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.
November 1st, 2013 at 2:04 am
I’m not sure that you can’t teach 70-IQ people algebra, categorically speaking. You can reduce algebra to a succession of concrete operations and have even dimwits memorize them. Probably how the “Stand and Deliver” guy managed it.
November 2nd, 2013 at 4:06 pm
You can’t even reduce it to a set of concrete operations for 90 IQ people, although I wonder at that level if incentive and effort would improve that outcome. I thought this would work, too. Doesn’t.
November 4th, 2013 at 11:36 pm
Really? Hmm. Working memory is pretty malleable, though, so if you gave 70-IQ kids 10 hours of training on the dual n-back per week, then reduced algebra to the set of concrete operations, maybe…Of course, math education is nothing more than a working memory exercise as is for most students.
November 1st, 2013 at 3:22 am
I don’t agree at all with Smith. But you typed a lot of words and did little more than give two case studies. I can’t imagine anyone in the world who would be convinced by that much evidence.
November 1st, 2013 at 3:24 am
Sigh. Why oh why do people think I’m trying to prove anything? It was Smith who made the unfounded claim. If he can do it, I can do. And I gave a lot more than case studies.
November 1st, 2013 at 3:42 am
I don’t know. I’m reading it again and you’re talking about how awesome and knowledgeable you are. The worst kind of appeal to authority is when you claim yourself to be the relevant authority.
And you cite a study published on twitter (???) and someone who tweeted that there is a correlation, which isn’t in dispute.
Also it’s strange to write 1500 words making an argument when you’re not trying to prove anything.
November 1st, 2013 at 3:53 am
I’m talking about how awesome I am? Really? I grant you I’m a superlative person. But where did I mention me at all in that post?
Dude, I write 1500 words clearing my throat. When I get to 3000 words, it’s long.
1) summarize issue 2) explain special ed to people who aren’t clear how it works. 3) explain what that means vis a vis IQ and high school teachers 4) give my data points 5) Explain why they are relevant. 6) give my own assertions and explain why I’d love to be wrong.
Don’t see much about me in there. But maybe you just need something to dwell on, to avoid mulling your shortcomings.
November 1st, 2013 at 6:35 pm
murphy, this is a topically focused blog. its author rightly assumes readers have accumulated background info from prior posts. attempts to make each post a self contained proof would be repetitive.
also, they’re called anecdotes, not “case studies”, you prissy douche. and they’re useful because ER is credible.
November 1st, 2013 at 12:28 pm
The historically slow development of algebra makes the claim that it can be understood by people with an IQ of 70 ludicrous. My God, Archimedes did not understand algebra!
November 1st, 2013 at 3:32 pm
If Noah Smith is in possession of a reproducible technique of teaching algebra to people with IQ’s as low as 70 the economic value of his knowledge is probably in excess of the economic value of knowing how to carry out cold fusion.
November 1st, 2013 at 3:42 pm
“My clients lose 50-100 pounds and keep it off. Permanently.”
November 1st, 2013 at 3:55 pm
Given the massive costs of Type II diabetes the economic value of that knowledge is pretty high.
November 1st, 2013 at 4:01 pm
Somewhere in the world there may be somebody who knows how to economically extract gold from seawater. But if you come across somebody who claims to know how to do so the likilihood is that that person is a charlatan. Noah Smith is almost certainly a charlatan.
November 1st, 2013 at 9:17 pm
“Remember with lots of reminders that 3-5 is a negative number, yes. ”
How much “g” does it take to represent “3” on a mental number line and then move backwards? How much “g” does one need to recognize that when one moves backward a greater number than three units one will pass “0” and enter negative territory?
Is that a “g-loaded” task, it seems so easily understood because it can be represented in a concrete visual format.
November 1st, 2013 at 9:20 pm
Go talk to any algebra teacher about the crazy making inability of kids to get negatives. Or you can read some of mine:
November 15th, 2013 at 2:33 am
Morris Kline, in his wonderful book “Mathematics: The Loss of Certainty,” covers in considerable detail the difficulties that some Western mathematicians had with negative numbers even as late as the 18th century:
(If the link doesn’t work, Google the phrase “many objections to negative numbers were voiced”).
November 1st, 2013 at 11:45 pm
To add support to the idea that negative numbers are not as trivial as one might think, I’ll quote Darren (from over at rightontheleftcoast.blogspot.com). Darren teaches high school math and writes this:
“I find problems [for my students] with both rational expressions and negative numbers.”
