Math (education) isn't a science, it's a religion!

November 15, 2009 12:21 AM

Math educators continue to dumb down curricula to be politically correct, argues Sandra Stotsky, blithely ignoring the lack of evidence for their methods -- and it's a serious problem for the nation.
posted by shivohum (30 comments total)

I came for the semi-coherent rambling, but I stayed for the bizarre sort-of-racist anti-hippy cartoons.

Wow.
posted by drjimmy11 at 12:27 AM on November 15 [3 favorites]

the bizarre sort-of-racist anti-hippy cartoons

what
posted by BitterOldPunk at 12:40 AM on November 15

I had a nice rant typed out about how we currently teach math (at least how it was when I was in school) but I'm not sure it's worth it. The author seems to be arguing against a ridiculous straw man.

How could anyone believe that her characterization of her opponents is the real driving force behind most math education in the U.S? Especially given the patchwork nature of the U.S. educational system. Remember, each school district, each state has their own guidelines for how things should be taught. That's the biggest problem with making sweeping statements like "Math education is like this in the U.S!" Normally you're only talking about what you're familiar with, which could be totally different from how average kids are taught.

But anyway, she's not proposing any solutions at all, just whining about liberals wanting to make math education "P.C" - a concept that makes no sense. What most people want to do is make math education modern. There's no real need to spend years and years drilling kids on pencil/paper techniques that are completely useless outside of an elementary school classroom. Teach kids some mental math to do in their head, and teach them how to use a calculator. Teach them how to program a computer to do the basic mathematical algorithms and then go on to teaching them Algebra.

Knowing pencil and paper arithmetic won't help you with algebra any more then a calculator will (IMO).

But the biggest "Cult" out there is the cult of know-nothings who think the way we taught math in the 1950s is the way we should be doing it now, even though the jobs where people would have used arithmetic have all been changed into jobs where people use Excel.

Is that what Sandra Stotsky, professor at the esteemed University of Arkansas wants? Well, she doesn't say. She just paints all her opponents as "Liberals" and well, we all know what to think about those kind of people.
posted by delmoi at 12:44 AM on November 15 [11 favorites]

There's no real need to spend years and years drilling kids on pencil/paper techniques that are completely useless outside of an elementary school classroom. Teach kids some mental math to do in their head, and teach them how to use a calculator.

I completely disagree with this statement. Teaching kids on pencil/paper techniques is to teach them how to problem-solve and -- more importantly -- how to think. Teaching kids how to think is, in my opinion, the most important function of school. It seems to be the very thing that we have moved away from doing. I don't think kids should be allowed to use calculators until they take calculus. Pencil/paper techniques teach logic. Calculators teach kids that there are magic ways of reaching solutions. Unfortunately in life, there are not always magic devices which give us solutions. Life often requires that we think our way through problems using -- you guessed it -- logic and other problem-solving techniques.

To say that you will never use what you learn in math class outside the classroom is to miss the point of math entirely. You will undoubtedly use the logic skills and problem-solving ability you gained in math class throughout your lifetime. I know I do.
posted by flarbuse at 1:05 AM on November 15 [4 favorites]

Teaching kids on pencil/paper techniques is to teach them how to problem-solve and -- more importantly -- how to think.

So does teaching kids mental math and how to program a computer, no?
posted by scody at 1:10 AM on November 15 [1 favorite]

The way math should be taught: Start with Peano in kindergarten. By the time they're seniors they need to be able to derive at least Taniyama-Shimura. That's not asking for too much, right?
posted by kmz at 1:11 AM on November 15 [3 favorites]

Pencil and paper comprise a simple computer. Build from there. Worked for me, despite (and occasionally thanks to) our shitty schools.
posted by runehog at 1:24 AM on November 15

To be serious though, I think there's middle ground between years and years of rote drills and giving calculators to kids in kindergarten. The key is to know the algorithms: once you know them inside and out, applying them either on paper or on a computer is easy.
posted by kmz at 1:30 AM on November 15

We want the higher math scores that other countries have? Then why not just do it like they do. Seems simple enough.

Anecdotally, my university offered two parallel series of math courses for calculus and differential equations: traditional and using Mathematica. Everyone I knew who took the Mathematica courses were much, much weaker when it came to applying the concepts to engineering problems. They had no fundamental understanding of how integrals and differential equations worked; all they knew was how to plug a formula in and change the numbers.

