Well, turns out that Noah Smith has made my last post for October an easy choice.
It all began when he and Miles Kimball declared that there’s only one difference between kids who excel in math and kids who don’t—the first group work hard, the second group doesn’t.
Robert VerBruggen did some neat research showing a strong correlation between ASVAB scores and algebra grades and even with my normal caveats about grades, that’s strong support for the notion that “smart” has something to do with “good at math”.
Then Steve Sailer chimed in with a great bit of snark on restriction of range, having picked up on a gem of a quote that I’d missed:
On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
Hahahaha. Oh. Okay.
But then, Noah Smith pops in and doubles down in the comments section:
Even students at the 20th percentile of IQ can do high school math pretty well. I’ve taught them to do it many times. Dumb as a box of rocks, but a box of rocks can do algebra.
I instantly asked for a cite. Then I saw he’d made a similar claim at his own blog:
But you don’t need to be a math whiz to do algebra. Someone with an IQ of 70 can handle that, I bet. Do you have any evidence to the contrary?
So I tweeted it and he responded—well, I have no idea how to link twitter conversations, but here’s some of it. Smith then went on to snark at me for not proving my claim, somehow forgetting that he’d made two claims that I was asking him to support. Hal Pashler of the Learning Attention and Perception Lab agreed that documentation of algebra proficiency in low IQ students is important.
The tone of Smith’s response makes me wonder if he understands what he has said—and what it means in the world of education. Similar claims include:
“All my clients lose 50-100 pounds and keep it off. Permanently.” said the nutritionist.
“Our little country town lives in perfect harmony with the Palestinians.” said the Israeli farmer.
“Well, I get 60% of black voter support,” said the Texas Republican.
“Oh, I just logged onto Healthcare.gov and signed up for a cheaper policy for my family,” said the Florida plumber.
“Yeah, I just dip lead into this little tincture I cooked up and shazam! gold.” said the alchemist.
I mentioned that I had taught two students with documented low ability. Smith misunderstood, I think: Is your only quantitative evidence the fact that you personally were unable to teach two kids algebra?
That’s not what I said, of course. I was emphasizing that I could document an experience of teaching low IQ kids, and it’s actually quite unusual for teachers to have that info. Because I write about cognitive ability as I experience it in the classroom, I have mentioned time and again that I work with students on the lower third to the middle of the cognitive ability spectrum. But perhaps I should make clear that I’m talking about the ability spectrum you see in high school, which weeds out the bottom. Math teachers don’t run into all that many genuinely special ed kids, as opposed to those with mild learning disabilities.
I believe most states have two broad categories of special education. The kids are either educated as part of the general school population or they aren’t. The kids with mild disabilities–executive function, attention deficit, dyslexia—are educated with the others. These are kids who have the same academic requirements as anyone else, except they have a legal document defining their accommodations: extra time on tests, sit up front, use of a calculator, whatever.
The kids with severe disabilities–emotional, mental, physical—who can’t be educated with the rest, have their own classes. In most schools I’ve worked in, there’s more than one class. There’s the class for kids with mild IQ deficits and emotional difficulties, the class for the severely autistic or severely retarded, and so on. At the high school level, we don’t really call it “mainstreaming”—that’s much more of an issue in elementary school, as I understand it. Some of the kids in “special day classes” are capable of attending general ed classes in their strong subject (remember that not all disabilities are cognitive), sometimes in math. But high school teachers aren’t ever dealing with severely disabled children unless they teach special ed.
So who goes into special day classes, and who goes to general ed? Specifying a particular IQ as a cutoff is like standing up and saying “YO! Sue Me!”. But an IQ of 80 is generally considered the cutoff between “normal low” and “borderline retarded”. So I’ve always assumed that somewhere between 75 and 85, kids are deemed better off in their own classes.
Then in the general population, in math, you know that the basement of your class will usually rise slightly with each step, so the lowest IQ in your math support or pre-algebra class is usually going to be lower than the lowest in your algebra class, which is probably lower than geometry class, and so on. Using what I knew about special ed unofficial placement, and what I know about my schools (usually 5 or 6 on the Great Schools scale), I have used 90 as a rough bottom of the range of IQs I teach in public schools.
But I never had any hard knowledge of that until last year, when through a complete coincidence I learned the IQs of two of my students.
Tre, who was in a math support class of mine last year, had phenomenal retention of any concrete fact he learned. Total inability to grasp abstract concepts. Couldn’t estimate. Couldn’t isolate x. Couldn’t figure out what the slope of a line was. I’d ask him things like “if you rolled a ball down this line, which one would go faster?” and he’d struggle for minutes just to figure out what I meant. If it wasn’t real, it didn’t exist. He got pretty good at percentages without actually understanding them—but 20% was divide by 5, 25% was divide by 4, 10% was divide by 10. He was motivated. Great kid, fantastic athlete, failing algebra for the fourth time kept him off the his strongest sports team his senior year and broke his heart. But he took up a second sport and made the state finals. He seemed a bit slow in conversation, but nothing that would mark him as really low intellect. He held a job, worked hard, was a popular kid. There was no way he would be passing the test, and when I communicated this to the AVP, she said, “He was not classified correctly, for various reasons”—one of the reasons probably being that Tre is black. She mentioned his tested IQ that his parents included in his file, and it was well south of 90, but still much higher than 70.
