The hubris of teachers

Today, kids left and right carry the label of some learning disability. Instead of telling kids that they are dumb or lazy, we narrow it down to some problem. It is clearly progress on the face of it. However, when I see that, in some schools, over 10% of all kids have received some kind of disability label by the time they graduate… I worry.

There might be some hubris at work. Do the experts know as much as they claim to know?

A favorite pet peeve of mine is the importance we put on grades as predictors of success. I have spent a great deal of time reviewing graduate students for scholarships in national competitions. I had a nearly perfect GPA myself. I was expecting the undergraduate GPA of students to be strongly correlated with the success at the doctoral level. What I found time and time again was that the correlation was weaker than I expected. Students who do very well as undergraduates often fail to shine as graduate students, and students who disappoint as undergraduates can sometimes do remarkably well as PhD students.

Given a choice, schools should prefer students students who got better GPAs. However, I would abstain from predicting the performance of a given student in graduate school given his GPA.

It is not that grades and tests do not matter, it is that we should use caution and humility when interpreting them. It is relatively easy to make statistical predictions, but it is very hard to translate these statistical predictions into reliable individual predictions.

In my opinion, the greatest mathematician of all times was probably Galois. Coming out of nowhere, he created a deep, useful and engaging mathematical theory that is still, today, viewed as highly original. You are using technology directly derived from Galois’ work today, even though he died in 1832 when he was 20 years old. However, we find that teachers regularly complained about Galois’ uneven results, lack of application, and so on. It seems that he could not focus for long on what his teachers wanted him to do. He was a pain as a student.

This is not uncommon, Gurdon, winner of the 2012 Nobel Prize in Physiology and Medecine, was similarly a difficult student:

“His work has been far from satisfactory… he will not listen, but will insist on doing his work in his own way… I believe he has ideas about becoming a Scientist; on his present showing this is quite ridiculous, if he can’t learn simple Biological facts he would have no chance of doing the work of a Specialist, and it would be a sheer waste of time on his part, and of those who have to teach him.” (source)

Everyone should use caution when judging others, but I believe that educators should be especially careful. They may not understand nearly as much as they think about the mind of their students.

6 thoughts on “The hubris of teachers”

  1. I had posted to you on twitter: ‘I agree with your closing statement, but I have a question: What percentage of “difficult students” become “Nobel Prize winners”?’ Twitter is a restrictive platform, and I tried to get more meaning out a tweet than is probably possible. I’ll try to expand on my real question here.

    The reason I asked about percentage is that I suspect the answer feeds into society’s cost/benefit calculation with regards to education. As I later said, I do believe negative labels are terrible and cause harm. On the other hand, even if we get rid of the negative labeling (and we should), I suspect society would still be willing to give up the potential long term benefits of shepherding “difficult students” for the short term cost reduction that comes from not handling “difficult students” specially. The smaller that percentage is in my original question, the more likely society just won’t care.

    I wouldn’t put much blame on teachers. The ones I know seem to be overworked. I do not blame them for not having time to deal with the “difficult students” and to cater to their educational needs when they have over a hundred other students following the rules (more or less), and the teacher would be punished for deviating from curriculum. (I’m assuming typical U.S. high school here, circumstances may vary.)

    My real question is how do we change the general approach that society has settled on for education? Our approach seems to be driven by a factory model that emphasizes efficiency of obtaining certain outcomes (test scores, grades, credentials etc.) that seem, as you’ve pointed out, weakly correlated with the outcomes that society (or individuals) would prefer. Anybody that does not fit that approach is neglected. How do we change this?

    Of course, perhaps I am merely projecting my own desires on to society. Perhaps society really does value the outcomes of the factory approach to education over other outcomes. Perhaps society actually doesn’t value Nobel Prize winners?

    As a final comment, I’ll just say that I benefited from some special handling as I was going through school. I was never labeled with a learning disability, but I was difficult in other ways. I nearly dropped out of high school, but my parents and a few others fought for me. People made a special exception for me. I was allowed to take math classes at a community college and allowed to take independent study AP classes (my school had worked hard to eliminate AP classes for some reason). I will always be grateful for those special efforts.

  2. @Charles

    In your comment, you refer to society as a being that has opinions and wishes. Can I meet this society? Who gets to decide what “society wants”?

    I was never consulted and my boys were certainly never given a say.

    I have a PhD in mathematics, and I do not get to even express an opinion about what my kids should learn in math and how they should learn it.

    Everything is decided by “experts”. Presumably because they know better. Do they?

    Who holds them accountable? What happens to them if they are wrong? How would we even know if they were wrong? Do we even know who they are?

    For example, most kids are given homeworks. As far as I can tell, there is no shred of evidence that homeworks are useful.

    My kids are told to memorize multiplication tables, but there is no hint of algorithmic thinking in their curriculum. Someone decided that memorizing multiplication tables was very important, but telling the kids about algorithms is not. How was this decision arrived at?

