The myth of “they weren’t ever taught….”

A year or so ago, our math department met with one of the feeder middle schools to engage in a required exercise. The course-alike teachers had to put together a list of “needed skills” for each subject, to inform the teachers of the feeder course of the subjects they should cover.

One of the pre-algebra teachers looked at the algebra “needed skills” list and said, “Integer operations and fractions! Damn. Why didn’t I think of that?” and we all cracked up. End of Potemkin drill.

All teachers working in low-ability populations go through a discovery process.

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.

It’s as if they weren’t taught at all.

But teachers are resilient. They redouble their efforts. They spend additional time on “warm-up” questions, they “activate prior knowledge” to reteach even the simple subjects that have apparently been forgotten, and they pull down all the kaleidoscopic, mathy posters and psychology-boosting epigrams they’d hung up in their optimistic naivete and paper the walls with colorful images formulas and algorithms.

They see progress in the areas they review—until they realize that the kids now have lost knowledge in the areas that weren’t being taught for the first time or in review, much as if the new activity caused them to overwrite the original files with the new information.

At some point, all teachers realize they are playing Whack-a-Mole in reverse, that the moles are never all up. Any new learning seems to overwrite or at best confuse the old learning, like an insufficient hard drive.

That’s when they get it: the kids were taught. They just forgot it all, just as they’re going to forget what they were taught this year.

All over America, teachers reach this moment of epiphany. Think of a double mirror shot, an look of shocked comprehension on an infinity of teachers who come to the awful truth.

End Stage One and the algebra specificity.

Stage Two: At this point, some teachers quit. But for the rest, their reaction to Stage One takes one of two paths.

Blame the students: The transformation from “these poor kids have just never been taught anything” to “These kids just don’t value education” is on display throughout the idealistic Teach for America blogs. It’s pretty funny to watch, since on many sites you have the naive newbies excoriating their kids’ previous teachers for taking money and doing nothing, while on other sites the cynical second-years are simultaneously posting about how they hadn’t understood the degree to which kids could sabotage their own destinies, or some such nonsense. Indeed, I once had a conversation with a TFAer at my school, and she said this to a word: “I’ve realized I’m a great teacher, but my students are terrible.”

Not that this reaction is unique to TFAers. Many experienced teachers who began their careers in a homogenous, high-achieving district that transformed over time into a Title I area with a majority of low income blacks or Hispanics have this response as well.

It’s easy to denounce this attitude, but teaching has taught me that easy is never a good way to go. These teachers are best served at a place like KIPP, where the kids who don’t work are booted. It’s not that the kids learn more, but at least the ones that stay work hard, and that allows the blamers to reward virtue. At comprehensive schools, the teachers who saw their student body population change over time respond by failing half or more of their classes.

These teachers please both progressives and eduformers, because they have high expectations. Their low-achiever test scores, however, are often (but not always) terrible.

Acceptance: Here, I do not refer to teachers who show movies all day, but teachers who realize that Whack-a-Mole is what it’s going to be. They adjust. Many, but not all, accept that cognitive ability is the root cause of this learning and forgetting (some blame poverty, still others can’t figure it out and don’t try). They try to find a path from the kids’ current knowledge to the demands of the course at hand, and the best ones try to find a way to craft the teaching so that the kids remember a few core ideas.

On the other hand, these teachers are clearly “lowering expectations” for their students.

Which is the best approach? Well, I’m an accepter. Not that I was ever particularly naive, but despite my realism, I was caught off-guard by just how much low ability students can forget. But as I’ve said before, that’s the challenge I see in teaching.

I could go into more on this, but this post is long enough. Besides, I don’t want to lose sight of the opening story and the pre-algebra teacher’s mockery of the entire point of the exercise. Of course they were teaching integer operations and fractions. Of course they were doing their best to impart an understanding of exponents and negatives. They didn’t need the list. They knew their job.

Teachers know something that educational policy folk of all stripes seem incapable of recognizing: it’s the students, not the teachers. They have been taught. And why they don’t remember is an issue we really should start to treat as a key piece of the puzzle.


About educationrealist

64 responses to “The myth of “they weren’t ever taught….”

  • Bostonian

    Shouldn’t we create what is effectively an elementary school diploma, award it to teenagers who can add 2+2 but not much more, and encourage them to find work? Currently we just stamp them as “high school dropouts” if they leave and award fake credentials if they stay.

    • educationrealist

      You read my mind! I’m actually a fan of a three tier system. One for 8th grade competency (or close to it), one for genuine high school level competency, and one for college readiness. And yes, that’s absolutely what we should do.