Now, maybe the students who were lazier gravitated towards the Mathematica series, so the output was less impressive. But the fact that they passed at all raises doubts, in my mind, about the structure of the "let's do it on the computer" courses.
posted by sbutler at 1:43 AM on November 15

I gotta say, whenever I hear someone using the phrase "political correctness," I really just turn right the hell off.

"Political correctness" is not, technically, something that exists. "Political correctness" is what you blame when you have neither the cerebral fortitude nor the intellectual honesty to face challenges that take you outside of your personal comfort zone. It's a handy catch-all stock phrase for people too lazy to engage in even the most limited degree of self-reflection.

I don't know if the phrase itself was used in the article, but the fact that it was used in the FPP made me flag it. But I didn't want to move on until I pointed out the silliness of "political correctness."
posted by hifiparasol at 1:44 AM on November 15 [21 favorites]

To be serious though, I think there's middle ground between years and years of rote drills and giving calculators to kids in kindergarten. The key is to know the algorithms: once you know them inside and out, applying them either on paper or on a computer is easy.

What they should be taught is how to do arithmetic in their heads. There are a lot of methods to do this and they work pretty well. I they are more prone to error then paper but does that matter that much in this day and age? Anything important is going to be done by computer. People are more likely to have a cellphone within reach then a pencil, when they're out shopping or whatever.
posted by delmoi at 2:01 AM on November 15

When I was in third grade, they taught us the most incredible stuff, multiple base arithmetic, set theory. Then in fourth grade, it was back to the same old arithmetic drills. I didn't see that third grade math again until I was in college.

Turns out it was New Math, and the parents didn't like it, because 1+1=10 was a very disturbing idea to them. So that one year was the only time we saw it.

I'm of the opinion that kids can learn a hell of a lot more mathematics than the simple arithmetic we stick them with, and the earlier you teach it to them, the better they'll understand it.

From the article: (my expertise is in reading research, K–12 standards, and teacher education)

Sounds like exactly the right person to be critiquing the math curriculum. No doubt she knows a lot more about teaching math than math teachers. Perhaps the NCTM could give her some advice on teaching reading.

I notice that while she is not shy about naming those she disagrees with, she can muster only one actual mathematician who possibly agrees with her...assuming his decade-old quote hasn't been pulled out of context.

On the one hand, she seems to be arguing for higher standards in math teaching. On the other hand, she seems to be very dishonest. So while I am happy to agree with the raising of standards, I am not so ready to jump on her hobby-horse of accusations.
posted by Jimmy Havok at 2:04 AM on November 15 [1 favorite]

The overuse/misuse of quotation marks "sucked", as did this quote:

Teacher-directed learning goes out the window, despite its demonstrated benefits for students with learning problems; instead, schools should embrace “student-centered” math classrooms.

Student-centred math classrooms must be directed by teachers. What would the teacher's role be if they weren't?
posted by pick_the_flowers at 2:05 AM on November 15

What they should be taught is how to do arithmetic in their heads. There are a lot of methods to do this and they work pretty well. I they are more prone to error then paper but does that matter that much in this day and age? Anything important is going to be done by computer. People are more likely to have a cellphone within reach then a pencil, when they're out shopping or whatever.

Mental arithmetic is fine and dandy (hell, I did UIL Number Sense in high school which is all about mental math), but you're not going to do long multiplication or division in your head. Learning math is not just for being able to balance your checkbook. You need to be at least familiar with the basic arithmetic algorithms if you want to be able to understand the more complex and difficult ones later on.
posted by kmz at 2:18 AM on November 15

The Royal Dutch Academy of Science looked into this, because there is a lot of criticism in the Netherlands on a popular math teaching method as well.

Turns out, it makes no difference in what way children get their math education, but it makes a lot of difference who teaches them. A lot of teachers lack basic qualities:

3. The key to improving mathematical proficiency lies in the teacher’s competences. Teacher training and post-graduate courses have been seriously undermined.
The Ministry of Education, Culture and Science should subject teaching training programmes to a thorough investigation and encourage post-graduate training in mathematics and mathematics teaching.

source: the summary on page 11 in this Dutch pdf.
posted by ijsbrand at 2:21 AM on November 15 [3 favorites]

Remember, each school district, each state has their own guidelines for how things should be taught. That's the biggest problem with making sweeping statements like "Math education is like this in the U.S!" Normally you're only talking about what you're familiar with, which could be totally different from how average kids are taught.

