The NY Times recently ran an article by Andrew Hacker asking “Is Algebra Necessary?” He stated that in a typical day 6 million high school students and 2 million college students are “struggling with algebra.” His argument was that algebra, geometry, and calculus “prevents us from discovering and developing young talent” and in his opinion was the “major academic reason” that around a third of all students fail to finish high school. Consequently, he believes we should not “force them to grasp” these concepts.
I’m an engineer, and I’ve never been good at mathematics, but I believe his argument is flawed.
Firstly, why does the number of people who drop out effect whether a subject is valuable in education? The number of people who drop out is affected by many factors. If a subject is valuable, and people are dropping out because of it, don’t ignore the subject, find ways to improve the teaching of it so that the value can be passed on.
Secondly, he doesn’t relay how failure rates have changed over time, and consequently he doesn’t know what other factors may play into the current failure rate, he just jumps to a conclusion.
Thirdly, giving and receiving an education is hard work. The brain is a muscle much like the others in the body. Using it burns energy and oxygen, and leaves you tired. Learning mathematics, a foreign language, or music theory all require an effort. Some people are better at some subjects and worse at others. While we should exploit the things we’re good at, it is the subjects we are weakest at that need the most work, not the least, or worse, none at all.
Fourthly, mathematicians are an essential element in the advancement of society, much the same as entrepreneurs, shopkeepers, and the people who collect the trash. We need everyone to have a functioning and evolving society. He sites
“Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics.”
I don’t know if 15,396 mathematicians is enough for our countries needs or not, but from my experience I would say we need more mathematicians, not less. The fewer students we expose to mathematics, the fewer mathematicians will graduate.
Fifthly, the USA is one of the more expensive countries in the world for manufacturing. Apple’s “Designed in California” claim is almost the best we can assert for many products, because it “costs too much” to manufacture in the US. Mental capabilities will be increasingly valuable in the future. Skimping on “intellectual” skills is a disservice to future generations.
One of the concessions Hacker makes to mathematics is that
“young people should learn to read and write and do long division, whether they want to or not.”
I’d argue that teaching of the basic operators doesn’t need to be emphasized because of the fact that the calculator has been common for fifty years. It’s akin to using all your time learning to spell and ignoring sentence structure and the construction of stories (which education also tends to do). Which is more important when even your mobile phone has a spell checker?
What is more important in mathematics is to have a feeling for the form of equations, when they should be applied, and how. These things give a better idea of the purpose and use of mathematics, and when people see a purpose to something they are more likely to become engaged.
Ok, I’ve whined on at Hacker’s expense, but what could be done? There are probably lots of things, but the biggest single thing I think we can do is
Talk about mathematics.
We learn to talk English, French, Spanish and all the other languages of the world as babies, toddlers, children, kids, teenagers and adults. We do it for the most part not by classroom teaching, but by continual interaction with other people. Most people’s everyday conversations do not involve much mathematics. Consequently, our children learn our language, but not mathematics. Learning anything requires persistence and practice. Parents have the greatest opportunity to influence children. Expanding family conversation to include discussing maths practice and concepts could make a significant difference in our children’s ability to cope with it in a classroom setting. Gestation is everything.
Simple maths topics are all around. Let children work out how long a journey will take. Get them to explain the equations they use. Talk about the units of miles per hour, meter per second. Ask them how long it would take if you went twice as fast. Talk about the difference between lines, areas, and volumes. Talk about distance, velocity, and acceleration, and how they are connected. Talk about the parameters that yield the form of the arc of a ball. Talk about probability. Talk about symmetry. Talk about the difference between rotation and translation.
Talk about anything but that maths is hard – because even if our children don’t turn into college professors – life is much harder without it.
Ok, you’ve suffered my opinions, but I’m off my soapbox at last, so now’s your chance to set me straight!
Giving you a hip bump to knock you off the soapbox, Nigel. Why? Because I want to add my piece of Pi to the argument in support of learning mathematics.
Think of the synapses in the brain that develop when one learns to extrapolate, break math from incomprehensible to logical steps, memorize the basics, and (in the brain’s subconscious core) store the path the brain took from problem A to solution Y.
I’m an unabashed logic puzzle and math and chemistry freak. I love problem solving. Those strong skills (IMHO) translate to other areas of my life that require quick cause/effect decisions.
I find the argument against learning problem solving skills illogical. And, now, I have to skedaddle for my NYT Sudoku problem solver. Learning is hard work, but I can’t imagine not waking to learn something new each day.
Pi … very droll. And you’re a logic puzzle, math and chemistry freak? Boy, you kept that quiet. I like solving problems. As you say, it’s one of the things that keeps our brains going. Well, that and wine, but I digress.
Hope the travels are still going well!
