Why the kids don't know no algebra

By Razib Khan | July 3, 2012 9:36 am

A few days ago I stumbled upon a really interesting post. And I’m wondering if my readers are at all familiar with the phenomenon outlined here (it was a total surprise to me), The myth of “they weren’t ever taught….”:

Stage One: I will describe this stage for algebra I teachers, but plug in reading, geometry, writing, science, any subject you choose, with the relevant details. This stage begins when teachers realize that easily half the class adds the numerators and denominators when adding fractions, doesn’t see the difference between 3-5 and 5-3, counts on fingers to add 8 and 6, and looks blank when asked what 7 times 3 is.

Ah, they think. The kids weren’t ever taught fractions and basic math facts! What the hell are these other teachers doing, then, taking a salary for showing the kids movies and playing Math Bingo? Insanity on the public penny. But hey, helping these kids, teaching them properly, is the reason they became teachers in the first place. So they push their schedule back, what, two weeks? Three? And go through fraction operations, reciprocals, negative numbers, the meaning of subtraction, a few properties of equality, and just wallow in the glories of basic arithmetic. Some use manipulatives, others use drills and games to increase engagement, but whatever the method, they’re basking in the glow of knowledge that they are Closing the Gap, that their kids are finally getting the attention that privileged suburban students get by virtue of their summer enrichment and more expensive teachers.

At first, it seems to work. The kids beam and say, “You explain it so much better than my last teacher did!” and the quizzes seem to show real progress. Phew! Now it’s possible to get on to teaching algebra, rather than the material the kids just hadn’t been taught.

But then, a few weeks later, the kids go back to ignoring the difference between 3-5 and 5-3. Furthermore, despite hours of explanation and practice, half the class seems to do no better than toss a coin to make the call on positive or negative slopes. Many students who demonstrated mastery of distributing multiplication over addition are now making a complete hash of the process in multi-step equations. And many students are still counting on their fingers.

The author is involved in education personally, so is posting their own reflections as well as what others report to them. In personal correspondence they explain that this phenomenon is common among children of average intelligence. The lowest quartile presumably would never have been able to master many of these rules in the first place. Some of the information resembles the stuff that a friend of mine experienced when he went in to do tutoring for disadvantaged students in Boston when he was getting his doctorate at MIT. At first my friend was totally taken aback at the level of ignorance (e.g., the inability to see the relationship between 1/10 and 10/100). Today he works at a major technology firm as a scientist, but continues to be involved in mentoring “at risk” kids. At some point you have to muddle on. He does his best, and does not indulge in the luxury of shock and disappointment. That helps no one.

This matters because American society is notionally obsessed with education. All this isn’t too clear or important to be frank when you aren’t a parent. It’s somewhat in the realm of the abstract. That changes when you become a parent. Suddenly you become immersed in the data of your local schools, and begin to weight various options to optimize your child’s schooling experience. Of course the real differences in school metrics have not only parental relevance, they matter in terms of national policy and attention. Both the political Left and the Right have their own pet solutions. More money, reform teachers’ unions, charter schools, vouchers, etc.

But the biggest problem at the heart of the matter is the fundamental populist drive to ignore human difference. American schools were designed to produce the citizen, and the citizen has the same rights and responsibilities from individual to individual. In some ways the public school system as it emerged in the 19th century was a project by the Protestant establishment to assimilate white ethnics, in particular Catholics (who of course created their own alternative educational system to maintain cultural separation and distinctiveness). In the 21st century the drive to produce H. Americanus seems quaint, rather, we want to citizens of the world with skills and abilities to navigate an information economy.

What American society on a deep philosophical level, no matter the political outlook, detests acknowledging is that a simple and elegant public policy solution can not abolish human difference. Some children are more athletic than others, and some children are more intelligent than others. Starting among conservatives, but now spreading to some liberals, is a rejection of this premise via blaming teachers. The premise is bewitching because it presents tractable problems with solutions on hand. Here is John B. Watson, the father of behaviorism:

Give me a dozen healthy infants, well-formed, and my own specified world to bring them up in and I’ll guarantee to take any one at random and train him to become any type of specialist I might select – doctor, lawyer, artist, merchant-chief and, yes, even beggar-man and thief, regardless of his talents, penchants, tendencies, abilities, vocations, and race of his ancestors. I am going beyond my facts and I admit it, but so have the advocates of the contrary and they have been doing it for many thousands of years

I think if Watson were alive today he’d have to admit he was wrong. Your ancestors are not destiny, but they are probability. If your father plays in the N.B.A., the probability that you will play in the N.B.A. is not high. But the probability is orders of magnitude higher than if you are a random person off the street.

With all this I am not saying conditions which are non-hereditary are irrelevant. What I am saying is that we can’t ignore the shape of the pre-existent landscape before we attempt to reshape it to our own image. Excoriating teachers for having pupils who can’t master mid-level secondary school mathematics is in some cases like excoriating someone for the fact that their irrigation canals from the plains into the mountains are failures. You need to level the mountains before your canals can work (or, barring that design and implement a mechanical system which will move water against the grade). Easier said than done. E. O. Wilson said of Communism, “Great Idea, Wrong Species.” The reaction of Communist regimes to this reality was brutal and shocking. Obviously the modern rejection of unpalatable aspects of human nature are not so grotesque. But they have a human toll nonetheless. I’m skeptical that this generation will pass before we have to acknowledge these realities and calibrate our policies accordingly.

