Required Reading for Math Teachers II

I’m excited and grateful about the positive response to Required Reading I. Therefore I’m a tiny bit trepidatious about my followup since it’s probably going to be a little more controversial. Be that as it may, I think it’s really, vitally important, so here goes:

Praise for Intelligence

Carol Dweck is a developmental psychologist who has made a career of studying how people’s beliefs about their traits influence their performance. She’s written a lot of good stuff but I want to call your attention to this article published in American Educator in 1999. The article summarizes research conducted by Dweck and others, most critically a study she and Claudia Mueller published in 1998 in the Journal of Personality and Social Psychology, 75 33-52 entitled “Intelligence praise can undermine motivation and performance.” I could not find the full text of the study online but the American Educator article summarizes the methodology and results.

Take-home lesson: Praise kids for what they have control over. Do not praise them for what they do not have control over. In particular, do not communicate to them that they’re smart, gifted, talented, intelligent, or the like, when they do something easily.

Telling kids they’re smart or gifted when they do something easily communicates to them that people will stop thinking they’re smart if they ever break a sweat. They become fundamentally afraid of struggle. This inhibits them from growing.

In the research Dweck presents, she and her colleagues took fifth graders and divided them into three experimental groups. All the students were given a set of puzzles that was designed to be “challenging but easy enough for all of them to do quite well.” Afterward, children in the three groups were told the following things:
Group 1: “Wow, you got x number correct. That’s a really good score. You must be smart at this.”
Group 2: “Wow, you got x number correct. That’s a really good score. You must have worked hard.”
Group 3: “Wow, you got x number correct. That’s a really good score.”

Afterward, the students were asked questions: how did they like the task? Would they like to take the problems home to practice? How smart did they feel? The three groups responded similarly to each other.

Next, all three groups were given a harder set of problems, on which they didn’t do as well. Then they were asked again how they liked it, would they like to take home the problems, and how smart did they feel? Lo and behold, the students who had been told “you must be smart at this” now did not feel smart at all, did not enjoy the task, and did not want to take the problems home. The students who had been told “you must have worked hard,” in contrast, enjoyed the task as much or more than the easier one. The third group had results between the other two.

Finally, the three groups were given a third set of problems similar in difficulty to the original set. The “you must be smart” group did the worst, and significantly worse than they had done on the original set. The “you must have worked hard” group did the best, and significantly better than they had done on the original set.

I think these results speak for themselves. If you think you are smart because you succeed with ease, you have a devastating and totally unavoidable conclusion to draw the minute you do not succeed with ease: you are not actually smart. There is nothing left to do but to desperately hide your struggle and hope no one finds you out. This is rough on your performance as well as your psyche. Meanwhile, if you find that your effort, your diligence, better yet your perseverance in the face of setbacks are what get the teacher excited about you, then a real challenge (meaning something you’re doubtful you can do) is actually an opportunity to enact your value. Dweck and Mueller also did some more experiments, fleshing out these details, that I won’t go into – the American Educator article (linked to above) is worth your read. But I have one thing to add. (Actually I have an unbelievably huge amount to add, but I had to limit it somehow.)

I take this research result to have very strong implications about how we should talk with kids about their performance. However, I take it to have no implications at all about what kinds of work they should be doing. For example, I think it challenges us to be very careful around the idea of “giftedness.” I would not mind if the whole idea of “mathematical giftedness” was given a rest for a good long while. But that doesn’t mean I don’t think children who love math shouldn’t get the opportunity to explore this love.

For example, if you are the parent or teacher of a kid who loves math and is breezing through her schoolwork, please please please give her opportunities to study mathematics that she finds exciting and challenging. But don’t tell her this is because she’s “gifted.” That puts her in Dweck’s experimental group 1 (“you must be smart at this”) and so sets her up to become freaked out and alienated from mathematics when the going gets rough. Tell her it’s because she’s excited by it. Praise her not when she flies through something easily but when she sticks with a problem past the point where she was ready to give up. Highlight her own sense of accomplishment when she does something that was really hard for her – “I was so proud when you did that because your patience paid off. I bet you’re proud too, huh?” Acknowledge resourcefulness – “I like how you looked for a new way to see it when your old way wasn’t working.” And show her that you value her enjoyment of the experience of doing math. When she first sees a pattern, she will be excited about it. When she figures out how to solve a new kind of problem, she will feel powerful. When she first sees a connection between disparate-looking objects, she will be in awe. These are the experiences that motivate a lifelong relationship to mathematics, so when she has them, let her know you value that. “Tell me what it was like when you saw that pattern.” If her enjoyment of math is bound up with being “gifted” it is fragile; so train her to enjoy math for its own sake.


13 thoughts on “Required Reading for Math Teachers II

  1. I’m afraid this is going to become a regular question of mine, but here goes: How do you think this extends to older students (adult/college-aged)? I’m a grad student teaching freshman calculus (for the first time, I might add, although I’ve done a lot of one-on-one tutoring) and I’m sure the same ideas about praise apply to them. I wonder if older students might be more inclined to be skeptical about a teacher’s praise, however.