Whoop. Forgot to confess that I’m also a dingbat, a klutz, and rarely more than one tune away from dancing alone in public.
dancing alone in public … nothing wrong with that!
So, we should give up because something is hard, or because it does not flow with our natural talents? Teach future generations to whine and wimp out?
My calculus classes always began the same way: a slow, numbing pain at the base of my neck. Like an allergic reaction, the pain would worsen and spread until, by the time the bell rang, my temples throbbed.
When we conquer an algebraic concept, we learn much more than x+y=z squared. We learn discipline, perseverance, confidence, problem-solving, risk-taking, method.
I view calculus as a gate-keeper separating the wheat from the mathematically-challenged (that would be me). Calculus has broadened my mind and strengthened my resolve. When life gets difficult, I know I will get through the ordeal because if I could survive calculus, then I can survive anything.
I’ve only once had to call on calculus. In a staff of higher-educated, higher-paid individuals than I will ever be, I was the only one int he marketing (read: creative) environment that could solve a particular problem armed with only pencil, paper and 3.5 minutes. There’s a line from CSI, King Kong on steroids. That was me that day.
I’m impressed! King Kong on steroids, indeed. A lot of people don’t even think to use what they’ve learnt when they go into a work environment that isn’t like school (eg, being in marketing and using calculus).
I agree that struggling to overcome an obstacle broadens peoples abilities. I think many people don’t realize they’ve grown after they achieve (or even only partially achieve) something. After all, who grew from (say) opening a packet of Pringles? (even though I like them 😉
This is really interesting, Nigel, because I utterly loathed maths at school. And yet, went on to use numbers every single day in my career – finance. The reason I loathed maths at school was the teacher and I had her for four hard, hard years. I scraped through my exams. But once out into the big wide world I flew because it all made sense and was logical. I flew through my bank exams and ran accounts for multi national corporations in the millions of dollars.
With my son, who had an aversion to maths, we sent him to Kumon (which is Japanese technique) when he was seven and by the age of nine he was faster doing calculus with a pencil and paper than his peers with calculators – he’s a whiz like Sherry Isaac.
It’s all in the teaching and unlocking the potential in the young.
Yes, something Hacker ignored was the nature of the teaching. Not that teachers are necessarily worse today than they were in the past, just that people’s expectations have changed and teaching methods haven’t. People have their greatest chance to learn when they’re young, and not making the most of it is a crime. Despite the pills, potions, and creams, you never get your youth back to try again (trust me I’ve tried 🙂
I’ve never herd of Kumon, I’m going to have to look that one up.
It is, indeed, how mathematics are taught that’s flawed and not mathematics itself. As a child, I was exposed, and pulled apart, by conflicting teaching practices and grew up with a loathing, and fear, of the subjects. As an adult, I was forced to look at the subject in a different way in order to make headway. What I came up with is this: Mathematics is about patterns, understanding the patterns, how they develop, how they relate to one another, and how they are applied. Once I removed the term “math” from my thinking, my understanding blossomed. The “just because it’s so” answers were always confusing to me. It was when I was able to finally look at equations and understand the concepts they were meant to represent that the light started to become brighter.
When my daughter was little, I was determined she would not be handicapped by the beliefs and perceptions that were foisted upon me. I used all the tools you suggest: calculating distance, exchange rates, weights and measures, etc. I am pleased to say that my child has become a young woman who understands the value of mathematics on a practical as well as a conceptual level.
How we teach…anything…is the real issue. Not the subject that’s taught. Thanks for a great post!
I’m glad to hear to worked with your daughter. I’m doing the same and I (egotistically) think it makes a difference. I truly hate it when her 7 to 10 yr old friends come round and ask her why she’s doing “stupid” things in her school holidays. At that age they aren’t really forming their own opinions, they’re just repeating what they’ve heard on TV and quite likely from their family.
I agree with you that mathematics is more about patterns than numbers and answers. Understand the forma and function is far more important and naturally leads to its application – which (to me) is far more interesting that abstract concepts.
Great post, Nigel. Math was always one of my favourite subjects because its predictability appealed to my hard-wired little brain. Follow the logical steps, and you’ll get the right answer. Not “sort of” right. Not 89% right. Perfectly, 100% right. Beautiful!
But I suspect Hacker’s rant against math is just another symptom of the flawed attitude that’s taking over our educational system. I don’t know what it’s like in the States, but here in Canada there’s a trend toward coddling our little darlings’ self-esteem to the point of ridiculous pandering. Kids here don’t “fail”. In fact, in some schools, they aren’t even assigned numerical marks anymore…. because getting a low mark might damage their self-esteem. In one case, a teacher was suspended for failing a student.
The result? A bunch of kids with no grasp of reality and a gigantic sense of entitlement. Kids who believe their very existence is worthy of awe and worship. Kids who believe they “deserve” better than a minimum-wage job slinging burgers despite a complete lack of skills and initiative.