CATEGORIZED UNDER: Culture, Evolution
MORE ABOUT: Education
  • mdb

    In many respects I agree with this, but the logical conclusion (which I also support) hasn’t gained much traction anywhere – and that is teachers don’t matter. Cut their pay and school budgets by 75% and spend it on something useful or better yet don’t tax it in the first place. Maybe in time.

  • https://plus.google.com/109962494182694679780/posts Razib Khan

    #1, i think what you’ll have is fewer teachers, supplemented by aides, human & technological.

  • Sandgroper

    You can tunnel through the mountains.

    I have clear memories of this sort of stuff happening in school, more so in primary school, I think. But seriously, some of that was the teachers – my older sister taught me more by doing a brain-dump on me every day after school than my teachers were achieving. I went to a high priced private secondary college by virtue of a scholarship, and a lot of the teachers were just plain duds, with a small scattering of brilliant ones. Going beyond my facts, I’d say it’s some of both.

  • https://plus.google.com/109962494182694679780/posts Razib Khan

    #3, i think the return-on-investment for good teachers varies about the kid’s ability level. really bright kids are probably more shaped by their peers than their teachers (no offense, but at elementary or secondary school levels they are likely to be brighter than most of their teachers). OTOH, not so sure about kids who are more average, and learn by rote and repetition.

  • simplicio

    I’m not sure genetic differences is really behind the problem described in the story. According to the teacher most of the kids were capable of figuring out addition of fractions with instruction. The reason that they didn’t know it later wasn’t lack of understanding but because they quickly forgot what they’d learned.

    Only a small part of the population is probably capable of being successful mathematicians. But I’d say in excess of 95% of the population is capable of figuring out how to add fractions. If a class of students doesn’t know how to add fractions, I don’t think you can subscribe it lack of innate ability.

  • Chris

    I don’t think taking away teacher’s salaries and school budgets will do anything helpful at all. What I wish we did earlier is differentiate children so that students who are able to, can learn faster, and different things are taught to children who do not learn as quickly. What it seems like we do, in Canada at least, is teach to the lowest common denominator until high school. This is very boring for children who are really great at math (or English, science, social science, phys ed), because they could learn the entire math curriculum in 1 or 2 years, rather than the 8 they have now. Differentiating is problematic, because children can be placed into the wrong category. They could be placed in a low math level, when they are capable of learning more. Instead of making this distinction we stick most children in a lower level than they are capable of and attempt to teach everyone the same material. I think this holds back our potential as a society. It is not just math we do this in, we do it in all subjects. I agree that it is not the fault of teachers that everyone cannot master everything. We all have strengths and weaknesses. In an ideal world, everyone would master every subject they could to the best of their abilities.

  • Dave

    John Holt had a more useful analysis of why students don’t learn–basically schools are prisons, places we force kids to show up and hear about stuff they’re not interested in. When kids are motivated to learn things because they’re interested, they damn sure learn them, except for a very few, if the things are as simple as we’re talking about here.

  • marcel

    How do you distinguish variation that is (almost) entirely genetic from variation in which environment plays or has played a large role. A rule of thumb, which I picked up somewhere along the way (so not pulling it out of my rear, but no documentation for it), is that the effects of poor nutrition on body size take about 3 generations of good nutrition to fully work themselves out.

    I think that this means the following. Consider a woman born to a mother who was herself poorly nourished her whole life (including in utero), and who (referring to the daughter) is poorly nourished through her childhood. Because of her mother’s experience, the daughter will be smaller than otherwise as a newborn, and in addition because of her own experience, she will be a smaller than average adult. Call her generation 1. She will give birth to a smaller newborn than she would have without her nutritional history, even if she is on a healthy diet through her pregnancy. If her daughter (generation 2) is well nourished through her pregnancy and childhood, she will nevertheless be smaller than she would have been otherwise, because of her mother’s experience, and, to some extent, so will her offspring. It is only with the following generation that the effects fully disappear. This length of time sure makes the small body size in the earlier generations appear to the casual observer to be genetic in origin.

    Do we know that the same is not true of intelligence or educability or whatever we should call it? That is a separate question from determining an appropriate response, but if it is the case, it surely informs that discussion.

    It is my impression that explanations of the Flynn effect rely on environmental changes that shift the distribution of IQ scores to the right[1]. If true, then why should policies not focus on implementing those changes?

    [1] A question about the Flynn effect that I’ve not been able to find with a quick web-search (I’m not asking anyone else to perform the search, but if you happen to know…) The explanations of the Flynn effect that I have seen mention that it raises mean scores on IQ exams, and since the convention is to map the raw test score to the IQ value of 100, the mapping between IQ values and raw scores on the tests used to measure IQ has to be redone every decade or so. It is also the convention to scale IQ scores so that 15-16 IQ points corresponds to one standard deviation in the raw scores. How is the Flynn effect effecting the standard deviation? Is it compressing or expanding over time, or not changing much at all? If expanding, is it remaining roughly a constant proportion of the mean score, so that the coef. of variation is roughly constant?

  • Sandgroper

    95% of the whole adult population? No way. I’ll take a bet with you on that any time.

  • Dm

    Elem-school and preschool children easily forget skills they once learned, but aren’t motivated to retain. My teacher spouse grapples with this problem all the time. And as always, strong confounding factors emerge. Kids of college professors tend to be a pleasure to teach, but many factors of these kids’ success are obvious and non-genetic. These parents motivate their children to do the homework, they sincerely appreciate their children’s success and don’t mete out discouraging punishments for academic failures. Generally they play mentally engaging games with their children, read with them, etc.