From this post: http://rightontheleftcoast.blogspot.com/2011/08/one-of-many-stupid-ideas-to-come-out-of.html (scroll down into the comments)
November 2nd, 2013 at 10:18 am
Not gonna lie, my first reaction to “well, everyone can do X, if they’d only work harder!” is “well, fuck you too”. This might be less unusual, but I find being told that something’s too hard for me less insulting than a strong implication that I’m lazy and feckless.
And can’t a lack of effort (inasmuch as it’s a real problem) be a perfectly rational response to standards being too high? If you’re never going to meet said standards, why on earth waste your time? Why hinder and annoy the people who have a snowball’s chance of doing well?
(“Progressive” “logic” on tracking: being put in classes that reflect your ability is just DEVASTATING to students’ precious self esteem. Being exposed to differences in ability on a daily basis, and holding the stronger students back, making your differences an active irritant and hindrance as opposed to just another difference: TOTALLY ossum. I have friends who still spit nails at the mention of the weak students who made their classes a living hell simply by slowing everything to a crawl – I suspect it explains a lot of hostility to and disregard for those on the left hand of the Bell Curve, and think Steve Sailer’s insulation plan works just as well for cognitive ability as race.)
Why shouldn’t weaker students focus on things they can do well – or at least better, or which at the very least are more fun? How is pricing them out of the market (I know what I mean) meant to make them work harder?
November 4th, 2013 at 2:19 pm
Yes, my thoughts exactly. We have the idea that lower performance simply implies lack of motivation and therefore if you put the unmotivated students in with the motivated students, maybe they’ll pick of the ‘learning fever’ so to speak, rather than say, assault/verbally abuse/cheat from the higher performers. There is also the idea that higher performers have all these advantages (so many books in their homes, richer parents, whatever the flavor of the month reason for achievement difference is) and therefore could use some time slumming with the regular kids in order to know what it feels like.
Having experienced the effects of both I have to say that I envied kids in special gifted schools when I was young but now that I’m older I find I’m more ambivalent about all the bullying. Really, I was lucky to be in a high-school where the kids weren’t more aggressive. I was beat up and systematically verbally abused but never knifed, so I’ve got that goin’ for me which is good. My experience leads me to think the exact opposite: that working with someone way over your level is discouraging and someone way below feels more like a puppy than a cohort, you worry more about them biting someone or soiling the carpet than you expect a meaningful contribution to discussion.
November 2nd, 2013 at 12:56 pm
If you’re ever outed – I hope those are not their real names.
November 2nd, 2013 at 4:04 pm
I never use real names. Minor details have been changed.
November 2nd, 2013 at 1:16 pm
First you have to know that all of you are on the same page and using a s.d. of 15 (as opposed to the s.d. 24 that’s used on Raven’s). This is important because a person so gung-ho optimistic as Noah will have the incentive backclaim the 24 s.d. as their claim (in which an IQ of 70 is equivalent to an s.d. 15 IQ of 81/82 – right in the center of the bottom quintile).
I also bet it not unlikely that Noah, if he’s validating his claims at all with his own students, is using local percentile achievement/NCLB test results instead of IQ test results to determine the bottom quintile (with corresponding dropping of the true bottom percentiles). I’d assume those statistics are much easier for a teacher to access. If not, then there is a professor (Australian – with it’s “tall poppy” culture) on the Chronicle of Higher Education who makes a proud claim to have purposely bombed his IQ test and received a 70. I’m sure he had no difficulty learning algebra. I’m also sure his IQ is 3 to 5 s.d. higher than his IQ score. But all you need is one student like that for a teacher to sincerely make the claim Noah made.
November 2nd, 2013 at 4:28 pm
I think you’re right about the possibilities. I think that Steve Sailer’s post about “restriction of range” is absolutely right. Noah Smith had no idea that the low ability kids he was dealing with were no where near the bottom of the range. If he was routinely helping kids who struggled with math to become successful at math, he probably never saw kids with IQs below 100. It’s not at all unusual for a kid to finally “get it” and go from far below basic to proficient. It just means that the kid was never an IQ of 90. Cail someone made the same point at Steve’s blog.
November 3rd, 2013 at 2:06 pm
I’m reading through the comments there now and they are good.
November 6th, 2013 at 1:06 am
No test uses SD 24 anymore, except the CCF, which is not frequerntly administered.
November 2nd, 2013 at 1:26 pm
It took a long time historically for negative numbers to become accepted so maybe the concept of negative numbers is pretty counterintuitive for most people.
