught, or adjusted?

      • JT says

        Logic can be taught. Here’s what I think is wrong with math classes: we have kids solve the answer, not the problem.

        At no point ever will anyone encounter a wild quadratic, step function, or some inequality just as part of their daily life.

        Instead, they’re going to encounter some system or problem that needs to be understood and the student will have to create the mathematical language to solve it. Basically, the “problems” listed in a math book are the solutions to problems, they are not the problems to be solved.

        I think we could make a huge impact on math education by reversing the thought process. Too many instructors start with non-logical explanations for basic math rules. “If it looks like this, then use this.” Great…learning “how” to do something will get you through a math course, but learning “why” you do something will get you through every complicated problem you ever encounter…and you’ll actually learn something along the way.

        I had the joy of attending a calculus class in which 90% of the class hated the instructor. I loved him. He was unlike any instructor I had ever had before. He didn’t just throw formulas on the board for memorization purposes. He’d go through the logical proofs for every problem, showing students how, if you had no idea what you were doing, you could do a simple logic test on a problem that you already understood. It changed my view of math forever – finally I found an instructor who actually taught mathematics as an entirely logical subject and not one to be mastered by rote memorization.

        The problem is that education, by default, has to teach kids what to think, since that can be taught to hundreds of kids at what time. Teaching kids how to think is a highly individualized thing. Therefore, math classes focus on the how as part of necessity, and never truly venture into the “why” – the most important part of any science.

        • says

          Math, in my not so humble opinion (which means less than Cameron’s if he chimes in considering he majored in it and I’m just a dumb Engineer), is an incredibly personalized subject. What worked for you won’t work for everyone, and what works for an engineer won’t work for a mathematician.

          Let me explain – while all of the math-using professions use some forms of advanced math, as an engineer it’s better off having a quick reference to move onto the next step. So, for us, we learn the theory behind one style of problem, and when a similar problem comes along we usually just match it up to the tables in the back of a textbook (for the millennial, we get it from our calculators).

          So, like Bryan implies, it’s sort of like cooking. I don’t need to calculate the exact amount of nutmeg to add to the dish, I look it up based upon the inputs. Consider a mechanical engineer… Every time he looks at a joist do you think he calculates the maximum deflection based upon the spans he measures? Of course not – he looks at the maximum in a table and makes sure it is less than that. Only when the answer hasn’t been calculated does he start to make manual calculations.

          So, I can see both sides from where I’m standing – the role of ‘cookbook’ style math learning for expediency, and the importance of theory for understanding ‘why’ something works a certain way. But, like I said, it’s both personal and dependent on profession.

          • sullivanb3 says

            PJ: What you said is very true when you say it is important to learn “cook book” style math, because in a professional environment, time is money… as in most circumstances! But, I find it very interesting when my girlfriend and I argue about things sometimes. She is a teacher and she sometimes asks me, as an engineer, what the best way is, to teach a math subject to the children. (very ironic because we had a conversation like this today about fractional addition.)

            I just cannot agree with JT enough. I think math is one of those things that is reached by many paths. We all may get to the same destination but the path is always different.

            When it comes to “theory”… For some it may be un-graspable at the time but there are many thing in life that we don’t understand until later, when we have time to “digest”. The rule will be taught as well… but the understanding is so much more important!

            - I find things very ironic sometimes because I often wondered the “why” we needed to understand very complex math… all the way up until differential equations. As an engineer, I have to disagree with JT, when he said “At no point ever will anyone encounter a wild quadratic, step function, or some inequality just as part of their daily life.” Definitely no disrespect there, because I think everyone thinks this at some point. But, we usually find a reason later.

            There are many complex situations when you have to “think outside the cook book” and use your own intuition to grow a new path.

  2. CameronDaniels says

    I know you used the term ‘especially’ but I need to point out that a lot of the ‘helicopter’ parenting and similar phenomena usually refers to students graduating high school this millenium, which will correspond with those born 1982 and later. It could be that we are on an even further negative trend.

    Whenever I think of the way parenting has changed and the way our children our raised, all I can think about is those ridiculous ADT ads. You know the ones: some mysterious hooded black man breaks into a house while an alarm goes off and a clearly frazzled white woman hugs her kids while crying. “SHOULDN’T YOU OWN A HOME SECURITY SYSTEM?”