    Some children of highly educated parents have problems with motivation to learn, and it’s easy to notice the lack of parental engagement (instead of playing or reading with their kids, these parents are online chatting with their friends, shopping, or exchanging pictures and videos purporting to prove how talented are their little ones) or true painful discouragement coming from the parents (from berating their “little idiots” for mistakes to promising, but not actually giving, memorable presents for the kids’ achievements).

    Being an educator of young children, one can’t help noticing how different they are in terms of their basic skills – but also how these difference change greatly over time. So I bet you that it’s going to be almost universally accepted among teachers that *every* kid can acquire basic skills, a year earlier or a year later (because that’s what they eventually see) … but that the role of parental engagement is huge (because that’s what makes their daily work fun or horror)

  • Hao

    @simplicio: I think 95% might be slightly on the high side, but I do believe a large majority could master fraction operations if properly trained. The problem I see is that a lot of them will likely forget it quickly (something you noted), and for some small fraction, the amount of time required is not worthwhile.

    I think if you asked the average US adult off the street to add two fractions with different denominators (esp. ones that don’t divide into 100), you’d get less than half able to do it within a reasonable amount of time. (and a smaller fraction unable to do so with unlimited time)

  • https://plus.google.com/109962494182694679780/posts Razib Khan

    Kids of college professors tend to be a pleasure to teach, but many factors of these kids’ success are obvious and non-genetic.

    all your examples have an obvious behavior genetic confound. don’t you see it?

  • simplicio

    @11 The 95% number was of course just pulled out of my ass. But I think its clear what I mean, its not some skill that only an elite few can master. And indeed the teacher in quoted piece seems able to teach it to children, the children just aren’t interested enough to remember it several weeks later.

    (How many “average adults” remember how to do it when pulled off the street isn’t really relevant though. I learned to program assembly many years ago, but haven’t used it since, and if you sat me down in front of a terminal and told me to write a program in assembly I wouldn’t be able to do it. That doesn’t mean I’m “incapable of learning assembly”, it just means I don’t remember technical skills that I don’t use).

    The relevant question is how many adults can add fractions after getting instruction.

  • Ron Strong

    I wonder how much of the pathetic performance of the average student is due to the education establishment’s phobia over using repetitious drill as pedagogical method.

    The vast majority of those who read this blog are probably in the top 5% – most much higher – as far as math aptitude. For such persons, less drill and more abstract instruction in earlier grades probably works just fine.

    But for the average kid and below – individuals who have nearly zero chance of ever performing in a profession that requires a good grasp of serious high school math such as calculus or probability and statistics – early grade repetitious drilling of the basics may be the best way to get them to the level needed to one day become a decent carpenter, mechanic, or other trade requiring a little arithmetic.

  • rmetric

    It’s easier for the parent to blame the teacher than it is for the parent to admit their own shortcomings, or the shortcomings of their children. A better course of action would be for the parent to take special care in identifying and encouraging areas of excellence.
    There are plenty of normal people out there, what the world needs is somebody extraordinarily good at solving problems in a novel way.

  • Dm

    #12 *we* all see genetic factors, did you miss it that I was trying to explain why the teachers see something different?

    My point was that the genetic factors, to a large degree, go hand in hand with environmental factors. I also tried to explain how the educators perceive “daily joy and daily disappointments” somewhat separately from “long-term achievements”, and how environmental factors may be more in play in the former category rather than in the later. But since it is the day-to-day struggles which affects the teachers’ life the most, they naturally come to appreciate the role of environmental factors the most.

  • http://perceivingwholes.blogspot.com Jane

    Do differences exist? Sure. Should they matter for teaching basic math? Absolutely not. See the results JUMP Math has been achieving. http://jumpmath1.org/jump_research (Scroll down to the before and after distributions.) With this curriculum, not only do all the students learn more but the gap between top and bottom performers becomes tiny.

  • Mark Plus

    I encounter people all the time who don’t know how to read calendars or follow directions to places they haven’t traveled to before. For some reason Latinas (women from Latin American ethnic groups), even the ones who speak good English, seem especially impaired in the latter ability. But then with those GPS devices in our cars, map literacy and direction-following skills have fallen into disuse. It wouldn’t surprise me if these same people struggled with basic arithmetic, the rules for adding fractions and the difference between positive and negative numbers in school.

  • dcwarrior

    Further to Dm’s comment up there, there seems to be a proportion of students who seem to delight in learning only what they think will be on the test and forgetting it the second the test is over. There are some of these among my co-workers as well.

    Whether that is personal, cultural or inborn, it may not be either a failure of teachers to teach or an inability to learn. Rather for some kids (I would say many), it might be a lack of desire to retain.

  • toto

    See the results JUMP Math has been achieving.

    According to JUMP.

    I’m with #5. If they really got it right once (which is how I read the article), then their lack of long-term assimilation sounds more like a problem with educational methods / environment than with raw genetic material.

  • Charlotte

    Are we all sure that there’s no agency on the part of the students here?

    I say this because I am familiar with the phenomenon described. I have been told that it goes on all the time in math classes on the K-12 level in my area (Southerm, rural, poor, culturally isolated).

    The local consensus is that students deliberately malinger in math class because they don’t want to have to do algebta.

    Students realize that if they can convince the teacher they don’t know simple arithmetic, they won’t have to move up to algebra. So they malinger, which allows them to stay with “easy” basic arithmetic all through high school.

    The schools then teach students test-taking “strategies” that allow them to get through their NCLB-mandated tests with passing scores, and allows their school to do the same.