November 2nd, 2013 at 1:52 pm
It is so fucking hard to “work hard” on the banal, on someone else’s idea of an academic good time, while simultaneously watching your dreams go further and further away. And while hearing that it’s good for you and is providing opportunities to you.
That their attitude will priviledge and encourage this set up, this catch-22, in formal schooling is one of the two worst things about Noah and Miles’ position.
Give opportunity to everyone, genuine opportunity to excel in their abilities and toward their dreams, not the “thank you sir may I have another” hazing ritual that is post-Socratic education (Socrates would not recognize the academy of today).
Sick jerks. They know not what they do in encouraging a “work hard” ethic instead of a “critically analyze and reject when proper” ethic.
November 2nd, 2013 at 1:55 pm
I’ve had a tiny bit of experience with retarded adults and I noted that sometimes they can seem fairly normal. I remember some with a good sense of humor. In general their brains are not totally shattered. Much of their neurological system is probably working normally but somewhere in this incredibly complicated system something is not right. It could be a tiny thing – a chemical reaction that is not occurring at a normal rate because the reactive locus of some enzyme is slightly distorted or something like that. With something as complicated as higher cognitive abilities a seemingly tiny defect or perturbation could screw up the whole thing.
November 3rd, 2013 at 11:19 am
I don’t even understand why Noah Smith would want to teach algebra to kids with low IQs; I guess rather his motive is to pretend that the world is egalitarian and high achievers are only so because of privilege.
An interesting feature of the modern, computerised world in my view is that the proportion of students that need to be good at STEM subjects is diminishing. In future we will need a relatively small elite who are able to innovate with the assistance of a deep understanding of science and technology, an intelligent managerial class, and a high proportion of the workforce that work in relatively unskilled roles providing services to the community. (Admittedly some of these service sector jobs will be highly skilled, such as teaching and healthcare.) Hence schools need to become much more vocational.
November 3rd, 2013 at 2:11 pm
From my POV, the issue with this is that the “relatively small elite” may not be the best people at those jobs, or those who would be most fulfilled at those jobs. I know that some people get Ph.D.s in the sciences because of family pressure, economic incentive, or because of the social cachet of the title and discipline.
Whereas those like me are genuinely fulfilled by the discipline, genuinely talented in the discipline, but can’t easily tolerate the authoritarian regime that awards the titles. Is our lot only ever to be the technician following someone else’s orders? Or the crank tinkering around in our bedrooms or garages?
November 3rd, 2013 at 4:59 pm
No one ever said life was fair! But fairer perhaps in capitalist systems than their alternatives. I agree with you though that life often unfairly rewards style over substance.
November 3rd, 2013 at 5:46 pm
Maybe in a couple more millenia human societies will evolve to the average level of interpersonal fairness of the stone age tribal societies. At least capitalism and communism both, and everything in between, are a hell of a lot fairer than the kingdoms of 2,000 – 4,000 years ago.
November 4th, 2013 at 6:52 pm
This idea (ER’s not the professor’s) is actually applicable at every IQ level. At each IQ level, there are some math concepts you cannot follow and work through, however hard you work. I am going through some Non-liner PDEs now, and it is killing me; I see that however hard you work, I cannot solve it. Same thing with REGEXes.
November 4th, 2013 at 8:43 pm
Me, too. I have a lot of trouble with spatial things, so both vectors and matrices are hard.
November 4th, 2013 at 11:22 pm
and functional programming, and biology, and statistics including R, and so on and so on. My self-estimated IQ may be too high.
November 4th, 2013 at 11:31 pm
Not necessarily. These days, people focus primarily on math ability, but high verbal is much rarer.
November 5th, 2013 at 12:55 pm
Any chance you have had difficulty with mental arithmetic as a child or adult? Contrast between my wife and I it seems to have a heavy spatial load when using arabic numerals and carrying. I doubt our working memory capacity is all that different, which is likely the other major component of mental arithmetic. Working with her for a few days we were able to come up with a strategy that worked (something that years of teachers throughout K-12 never taught her).
November 5th, 2013 at 1:56 pm
No, I had good mental arithmetic skills. I was “good” at math, but had trouble as it got more advanced. WHat I learned to do later in life was compensate, using logic for spatial. I could probably do that with calc, vectors, and the matrix, but it would take time. One of my best students wants to learn vectors on his own time, so I’m going to give it a shot. Will report back.
November 4th, 2013 at 11:35 pm
That’s true. I’ve never met anyone even close to my verbal IQ, but I know quite a few who are vastly superior to me in terms of mathematical or visuospatial ability.
