I saw that Andrew Hacker is making the rounds for his new book, The Math Myth: And Other STEM Delusions. In one way, I’m very much in agreement with him. The reason that most people focus on math and science is because they think of them in terms of job training. If you know math, the theory goes, then you will get a good job. I hate this idea. But the problem here is the way people think about science and math — not the subjects themselves.
Let’s consider STEM for a moment. It is an acronym for Science, Technology, Engineering and Math. These are not the same things. When I was in college, technology and engineering were in the School of Engineering. Physics and math were in the School of Liberal Arts. Right now, University of California, Berkeley has a School of Letters & Science, “Berkeley’s largest college includes more than 60 departments in the biological sciences, arts and humanities, physical sciences, and social sciences.” That’s how people should think of math: the same way they think of history or philosophy.
The problem I see in math is not that it is hard or that people hate it. The problem is that the teaching of it is absolutely horrendous. I used to do tech work over at a church and they had a tutoring program. It didn’t surprise me that the tutors were mostly horrible. But it did surprise me that children were forced not just to solve problems but to solve them in a specific way.
This is ironic given that I always liked the subject when I was younger because I could approach it in any way that I wanted to. Math, in its natural form, is extremely creative. But our focus on test scores has turned math into the most boring, brain dead thing imaginable. At the same time, when I was a kid, I hated grammar because it was taught in the same way math appears to be taught now.
Math and Grammar
As it is, I’m not very good at knowing the names of things. What I’m really good at is making language work. And the reason for that is because I have my own system for the way English works. But that did me little good in school. A student who knew exactly what an infinitive was and that they should never split one was likely to do very well in school and on standardized tests. I, on the other hand, lump infinitives in with similar constructs and know what works well and what does not.
For example, very few would mark you wrong if you wrote, “He tried to calm the rowdy class down.” But it’s a horrible sentence. It’s the sort of thing that people say but should always avoid writing. It should be, “He tried to calm down the rowdy class.” “Calm down” is a phrasal verb. Splitting phrasal verbs is usually much worse than splitting infinitives. For one thing, I commonly come upon phrasal verb split by ridiculously long objects. For example, “His plan was to take the whole town — the government, the business community, even the schools — over.” But I’ll bet you’ve never been told not to split an phrasal verb — or even what a phrasal verb is.
Math Is Fun
The reason that I know to avoid splitting phrasal verbs is because I find the English language fascinating. But this is not thanks to my English teachers. We have created an educational system that is more focused on social discipline than anything else. And that is the problem. The problem is not that math is hard. I’ll admit: math is hard. And so is English. And so is art and music and theater. Yet people get good at all these things because they are also fun.
The biggest educational problem we have is that we see the purpose of childhood as being preparation for becoming a good adult worker. And that’s what’s going on with the fetishization of STEM subjects. Math is really useful. But that’s not why I love it. But that’s why the Michelle Rhees of the world think that children ought to love it. And that’s why they are destroying education.
Phrasal verbs- I can do you one better. My wife and her family will say, instead of “behaving,” “being have” (rhymes with brave).
As a mathematician, I more or less agree with this. I recently read an article that makes very similar points: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
I take some issue with his dismissal of teacher education, but the math points are excellent.
That’s a lovely essay, really passionately written and effective. I adored this gag:
TEXTBOOK PUBLISHERS: TEACHERS ::
A) pharmaceutical companies : doctors
B) record companies : disk jockeys
C) corporations : congressmen
D) all of the above
(Although it should be “congresspersons,” but we’ll let that slide!)
I agree with almost everything in it. As for teacher education, I think the problem is how our system is structured, not the individual qualifications for teachers. I believe in Finland the top thing teachers are asked to do is engage students; a “bad teacher” would be one who basically doesn’t love teaching. They use far less homework and tests. Naturally, their results far surpass ours! (But then they make life manageable for working families as well, which contributes hugely to kids being refreshed and engaged at school.)
There’s a BBC show, “The Story Of Maths,” which is on Netflix and kinda fun. Unfortunately it tends to use a linear approach towards math history — culture A produced solution 1.0, culture B improved upon it to create solution 1.1, and so on.
However almost everything in it was new to me (math ignoramus that I am), and the creativity some ancient societies developed towards problem-solving is truly amazing! And while their methods may seem cumbersome to us today, I’m sure they’d say the same thing about ours. Just like runeform lettering seems confusing to us and probably made perfect sense at the time.
I agree with you about the systemic problem. I do know that in grammar school I had teachers who hated math and were poisoning all their students. But in general, that isn’t the problem.
