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Failure Actually IS an Option

The One Laptop Per Child wiki may seem like an odd place to find an essay titled What Makes Mathematics Hard to Learn? but that’s exactly where the folks at Mental Floss found it.

The writer, Marvin Minsky, a “cognitive scientist in the field of artificial intelligence”, says the problem is not in learning math but in the way we teach it.

Why do some children find Math hard to learn? I suspect that this is often caused by starting with the practice and drill of a bunch of skills called Arithmetic–and instead of promoting inventiveness, we focus on preventing mistakes. I suspect that this negative emphasis leads many children not only to dislike Arithmetic, but also later to become averse to everything else that smells of technology. It might even lead to a long-term distaste for the use of symbolic representations.

Minsky offers some excellent suggestions for improving the way we teach math, especially at the elementary level.

First among these is encouraging kids to experiment with concepts and processes instead of always expecting them to memorize and apply algorithms over and over (and over!).

At the same time we stigmatize the concept of “failure” by drilling into their heads the absolute need to right, each and every time.

There is a popular idea that, in order to understand something well, it is best to get things right from the start–because then you’ll never make any mistakes. We tend to think of knowledge in positive terms–and of experts as people who know exactly what to do. But one could argue that much of an expert’s competence stems from having learned to avoid the most common bugs. How much of what each person learns has this negative character? It would be hard for scientists to measure this, because a person’s knowledge about what not to do doesn’t overtly show in that individual’s behavior.

In the real world, people learn from their mistakes and build on their failures as well as their successes.

In school, especially in how we teach arithmetic, mistakes are not permitted. Everything is right or wrong. There is no other option.

It’s no wonder, by the time students arrive at high school, most pretty much hate the thought of anything called “math”.

education, math, olpc, learning


  1. Ted Bongiovanni

    I was a math flunkie in grammar school. I’ll never forget Ms. McArdle’s 10 question computation tests, where we had to add, subtract, multiply and divide eight digit numbers by hand. In spite of regularly failing these tests I managed OK — but just OK with my graduate statistics and economics classes. I’m *still* intimidated by math–but now it’s my problem. (Pun somewhat intended.)

    I think the promise of OLPC in Math education is that it has the potential to make learning about math fun–to allow for that expert playful experimentation to which you refer. If you want to draw a line for a game so that a character can scale a wall, then you’ve had to learn about plotting coordinates on a grid, slope, and all these other concepts that are so hard to make real.

    Great post, and I think there’s amazing potential here. I just hope we can find a way to overcome the inertia of teaching to avoid mistakes–if mistakes were rewarded, I’d have been a better student. :)

  2. Betty

    When I taught math, I encouraged students to learn from their mistakes. The biggest problem was having to move so fast through the objectives in order to be prepared for the state test held each spring. I do think that memorizing basic facts is essential, but kids need to be given time to use their knowledge before being assigned another set of facts to memorize.

  3. Charlene

    I agree with Betty about moving too fast. I also agree that there are some who tend to teach little guys with a zero tolerance for mistakes. On the Connections site: http://cnx.org/content/m14660/latest/ one module called “Make School a Safe Place for Taking Risks and Making Mistakes” shares some ways to help students feel okay about their attempts to solve problems. “This task is to teach and model that we all make mistakes and our schools and classrooms are safe places to make mistakes. If we have a zero tolerance policy, it is zero tolerance for not learning from mistakes. Set the expectation that students will learn to problem solve and we are there to guide and assist. Recognize the progress of students who learned from their mistakes. In our interactions and conference with students, focus on the learning, not the mistake. ” This sounds so basic, how we would want our parents, employers, and friends to treat us in our work. Now if we could just get our students’parents on board with this line of thinking about learning.

  4. Carolyn Foote

    Interestingly, I’ve been reading Dewey’s books and he talks about the same thing (only many years ago!).

  5. Jenny

    I’ve just read this article and found it fascinating. It’s one I need to go back to again because I don’t know that I agree with everything in it, but it has given me a lot to think about. I feel as though math is an area we do not teach very well in this country. We have done much better work in reading and writing. We have a lot to learn about teaching math.

  6. Louise Maine

    We definitely miss the boat in Math and also with other subjects. As we learn from failure, we could do so much better than insisting upon perfection right away. How do we do this when testing students to death is the current norm?

  7. Marvin

    Thanks, Jenny! Could you give me a pointer to where Dewey talks about these things?

    In my essay, I forgot to acknowledge how many great math teachers there are out there. I owe a lot to the encouragement I got from Mr. Lepowsky and Mr. Pieters (as well as from books like Lancelot Hogben’s “Mathematics For The Millions”).

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