November 5th, 2013 at 5:50 pm
Can you or educational realist explain the meaning of verbal IQ? I am not arguing against or for it, but he mentioned high verbal is rarer. What is the import of verbal IQ upon cognitive ability? Can people with higher verbal IQ read and understand better?
November 5th, 2013 at 5:58 pm
No one really knows. I wrote about this here: https://educationrealist.wordpress.com/2012/01/28/the-gap-in-the-gre/
November 4th, 2013 at 7:11 pm
vijay – What does REGEX mean?
As for non-linear PDE’s does anyone know much about them?
November 4th, 2013 at 11:24 pm
Regular expressions; just google them.
On Non-linear PDE, exactly! I have been staring at a few for 2 days now.
November 5th, 2013 at 1:30 pm
Oh vijay – Are regular expressions or regular languages covered in Eilengberg’s book on automata and languages?
November 5th, 2013 at 3:12 pm
You are way past me; I am an engineer who might have difficulty understanding that book.
November 6th, 2013 at 1:03 am
Having taught computer science to gifted high schoolers and also having taught 5th and 4th grade at a school for children with LDs (small classes with student IQs high lighted in their records). I think many teachers have no idea about teaching children with 70 IQs.
I have taught math classes to student who could hardly read but had high IQs (135 and above). Math is where they excelled. Drop the IQ to below 85 and math ability dropped. (By the way I never looked at a child’s IQ until I had taught them for a few months. Some children, especially cute kids with good social skills seem bright until they have to learn something. Others may not seem so bright until you have them in a class and realize the kid may have difficulty expressing herself but she is brilliant.I got to the point where I could guess a kid’s IQ with in 6 points before looking it up.)
There are 5th graders who can’t hold up 8 fingers without counting them. These students were doing multiplication but they didn’t really understand it despite using computers, munipulatives, etc. Yeah, they sort of knew multiplication was equal groups of stuff, but if they said 8 times 3 was 32 and were told that 8 times 4 was 32 (as a hint) often they would wildly guess: 53, 88, 74? They might know 9 + 2 was 11 but 29 plus 2 wasn’t obvious.
Multiplication was often easier than subtraction which had to be relearned when they got to long division. These are children who can’t apply what they have “learned.” Some of them were hard workers and some had more or less given up. Most of them are a year older (having repeated kinder) so we are talking 12 year olds having difficulty with basic arithmetic, while in other classes some 13 year olds are being introduced to algebra.
Many of these students were sweet, sometimes talented children. Some were great at sports, or art, or drama. Most didn’t not appear to have low IQs until they had to learn something academic. Another problem with teaching students with low IQs is that they often have limited vocabularies. I can’t imagine getting through algebra with students who don’t know what the word slope means.
I am not saying that none of them could have learned algebra sometime in their life. I question the effort that would have gone into trying to teach them algebra. I also question the definition of “learning algebra.”
November 6th, 2013 at 11:06 am
If “Clever Hans” could be taught arithmetic maybe kids with IQ’s of 70 can be taught algebra.
November 17th, 2013 at 2:02 pm
“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. ”
This is a very common thing in Internet Argument, and it drives me up the bloody wall. It’s like, “you’re playing it up like you’re my intellectual superior and yet you’re forgetting that the burden of proof lies on the positive claimant?”
January 1st, 2014 at 3:12 pm
[…] what they were taught, that teaching algebra is like banging your head with a whiteboard, and that no one has had success teaching advanced math to the moderately retarded, but I also talk about the joys of teaching kids with low motivation and low (for high school) […]
January 14th, 2014 at 2:04 am
I teach in Pennsylvania, where we now have the “Keystone Algebra 1” test that all our 9th grade students must pass. I currently teach Algebra 1 to 14 students, and our curriculum has several levels of Algebra 1, with this one being the lowest. I have several students with IQs of 80 (or lower) in this class. *Most* of the students I have cannot retain material for more than a few days – is that due to their IQ, their study habits or lack thereof, or general motivation? While I realize that studying and teaching gifted math students is much more fun and interesting, I feel that we neglect the other side of the curve because we can’t understand *why* our students don’t understand.
January 14th, 2014 at 2:11 am
Interesting! They were probably all classified incorrectly, if it’s IQ.
I think we neglect IQ because it’s way to touchy to mention. In earlier years, we studied IQ but in those days low IQs were just expected to drop out. So there wasn’t a lot of research done on teaching them. That’s got to be a frustrating class.