From what little I understand of the issue, this is not generally true; there really is a de facto national curriculum due to how the textbook publishing world works. It stems from the fact that certain states (22 out of 50) are so-called 'adoption' states, which means that on a regular six year cycle they approve a list of texts for use statewide. If a publisher doesn't make the list they can't sell any textbooks in that state for that whole cycle, which is ruinous to profits. Since it's also too costly to develop multiple parallel editions, this means publishers essentially only worry about those 22 states' curricula and ignore the other 28. To make matters worse, Texas, California, and Florida (all adoption states) account for approximately a third of all total textbook sales so the publishers further narrow their focus to producing something that must absolutely comply with the requirements of the boards of education of those three states above all else. If the Texas curriculum states that math is taught a particular way, there's a good chance that means that it's taught that way nationwide as a result.
posted by Rhomboid at 2:26 AM on November 15 [1 favorite]

If the Texas curriculum states that math is taught a particular way, there's a good chance that means that it's taught that way nationwide as a result.

And everyone knows that Texas is a hotbed of liberals.
posted by Jimmy Havok at 2:29 AM on November 15

You need to be at least familiar with the basic arithmetic algorithms if you want to be able to understand the more complex and difficult ones later on.

I disagree. Kids should understand the basic ideas behind natural numbers, like prime factorization and so on, but I don't think knowing long division is very helpful. I never needed it in high school and college, when I had a calculator that worked on polynomials just as well as it did on integers.

But the point is there is a difference between "knowing" the basics of the algorithm and being forced to apply it over and over and over again in order to get "good" at something you will never use outside of an elementary school classroom.
posted by delmoi at 2:29 AM on November 15 [1 favorite]

If you know math, you have superpowers.

I know math, and I have superpowers.

Give me a two digit number that ends in a five and I will square it for you in my head. It's an easy trick that depends on the fact that (a + b)² = a² + 2ab + b².

Drop a ball from a height and I can tell you when it hits the ground. I can tell you how much beer and how much whiskey to blend if you want a nasty drink with same alcohol content as wine, because that's just a system of two equations in two unknowns.

I can blow your mind. I know about higher orders of infinity and I'm completely at home with higher dimensions. My superpowers might crush weaker minds, but they also lead to exquisite beauty. I see patterns. Patterns in nature are my friends.

If you know math you will have superpowers beyond anything you could ever have in a video game.

That's worth it, kids.
posted by twoleftfeet at 3:02 AM on November 15 [3 favorites]

Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x].
posted by netbros at 3:21 AM on November 15

Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x]

People have actually wasted time on that one when they could have been worrying about why the golden ratio =-2 sin(666)
posted by twoleftfeet at 3:37 AM on November 15

Oh how I loathe the phrase politically correct.
posted by molecicco at 3:38 AM on November 15 [1 favorite]

delmoi, your comments give you away as someone who has never stepped foot in front of a group of students to teach them anything remotely concerning math. I'd give you two minutes in front of a group of 15 year olds before pulling your hair and screaming "what do you mean you don't understand what one over three means, it's a fraction! What do you mean what's a fraction? Okay, just stop. Can anyone tell me what 7 times 4 is. DON'T COUNT ON YOUR FINGERS, HAVEN'T YOU MEMORIZED IT!"

I sometimes teach an SAT prep course at this all-girls boarding school, and about half of the girls are from China and half are Americans. When we get to the math, I just have the Chinese girls work on their vocab flashcards, because they're so bored by the math, while the american girls need a five minute lecture on what a "variable" is. When the American girls ask the Chinese girls why they're so good in math, they just sort of roll their eyes and go, "we learned this stuff, like, TEN years ago." It's really embarrassing, to be honest.

The fact is, our childrens ain't be learning basic stuff, and that's a problem. I blame horrible teachers and poor curriculum, but to suggest that we just stop teaching kids paper and pencil arithmetic ignores the fact that until a student the basic principles of arithmetic and then algebra, nothing more can really be taught. Once they're lost on fractions, or variables, or linear equations, or whatever, they're lost.
posted by billysumday at 4:23 AM on November 15 [4 favorites]

I'll tell you the sentence where I stopped reading:

Some influential educators sought to dismiss the traditional curriculum altogether, viewing it as a white, Christian, heterosexual-male product that unjustly valorized rational, abstract, and categorical thinking over the associative, experience-based, and emotion-laden thinking supposedly more congenial to females and certain minorities.

