Why Americans suck at it:
American institutions charged with training teachers in new approaches to math have proved largely unable to do it. At most education schools, the professors with the research budgets and deanships have little interest in the science of teaching. Indeed, when Lampert attended Harvard’s Graduate School of Education in the 1970s, she could find only one listing in the entire course catalog that used the word “teaching” in its title. (Today only 19 out of 231 courses include it.) Methods courses, meanwhile, are usually taught by the lowest ranks of professors — chronically underpaid, overworked and, ultimately, ineffective.
Without the right training, most teachers do not understand math well enough to teach it the way Lampert does. “Remember,” Lampert says, “American teachers are only a subset of Americans.” As graduates of American schools, they are no more likely to display numeracy than the rest of us. “I’m just not a math person,” Lampert says her education students would say with an apologetic shrug.
Consequently, the most powerful influence on teachers is the one most beyond our control. The sociologist Dan Lortie calls the phenomenon the apprenticeship of observation. Teachers learn to teach primarily by recalling their memories of having been taught, an average of 13,000 hours of instruction over a typical childhood. The apprenticeship of observation exacerbates what the education scholar Suzanne Wilson calls education reform’s double bind. The very people who embody the problem — teachers — are also the ones charged with solving it.
…Left to their own devices, teachers are once again trying to incorporate new ideas into old scripts, often botching them in the process. One especially nonsensical result stems from the Common Core’s suggestion that students not just find answers but also “illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.” The idea of utilizing arrays of dots makes sense in the hands of a skilled teacher, who can use them to help a student understand how multiplication actually works. For example, a teacher trying to explain multiplication might ask a student to first draw three rows of dots with two dots in each row and then imagine what the picture would look like with three or four or five dots in each row. Guiding the student through the exercise, the teacher could help her see that each march up the times table (3×2, 3×3, 3×4) just means adding another dot per row. But if a teacher doesn’t use the dots to illustrate bigger ideas, they become just another meaningless exercise. Instead of memorizing familiar steps, students now practice even stranger rituals, like drawing dots only to count them or breaking simple addition problems into complicated forms (62+26, for example, must become 60+2+20+6) without understanding why. This can make for even poorer math students. “In the hands of unprepared teachers,” Lampert says, “alternative algorithms are worse than just teaching them standard algorithms.”
No wonder parents and some mathematicians denigrate the reforms as “fuzzy math.” In the warped way untrained teachers interpret them, they are fuzzy.
It’s a long, but interesting, and depressing article.
I should note that I was one of the kids who suffered from the “New Math” in the sixties, but I had a great algebra teacher in junior high (I forget her name, but she was a black woman), and good ones in high school as well. We actually learned calculus and analytic geometry from Mr. Troyer.
[Update a while later]
The more I think about this, the more furious I get that we have these worthless schools of “education” that don’t even teach teachers to teach.
Let’s hope Salman Khan and other YouTube teachers can make an end run around the teacher’s guild.
The whole process of training teachers, particularly the process of qualifying candidates for teaching degrees, needs to be seriously overhauled. I am seeing some progress at the college level now, although with the Fed takeover of Common Core it looks like that could set back progress for another decade or more. I can’t think of any better first step than eliminating the US Department of Education.
YouTube can definitely be a great resource these days for parents and their kids. Years ago before that was an option, our son was struggling with a middle school math class. He loved math, excelled at it, but he just could not connect with this particular teacher on this material. I was discussing this with my brother in law who suggested I take him up to Barnes and Nobles and look at titles in that area; “most of the books are probably written by someone who is really skilled at teaching that subject, and their friends encouraged them to write a book”. He was right, we bought the one we liked best, and with that book my son sailed through the rest of the class. YouTube is even better with the full multimedia experience.
American students rank 25th in the world in math. But hey, it’s not so bad. At least we’re still in the top ten.
Another keyboard in the trash…
Rand, thanks for finding that very interesting article. A few thoughts, kind of related-
1) I hate to say it, but there is a gap of about 15 points in the mean IQ between the kids in a Japanese school and the kids in a typical American big city school. The statement in the article about how the students in the two countries aren’t different is false.