In some of my reading for this article I came upon a comment that one reason that math was focused on so much was that it was easy to test for. I think this is insightful. I remember a physics professor I had talking about the difficulty of tests. Maybe he had just asked the wrong questions. He was a thoughtful man. But we are now arranging our educational system around tests. Tests should only be a tool of education. But they have become an end. It’s disgusting.
I don’t have time to read it right now, but I’ll try to get to it. One funny thing is that traditionally, there has been a strong current in mathematics of people who loved it because it wasn’t practical. That’s one reason I don’t like to hear people say they don’t like math; in most cases, they don’t even know what math is (which isn’t their fault).
Very interesting about “being have.” Apparently, the word comes from Middle English “behaven” where “haven” means to have or hold onto. So that construct, although idiosyncratic, makes sense.
I checked out that PDF, and it is full of errors and misconceptions. Certainly I’m with the author, and with just about everyone here, on the pleasure and vitality of mathematical play.
But as far as elementary and secondary education, the author does not know what he is talking about. He asserts that students are introduced to the triangle area formula with no context or motivation. In reality, maths books usually introduce the formula exactly as he recommends, by seeing a triangle as half a rectangle. Similarly for the negative exponents example. The author asserts that students learn formulas and drills with no motivation as to their meaning or why they are required. Again, the stuff he recommends and falsely asserts is not taught, is in fact taught, every time. That’s exactly what is done; negative exponents are introduced as an extension of the initial idea, just as he recommends.
In short, he says: they do X but should do Y instead. In reality, books and teachers do Y already. He doesn’t know what he’s talking about.
I’m afraid that my view is simpler and much less complimentary to human nature. The vast majority of children, teens, and adults alike, don’t enjoy mental effort. See, the kids don’t care about the great concept that is negative exponents. They want their Justin Bieber. Don’t care about how easy it is to grasp the area formula by looking at pictures. They want their videogames.
I don’t enjoy holding this view; I wish I did not. Please, prove me wrong. I’m not being sarcastic; please give me a rationally compelling reason to change my opinion.
We have a fundamental disagreement on this matter. Go look at Wikipedia. The amount of creative thought and analysis that goes into understanding Harry Potter is amazing. It’s not always obvious. But as long as people find thinking relevant to them, they take great joy in it. This is one of the reasons that we have thrived as a species.
Relevance is the key. I certainly don’t want students to do ‘dead memorization’ (staring at numbers until they ‘know’ it). I want them to be introduced to contexts that will make them see for themselves by mathematics (and calculation) are valuable.
I stand by my conclusions on the PDF though; the author is dead wrong about the omission of the good, motivating, playful considerations that lead to understanding (as opposed to obedience). That stuff already is in the books! Check for yourself!
I read portions of this to a music teacher friend, and the response was “nail. Head.” But my friend only teaches music to students who want to play piano for fun; students seeking training for competitive performance are referred elsewhere. And of course we’re slashing art, music, theater education because they have little professional use (except to a handful of people.)
Everyone I know who hated math in school (and that’s most people I meet) enjoyed one math class. Maybe it was geometry or algebra or statistics. They just hated the other required classes. Which begs the question; why do we force teenagers to take all of the above, and threaten them with a poorer GPA if there’s one they simply dislike? Because any math subject you take in school, if you don’t use it after the class is over, is lost training. You’ll simply forget it. As, honestly, I forgot 99% of the history I learned in high school (since, with the exception of one year’s teacher, history was taught in the same brain-numbing fashion.)
I imagine so much of this has to do with our meritocracy religion. Since society should reward the “exceptional” and punish the “lazy,” education should not encourage learning as fun, as its own reward. It should weed out the good order takers from the less pliable. And if that results in declining graduation rates for students in poorer districts, it proves meritocracy is correct; they are poor because they lack discipline.
That’s a very important point about meritocracy. It’s all about deciding who goes to Harvard, who goes to Portland State, and who goes to work check-out at Walmart their whole lives. And the funny thing is that people are very comfortable with individuals being great at one thing and terrible at another. I think it is all about interest: anyone can be good at anything. I have no natural talent at basketball, but if I had spent my whole childhood doing it, I would be competent. So who really cares? As it is, I had a terrible time learning to read, and only really got into reading because I was interested in magic and so had to read these (incredibly technical) books. So I think it is interesting that just allowing me to do what I wanted (magic tricks) led to my being a writer. We would be better off just leaving kids alone. Adults assume that children are as incurious as they are; that’s just not true. If learning weren’t fun, we would have gone extinct by now.
My music teacher friend has a deaf niece, and there are interesting challenges in educating deaf children. One being that ASL grammar is utterly different from English grammar, so reading and writing are harder for deaf children to pick up. (Although considerable research shows that deaf children who learn ASL have an advantage over children whose parents do not sign, make the child take “lip reading” instruction, etc.)