    In more seriousness, if freshman math (at some schools pre-calc or dare I say ‘Mathematical Concepts’) is the most severe impediment to graduation, then we should place more of the onus on teaching and instructing proper mathematical understanding or continued high expectations. Take it from two writers who majored in Computer Engineering and Mathematics: math sells.

    One of my favorite books ‘Innumeracy’ by John Allen Paulos (which, coincidentally, I should write an article reviewing) expounds the absurd double standard for English and Math in popular culture. At dinner parties, at grocery stores, at political debates people have no qualms claiming ‘I have never been good at math’. I can simply imagine the shame of the person in a social setting claiming ‘I have never been good at speaking or reading or writing’. Why the double standard?

    Sandbagging a certain post with Poe’s law?

    • says

      Fine, 1982, no quibbles. We can then blame helicopter parenting on all of the Boomers (since they catch flak from everyone else!).

      I’ve actually mentioned John Allen Paulos twice on the podcast – you should definitely review his book. Get that innumeracy out of the mainstream, if only so i don’t have to wait 60 seconds for people to bust out a smartphone to calculate a 15% tip.

  3. says

    Algebra wasn’t a subject I loved, but I didn’t hate it. It was necessary, and that was it.

    I think it is the most ridiculous thing I’ve ever read. Only in America could you think of banning advanced math because it’s too hard for kids to learn.

    Why don’t we just give kids prizes and perfect grades for showing up in class and breathing? Even as a Millennium Kid with Boomer Parents, I always wondered how some kids in my class had ancestors who made it through life without having been eaten by dinosaurs early on.

    As someone who has a mother who is a teacher, I have a whole slew of horror stories about how teachers have to ‘accomodate’ children during school (read: baby them) and give them falsified grades because their parents threaten to have you fired, but when they reach high school and their parents realize they don’t know jack squat, they try and sue the school board for the teachers having accommodated their lazy and/or less-intelligent kids too much.

    Why don’t we just all come out and admit that some kids are not meant to go on to higher education, and they should go to trade school, become plumbers and make a sweet $100,000 a year?

    Dropping out is acceptable in my books, because it filters out those kids who CAN do and those who CAN’T (the reasons, of course, are debatable whether it is the kid, society, school or parenting that caused it) and have to learn how to live with the reality that they are not all budding geniuses.

    • says

      There’s nothing wrong in my books with so-called “blue-collar” professions, and I know that I pay contractors a lot more to work on my house than I would certain majors to come talk to me (ha). And yes, that factors in all the work I do myself.

      Even better than dropping out is being realistic in the first place about whether your Underwater Basket Weaving degree has any practical application, and whether it’s worth 6 figures of debt to achieve. Full scholarship? Go wild, but I’d still keep an eye on the ‘average salary’ after graduation, ha.

  4. sullivanb3 says

    In regards to your comment about no losers in youth soccer: I seriously remember the exact trophy at my house that I got when we didn’t have a winning record or anything back in minor league baseball (5th grade). It really made me angry too because it was bigger than a few of the ones that I had won at tournaments. I won many more after that but I still had a mental asterisk next to that one hahaha.

  5. Funny about Money says

    oooohhh gawd, don’t get me started!

    Yes, freshman math probably IS the biggest impediment to graduation, because the poor kids haven’t learned to add on their fingers by the time they get to the course. I teach those students English, and I can assure you they haven’t learned much else, either. My son, who graduated from an elite liberal arts college, took that course by way of picking up some lock-step requirements to get into a graduate program outside his undergraduate major; he reported that the professor spent a fair amount of time trying to teach the students fractions. They couldn’t figure out how to do percentages, and most of them, presented with the question “12 is what percentage of 28,” hadn’t a clue.

    It gets better. School administrators nationwide have decided to stop teaching kids cursive. It’s just so HARD and most of them never use it anyway, because they all type on keyboards.

    Heaven help us.

    • says

      I can tell you that I rank algebra above cursive, but I agree with your point on the inadequacy of pre-college education – it’s tough to compare across schools objectively, but pretty obvious once students from various high schools come together in college. It’s why colleges rely so much on standardized tests like the SAT and ACT (and their various analogues in graduate school) – they aren’t perfect, but they do give you an idea of the skills of incoming students in ways that GPAs and transcripts can’t.

      It makes me want to be a teacher… well, after my day job has run its course. Second career?

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