Teaching Perseverance

Reading an Alfie Kohn’s article on what kids learn from failure made me think of the most common question I hear from teachers about the Common Core Practices:

How can I teach perseverance?

It’s an excellent question, and the answer isn’t necessarily obvious. As Kohn points out, experiencing failure and having a teacher prod you to keep trying isn’t—or letting you hang—isn’t necessarily helpful. He write that

studies find that when kids fail, they tend to construct an image of themselves as incompetent and even helpless, which leads to more failure… if an adult declines to step in and help when kids are frustrated, that doesn’t make them more self-sufficient or self-confident: It mostly leaves them feeling less supported, less secure about their own worthiness, and more doubtful about the extent to which the parent or teacher really cares about them.

This illuminates a real pitfall of the unsubtle approach to teaching perseverance. You can’t simply throw students into a situation where they’re likely to fail and let them founder. When I think about being productively stuck, it’s worth remembering that there’s two ways to get out of balance, and both are pretty unproductive. If there’s no challenge, there’s no real learning. If the challenge is—or feels—insurmountable, there’s no real learning either.

And the best medicine for those about to face a particularly tough challenge, and want to stave off the feelings of failure that threaten to derail them? Start with a few easy successes. Seriously. I’ve realized that I do this myself, and when I help kids do it, they can work longer and with more focus.

I start with easy cases. Ridiculously easy. Say I’m trying to figure out the problem of how many squares are on a chessboard.

There are 64 small squares. Is that they end? No, wait, the whole thing is a square. So that makes 65. But then there are middle sized ones. Suddenly, the problem seems insurmountable. Many kids, once they realize they’re facing a cacophony of counting, give up.

What I do is ask myself how I could turn this into a problem that I could have some success with. How easy could I make this problem? And here’s the interesting thing. I’ll ask kids that question (even prompting them, if necessary, that eight by eight is a pretty big situation to start with) and what they usually say is to try on a four by four board instead. Sometimes they’ll say to start on a three by three or a two by two.

Do you know where I start? Zero by zero.

It’s shameless, I know, but why should I feel shame? I’m just thinking, playing, messing around, and giving myself the gift of instant success.

Because I can see immediately that there are zero squares on a zero by zero board. There’s no board.

And then I go to a one by one board. Which has one square.

So at the point others are giving up, I’ve now experienced two successes. And so have my students, with my help. I didn’t give anything away, didn’t rob them of the challenge. Just modeled how to start simple, bolster yourself up, see what you know. And there’s a way forward, a pathway from simple to hard that seems, maybe, passable. I can see a way to slowly ratchet up the difficulty, going to two by two and then to three by three. Maybe I won’t get where I’m going—believe me, I’ve worked on some problems that go from easy cases to ridiculously hard ones quick enough to give you whiplash—but this is part of what learning perseverance looks like. It’s knowing how to reframe things, make things simpler, change focus to see if you can get new ideas. And the taste of success keeps me going.

Thinking over this, there’s something really interesting happening in the pacing. I could have said

0 squares on a zero by zero chessboard.
1 square on a one by one chessboard.
How many on an eight by eight chessboard?

 

The information and the problem are identical. But the experience is profoundly different. That’s because the act of making a problem simpler is empowering. It shifts the situation from one of impending failure to one of success, even if the success is paltry. We go from hanging from a cliff face to standing calmly at the bottom of the mountain, considering our path forward. And no matter how you slice it, falling from a mountain hurts, sometimes in ways that you don’t recover from. Flailing shouldn’t become failing.

In other words, the actual skill we want to teach is how to shift from the despair of feeling like you’re about to fall off the cliff into ignominious ignorance to being back at the start, thinking about your options, considering your possibilities, and know that you can take at least one step without falling down in your journey of however many miles it will be.

Want to teach perseverance? Teach how to start a hard problem with simple case.

This entry was posted in Math Musings, Problem and tagged , , , . Bookmark the permalink.

3 Responses to Teaching Perseverance

  1. dave Gardner says:

    Hi, Dan –
    In regard to the “How Many Squares” problem in your column on perseverance: This problem is a wonderful opportunity to introduce patterns and the value of using them to solve difficult problems such as this. For example:

  2. dave Gardner says:

    Hi, Dan –
    In regard to the “How Many Squares” problem in your column on perseverance: This problem is a wonderful opportunity to introduce patterns and the value of using them to solve difficult problems such as this. For example:
    1 square = 1 square
    4 squares = 5 squares
    9 squares = 14 squares
    16 squares = 30 squares
    The first pattern, of course, is square numbers. The second pattern goes up by square numbers. I’ll add this problem to my math tool box.

  3. peter sills says:

    I am collecting information on how to teach kids perseverance. If you know of any other methods lime this one, let me know!

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>