Why Math teaching never improves


Never improves? I don’t think that’s true.

My kids have a flipped classroom. Rather than be taught a lesson then sent home with a bunch of homework, their homework is to watch a video on the material and then they do problems the next day in class. It’s working much, much better for them because I think the lesson video just plants the idea and the real learning happens when working through problems. That’s just a guess though and I bet the traditional model probably works better for some of the kids.

Plus, a lot of teachers aren’t very good at teaching. If the teacher’s video isn’t clear, then they watch a Khan Academy lesson which is almost always excellent.

The people who really like school, go on to become teachers. Those of us who struggled in school despite testing high in IQ, are not going to become teachers. It’s a positive feedback loop that won’t be broken.

Looking back at my math classes, the teachers got defensive when I’d ask a question they weren’t expecting. I eventually learned to stop asking questions in class. Today I still love mathematical patterns, just don’t make me use numbers.

It was hardly just math class, every time I connected with a teacher, invariably, they would be fighting the administration just to keep doing the stuff they did best. The office politics was a powerful force in my high school, and convinced me teaching was the last place I’d ever want to be.


Math. Math never changes.


The real problem is buried in the article, and it’s nothing to do with teachers needing more guidance. It’s this sentence: “Without the right training, most teachers do not understand math well enough to teach it the way Lampert does.”

No one should be teaching maths (except perhaps at the kindergarten level) without a maths degree, and thus maths teachers should understand maths well enough to teach it properly and understand new methodology without needing any further training or guidance. Of course, that means that you have to pay maths teachers more than other teachers, which tends to be unpopular with the educational establishment.


Purely from my own anecdotal experience, this is not true. I have a ton of teacher friends, and they are fairly evenly split between people who loved school and people who didn’t. I loved school, excelled at most things (but especially math), but learned early on (through trying to tutor classmates/younger students in school) that I have absolutely no idea how to teach, so never even considered being a teacher.

I love hearing UK (or UK adjacent, like Ireland) people call it “maths” instead of “math”. As if you are teaching more than one mathematic to people. It’s one of those weird linguistic things that always sounds so jarring to my North American ears.

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Except for when dealing with sufficiently large values of Math…


I recall a couple of people who had to repeat basic algebra a couple times in college before finally squeaking by with a passing grade – both were education majors.

Tell that to my wife’s Facebook feed full of people who won’t stop bitching about the “new math” Obama is forcing every kid to do at gunpoint or something.

It’s infuriating because what they’re complaining about is a completely sensible approach to certain problems (subtract 175 from 210 by splitting the difference and getting 25 + 10 == 35 instead of doing long subtraction) and the people are treating it like the teachers are forcing the kids to learn witchcraft in order to pass the class.

Maybe Math teaching never improves because every time you try to improve it there’s a huge outcry from dumb but well connected people?


Totally agree. I am a math lecturer at a university and I have two daughters who went through a phenomenal string of bad math teachers in the public schools. Teaching remedial college math made me realize how many students are poorly prepared. Seeing the abysmal quality of math teachers made me realize it’s not their fault. Many years ago when I was in school and had great math teachers, teaching was respected and it must’ve paid better than now. Now the pay is so low in my county that they almost can’t hire a qualified math teacher. Education reform is going in the wrong direction, siphoning $ off to computer manufacturers, testing companies, publishers, and private charter school companies. And online education companies (test scores were so low in a nearby county that they are about to close that down, thank goodness).

Pay teachers well and treat them well so that a better-educated class of people will become teachers. That’s the solution.


Maybe. Even with good pay teaching is a specialized profession.

Someone who has a lot of expertise may prefer to be out in the world discovering new proofs or building systems instead of teaching. Both professions are valuable and necessary, but they don’t necessarily have the same appeal.

No one should be teaching maths (except perhaps at the kindergarten level) without a maths degree
You have a point, but in the North American system at least, students in the first five to six years of schooling don’t have specialized teachers for different subjects in general – instead they have a single teacher who is supposed to cover all subjects and who probably decided to be a teacher “because they like children” rather than any love of a particular subject. It’s not until 6th or 7th grade that most schools start to have math teachers who were math majors, history teachers who were history majors, etc.


This. This is the point when a (sufficiently perceptive) student learns which teachers have any real understanding of their subject matter. I’ve had teachers (not just in math) continue to insist they are right even when, after class, I (correctly) derived the negation of things they said. Some get angry and refuse to even let you ask the question.