      • johndraper

        It’s rapidly becoming a moot point though: most of these kids just aren’t smart enough to ever become economically productive members of society. Who needs security guards and grunts when you’ve got AI and drones?

        But yes, we should definitely have a skills-based rather than time-based system. Not really possible in our current system, but flipped classrooms with Kahn Academy type stuff + tutoring should make it easier.

    • OM

      “You are basically saying that low-IQ kids are not educable beyond a certain point. Agreed. Shouldn’t we create what is effectively an elementary school diploma, award it to teenagers who can add 2+2 but not much more, and encourage them to find work? ”

      What type of “work” hires people who can add 2+2 but not much more?

      And just because someone sucks at math doesn’t mean they are low IQ. I suck at it and I’m currently writing a very long philosophy book full of abstract concepts.

      Why do you perceive mathematical ability to be the pinnacle of intelligence?

      • educationrealist

        Actually, I doubt you “suck” at it. Most people of above average IQs don’t understand what even slightly below average (say 95-100) look like.

        I don’t perceive it to be so. You might read it more closely, or perhaps you “suck” at reading, too? Just checking. Read the 4th paragraph again.

  • Why the kids don’t know no algebra | Gene Expression | Discover Magazine

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  • DYSPEPSIA GENERATION » Blog Archive » The Myth of “They Weren’t Ever Taught….”

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  • Jim Stephenson

    About 8 years ago a math teacher in my son’s high school told me that they were addressing state-mandated standards by teaching a section and then immediately giving a test on it. Thus, they banked a “Pass” for that concept. Implicit in this, of course, is that by the end of the year the students would not be able to pass the exams.

    And this is in honors courses in a school with a relatively strong academic reputation! I can only imagine that the situation is worse now.

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  • klejdys

    So what you’re saying is that National Review had no idea what it was doing when it fired Robert Weissberg?

    Heaven forfend. If they are wrong on Weissberg…what if they were wrong on the Derb??? //head explodes

    Great thoughts. Should be read by anyone who has a student in school or is a teacher.

    • educationrealist

      Well, you have conflated race with ability. I agree that ability doesn’t seem to be evenly distributed by race, but the students in my classes that do the “learn and forget it” are of all races, including Asian.

      However, I think the reason we ignore cognitive ability is because of our fears about the racial distribution.

  • Pincher Martin

    Congrats on getting this post recognized so widely across the blogosphere.

    • educationrealist

      Thanks! It occurred to me that most of the people I read on the subject of cognitive ability have very little idea what it’s like to teach kids of low to average IQs relatively advanced concepts.

  • Jouyin Teoh

    I think it’s like getting a square peg to fit into the wrong hole – the problem isn’t with the kids, the problem isn’t with the teachers. The problem is with the system. I’m an occupational therapist with experience teaching intellectually challenged children – if students are put into a system which focuses on discovering their strengths and cultivating them, they stand a better chance of succeeding than being forced to comply to a standard, uniform system. Each of us have a role to play in the world, for these kids – maybe they’re just not meant to play roles that involve complex maths. I know I wasn’t meant to, and I’d be a lousy engineer, but I’m good at what I do. 😛

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  • Min

    One question that I have is the extent to which students are playing Whack-a-Mole in order to get easy classes for a week or two.

  • Min

    “Many students who demonstrated mastery of distributing multiplication over addition are now making a complete hash of the process in multi-step equations.”

    That kind of thing is not unusual. Even professors of logic have gotten the Wason task wrong. Context matters. One of the strengths of mathematics is its meaninglessness. That means that the same math can apply to different things. But its meaninglessness also makes it difficult to learn. It also means that learning the distribution of multiplication over addition does not mean that the student has learned how to apply it in different contexts.

    • educationrealist

      Since it’s half the class, it would hardly be unusual now, would it?

      It also means that learning the distribution of multiplication over addition does not mean that the student has learned how to apply it in different contexts.

      Yes, it would. I think I pointed that out.