    Because this is an area of low educational attainment, the consequences of using this strategy are not felt to be serious for the students. (“You’re never going to use algebra in the real world” — so why not game your way out of learning it in school?)

    The local emphasis is on after-school sports, and an “easy” high school curriculum that requires little homework and leaves plenty of time for sports is valued. The International Baccalaureate program locally has a struggle. Parents don’t like it because IB homework leaves little time for sports.

    Most local high school graduates go to the area community college, and of course most of them have to be remediated in math once they get there. This disappoints a few students who had hoped to become engineers or doctors, even though they knew no math beyond basic arithmetic. They now realize that the 2+ years of remediation they will need to reach freshman-level competency in math is going to put the M.D. or engineering degree out of reach.

    But most students go into nursing or allied health professions these days, where nothing but basic arithmetic is required, or get technical certificates.

    I just want to raise the possibility, then, that, strange as it might seem to parents who have middle-class aspirations for their children, these students act to benefit themselves when they “kill” the difficult algebra curriculum by pretending not to understand basic arithmetic. They can coast on “easy” basic arithmentic for another year. Their parents don’t mind. There’s no stigma in the local culture if you never get to calculus; on the contrary. The technical training classes they go into don’t ask for anything more than basic arithmetic. And their teachers are usually helpless against the united opposition of the class.

  • Richard Harper

    IQ measures were designed originally around educability, to select those who could not keep up with coursework and so should be excused to work on the home farms instead. Later during the Cold War they emphasized finding the best brains to beat the war-arms technology race. In both cases they sought measures independent of previous training and cultural knowledge accumulation, so they emphasized working memory and cognitive-speed. (The latter useful for the automation of industry.) The effectiveness of those measures at predicting the capacity for developing expertise seem to quite possibly be only slight, and perhaps mostly correlational. I suspect the USSR practice of giving weight to admitting students to top universities who had demonstrated an ability to develop expertise at chess may have been more effective at promoting talent in the so-called “hard” sciences than is generally appreciated. The extreme absence of the memory of math procedures learned in the vast majority of students was certainly my experience from that age (.. which I remember quite clearly, by the way.)

  • JR

    How could a government tailor education for each specific and distinct student and still allow for the socialization that comes with grade levels? (People have different, heretable skill sets at socialization, as well)

    There are limited resources and seemingly unlimited differences between children. Sure, we try to provide the “gifted” and those with special needs with additional resources, but on a large scale, the system seems inadequate.

    One way, perhaps, to provide exactly the education a student needs would be to let students complete a K-12 curriculum at their own speed, diploma in hand as soon as they are done. Most students, genetic probability seems to show, would finish at about the same time, but would complete different subject areas at different speeds.

    I foresee that the economic cost of such a process would be astronomical, and the socialization cost to those who either fall behind or rocket forward would be a detriment to their ability to reach their fully socialized potential.

    In short, a solution for our PUBLIC schools seems light-years away.

  • Charles Nydorf

    When I 12, I participated in an experiment where a group of children deemed “gifted” learned elementary calculus. When my grandfather heard of this he was shocked and said “You are building the roof before you are laying the f0undation” to which my uncle countered that you would do that if you were digging a well. My uncle had a point, which is that the order in which you acquire math skills is not that relevant. A motivated student who lacks the prerequisites to tackle a problem will back up and master them pretty quickly.
    What teachers can learn from this is the principle of covering a wide variety of math topics and not worry to much about the order in which they are introduced or learned.. One topic or another is likely to capture a student’s interest and he’ll then start mastering other aspects of the subject. Once he starts thinking for himself about the subject he won’t need to memorize a lot of rules because he will be able to figure them out for themselves.
    Difficulties are also teaching opportunities. If the student can’t tell the difference between 5-3 and 3-5 you can teach the concept of commutativity and mention that their are systems in which the elementary operations do not commute. The sense in 1/10 and 10/100 are the same is really profound and any student who can explain it is on his way to becoming a philosopher.

  • Dm

    #24 Charles, that’s funny in a way, at the age of 12 I was in a gifted math-centered program where we started a multi-semester course of group theory (sans LA) because the curriculum people wouldn’t let anyone start on calculus w/o “proper foundation” :)

    But it was my third school in as many years. I’ve been totally failing at the first one and left with sub-1 GPA & a referral to a special program for children with learning disabilities, which Mom fought hard to quash. Which of course constitutes only anecdotal evidence but still kind of convinces me that the environment matters … at least the bad environment, with incompetent teachers and violence, matters for one’s educational success. Often it just takes one teacher who hates the kid…

    Good environment IMVHO matters a lot in high school (which is IMO the only segment of the American school system which is, at its core, about education as opposed to, let’s put it this way, child care). But it is scarce. Incompetent math and science teachers steer scores of high-schoolers away from deeper learning.

  • expeedee

    Here is an interesting article on the education gap by P. Buchanan that I think is worth reading:


  • expeedee

    Perhaps there really is nothing really wrong with our educational system after all. Here is an interesting article on the education gap by P. Buchanan that I think is worth reading:


  • van Rooinek

    When I was in gradschool I was a teaching assistant for Chem 102, Chemistry for the NonScientist. It was the only science course a lot of these kids would ever have.

    I recall one determined student who showed up regularly for tutoring at my office hours. She was truly a hard worker, one of the few, and honest — indeed she tipped us off about a cheating ring. By her work ethic she far excelled most of the class. But… One day I was trying to explain how to balance a chemical equation, and I explained it slowly and patiently, several different ways, and she just wasn’t getting it. Finally she asked a question which clarified the problem: It wasn’t the chemistry she had trouble with — she didn’t understand the simple ALGEBRA needed to solve the problem!