Not all. Definitely not all. But too many.


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and that’s Wenjun Wu
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Unfortunately, this is a widespread problem in the US. There were multiple subjects I disliked in high school due to bad teaching that I’ve come to appreciate since then. In a capitalist society, poor pay and low prestige attracts the corresponding level of applicants (obviously, there are exceptions, but those are uncommon). The solution should be obvious, but apparently education is only a priority when it comes to making speeches.


This is background for an anecdote: I always considered myself bad at math as a child, though my family required me to keep my nose to the grindstone and keep trying. Got through calculus in college, and then was allowed to stop.

Toward the end of my senior year in college, a school friend from my grammar school days who now went to a different school asked me to help her review trigonometry for her final exam; I had studied it the year before. Now, I had barely pulled a B in that class, but I gamely agreed. And we spent several hours with me showing her every mental trick and cheat I knew (including the Indian princess, Sohkahtoa, who was news to her) or had figured out.

It was an interesting experience, because I discovered I knew a lot more trig than I thought. And she told me she learned more working the problems through with me than she had in a year of class. She wound up pulling a good grade.

I firmly believe that it was because I had struggled so that I understood how to show someone else who was struggling how to learn it. Because understanding hadn’t come easily for me.

Of course now I haven’t used trig in decades, so I wouldn’t be able to teach it to anyone if my life depended on it. But there’s a lot to be said for being allowed to work things through with another student.

The problem is that the parents don’t understand that method. If all you have been taught is the long subtraction way or to use a calculator, using a method that has more steps but is easier to do in your head is going to seem weird and convoluted.

We are taught that math is hard, and have been taught in a way that makes it hard. That’s the real problem.

I respectfully disagree. It might help in teaching subjects like algebra and beyond, but no one needs a degree in mathematics to teach arithmetic, just as no one should need a degree in English literature to teach children to read.

In my mind, about the only grade-school subjects that truly benefit from a teacher with additional training in the field would be history (someone with a degree in history could help compensate for the abysmal history textbooks we have), science, and those topics where trained skill is particularly helpful: art, music, and physical education.

It’s a different story with older children, of course.

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My problem has always been either way, by old school carrying ones, or as you described by breaking up the problem, in the long run I am going to royally eff up the arithmetic and get the wrong answer. I did fine in all my 300 level college math classes as they were about proofs or algorithms in the case on numerical methods classes. But if I actually have to compute numbers in my head forget it, get me a calculator and be done with it, my wife and kid can go yeah thats ‘2659’ while I am still just parsing the numbers.

You’re completely wrong. Excellent teachers persevere despite poor pay and low prestige, because they love to teach. And what you call the “uncommon exceptions” are most of the teachers who have ever taught my son. Looking back at my own childhood, there were a lot of good, committed people there too.

There is a crisis in education, but it’s not a crisis of stupid lazy teachers. It’s a crisis caused by people who have found ways to make education profitable. In order to turn a profit, they have to work hard to blame and demonize professional teachers. That way, they can cut wages and benefits and increase profits.

I used to live in Pennsylvania, where these folks managed to pass a law allowing any taxpayer to pay tuition or make a donation to a for-profit school, and receive a 100% tax credit. It was a law clearly designed to shift funding away from public education and into the pockets of private school owners. In order to make it more attractive, they needed a narrative about stupid lazy government workers - they even made a movie about it.

And so, public school gets less and less funds, and then it’s blamed when performance suffers, so funding is cut further. Meanwhile, for-profit schools are not held to account for results, nor do they produce results, nor do they face any kind of funding cuts. A campaign contribution goes a long way at the state level.

Both kinds of schools have excellent, highly motivated teachers, in a system that is designed to punish them.


From the article:

“Instead of having students memorize and then practice endless lists of equations — which Takahashi remembered from his own days in school — Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math’s procedures, properties and proofs for themselves.”

I think it’s insane that the most effective tools for working out math problems, fifty years into the computer age, is a fucking whiteboard.

When kids can compose, manipulate, test, visualize, and communicate expressions using open technology on their smartphones, math education will begin to improve. Not before that time will much progress be made, notwithstanding the stupidity of the lobbying industry which promotes ed-materials/private-education/right-wing-religious-censorship. Teachers don’t have the tools, students don’t have the tools, and for twenty years math ed technology has been left to Texas Instruments.