Another is that deaf students can easily block the teacher out merely by shutting or averting their eyes. So to hold their attention, the teacher must engage their curiosity. In the case of this niece, it was falling in love with the “Narnia” movies, which naturally made her want to read the books. I imagine lots of kids were similarly inspired by the “Harry Potter” movies taking so long to be made!
Martin Gardner’s “Mathematical Games” column in Scientific American from 1956 to 1986 is just one example of how we can play w/ math.
Absolutely. I loved his books when I was younger.
Yeah…I got nothing. I hate both grammar and math.
The next two math classes are agony already and I haven’t even taken them.
The ONLY value in grammar classes is it does help with learning a new language to know what the hell a “pluperfect subjunctive” is. Otherwise they’re pointless. (And even with languages you can get around knowing the technical grammar terms if you have a good teacher.)
Incidentally I have one “F” in all my years of school records, and it was a college grammar class.
I honestly don’t see the point for most academic requirements outside one’s chosen field the way we teach them now. At one point in college I had to reteach myself basic physics and chemistry to pass those courses six years after I finished high school. It worked, I got my As, and if I took those courses now, I’d flunk (unless I retaught myself again.) Because it was just so much rote bulls**t, I had no interest in keeping up with it.
Now, I actually think physics is cool, and I wish I had kept up with it! If I ever have you leave me a billion-doillar fortune (obviously, I do not rely on you for this — any benefactors may apply), I’m going to reteach myself calculus so I can learn me some physics!
There’s so many fields we could teach differently. For example, I remember taking one course, “Geology For The Non-Scientist.” What a great idea for a course! Geology is fascinating (this app is absolutely a gas for rock nerds.) Make it fun, and students will remember what they learn! But no, it was more go**amn memorization, only less demanding than the regular geology courses so football players could fulfill their science requirements.
Why are we requiring people to “broaden their education” outside what they want to study, and then making those new subjects intolerably dull? I don’t get it.
You can probably get yourself back up to math speed with a few simple textbooks and sample problems. Maybe ask a librarian to help you try some books, and if there’s one you like, get it used on Amazon?
I kind of think the opposite (but both are true): studying another language allows you to understand your own language. My love of grammar started with an excellent Spanish teacher. I didn’t learn much Spanish from her, but I learned more about grammar from her than from any other teacher. And she’s the one that made me love grammar, which is how I learned a lot about it. John Lennon was right: love is all you need.
When I tutored math, I constantly ran into this problem where the student was having difficulty because of things they were supposed to have learned before. But we don’t allow the flexibility to address that problem. All education should be like writing a book. If you were writing a book about WWII, there would be lots of twists and turns. At some point you might realize that you need to understand the rise of Nazism. So you study that. In the end, your book might be about Kristallnacht alone. From a social standpoint, it’s much better to have a diversity of knowledge than a bunch of people who all know the same thing to varying levels.
Great article, Frank! I really enjoyed it. I’m reading the article that Jurgan linked, and I find it fascinating. I do think it’s sad that so much of our education has been taken over with the idea that everyone must grow up to become a good little worker bee. I feel that the same reason people hate poetry is that it’s taught in much the same way as math. There is a complete lack of imagination to how it’s taught–it’s just used as “gotcha”. There’s no room for free exploration or discussion of metaphorical themes. If you don’t “get” the right meaning of a poem you’re a stupid, wrong person. It’s used to shame kids. No wonder no one likes it.
That’s a great point. I hadn’t thought about poetry. And the weird thing is that kids love poetry: Mother Goose and Dr Seuss and Shel Silverstein. And then they go to school and have all that loved destroyed. I think a big part of what you’re talking about is this idea that you need to get the “right” thing out of a poem. But the thing about a great piece of art is that it works in a multitude of ways. What I most love about your poem For Dolly Arthur is how clear it is in my mind — it’s like I’m there: both with you and in the distant past with Dolly Arthur. But that’s just one aspect of it. I think in a lot of cases, a teacher doesn’t know much about poetry and so just goes by the course book and the course book says… whatever. If there’s going to be a two week section on poetry, the schools would be much better off hiring a local poet to come in and teach it.
That reminds me: I remember being told by a teacher what “The Road Not Taken” meant. I didn’t think much about it then, but what a vile act of artistic desecration. But if you tell a student what a poem means, then you can test them on it. Interestingly, Frost said he saw the poem as playful — the funny thought that taking one road would make a huge difference. That’s not to say that he is right. It’s just to note that he would have failed the test on what his poem “means.”