2) Some of the more abstract ways of doing problems are probably just inaccessible to many kids, because they rely on kinds of thinking that are too tough for the typical below-average IQ student.
3) I’ve been thinking a lot about the Common Core and Next Generation Science Standards lately. The way they’re aimed at higher levels of thinking is nice in Perfect Happy Land, but not so good for the real world, where half the kids are below average. I suspect that when more states start giving tests aligned to those standards, the tests will be shown to be essentially proxies for IQ tests. There’s already really good evidence, from New York scores, to support this idea.
4) By teaching math so abstractly, low-end students will be deprived of the kinds of rote math in which they could have had some success. My gut tells me that in a decade, our kids will be even worse off than now, because longhand, mindless, rote math (the staple of how I learned it, back in the 70’s, for example) won’t be taught in any form. Even the slower kids could do multiplication and division back in the day. But I suspect those children will be totally left in the dust in a school that teaches with these new methods.
The single most important math class I had was the day the teacher covered compound interest. A lot of kids in my class didn’t get it then, 30 years ago, and we did have a proper grounding in longhand multiplication and division. The kids suffering under Common Core (we’ve adopted something nearly identical in Alberta) have no hope of understanding compound interest, not even the diligent students.
That’s a feature, not a bug, for our self-appointed ruling class. The commoners won’t understand that their wealth is being confiscated.
I think the biggest problem with math in the US is the kids just don’t want to do it, and you can’t learn something when you don’t want to. And, a lot of that reluctance is due to cultural influences. Math just isn’t cool.
I just cannot resist:
http://www.bing.com/videos/search?q=new+math+tom+lehrer&FORM=VIRE3#view=detail&mid=98B189722A24C39DBB2F98B189722A24C39DBB2F
I do agree that kids today are lazier (well, certainly more distracted) than kids of my generation, but I won’t blame the kids for all the troubles. And while catastrophic home environments aren’t something the education system can’t fix, many of the problems are rooted in the system itself.
We aren’t Finland, but we could make more effort to get smarter people interested in teaching. Average education major IQ in the US is just above average (estimated at 110, from the study I saw). If you want teachers teaching high-order reasoning skills, the teachers should be easily able to use those skills themselves. In the NYT article Rand linked, there’s a comment that the US invented all these great teaching methods, but we don’t use them. I strongly suspect a lot of teachers just don’t have the capacity to teach that way. So if you pair barely-above-average ability teachers with below-average students, that’s not a mix destined for success. Radical thought: take masters and doctoral students and orient them towards teaching as a career. There aren’t enough jobs in universities for them anyway. Give them decent starting pay, maybe forgive some loans so it’s economically feasible for them, and see what happens.
Also, for specialty subjects like the STEM disciplines, state licensing requirements are onerous. If I were trying to design licensing requirements to keep experienced STEM people OUT of the teaching profession, I could hardly do a better job than the states have managed (at least, my own state). Going back and getting a teaching certificate can take a couple of years and cost $20,000 in some cases. For a mature adult with a family, that’s not feasible. (I suspect a lot of this is the unions trying to keep out the unwashed heathen rabble, but that’s another discussion.)
Finally, I think the Brits have it basically right with their exams that sort students. Trying to teach every student as if college is the expected outcome is silly; about 35-40% of high school graduates won’t go to college, and many of those who do, won’t graduate. Maybe that’s for economic reasons, but I suspect often they weren’t really capable of working at the college level anyway.
My gut tells me the public K-12 education system is just hopelessly messed up at the national and state levels, and in most big cities as well. There are some good districts out there, well-funded (though money isn’t everything) and with enough students to be able to offer high-end classes. Private schools, which are usually not bound by state standards, are more able to innovate and more easily separate ineffective teachers. They can still provide a good experience. There’s a reason politicians’ kids so often go to private schools…
Typo in prev post, should read, “And while catastrophic home environments _are_ something the education system can’t fix, many of the problems are rooted in the system itself.”