    Like I said, she was one of the good ones, who deserved respect and all the help I could give. And even if she hadn’t been, I was still too polite to voice the question that I wanted to scream: “WHAT ARE YOU DOING IN COLLEGE?” At the time I blamed the k-12 educational system for sending her to college without a clear knowledge of algebra… but now, decades later, I realize an alternate possibilty: maybe she’s just one of those people who innately can’t do it, or can’t remember it, like the kids described above.

  • van Rooinek

    PS… now that I think about it more…. She was about a decade older than the rest of the class, married with a family, and was a “returnee” to college, rather than fresh out of high school. So maybe, maybe, she just *FORGOT* algebra during that long gap. Maybe.

  • gaddeswarup

    Thinking again about fractions, I feel that the concepts are difficult and take a long time and repetion to teach. I wonder how they teach division of a fraction by a fraction.

  • MrsRobinson

    The staff in my schools killed it for me. I was 3.5+gpa until 8th grade. I was in four classes two years advanced and loving the learning and the challenge ( I actually got a B one time.) Then I transferred to a new school in a neighboring state. They refused to acknowledge my advanced status and put me right back in basic classes.

    You know what its like to be taking Algebra II and Biology and then being forced back into basic math (+-*/) and science and then ridiculed by the super for asking he look at my transcript again to please correct this error?

    I’m not saying teachers Are the problem but some of them definitely are. I dropped out two years later, tired of the crap. Then I was refused my GED test until I was 18, which I took (no studying required, dur) and came out 5th in my class (figures I’d loosen my grip on geometry in two years time, ha!)

    Education system needs afixin’.

  • http://wulfkurtoglu.blogspot.com/ Wulf Kurtoglu

    One benefit that educated parents can give their children is a connection between school subjects and the real world. Being more of a Humanities type, I take my example from there – I had the happy feeling, by the time my daughter was about twelve, that she lived in the same world that people like da Vinci, Virgil and Shakespeare had lived in. These were people who had done stuff that was still tangible and formative for her family and therefore for her. Conversely, it’s very easy for kids to have the impression that everything that happened before they were born is completely irrelevant to their lives and exists only within the walls of the school.

  • Karl Zimmerman

    I think the example of Finland’s school system is interesting, in that despite having a fairly short number of hours in the classroom, and regular school not beginning until seven, students have high performance, and formerly high gaps due to socio-economic status have been reduced (there are still huge gaps for immigrants). Still, neighboring Norway has similar education policies to the U.S., and similar middling scores to the U.S. Since the ethnic stocks are roughly speaking similar, there is no biological reason to assume the Finns are smarter than the Norse – it really seems their education system is superior.

    How did they do it? The main cause was the transformation of teaching into a highly-paid, high-prestige professional position. Teachers must have a masters degree, and the programs themselves are highly competitive, with only the top 10% of college graduates allowed to enter the most selective programs. They are also given a lot of autonomy on the job. It seems safe to assume, since a higher IQ is correlated with better job performance in virtually every job, this also would be the case for teaching, and the Finnish example bears this out.

    Sadly, we’re headed in the opposite direction. National consensus is heading towards teachers being the problem, but the solutions being offered – cutting pay and benefits, increasing hours, and reducing prestige and independence even further – will only ensure an even lower caliber of applicants becomes teachers in the future. Biology is destiny goes both ways. A teacher can only do so much with a dumb kid, but a dumb teacher can do even less.

  • April Brown

    I always felt kind of bad for my teachers who blamed themselves when I knew that it was a deficit on my part. Tragically, one of the best teachers I had in high school taught both accounting and physical education, both of which I flunked out of. Poor guy was at a loss to figure out a way to compensate for my horrifying number dyslexia (turns out that’s a deal breaker in a subject that involves writing columns of numbers by hand and doing something useful with them) and a frail anemic physique that couldn’t do any of those stupid presidential fitness tests.

    No matter how great a teacher I had, there was no chance in hell, courtesy of genetics, that I could have succeeded at either class. Bothered me that my teacher took it personally, and I hope he never got blamed for having a student that flunked both his classes simultaneously.

  • Tom Bri

    I spent 15 years teaching, mostly Asians. I found there is a small number of people, even very smart people, who just cannot learn a particular subject. But I was also convinced that the great majority can learn if motivated. I taught kids to speak and read English, whose only practice was a few hours a week with me. The key is motivation.
    I wrote an article on this. http://hub.me/acMvM

    Incidentally, I had always thought of myself as someone who was unable to learn math. But last year I decided to take some science classes at the local jr college, and discovered that my college classes were so far back in the distant time that they didn’t accept them as pre-requisites. I had to learn algebra to pass the placement test. I learned enough to pass the test in about two weeks. Then immediately took chemistry where I used the basic algebra I had just learned. The difference was motivation. I now wanted to learn algebra, whereas I had never before. That also convinced me that math instruction, at least as it was done 40 years ago in my school, is awful. I learned about as much algebra in two weeks as a typical high school kid is expected to learn in a one year course.

  • http://https//roc.iwcc.con Jan Lunde

    American students lack foccus and patience; they want instant kudos for average effort/quality. They know the public school culture is dominated by Friday Night fotball fever, lax pareting which permits underage drinking equals hormones gone wild and unispired and uninspiring staff & administration. Students “get” it. Those who hang in until graduation just put in their time and look forward to being entertained/distracted rather than doing Hard Time academucally.