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  • Lynn curious parent

    I really enjoyed this article, and several of the others on this site. It made me laugh out loud. Usually when I read educational stuff (a lot) it makes me roll my eyes. The hook that got me to leave this comment was the last line – ‘and why they don’t remember is an issue we really should start to treat as a big piece of the puzzle’. We have a challenging son who is a challenging student – he is part gifted, part learning difficulties, part teenager. The best I can do as a parent is provide a loving and secure home environment. We have both had a dismal experience of his high school years so far. Anyway, back to the article. In the interests of providing data for ‘why they don’t remember’ I can relate this episode from last night. Son’s teacher contacted me to say there is a trigonometry test tomorrow, son hasn’t done the revision in class, can I help him at home. I did, we went back to basic concepts, we did some examples, we worked out how to use the computer calculator to do inverse functions…. all stuff we did last year for trigonometry. Son didn’t remember any of it “I remember doing it last year but i forgot about it straight afterwards because it wasn’t relevant to what I want to do – it went straight to the delete file in by brain”. (He talks a lot in computer language, he wants to design computer games). I suspect the trash can folder will be emptied again as soon as the test is done. My reason for searching the internet and thankfully coming across this site was to try and find out if there is any relevance to learning trigonometry, for our son anyway. Haven’t found anything yet, so at this stage I have to agree with him.
    Thanks for the articles, thoughts, humour etc. It has given me hope again (for today at least).
    From Lynn curious parent.

    • cathyf

      I have been a professional videogame developer, and trigonometry is absolutely basic. Without it, the physical motion in your game looks wrong. And you have no concept of proper scoring.

      Tell your son that math is the difference between being a PLAYER of games and a BUILDER of games. Or, in money terms, math is the difference between paying to play games and being paid to build games. Because nobody is going to pay anybody to play games…

      • Lynn curious parent

        Thanks cathyf for your reply.
        Have just had a great conversation with son, who is now at home “unschooling”. We are discovering all sorts of possibilities that are outside the usual pathways (re school systems and work). The best thing for him is learning/knowing he CAN pursue what’s relevant to him – probably not through mainstream channels. And for me it’s making sure he has the skills to do it himself. Mind you, his ideal workplace would still be to be paid to play games – and he has investigated the possibilities! I observe no income yet however.

      • cathyf

        Tell your son that there ARE videogame jobs where you play games all day. Imagine playing “Barbie’s Dream House” for 70 hours per week.

        For six months.

        Videogame houses are terrible places to work. The pay sucks, and it’s ALWAYS “crunch time” because management knows that there is an infinite supply of starry-eyed kids willing to work for peanuts so that when they burn out this crew there are always more suckers in the pipeline. The PC gaming industry is dead, killed off by software pirates, and console games are like movies with incredibly detailed specs and individual workers are cogs in this giant machine who have no control over or even access to the overarching design of the game. (I heard a comment once by an artist who worked on Monsters, Inc. It went something like — remember the scene where Sully sneezes? The 1-second cloud of snot, 18 months of my life! Games are a lot like that, too.)

    • caroljm36

      Jeez he’ll be using Trig functions all through Calculus. Why would you skip that? Unless he’s going to be a business major.

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  • Robert in Arabia

    IQ tests? We don’t need no stinking IQ tests.

  • Ariel

    I’m coming to this conversation a little late, so apologies for that. I was searching for something else via Google and ended up here and I’m glad I did. What you explained in your post as “What-A-Mole” describes perfectly how I felt taking “learning support” math upon my return to college. I took my first math course this fall after thirty-plus years. Even in high school I didn’t do all that well in math, so you can imagine my dread and fear of taking math – even sweathog math – in college. I’m one of those creatures who ended up with near-perfect verbal SAT scores but to describe my performance in math as “dismal” would be rather generous.

    Before entering college this year I took the COMPASS exam and did not pass the math section by 2 points, but received a perfect score on the language portion, a re-run of where I left off back in the ’70s. I’ve been a relatively successful businessperson (even with only a high school diploma) and consider myself smarter than the average bear, but when it comes to mathematics, I cannot seem to retain lessons, or at least have not learned how to retain them. Then again, neither have I been taught. Under advisement from my university counselor, I took the ALEKS online course, supposedly so I could “learn at my own pace”. That sounded good since in my entire life I had one year of algebra in high school – back in 1976! Even had I managed to pass the COMPASS it seemed ridiculous to enroll in a college-level math course when I basically know almost nothing.

    The problem is… I am not sure I really learned very much, even though I did manage to pass what ALEKS describes as “beginning and intermediate algebra” in one semester. I think if placed in your 9th-grade class I would probably pass… probably. I am very afraid that what I learned was how to use ALEKS, not the actual algebra.

    Your description of kids enthusiastically working out problems one day and then looking glassy-eyed when faced with those same problems two weeks later is painfully relevant to me. I’m one of those glassy-eyed ones.
    I doubt by Spring term I would be able to pass the final exam from the class I just completed, and by that I mean the very same exam.

    So I can relate to those kids. Do I blame the ALEKS program? No, not really, it did basically what it advertised. Do I blame myself? No, I worked very hard on this class – I logged in 173 hours just in ALEKS, and of course studied outside that login time (as well as took two other classes).
    I understand blame is not a particularly useful concept, but it would be good to know why I spent so much time and effort and feel I have gained very little effective knowledge.