Mohammed was in another of my math classes last year. Unlike Tre, does not communicate his mental disability immediately. He talks quickly, cracks decent jokes, likes people around, while Tre was happier off in a corner listening to music. It took me a while to realize that Mohammed, who is neither black nor Hispanic, wasn’t retaining any information at all. Once I did realize this, I looked more closely at his IEP and saw he was a special day students with an IQ in the mid-80s. Also an excellent athlete, but very different from Tre. No fact grasp at all. He couldn’t remember what you told him five minutes ago, much less yesterday. But he could solve a simple algebraic equation with a calculator. He’d have to relearn it almost every day, but he had the ability to abstract that Tre lacks. He very badly wanted to move on to the next math class in the sequence, against the recommendation of his special ed adviser, and nagged me constantly to support him in this quest. I was willing to help him try, but his sport kept him out of the classroom a couple days a week for nearly a month, and everything I’d managed to do to keep him not rolling backwards was undone. So I passed him and talked him into an easier course.
The point is this: Tre and Mohammed, while not obviously or actually “dumb as a box of rocks”, as Smith indelicately put it, were noticeably less able than almost all my other students in five years, despite considerable motivation on their part and a huge amount of support on mine. I have probably had a couple other students with as low intelligence, but couldn’t be sure because they were never around or made class miserable by misbehaving. This suggests to me that my rough approximation of my students’ cognitive ability is correct. I haven’t taught many kids with IQs south of 90, and most of them my lowest IQ kids were in my Algebra I classes.
And the bottom of my particular class distribution is not capable of algebra mastery. Algebra survival, sure. Ability to solve a simple equation with advice on how to turn it concrete, yeah. Remember with lots of reminders that 3-5 is a negative number, yes. Remember with lots of coaching that y=mx + b is a way to describe a line, okay. But not anything approaching knowledge, and you’ll have to cover it all again in the next year.
Since I began this, Robert VerBruggen did additional ASVAB crunching and found that kids who scored low on the ASVAB (2%) got mostly Ds and Fs, but some As in Algebra II. But he also pointed out “Not really clear that all of them both (A) genuinely have IQs that low and (B) genuinely learned algebra.” And here I’ve already linked in my post on fraudulent grades. As we teach algebra today, a kid with an IQ of 90 can’t get an A in algebra I, much less algebra II, unless his teacher is lying.
I’d be surprised if many 70 IQs got around to taking the ASVAB, but the caveat is this: 70 IQs would not be uncommon in a predominantly black population. My current school is 10% black and that’s the highest African American population in any school I’ve taught at. My sample size for blacks, total, is maybe 100—tutoring, teaching, everything–in 11 years. And most blacks in this area are high functioning. It would not surprise me at all if I only ran into blacks whose IQs were 80 or higher. I have many excellent black students who are top performers.
I do not believe that a 70 IQ of any race can master Algebra I, much less Algebra II. But I want data. I have been asking nearly as long as I’ve had this blog if anyone can show evidence of successful mastery of algebra by IQs less than 100. I don’t believe it exists, at least not since 1975, when we began ignoring IQ. And I’m absolutely shocked that anyone, even a liberal, even someone who sneers at IQ, would openly brag that it was no big deal to teach advanced math, much less algebra, to kids with IQs below 90.
Maybe Noah Smith is already trying to walk this back. I can’t find the original tweet to me in which he said math tutors are having great success with kids of 70 IQ. Here’s my response to it, but I can’t find the original tweet. Apologies if it’s there and I missed it, but most of the rest is there. He’s now saying to Robert VB (don’t make me type it out again!) “some” kids could pass but of course, this all began because he said an IQ of 70 could handle algebra and that he routinely teaches algebra to kids in the bottom fifth.
As I tweeted, if Noah Smith were right, we’d never need special education. We’d be teaching kids with 70 IQs algebra, a little geometry, maybe writing analytical essays on Of Mice and Men. But Jim, one of my commenters, had a much better analogy: the Supreme Court has made it functionally impossible to execute murderers with an IQ below 70. So someone with an IQ of 70 knows—barely—that it’s not a good idea to kill people, but can handle the quadratic formula and rational expressions, no sweat? Really?
It’s really quite simple: Noah Smith is almost certainly talking out of his posterior. But boy howdy, would I love to be wrong. Show me these IQ 70 kids learning algebra. Please.
I was bound and determined to get this in before my WordPress account thought October was over. Apologies for typos, I’m cleaning it up.
Second note: Tre and Mohammed are both pseudoynms, and I changed details about each. I went back in and changed even more info, just to be certain.