  • gcochran

    Those kids are dumb, but they’re probably not as crazy as most of the posters here.

  • Kevin

    Teacher quality does matter.

    A teacher one standard deviation above the mean effectiveness annually generates marginal gains of over $400,000 in present value of student future earnings with a class size of 20 and proportionately higher with larger class sizes. Alternatively, replacing the bottom 5-8 percent of teachers with average teachers could move the U.S. near the top of international math and science rankings with a present value of $100 trillion.

    From the underlying paper (pdf):

    The results suggest that the effects of a costly ten student reduction in class size are smaller than the benefit of moving one standard deviation up the teacher quality distribution, highlighting the importance of teacher effectiveness in the determination of school quality.

  • http://educationrealist@wordpress.com Education Realist

    Thanks, Razib, for the great comment. That’s exactly the point I was making.

    #1, 2: That’s way too much of the IQ is destiny mindset for me. Of course, IQ matters, but technology won’t solve the problem of unmotivated kids. Teachers can, as can external goals that motivate a kid even with a less than inspiring teacher. What we need is more realistic curriculum for lower to mid ability students, and a meaningful goal.

    #3 and others with a similar point: You read this blog. You respond about your own educational experiences from a, dare I say, metacognitive perspective. Almost axiomatically, you have nothing in common with the students under discussion so your own experiences aren’t relevant. There’s a huge difference between a otherwise high ability kid struggling with math and a low-mid ability kid struggling with math.

    #5–Suppose you ask me for instructions to the store. I give them to you. You remember them for a week, and then you ask again. We repeat this 80 times in a year and at no point do you ever remember the way to the store. Are you saying the only problem is that you just forgot the instructions? Of course not. The problem is that you didn’t (as we say in teaching) internalize the information and process it into something you can use. The problem with teaching math to low and mid-ability kids is that they are given too much information in a form that they can’t internalize. If you read the last part of my post, I talk about the teachers who accept this. One of the things these teachers try over and over to do is to figure out ways to help students internalize the information so that they won’t forget it. And we have our successes! That’s the big fascinating challenge of teaching. But we would need to teach much less, and cover it more slowly. At least, that’s what I think. It’d be nice to see research, but it’s much less controversial to research cognitive ability in teachers than it is to do it in students. Oh, and as others have said, you are absolutely incorrect that 95% of the population can master fractions. I do agree that we could get the number higher than it is now, but not if we keep treating low and mid ability kids like high ability ones.

    #24–As the opening anecdote of my post says, “Damn. Why didn’t I think of that?” Oh yeah. I did. We do. They are taught about the properties constantly in school, and if you notice in the part Razib quoted, equality properties are one of the items on the list. It’s covered CONSTANTLY. That comment is one of the reasons that teachers know the outside world doesn’t get it.

    #33–There is next to no evidence that teacher cognitive ability improves performance. I suspect that the research would show otherwise IF student cognitive ability were taken into the equation, but I am also fairly certain that the relationship would not be linear. Besides, as I’ve pointed out before (and Razib discussed this post, too), secondary teachers are in the top half of the college grad pool in their subject.

    I think I missed some great comments that I should have responded to, but I have pies to make. Thanks for the discussion and happy fourth!

  • Mike

    If half my class wasn’t able to understand common fractions, or forgot after two weeks, I’d assume they were smoking pot.

    In a large number of cases, I’d probably be correct.

  • Sam Koritz

    Education Realist’s personal observation that slow kids forget what they’ve been taught is backed up by research. The Johns Hopkins study “Lasting Consequences of the Summer Learning Gap,” for example, claims that most of the difference between high & low SES kids’ learning can be explained by low SES kids forgetting over the summer & and high SES kids continuing to learn: http://www.nayre.org/Summer%20Learning%20Gap.pdf

    Re the value of high quality teachers, we do know that low quality teaching is keeping US students from reaching their potential. See, for example, Teacher Quality Moderates the Genetic Effects on Early Reading: http://www.sciencemag.org/content/328/5977/512.short
    I don’t know of any studies that separate actual teaching skills from other classroom factors — disruptive kids, etc. — though, so it’s possible that most of the damage is being done by the latter.

  • simplicio

    @39 “Are you saying the only problem is that you just forgot the instructions? Of course not.”

    Not sure where you got that from. I wasn’t denying the existence of a problem, I was questioning whether the problem was really the one Razib seemed to perceive it to be.

    “The problem is that you didn’t (as we say in teaching) internalize the information and process it into something you can use. ”

    This I certainly agree with. I just don’t think the (primary) reason for that problem is a difference in raw intellectual ability. Smart people and dumb people alike remember and internalize those things they find interesting or useful and quickly forget those that they don’t. I suspect your kids come from backgrounds that haven’t given them cause to believe that adding fractions is interesting or useful, and so they quickly forget it. Schools can and do address this to some extent (indeed its much of the point of the whole system of grades and GPAs), but there’s obviously only so much you can do in the context of a classroom to make kids value intellectual understanding.

    Enjoy your baking.

  • http://educationrealist@wordpress.com Education Realist

    #42 I know you aren’t denying the existence of the problem. You specifically said that the problem was that they forgot what they’d learned, and that this was not “genetic differences”. Best I can see, no one mentioned “genetic” until you did. If we assume that you equate “cognitive” with “genetic” (which is the only way your original post is coherent), you are saying that the problem isn’t cognitive, but rather a failure to remember.