    Now, we take whatever “society” decided was important… remember that we do not know exactly who this “society” is… and then we test students according to this ideal… without really knowing why it is an ideal…

    “We” decided that all kids should learn at a comparable rhythm in all subjects. Who is this “we”?

    Do these people ever question themselves? Are they being held accountable?

    When they rank students, what does this ranking expresses? What “society” thinks is best? Where is this society we refer to?

    I’ll just say that I benefited from some special handling as I was going through school. (…) People made a special exception for me.

    Why should that even be remarkable? Who got to decide that we should all be treated the same… and be grateful whenever we are allowed to differ?

    Since when is being different a fault? Who gets to decide that it is a fault?

  3. “I was never consulted and my boys were certainly never given a say.”

    Yes, you were. The Common Core State Standards put out several public requests for comments.

    “I have a PhD in mathematics, and I do not get to even express an opinion about what my kids should learn in math and how they should learn it.”

    I also have a Ph.D. in mathematics, and I do get to express such an opinion, because I have decided to do so. As a Ph.D., you should know that Ph.D.s mostly only get the work they assign to themselves. If you choose to take the time out of your schedule to have an impact, you can certainly do so. Much of the Common Core committee is made up of mathematicians. The MAA has several groups of faculty, such as CRAFTY, that deal with education. The AMS has a group of mathematicians write the MET and MET II, widely used guidelines for designing programs that train teachers. Additionally, you could work independently. Write a grant to work with a school, get involved in changing education at a grass roots level. Run for a position on the school board. You have lots of options to use your expertise.

    “Everything is decided by ‘experts’. Presumably because they know better. Do they?”

    Well most of these experts have exactly the same qualifications as you: a Ph.D. in mathematics and experience with students, so I’d be more careful about disparaging their expertise.

    “Who holds them accountable? What happens to them if they are wrong? How would we even know if they were wrong?”

    Most of them have tenure, so nobody.

    “Do we even know who they are?”
    A list of CCSS comittee members took literally to less than 30 seconds of googling.
    http://www.corestandards.org/assets/CommonCoreReport_6.10.pdf

    “For example, most kids are given homeworks. As far as I can tell, there is no shred of evidence that homeworks are useful.”
    Well, it depends on the content of the homework, doesn’t it? Asking if homework is useful in general is like asking if drugs are useful in general. It depends on which drug, used to treat what condition, in what patient.

    “Someone decided that memorizing multiplication tables was very important, but telling the kids about algorithms is not. How was this decision arrived at?”

    History of Mathematics. The first documented case (that I know of) of an author claiming that memorizing multiplication tables was necessary is the unknown author of the Treviso Arithmetic. The first printed book on mathematics, from 1478.

    Translation here:
    http://www.opencourtbooks.com/books_n/capitalism_arithmetic.htm

    “‘We’ decided that all kids should learn at a comparable rhythm in all subjects. Who is this ‘we’?”

    I am unaware of anyone making this decision. In fact, I’m not sure what you mean by “comparable rhythm” at all.

    “Do these people ever question themselves?”
    Well, yes. These are people working with children. Almost all of them are also parents. They question themselves, and worry, and doubt just as much as any parent. In addition, many of them (particularly the designers) are scientists, so they carry with themselves a scientific doubt of their own work at all times. Many of them mask all of this doubt and skepticism in certainty, because a) It’s actually quite difficult to be that skeptical of yourself all the time, some self comfort is needed; and b) Parents are in general so worried that their child will be the one that a mistake is made with that they will only listen to anyone who sounds confident and certain, but someone who is honest about the scientific skepticism involved in the process (or the uncertainty inherent in working with extremely complex and not fully understood biological systems) will not be listened to. Confidence must be faked in order to get anything done.

    “Are they being held accountable?”
    I usually interpret this as “are people being punished for mistakes?” For the most part, no, and I don’t really support “accountability” in that sense, because it prevents people from taking risks, and risks are important to growth. But if you really have a need for punishment, you can take comfort in the idea that a conscience is a very cruel and unforgiving master. No failure in this field is ever forgotten by the person who made it.

    “When they rank students, what does this ranking expresses? ”
    This is a change in subject. Developers and experts do not rank students, teachers rank students. For the most part, it expresses an ability to fit into the cogs of society: to meet a bare minimum work ethic, do things that are required regardless of whether or not someone wants to do them, and generally hold an entry level type job or apprenticeship. Now that doesn’t work for everybody. There are a tiny number of exceptional people who could benefit from other treatment, but for the most part, the most valued skill in society is the ability to buckle down, do you work, and meet your responsibilities. That’s what homework is about. Well, that and repeated reasoning for reflecting abstraction, but I’m not going to teach a graduate course in learning theory in an internet comment.