This kind of content-free strawman tirade has no place in an article meant to be taken seriously. The ironic thing is, I have a degree in math. I might actually have agreed with the author -- if her article emphasized the mathematical shortfalls instead of appealing to the conservative social idea that it's all PC educators' fault.
posted by cotterpin at 4:47 AM on November 15 [1 favorite]

TIME Magazine currently has an article about Five Things the U.S. Can Learn from China which includes some obvious stuff about how the U.S. should try to be at least as good as China in mathematics.
posted by twoleftfeet at 4:50 AM on November 15

The reason hippie-sounding methods were adopted by teachers is because they worked better than standardized methods. Since the 80s, conservatives have busily attacked student-centered methods and every time they win, they make education shittier, then blame the hippies for education's shittier state.

Up here in Ontario, we instituted a stern, standardized-test system. This kicked hundreds of students out of the school system. Now the province is desperately inventing methods to get them back, including special diplomas for basically showing up and continuing to breathe for the entire assessment period.

See, conservatives want their descendants to feel just as smart as they did in the 50s and early 60s, when they learned by rote and anyway they could get in as a legacy or enter Dad's business. Who gives a shit what happens to the kid with crappy shoes?

The problem (besides the reprehensible nature of this viewpoint) is that the 50s and 60s featured a society that thrived on caste-based education so that rather than getting uppity ideas about knowing things, the underclass could jump right to mines and canneries and whatever other crap poor people do. But now, more jobs require some sort of education so it doesn't work.

In other news, you can find a shitheel with a degree to say just about anything. Sandra Stotsky is an enforcer for that most odious of conservative education causes, the charter school. Charter schools are shitty schools that tend to subtly resegregate and are often run as for-profit enterprises, but are funded by the government -- y'know, like the way prisons in the US get managed. Listening to her talk about education is like listening to global warming opinions from scientists in the fossil fuel sector.
posted by mobunited at 4:54 AM on November 15 [4 favorites]

but to suggest that we just stop teaching kids paper and pencil arithmetic ignores the fact that until a student the basic principles of arithmetic and then algebra, nothing more can really be taught.

I think I have made it very clear that I don't think they shouldn't be taught "the basics" but you're making a kind of error yourself when you consider "pencil and paper algorithms" to be "the basics". I've never "memorized" a multiplication table, Although I did happen to know 4*7 off the top of my head.

Obviously someone who learns mental math, which is what I was advocating would have no trouble knowing what 4*7 is or what 1/3 "means". Duh.

The whole reason that those kids don't know any math is because it's socially acceptable for people not to know any math. A big part of the reason, I think, is that it's just not really applicable to most people's lives anymore. Hardly any jobs actually require arithmetic skills. Any math that's done in business is going to be done in excel, or more advance tools.

Obviously people need to understand the concept of addition, multiplication, division, and exponentiation in order to understand Algebra. But I don't see why you think knowing these pencil and paper systems are necessary.

In my view "the basics" of math is actually stuff like set theory. Kids would be better off learning that, which aside from being more interesting would actually provide them with a much stronger basis to learn higher math.

But my over all point is that there is a difference between "knowing the basics" and being able to crank out 30 long division problems an hour or whatever.
posted by delmoi at 4:54 AM on November 15 [1 favorite]

I'll tell you the sentence where I stopped reading:

I actually read the whole thing, because I wanted to make sure my rant about how 'traditionalism' was the real problem applied. But it turned it it didn't apply because she made no concrete suggestions whatsoever. So I couldn't complain about her arguing for traditionalism, because she made no such argument. She didn't argue for or against any particular technique at all.

It's all just a rant about stereotypical "liberals" (although she doesn't use that term) that only exist in the minds of rush Limbaugh listeners.
posted by delmoi at 4:58 AM on November 15

The problem (besides the reprehensible nature of this viewpoint) is that the 50s and 60s featured a society that thrived on caste-based education so that rather than getting uppity ideas about knowing things, the underclass could jump right to mines and canneries and whatever other crap poor people do. But now, more jobs require some sort of education so it doesn't work.

Oh, and of course they didn't have computers. That was the real issues Businesses needed people who would just sit, all day long and calculate math problems. In fact their job title was often "computer". Computer was a job before it was a thing. It makes a lot of sense, if you have business like a bank or something that depends on accurate math and you don't have a computer, to use a pencil and paper technique.

But that's the real change.
posted by delmoi at 5:01 AM on November 15 [1 favorite]

I had an encounter with student centered learning in my high school honors geometry class. I still know nothing about geometry. It just didn't work for me.
posted by dortmunder at 5:01 AM on November 15