    Before anyone dismisses kids as stupid, lazy, manipulative or other negative traits though, I would encourage them to take a course in a subject they found challenging in high school or college the first time around. It might give a different perspective.

    I have no answers for you on how to remedy the Whack-A-Mole situation. I just empathize with those kids and want to say yes, some of them are probably just lazy, “not bright” or disinterested but some, like me, may want desperately to learn but maybe just don’t know how to *learn* it.

    Thanks for a thought-provoking post!

    – Ariel

    • educationrealist

      You’re welcome. One thing to remember–there’s a big difference between a high cognitive ability person with math issues and a low cognitive ability person who struggles with all abstract learning. I know more than a few people like you, and it’s a whole different problem than the one I’m describing here (although the symptoms are the same).

      You may want to check out my linear modeling posts. I’m going to do more on that subject as well.

      • DensityDuck

        It does seem to me that knowledge retention might be both a learned skill and a genetic factor.

        Some people can go to the gym for six months, work hard every day, get their weight down and their strength up, and if they stop going then six months later they’re a slack-armed pudge again, even if they stayed on the diet. Other people are just generally fit and strong their whole lives without really trying. The ability to stay in physical condition is genetic; why ot expect to see the same in knowledge retention?

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  • Robert Miller

    I did poorly in math (algebra, geometry, trig etc) in high school. I just would not sink in. While in the Army, I began to take courses in college subjects, and had to take refreshers in Algebra, trig etc, and I excelled in it. It was if some switch in my brain was turned on. I still can do complex problems in trig and calculus, et al. Maybe the problem is that the “switch” is turned off. I have talked to others about this. Some got math in high school, but other areas were a complete mystery to them, such as reading, etc.

    • surfer

      There is something about the military. Have seen a lot of great technical courses from there. Not great like an MIT course at the highest level and stuffed. But great at efficiently transferring info and training students.

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    I have taught mathematics and science at international prep schools in China and Vietnam. I can assure you these students exist at the highest socioeconomic levels. Being able to do mathematics does not vary proportionally with how many fancy toys your mommy and daddy can buy you.

    Whatever the problem is, it’s not reducible to wealth and poverty.

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  • surfer

    [This is weird but I’m commenting on a comment from the GeneXP blog, don’t want to sign up for Discus]

    A commenter there talked about algebra and chemistry:

    “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&#39t getting it. Finally she asked a question which clarified the problem: It wasn&#39t the chemistry she had trouble with — she didn&#39t 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&#39t 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&#39s just one of those people who innately can&#39t do it, or can&#39t remember it, like the kids described above.”


    I’m surprised by the lack of awareness and empathy.

    I got a 5 on the AP exam (in the 80s, at a top school) and tutored it as a TA in college with students much better than his. (general chem, top 25 school, more than 50% pre-MD). So I know general chem as a student and briefly a tutor.

    OF COURSE chemistry is applied algebra. The subject is rife with it (stoichiometry, equilibrium [general, acid-base, and solubility product], reaction rates (both concentration and temperature variations), gas laws, thermodynamics, as well as all kinds of unit conversions. Yes, there is some descriptive chemistry and bonding concepts, but I would say easily 50% of it is tricky applied algebra.

    I actually had a (smart) girl at the top 25 who was irked that she did not place out of G chem and then more irked at having a B+ (straight As in high school). Was working practice problems with her and at one point she looked at me and said, “you know this stuff isn’t chemistry, it’s ALGEBRA”. I tried to give her some PC stuff about chem concepts, but she looked me dead in the eye and said “this is just algebra and know that I realized this, I am going to ace your course”. AND SHE DID.

    So, it’s not even the concept of how algebraic general chem is. It’s that this fellow didn’t realize it. Didn’t even realize it himself. And it is possible to be pretty darned good at math and science and still have to pause a bit and work through some tricky algebra, particularly in chemistry word problems. Even for the strong students.

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  • Not Negatives–Subtraction | educationrealist

    […] not like the curriculum was a surprise: integer operations and fractions played a big […]

  • Mike

    Reminds me of the movie “Stand and Deliver” from 1988 and Reagan 1983 report “A Nation At Risk”!
    We look for scapegoats, especially Feds & new ed reforms, instead of discussing meaningful solutions!

  • Ten Most Read, Ten You Should Read | educationrealist

    […] The myth of “they weren’t ever taught….”— July 1, 2012 This is one of my favorite pieces. It’s all true, still. Every word. And new teachers have to come to grips with it every year. ignore me, lazy way to space […]

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