    “Who got to decide that we should all be treated the same… and be grateful whenever we are allowed to differ?”
    Nobody decided that. What you’re seeing is the emergent behavior of many individual decisions. As to while people should be grateful for being treated differently, that should be obvious. Special treatment requires additional effort. Enough additional effort that (with the current teacher-student ratio) not everybody can be treated individually. So a teacher has to decide who gets that extra attention and who does not. One should always be grateful for special treatment, because it’s special. It does not go to everybody. And doubly grateful because that extra work is unpaid. The teacher gets the same salary whether they do that extra work on your behalf or not. So, a student who wants to be treated differently has to communicate to the teacher that it is worth the teacher’s time to do so. You may think you were special, or that your children are special, but what evidence does the teacher have that treating you that way will pay off in terms of additional benefits to you or your children? Why should the teacher decide that out of the 30-150 students, and 60-300 parents they deal with every year, you should be treated specially? If you provide that evidence, if the teacher has a suspicion that it will pay off, then they will take the time. Otherwise they won’t. It is the job of you and your children to provide that evidence, and then be grateful for the additional optional and unpaid work the teacher does on your behalf.

    When I was a child, I was always told that I was very smart. When I went to graduate school, nobody listened to my ideas. I thought “I’m smart, my ideas are good, why is nobody listening to my good ideas.” But that was self centered thinking, barely above the level of a self-obsessed teenager. The real question that mattered was “How do other people see me? I’m in a city full of strangers. They don’t know who I am. I don’t have any credentials. What reason am I giving them to trust me and my ideas?” Then I realized that what I had to do was work to provide evidence that my ideas were good. And guess what. Some of those ideas were good, and some of them weren’t. So the skepticism I faced was warranted.

    The same thing is going on here. If you know you or your children are special and should be treated differently, that’s fine, but how would SOMEONE ELSE know that? What evidence do you provide for others to see? And it has to be more than “My children are getting bad grades,” because there are lots of reasons to be getting bad grades. Being a future Nobel Prize winner is one of the least likely, but that doesn’t mean it’s impossible. It just means you have to give credible evidence that you’re worth the effort.

  4. @Carlos

    it has to be more than “My children are getting bad grades,” because there are lots of reasons to be getting bad grades.

    My own children are not getting bad grades.

    “I was never consulted and my boys were certainly never given a say.”

    Yes, you were. The Common Core State Standards put out several public requests for comments.

    I am not American and I barely know what Common Core is. In Montreal, the curriculum is set by the minister and there is no open deliberation of any kind.

    It is great if Americans openly debate their educational choices… but, even so, why should one committee get to decide what millions of kids should learn? On what moral basis? It seems pretty close to hubris if you ask me.


    “For example, most kids are given homeworks. As far as I can tell, there is no shred of evidence that homeworks are useful.”
    Well, it depends on the content of the homework, doesn’t it? Asking if homework is useful in general is like asking if drugs are useful in general. It depends on which drug, used to treat what condition, in what patient.

    If you are going to prescribe drugs to people, you have to prove to a reasonable degree that it is efficient.

    If you are going to ask 50,000 students to each complete 30 minutes of homework each day of the week for a year… shouldn’t you have to show that it is reasonably efficient?

    “‘We’ decided that all kids should learn at a comparable rhythm in all subjects. Who is this ‘we’?”

    I am unaware of anyone making this decision. In fact, I’m not sure what you mean by “comparable rhythm” at all.

    All students of the same age have to cover the same subjects at about the same level, plus ou minus minor variations.

    The same thing is going on here. If you know you or your children are special and should be treated differently, that’s fine, but how would SOMEONE ELSE know that? (…) you have to give credible evidence that you’re worth the effort.

    We formally expect all students of the same age to achieve the same levels in all subjects.

    Now you say that the burden of the proof should be on the student to show that this might not be applicable in him because he is worth the effort? Why do the student get the burden of the proof?

  5. My academics record shows ridiculously extreme ups and downs. As the post shows observer’s view, I just had to reply with subject’s view. At SSC I underperformed as any introvert high school person is too inexperienced to figure out how to handle bullying by the then mayor’s son, a class-mate, in time to save one’s career. After my own family labeled me idiot, I found solace being pushed around and hero-worshipping kids with rebellious attitudes. Recognizing programming as my only interest from school, that can be profession too, I went to do diploma in Computers, having fared too poorly to do bachelors in engineering aligned with my family’s brilliant background. The subjects that naysayers said were beyond my ability wasted my time only because I had become a freak by overvaluing everybody’s opinions. Still I did manage to enter BE, but now I began seeing how everyone from my past had fared, and completing the feedback loop messed up my priority to make living vs. study, making me crash mid-way, when I finally was doing great. After fixing the coefficients on the feedback loop I easily breezed through M. Tech. with stipend, that too from the premier institute where my grandfather studied, if not from one of handful elite institutes, still better than most. My ease from being well-organized was misinterpreted by some class-mates to block my name being forwarded for worthwhile campus placement offers. My family elders constant worry regarding family future then compelled me to return home. Though some wanted me to start a family, its all work no play building career suited with my education, i.e. the indie developer’s startup challenge. So success indicators, my hunch is, can only be obtained by observing enough closely as to intrude my privacy.

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