April 25th, 2014 at 12:49 pm
My son, adopted at age 5, never got an Iq score above 80 and sometimes even 79. He wasn’t in modified high school courses till 12th grade, mainly because (even though he had an IEP) we were never told that modified classes were an option. All students who were not in modified classes had to pass Algebra 1 to get their high school diplomas, with at least a grade of C. It was NOT an easy or watered down class. He passed, although he did have to meet with a math tutor twice a week to pass the tests. She had no idea he’d tested at low intelligence so she was sometimes impatient with him. He did- and does- feel “stupid” compared to others. But no one held his hand when he took those exams. So I am confused.
April 25th, 2014 at 12:59 pm
I also want to add that his tests were administered since he was 5 years old and from several different locations known for working with children- and later teens- with learning challenges. At age 5 he was classified as Borderline retarded? After all, is there a significant difference between an IQ of 79 and 80? I find that hard to believe. At age 22 he just obtained a score of 80 and yet, before that, he recently passed the written test for his drivers’ examination ( which was actually a computerized multiple choice exam). He could not sit still long enough to take standard classroom driving education classes so he did the online, state certified option ( which was as rigorous as the classroom exam). He then took the required driving class, although one on one with the instructor (no other students in the car).
April 25th, 2014 at 1:15 pm
I want to add that in spite of his achievements this far I know, from all the years raising him, that he will need supervision. I want to add that at age 6 he learned to read fairly quickly ( at a younger age than one son who is a lawyer) . As far as life skills go, he can prepare frozen pizzas and spaghetti, does his own laundry, can clean his room, is obsessive about his grooming (showers daily without being reminded, focuses on looking good and wearing “cool” clothes, et). He can takes leftovers from dinner to work and heat them properly in a microwave. He can drive to work with supervision (he hasn’t yet taken the road test to get his full license).
April 25th, 2014 at 5:59 pm
Yes, an IQ of 80 does not mean he is totally unable to function in society.
Pedro Guerrero has an IQ of 70, and was able to be a Major League hitter and position player.
Also, reading itself isn’t that “g-loaded” since it is just decoding the words and pronouncing them.
April 25th, 2014 at 1:25 pm
But he will never have the math skills to balance a checkbook. We have practiced this with him. Nor can he handle a budget although, with motivation ( having gas money when he gets a car), he saves some money from his paycheck (he can do this because he lives at home and doesn’t support himself). He also had to take vocational rehab classes to get a repetitive, simple factory type job at an institution for intellectually challenged employees. He was transitioned to that job through vocational rehab. Although we intend to set up a Special Needs trust for him, we are very worried about his future. He is also concerned and asks us often ” how will I get by without you guys?” We reassure him about his capabilities but I don’t really feel confident. I hope it is obvious that we have supported his independence, required him to hold a job, etc. He is often bored outside of work and has only one friend (who is of normal intelligence) and that friend, who has been there since grade school, may be pulling away. This hurts my heart. What do we do from here? We have been told he “falls in a gap” and is too intelligent for special needs housing. Any advice would be appreciated!
April 25th, 2014 at 1:32 pm
Until recently, he had a drug habit (pot) but stopped that on his own when he began to worry about his future, getting a better job some day, having money when he drives. We knew we could not monitor a 22 year old about pot, not unless we hovered and watched his every move (we don’t). He is obsessed with getting a girlfriend and spends much time on Instagram (I’m not crazy about that). But his social life? How do we help him find one?
April 26th, 2014 at 11:48 am
I don’t know how to answer your questions. I’m sorry for your stress. It seems to me that you are doing all you can. However, when you say he passed his algebra class, what were his test scores? Not the teacher grades, but the state tests. The rest of your description is consistent with someone who could not pass algebra.
I would accept that for some reason, your school system was reluctant to classify him. There are plenty of people out there with similar IQs. The problem is that many people with those IQs are smoking pot, leading purposeless lives, and thus far you’ve managed to avoid that for him. So you’ve been successful in helping him escape a lot of the downside risks, but at the cost of his feeling alone and isolated. I feel sure there’s a way through that, finding him the successful or motivated people in his peer group.
However, his job seems appropriate for him. Is he happy?
May 31st, 2016 at 1:51 am
[…] not a matter of trying harder, or teaching better, or that the kids weren’t taught. They lack any real understanding of the layers of cognitive ability. They don’t realize there are perfectly normal folks who […]
October 9th, 2017 at 1:56 am
[…] in those tiers. My various occupations have given me access to the entire range of IQs, from the occasional low 80s to third standard deviation and possibly beyond. As a result, I don’t know a 98 from a 105, […]