    1. I’m excited to give a look to the book JYB recommends but in the meantime here are my thoughts:

      The exact same principles apply to college students. The important difference is that their ideas about themselves and math and their relation to it are a lot more entrenched. This means a student whose love of math is based on feeling smart by doing things more easily than peers has had a lot of years to become invested in this identity. Likewise, the more common dynamic of feeling dumb because you see peers doing things more easily than you has had a lot of time to embed itself in your psyche.

      From your point of view as a teacher of college students, the lesson of Dweck’s research is the same: don’t praise ease. Praise persistence, resourcefulness, tolerance of frustration, commitment to seeking logical satisfaction, and other mathematically powerful behaviors. Here are some specific ideas, to take or discard as you see fit:

      Jump all over it delightedly when a student takes a public risk. “Thanks for having the guts to try out the problem even though you’re not sure you know how to solve it. We’re all gonna benefit from your courage.”

      Or when a student voices something that’s confusing them. “Awesome question. Asking this kind of question is what’s going to earn you deep understanding. Let’s figure it out.” Or, especially if they seem shy about troubling everyone with the question: “I love it. You’re a warrior for your understanding. Let’s figure it out.”

      Or when a student continues to probe a problem after they’ve already found an answer. I saw a veteran teacher (David Hankin, for you New Yorkers) respond to such a student by saying delightedly to the class “He wasn’t done with the problem when he had the answer!” The student abashedly noted a calculation error in his further work, to which the teacher said, “That’s just arithmetic. That only matters on math contests.” This communicated that the point is to savor and explore the math, not to avoid ever making mistakes.

      These are just a few ideas. I’d be interested in other people continuing this brainstorm…

      But because they’re in college and not elementary school, you won’t see change as quickly. In a room of middle schoolers, two weeks of consistently valuing persistence and not valuing ease is enough to turn the culture of the room around. With college students, change will be much more gradual.

  2. When I first encountered Dweck’s research a couple years ago it was a transformative moment for me. I’ve changed the way I approach feedback and grading. Giving my students the article on how your brain grows when you learn new things from the Dweck, Blackwell intervention study is the second thing we do in my class. The first is the writing assigment from the Cohen study on stereotype threat.

    Side note: She’s actually really helpful and has sent me some resources and we’ve had email conversations a few times.

    @musesusan: There’s a book I really like called How to Give Effective Feedback to Your Students by Susan Brookhart. It focused on feedback which I have found more applicable as a teacher. She cites Dweck’s work in the book and also recommends a book called Choice Words by Johnston which I haven’t read but might have more information on praise itself.

    Article by author:

    The book can be found on the same website.

  3. This paragraph from the article deals with the question raised about college students. I’d like to see the film mentioned:

    Some exciting new research shows that even college students’ views about intelligence and effort can be modified—and that these changes will affect their level of academic achievement. In their study, Aronson and Fried taught minority students at a prestigious university to view their intelligence as a potentiality that could be developed through hard work. For example, they created and showed a film that explained the neural changes that took place in the brain every time students confronted difficulty by exerting effort.

    1. @Sue. It was an excerpt from an ABC news show. It’s older so it’s on VHS only. I don’t have a VCR in my room so never tried to buy it.

      It’s called Common Miracles: New American Revolution in Learning.

      A good one I’ve shown is called “Why Reading Matters” it was produced by the BBC. It’s about reading specifically but I try to make sure my students know that it applies to any complex activity.

      1. I just noticed that perhaps we’re referencing different studies. This is the one that Common Miracles is from:

        Reducing the Effects of Stereotype Threat on
        African American College Students by Shaping Theories of Intelligence

        You seem to be talking about newer research I don’t think I’m familiar with. What’s the citation?

      2. Sue is quoting the Dweck article I linked to. Dweck is citing Aronson and Fried (1998) “Reducing stereotype threat and boosting academic achievement of African Americans: The role of conceptions of intelligence.” Is that the same thing?

  4. This is so interesting! As a kid I remember being put into accelerated (read: gifted) math and feeling SUPER nervous if I didnt get something right away because I assumed my class mates were just breezing by it. I eventually worked through it but I recall being told I was ‘smart’ much more than being told I was ‘hard working’ or capable.
    And of course the kids in the non-accelerated class assumed they couldn’t hack it, that having to work hard to grasp math concepts meant you were deficient, so they had it even worse.

  5. Ben I don’t think you’re going to get much of an argument on this one from the blogging math teacher crowd. I really like the examples in your comment though. I’m determined to call someone “a warrior for your understanding” TOMORROW.

    1. Yay! As far as the apprehension of controversy I was thinking of the exchange with Unapologetic a few weeks back on Jesse’s blog. I may have been consciously politic in writing Required Reading II because of this. Recently I’ve been coming to see the romance of mathematical giftedness not only as a major impediment to improving math education but also as a sort of central tenet of American culture’s relationship to mathematics (Good Will Hunting anyone?). So I’ve been figuring it’s a wall that has to come down brick by brick.

  6. Fascinating.

    Reflecting on my practice, I don’t think I ever cross over to that “gifted” language. I may be a bit stingy with praise, but when it comes, it comes for the answer or the work, not the kid.

    I especially like identifying strong insights that are part of wrong answers. And I’m generous with compliments for good questions (they can be good, they can be perceptive, they can go beyond where we are quite ready to go, they can raise important issues, etc, etc.)



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