Malcom Gladwell on Math and Persistence (1)
Wednesday, December 16th, 2009I’ve really been enjoying Malcolm Gladwell‘s excellent book, Outliers. There’s so much good stuff in this book about the relationship between learning math and: language, cultural attitudes, and agriculture (?!!) that I can’t even describe it all here–you should really just read the whole thing!
One juicy niblet in particular from the book really struck me:
A few years ago, Alan Schoenfeld, a math professor at Berkeley, made a videotape of a woman named Renee as she was trying to solve a math problem. [… ] Twenty-two minutes pass from the moment Renee begins playing with the computer program to the moment she says, “Ahhhh. That means something now.” That’s a long time. [The researcher Schoenfeld remarked,] “If I put the average eighth grader in the same position as Renee, I’m guessing that after the first few attempts, they would have said, ‘I don’t get it. I need you to explain it.’” Schoenfeld once asked a group of high school students how long they would work on a homework question before they concluded that it was too hard for them to solve. Their answers ranged from thirty seconds to five minutes, with the average answer two minutes.
But Renee took twenty-two minutes! Gladwell goes on to explain:
We sometimes think of being good at mathematics as an innate ability. You either have “it” or you don’t. But to Schoenfeld, it’s not so much ability as attitude. You master mathematics if you’re willing to try. That’s what Schoenfeld attempts to teach his students. Success is a function of persitence and doggedness and the willingness to work hard for twenty-two minutes to make sense of something that most people would give up on after thirty seconds.
Gladwell doesn’t try to explain what made Renee so exceptional. But it definitely made me wonder what I can do to help my students cultivate these qualities in themselves.
I’m not surprised about the typical high school student’s patience limit for solving a problem because of the formulaic nature of math problems that are given. In virtually every math textbook, the examples are structured so that if a student sees a problem of type X, they apply theorem Y or method Z to get the answer. This is probably encouraged by typical teaching practices that involve teaching the different ways of getting the answer, rather than problem solving strategies in general. When you have 8 years of this experience, it’s not surprising to find that students will give up after just a few minutes of effort. At that point, it’s a very reasonable assumption that they simply don’t know the right theorem or method for solving the problem.
In contrast, one of the most basic things students who do math competitions learn is a set of problem solving strategies based on trial and effort. Polya’s classic book, How to Solve It, remains an excellent introduction to this different way of thinking.
Thanks for your insightful comments!! I’d never thought about it that way before… that it is a reasonable assumption. I’m always interested in ways to teach actual problem-solving skills instead of just algorithms. I haven’t yet read Polya’s book, thanks for the recommendation!
Also, I checked out your website. CS and experimental psychology — that’s really cool!
What are your thoughts on the prevalence of training students in the automization of math facts? My daughter is in 3rd grade and is being tested in “rocket math” where she is timed on math facts. If she cannot pass one leven she does not move onto the next level. The result was that she did not start learning multiplication until the end of 2nd grade although I know she is capable of learning it.
Most of the research this is based on was done in the 1980’s. Is there any recent, relevent research out there about what is the best way for elementary kids to learn math?
Dear Yolanda, Thanks so much for stopping by! That is a great question. I’m not familiar with “rocket math.” I do think it’s valuable for students to know math facts automatically. When you don’t have to stop and agonize over a basic math fact, it’s much easier to learn more advanced material. And psychologically, students do feel more confident when they know their facts cold. That said, automization of math facts isn’t the end-all be-all. There are many other ways to approach and use math, and only approaching it as memorizing facts is not the best way, in my opinion.
One thing I’ve noticed about methods that focus on quizzing students a lot about the facts is that while that certainly helps to reinforce facts students have already learned, it doesn’t help students who haven’t learned the facts. It’s like if I didn’t know the capital of Alaska and someone tried to teach it to me by quizzing me on it over and over and over. That wouldn’t help me learn it, it would just remind me that I didn’t know the answer!
So instead of just asking the same questions, trying to teach the answers – visually with blocks or pictures, or with stories, or songs or rapping, or however worked for the individual kid – to me, that seems a more reasonable approach.
It sounds like you feel like you may be concerned that the rocket math approach isn’t working for your daughter. There are definitely ways for her to start learning multiplication facts outside of the rocket math system! I would recommend checking out the Rockin’ the Standards skip counting songs. That way she could memorize her skip counting facts and prepare to do multiplication in a way that is fun and confidence-building – and a super-helpful memory aid! You could also practice “building” multiplication facts using math blocks or legos. Basically, if you feel she is ready to start working on multiplication, you don’t need to wait for her to pass into the next level of rocket math.
I’m not sure what you’re referring to when you say most of the research this is based on was done in the 1980s. Are you referring to Malcolm Gladwell, or rocket math, or … ? I don’t know of any research about the best way for elementary kids to learn math, though if I come across any, I will be certain to tell you!
In my experience tutoring students for over seven years, there is no “best way” because everyone’s brain is a little bit different. So it’s really a question of figuring out how your daughter learns best and then trying to do more of that. If rocket math doesn’t seem to be working, there are plenty of different ways to approach the material and lots of other things to try!
I’m happy to explore this with you and help you find something that works for your daughter, so please feel free to continue this conversation here in the comments, or via email, or give me a call at 617-888-0160 if you’d like to talk on the phone!
take care and keep me posted!
REBECCA
Rebecca,
I also tutor math and SAT, ACT prep online. I work with students locally, nationally, and internationally. I love your website. Who designs it for you?
What meeting program do you use? I use Webex.
I’d love to talk with you.
Sandy Lieberman
Hey, Sandy! I use teamskrbl. I’ve never used WebEx–tell me about it!
[…] just read a great story posted on a blog about Malcolm Gladwell’s comments about Alan Schoenfeld’s research on persistence in problem solving in Gladwell’s book Outliers. In this story, a young woman […]