Hacker’s right: math is holding these kids back. And that’s a good thing. Any course that teaches logic, discipline, and perseverance while providing quantifiable feedback on performance is valuable far beyond the ability to do long division and calculate sales tax in your head.
I’m with you: Make ’em suffer! It’ll do us all a favour, because these kids will be running our countries in a few short years. And I don’t know about you, but I think I’d prefer some logic and discipline in our leadership.
…oh wait, we don’t have that now, do we? Maybe we should force our political leaders to pass calculus before they can be elected…
Never mind. Getting off my soapbox now.
Maths was one of your favorite subjects? I knew there was a good reason why I like you! You’re right that maths is the only field where there is a true concept of right and wrong. I often use the converse to encourage people in creative writing.
I think removing the potential for failure is pretty much a guarantee that people won’t try. If there’s nothing at stake, why bother? Furthermore, if you don’t objectively grade people, how do you know who needs help?
Calculus for politicians?! Now you’re talking. Boy, that would be good. Perhaps we could throw in basic spelling (starting with potato). It would certainly thin out the tooth-straightened, backed by millions, schmoozers we’ve got at the moment. Their only brush with mathematics is to tell their accounts to make sure they don’t pay any taxes!
I have actually told my kids that while I have absolutely no use whatsoever for the trigonometry I took in high school, I use algebra every day. I don’t actually write out an equation with “x” or “y” in it, but the principles are there all the time in reconfiguring recipes for a different number of servings, calculating distance or gas mileage, figuring out my personal finances, and much more. I think you are so right, Nigel. If the kids aren’t getting it, let’s rethink how we’re teaching it.
Hey, it can be hard to potty train kids too, but we don’t say, “No problem there, junior. Just wear this diaper for the rest of your life.” Great stuff!
Julie, “No problem there, junior. Just wear this diaper for the rest of your life.” — that’s inspired.
Yes, even when were not thinking of x and y, were always using algebra. Will my car fit through that gap? Do I have enough to buy lunch? Has this shrunk in the wash? As you say, it everywhere.
I’m hoping that Hacker’s article stirs up enough counter argument that something might actually get done.
I am so tired of all these lazy attitudes. I agree, if children are having trouble learning then we need to look at how they are being taught. My son’s school switched their approach this last year after teaching the kids math the same way for three years. It was a horribly hard year on all the kids. It was like the rug had been yanked out from under them as they were all the sudden told, “Forget the way you were told to do math all these years. Now do it this way.” Even all the parents had no idea what we were doing so we had a hell of a time helping with the homework. I think something like that needs to start at the beginning, with the first grade, not in the middle of fourth or fifth. My son thinks differently than I do so teaching math to him can be a challenge. I never had a problem in the subject. I know there is a large increase of asperger and autistic children in the system (some or many undiagnosed) now and it’s clear to me that they might see the problem differently than we do. At least, my son does. So, that might be adding to their statistics. He’s smart, but his learning process is different. He hates to sit down and do math. I loved math in school. It was the one subject I was always sure of. Go figure.
That doesn’t sound good – changing methods between years. One of things I wonder about is how children are taught one thing or way of doing something, then re-taught later because the first time wasn’t comprehensive or complete. Everyone learns in a different way and at a different speed, and schools very often don’t cater for this variation.
Glad to hear you liked maths 🙂
The fact of the matter is that ANY mind can grasp mathematics. The hinderence is that not just any mind can teach it. Teachers today are often trained to teach in only one method so as not to confuse kids. To the point that my friends (who had homeschooled their children until the oldest was ready for the third grade) were told explicitely NOT to help their daughter with her math homework, as they would only confuse the girl.
I work as a substitute teacher, but the way I was taught to do math was far different than the way my students are taught. You see, I was taught math by a woman who is a self proclaimed “mathematical idiot.” Yes, I was homeschooled. When I was ready for the sixth grade, I had moved passed my mother’s ability to teach me math, but the tricks that she memorized in order to get me that far are what I know to this day. These are the same tricks that I show my students. More than once I have gotten a confused look and changed my teaching tactics to be suddenly rewarded with understanding nods. I frequently have students come up to me in the grocery store and say, “Miss, I still don’t understand how my teacher works those problems, but I do it the way you showed me and I get the right answer every time.”
Teachers must understand that the relationship between student and teacher works much like the gears in a mountain bike. If the gears don’t mesh, nobody moves forward. The trick is to be willing to adjust your teaching method to that of the students learning method. The student doesn’t know how to change. It falls to the teachers.
Unfortunately, we place this responsibility on the teachers, then we severely underpay them, cut funding for classroom supplies, and over populate their classrooms. I have literally been in more than one classroom where students were sitting in the window sills and sharing books. The only reason that they weren’t acting up was out of respect for a compassionate teacher who gave more to her class than she could possibly afford.