    But failure to recall information is a cognitive issue. While there are people with high cognitive ability and low recall, they are an exception. Our school system is designed with the assumption that students have a certain recall level. They don’t.

    I am all for reasoning and rarely one that relies purely on personal experience. However, I live in a very high IQ area, and have worked with smart people all my life. Since I became a teacher, I have become sharply aware that the vast majority of people discussing teaching have literally no clue what it’s like to teach low to mid-level cognitive ability students.

    I also find it interesting when people resist the idea that low cognitive ability exists. Apparently, all students are smart and just uninterested in learning. Who knew?

  • simplicio

    @43 “Best I can see, no one mentioned “genetic” until you did.”

    -Razib did (or at least, he talked about human differences that he contrasted against “non-hereditary ” differences, which sounds pretty genetic to me). As I said, my initial post was replying to his take on what the problem was.

    “But failure to recall information is a cognitive issue.”

    -I’m sure that’s true to some degree. But stupid people remember things. Just because there are cognitive differences in memory doesn’t mean that everything stupid people don’t remember is due to a lack of cognitive ability.

    No doubt there are many facts and skills that are important to them that your students remember for much longer then the few weeks you describe them being unable to remember how to add fractions. The forget fractions because they don’t care, not because they are incapable of remembering stuff for more then a few weeks.

    On the converse, I have a hard science PhD and would consider myself pretty smart. I have a group of friends that are really into card games, and because I like the company, I play with them every few weeks even though I find the game itself kind of boring. They make fun of me because they end up having to reteach me the rules and basic strategy every time, even when my job requires me to remember much more complicated skills over much longer streaches of time. The reason I don’t remember the card game isn’t because I have some “low card-game specific cognitive ability”, its because I don’t like the stupid card game and don’t feel like expending the mental effort of really internalizing how it works.

    “I also find it interesting when people resist the idea that low cognitive ability exists. Apparently, all students are smart and just uninterested in learning. Who knew?”

    -Is this in response to me? I didn’t reject the idea that low cognitive ability exists or say that all students were smart. I just don’t think that’s the explanation for the specific issue you described. Its possible to accept cognitive differences and not see them as the answer to everything.

  • http://educationrealist@wordpress.com Education Realist

    #44–Really? You don’t see cognitive ability as the most likely reason that high schoolers, who have been taught fractions, negatives, commutative property, integer operations, and basic math facts for four years or more, are incapable of remembering them? Given all the incentives that they have, particularly when younger children, to memorize these facts?

    In my experience, people who find cognitive ability an unlikely explanation are people who haven’t been exposed to this behavior. I truly believe that we can find a way to get some of this information to stick. I’m not being hopeless about it.

    So let’s put it this way: what I want, the research I want to see, is whether or not low to mid-level IQ predicts the behavior I describe. I am almost certain it does.

    I would probably be like you–in fact, I probably had the same response as you, before becoming a teacher. I do not say this lightly: People who haven’t seen or worked with the population under discussion should not assume they can explain it better than those who have. That’s why I wrote this post, to tell high ability people that they don’t know what it’s like and can’t use their own experiences as a guide.

    As to your own experiences, see my original comment reply to #3. And I see now where the “genetic differences” response came from, sorry.

    And the pies came out great, thanks!

  • Bob

    Fact: Teachers are dumb. The lowest of the low GPAs in college go into teaching.

    Opinion: Those teachers are lazy. My wife (a history major, not education) would go into school at 7:00am and monopolize the Xerox machine for the day’s handouts. Others, the majority, would arrive at achool just before the bell – and leave immediately after school. Those same ones made extensive use of mocies, computer games, fielf trips: anything that didn’t require work. The kids’ papers weren’t sent home, of course. Mothers slit each others throats to get their kids in my wife’s class.

    Conclusion: It’s a downward spiral with no solution.

  • FrustratedTeacher

    @45- EducationRealist how long have you been teaching? I see your attitude a lot with recent teachers, especially later-year Teach for America types (call it the immediate exposure to your very well explained ‘they-never-learned’ fallacy). If a student hasn’t learned fractions by rote by the time they get to highschool, a two week refresher tacked on to the syllabus isn’t going to help.

    One thing to keep track of is who previously taught students entering your class. I’ve found that one teacher whose class feeds into mine has students who are consistently more capable than most of the other teachers who feed into my level. The consistency of this pattern has lead me to believe that a teacher can make a difference, and its possible for students to retain more of the information then they currently are. Unfortunately, looking at how my students go on to perform, I know that a lot of what I’m currently trying doesn’t work.

  • simplicio

    @44 “Really? You don’t see cognitive ability as the most likely reason that high schoolers, who have been taught fractions, negatives, commutative property, integer operations, and basic math facts for four years or more, are incapable of remembering them?”

    -Really. To go back to adding fractions, assuming you know how to multiply (or have a calculator), then in order to add fractions, you really just need to remember three steps. I think all but the very lowest level of cognitive ability found in a HS, even a low achieving HS, is able to remember three steps for more then a few weeks [i]if that person wants to[/i]. It takes more then three steps to drive a car, but I imagine your students can remember how to do that.

    “Given all the incentives that they have, particularly when younger children, to memorize these facts?”

    – I think you overestimate the incentives for kids to learn stuff they aren’t interested in. If your unlikely to go to college, and unlikely to hold a technical job, and neither your peers nor family show any particular interest or admiration for intellectual pursuits, then why do you care whether some file somewhere says you got an F or an A in algebra?