Solution: Don’t get lazy. Fund the schools. Make it possible for those who CAN TEACH, to do their jobs. Quit making them teach to the test. Standardized tests are a waste of money as nearly any child can memorize facts. I know this from first hand experience, I taught an illiterate 15 year old, who couldn’t add two digit numbers, which buttons to push on the calculator when he saw the pythagorean theorom. He didn’t know what he was doing mathematically, but he looked damned good on those stupid tests.
Let teachers be teachers and we will see a better tomorrow.
Thanks for your teachers perspective. I think you hit the nail on the head with “funding.” On top of that I’d add the correct use of funds, I hate it when I hear another school proudly boating about installing half a million dollars of football field and jumbotron. I’m sure that makes all the difference to the education they’re supposed to be providing.
From my non-teacher perspective, teachers seem to have a lot of “non-teaching” paperwork, meetings and processes to load up their time. Add full classes and its not a recipe for success.
I agree with almost everything said here. All I would add is that I don’t think that calculus is as important for a high school graduate as statistics. I would teach algebra, geometry, and a heavy dose of stats as a basic high school math curriculum. Then students would understand newspaper articles about political polls, drug studies, etc., much better.
I’m not sure how much stats is taught at schools these days. I do wonder about the number of people I see taken in by the statistics quoted on TV and in adverts. A bit like a number out of a computer, lots of people believe that it must be correct.
I hated math all through school, though for some reason people assumed I was good at it (despite my nearly failing it several times). I’ve since learned better… Math is not only great and necessary, but it tickles the mind wonderfully.
Bad teaching. Teaching to test. Not adapting methods to students. And… to be honest, an obsession with repetition and solving operational problems over and over again because the number in the answer was always given more value than the process nearly killed a love affair for me. Could it possibly be that I’m not the only one?
Likely…. And people like this Hacker who sees little value in things solely because he does not know how to best use them…. people like that don’t make better teachers come available; they do not make good matchmakers for those who don’t know where to find their passion.
So only some 15K graduated with Math degrees in the past few years. A lot of people graduated in the last few years with MBAs too. And while I’m sure we do need people who know Business and Management and Finance… A lot of those degree holders are waiting for jobs just like the math majors. Indeed, many of them when for the MBA major because they’d been led to believe that it would be the fastrack to a job, not because they had a passion for Business. They didn’t go for Math because they’d been told their only options would be for teaching or further academic study….and they needed the job to pay their student loans.
I’m sorry, I should not be ranting on your blog, Nigel, but this anti-higher learning attitude keeps getting stronger and stronger….. and I just hurt. 🙁
Ha! Feel free to rant 🙂
MBAs? While there are probably lots of people who benefit from these course, I feel their popularity has more to do with the advertising by the people who sell these course. A lot of companies think that an MBA is a clear distinguisher over non-MBA candidates, whereas I’d rate as a minor add-on to the rest of their education and experience. The majority of good PMs and mangers I know don’t have these sort of degrees, but have considerable experience in dealing with customers, and programmatics that they have gained over time.
As you say, the more I think about Hacker’s argument, the more it seems more to do with him having a problem explaining failure than the worth of what’s being taught and addressing that.
So, by Hacker’s logic, anything too challenging should just be eliminated from school curriculum then? That’s insane. We really are only a few steps away from becoming the dumb, lazy slobs in Wall-E.
You’re so right, Nigel—exposing kids to it at an earlier age, and continuing the exposure, is the only way to keep people using it. By removing that exposure, we’ll all just become pods.
This article is just further evidence to me that the writers at the New York Times are, increasingly, stupid hacks.
Yes, removing the obstacles to passing seems to be his objective. On that basis I guess we should be glad he didn’t advocate abolishing the pesky need to turn up at school. After all, you still get much the same education when sat in your underwear playing xbox all day, don’t you?
I’m a big fan if gestation and consistent practice in education. I don’t mean it to be repetitive, but lots of people far greater than me have found numerous ways to say practice makes perfect. I add gestation because I’m convinced that after you’ve been exposed to an idea, even if you don’t understand it at the time, it won’t be as frightening the next time, and then you’ll be more receptive and less likely to put up a wall to your learning.
“…the writers at the New York Times are, increasingly, stupid hacks.” … or Hackers in this case?
Have a great weekend. I insist.
Absolutely agree on the gestation theory—part of why people dread things is because they aren’t familiar with them. So with consistent exposure, they becomes less intimidating. But hacks like Hacker (ha!) obviously just think about taking shortcuts. Because hey, if something is too challenging, why not just not do it? If you don’t try, you don’t fail!
You have a good weekend too, NB.