    You see this even in relatively smart kids that will go to college. They have an incentive to keep their grades up to get in a decent school, but as anyone whose taught a Freshman Undergraduate math class, the amount of arithmetic and algebra they manage to forget even after spending four years getting decent grades in HS math classes can be pretty stunning.

    “In my experience, people who find cognitive ability an unlikely explanation are people who haven’t been exposed to this behaviour.”

    -OK, but what specifically in your experience makes you think its a cognitive deficit and not simply a lack of interest in engaging with the material? I’ve seen what sounds like a similar, if less severe, phenomena teaching undergrads who have good GPAs and decent SAT scores. Its clear that they’re smart enough to remember how to find the roots of an equation if they particularly wanted to, but they don’t so they don’t.

  • Konkvistador
  • http://educationrealist@wordpress.com Education Realist

    #46–No, that’s incorrect. See my original comment #39 and I guess I’ll just go ahead and quote Razib who quotes me: http://blogs.discovermagazine.com/gnxp/2012/01/physical-education-teachers-are-not-smart/

    #47–As I say in my post, the attitude is extremely prevalent among TFAers, but no,I’m an accepter. I’m about to start my fourth year teaching, but I taught test prep to disadvantaged, low ability kids for years. I’m not disillusioned at all. I just want others to understand, because it’s incredibly common for eduformers to do the same thing as these early teachers: they point to teachers of kids with low test scores and say, “These teachers didn’t teach them a thing.”

    #48– Any teacher working with kids knows the difference between “low ability” and “low motivation.” In my specific case, I’ve also taught kids SAT/ACT prep for a decade, and there is an enormous difference betweeen a kid who, with hard work, can hit 450 on an SAT section, and a kid who, with hard work, can hit 600 on the same section–much less kids who start off at 650 per section and then fine-tune up. In short, as I’ve said before, routine exposure to low-mid ability kids provides teachers with a much better sense of what the term means. I suspect your version of “decent” starts at the high 500s per section, which puts your people way out of the league I’m discussing.

  • simplicio

    @50 “I suspect your version of “decent” starts at the high 500s per section, which puts your people way out of the league I’m discussing.”

    -That’s my point. I see the same problem with kids quickly forgetting what they’ve learned with kids who presumably have higher cognitive abilities that you describe with lower ability kids. Hence my thesis: that the bulk of this specific problem isn’t due to a difference in cognitive ability.

  • edcrazy

    1.I’m not as well-spoken as most of the writers here, but I do have my own educational experience from which to draw some opinions. Tracking. What a way to let students achieve to their abilities, allowing entrance and exit from said tracks due to teacher-suggested migration, without the drag on learning from teaching to multiple learning levels within the constraints of a 48 minute class.
    2. My summer-school attending child, sitting among many of her previous classmates who are also at their wits’ end in trying to grasp higher than general math concepts, also has to ignore squirt gun battles at 9 a.m. I mention this because behavior/respect/responsibility cannot be eliminated from the burden of teaching with tax dollars or resolved by testing teachers for accountability.

    Thanks for this interesting blog, bythe way.

  • Luciano

    Try come to Brazil. Here, the presumption of equality is almost a law. And, of course, the blame is all on the teachers if students don’t learn.

    I wonder why we should teach people things they don’t want to learn. For 3/5+5/8 just use a calculator. If you know how to press the buttons and read the numbers, what’s all the fuzz about it ?

  • edcrazy

    @ luciano: i’d like to have the informed option to sign off the graduation REQUIREMENT for a math subject that I am most certain will never be approached in my kid’s future. otherwise, I’m conspiring with torture…figuratively speaking(?)

  • Luciano

    Exactly, edcrazy. It’s just torture.

    How long people will have to live with that ? Frankly, why would a bus driver or office clerk ever need to learn how to add fractions, let alone solve quadratic equations ? And speaking of this, why would they be interested in knowing anything about the spanish inquisition (not joking, monty python fans) or monocotyledons ?

    Why try to teach people things they don’t wanna learn ? Let them just get along in life and be happy their own way.

  • Theresa

    1. I thought the whole point of taking all of these classes is that you don’t know what you are going to end up doing in life. As it turns out, the job I’m in right now I don’t need the Trig/Math Analysis that I took, but I enjoyed it. I miss learning and the challenge. I know where to find information to refresh my memory should I need it.

    2. Has anyone done a study to see if these kids who “forget” so easily are more likely to have problems with Parkinson’s, dementia, and/or Alzheimer’s later in life?

  • Kyrilluk

    @55. It’s very difficult to predict the future. That’s why it’s a good idea to get as much people as possible to learn to “add fractions, let alone solve quadratic equations”, etc.. Not everyone dream of becoming a “bus driver” when they are young.

    Regarding the subject, I would agree with simplicio. When you don’t use a skill, you tend to forget it. So having a kid not remembering -even after 4 years – the algorithm behind adding fraction is not necessary a sign that they this is a mid to low ability kid.

    But for a group, this is more worrying . Like Charlotte says in post @21 there might be a specific cultural trait here. Or that on average, there are more low IQ kids in this group which in turn discourage the mid to hight IQ kids to remember these skills.

  • Luciano

    But, Kyrilluk, honestly, where do you need to solve quadratic equations ?

    I think not even engineers need to do that. It’s just a curiosity. Why torture kids with this ?

  • Sandgroper

    We do.

  • Sandgroper

    I mean we solve quadratic equations, not torture kids.

    Well, both, really.


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About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at http://www.razib.com


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