TEDxNYED
Dan Meyer: Math class needs a makeover
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Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.
Double-click the English transcript below to play the video.
00:15
Can I ask you to please recall a time
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when you really loved something --
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a movie, an album, a song or a book --
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and you recommended it wholeheartedly
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to someone you also really liked,
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and you anticipated that reaction, you waited for it,
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and it came back, and the person hated it?
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So, by way of introduction,
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that is the exact same state
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in which I spent every working day of the last six years. (Laughter)
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I teach high school math.
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I sell a product to a market
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that doesn't want it, but is forced by law to buy it.
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I mean, it's just a losing proposition.
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So there's a useful stereotype about students that I see,
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a useful stereotype about you all.
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I could give you guys
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an algebra-two final exam,
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and I would expect no higher
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than a 25 percent pass rate.
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And both of these facts say less about you or my students
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than they do about what we call math education
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in the U.S. today.
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To start with, I'd like to break math down into two categories.
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One is computation; this is the stuff you've forgotten.
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For example, factoring quadratics with
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leading coefficients greater than one.
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This stuff is also really easy to relearn,
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provided you have a really strong grounding
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in reasoning. Math reasoning --
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we'll call it the application
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of math processes to the world around us --
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this is hard to teach.
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This is what we would love students to retain,
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even if they don't go into mathematical fields.
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This is also something that, the way we teach it in the U.S.
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all but ensures they won't retain it.
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So, I'd like to talk about why that is,
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why that's such a calamity for society, what we can do about it
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and, to close with, why this is an amazing time
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to be a math teacher.
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So first, five symptoms
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that you're doing math reasoning wrong
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in your classroom.
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One is a lack of initiative; your students don't self-start.
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You finish your lecture block
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and immediately you have five hands going up
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asking you to re-explain the entire thing at their desks.
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Students lack perseverance.
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They lack retention; you find yourself
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re-explaining concepts three months later, wholesale.
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There's an aversion to word problems,
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which describes 99 percent of my students.
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And then the other one percent
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is eagerly looking for the formula
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to apply in that situation.
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This is really destructive.
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David Milch, creator of "Deadwood" and other amazing TV shows,
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has a really good description for this.
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He swore off creating
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contemporary drama,
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shows set in the present day,
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because he saw that when people fill their mind
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with four hours a day of, for example, "Two and a Half Men," no disrespect,
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it shapes the neural pathways, he said,
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in such a way that they expect simple problems.
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He called it, "an impatience with irresolution."
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You're impatient with things that don't resolve quickly.
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You expect sitcom-sized problems that wrap up in 22 minutes,
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three commercial breaks and a laugh track.
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And I'll put it to all of you,
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what you already know, that no problem worth solving is that simple.
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I am very concerned about this
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because I'm going to retire in a world that my students will run.
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I'm doing bad things
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to my own future and well-being
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when I teach this way.
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I'm here to tell you that the way our textbooks -- particularly
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mass-adopted textbooks -- teach math reasoning
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and patient problem solving,
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it's functionally equivalent to turning on "Two and a Half Men" and calling it a day.
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(Laughter)
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In all seriousness. Here's an example from a physics textbook.
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It applies equally to math.
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Notice, first of all here,
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that you have exactly three pieces of information there,
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each of which will figure into a formula
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somewhere, eventually,
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which the student will then compute.
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I believe in real life.
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And ask yourself, what problem have you solved, ever,
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that was worth solving
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where you knew all of the given information in advance;
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where you didn't have a surplus of information and you had to filter it out,
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or you didn't have sufficient information
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and had to go find some.
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I'm sure we all agree that no problem worth solving is like that.
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And the textbook, I think, knows how it's hamstringing students
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because, watch this, this is the practice problem set.
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When it comes time to do the actual problem set,
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we have problems like this right here
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where we're just swapping out numbers and tweaking the context a little bit.
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And if the student still doesn't recognize the stamp this was molded from,
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it helpfully explains to you
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what sample problem you can return to to find the formula.
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You could literally, I mean this,
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pass this particular unit without knowing any physics,
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just knowing how to decode a textbook. That's a shame.
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So I can diagnose the problem a little more specifically in math.
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04:31
Here's a really cool problem. I like this.
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It's about defining steepness and slope
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using a ski lift.
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But what you have here is actually four separate layers,
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and I'm curious which of you can see the four separate layers
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and, particularly, how when they're compressed together
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and presented to the student all at once,
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how that creates this impatient problem solving.
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I'll define them here: You have the visual.
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You also have the mathematical structure,
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talking about grids, measurements, labels,
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points, axes, that sort of thing.
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You have substeps, which all lead to what we really want to talk about:
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which section is the steepest.
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So I hope you can see.
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I really hope you can see how what we're doing here
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is taking a compelling question, a compelling answer,
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but we're paving a smooth, straight path
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from one to the other
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and congratulating our students for how well
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they can step over the small cracks in the way.
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That's all we're doing here.
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So I want to put to you that if we can separate these in a different way
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and build them up with students,
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we can have everything we're looking for in terms of patient problem solving.
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So right here I start with the visual,
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and I immediately ask the question:
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Which section is the steepest?
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And this starts conversation
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because the visual is created in such a way where you can defend two answers.
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So you get people arguing against each other,
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friend versus friend,
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in pairs, journaling, whatever.
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And then eventually we realize
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it's getting annoying to talk about
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the skier in the lower left-hand side of the screen
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or the skier just above the mid line.
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And we realize how great would it be
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if we just had some A, B, C and D labels
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to talk about them more easily.
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And then as we start to define what does steepness mean,
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we realize it would be nice to have some measurements
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to really narrow it down, specifically what that means.
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And then and only then,
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we throw down that mathematical structure.
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The math serves the conversation,
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the conversation doesn't serve the math.
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And at that point, I'll put it to you that nine out of 10 classes
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are good to go on the whole slope, steepness thing.
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But if you need to,
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your students can then develop those substeps together.
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Do you guys see how this, right here, compared to that --
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which one creates that patient problem solving, that math reasoning?
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It's been obvious in my practice, to me.
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And I'll yield the floor here for a second to Einstein,
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who, I believe, has paid his dues.
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He talked about the formulation of a problem being so incredibly important,
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and yet in my practice, in the U.S. here,
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we just give problems to students;
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we don't involve them in the formulation of the problem.
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So 90 percent of what I do
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with my five hours of prep time per week
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is to take fairly compelling elements
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of problems like this from my textbook
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and rebuild them in a way that supports math reasoning and patient problem solving.
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And here's how it works.
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I like this question. It's about a water tank.
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The question is: How long will it take you to fill it up?
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First things first, we eliminate all the substeps.
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Students have to develop those,
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they have to formulate those.
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And then notice that all the information written on there is stuff you'll need.
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None of it's a distractor, so we lose that.
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Students need to decide, "All right, well,
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does the height matter? Does the side of it matter?
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Does the color of the valve matter? What matters here?"
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Such an underrepresented question in math curriculum.
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So now we have a water tank.
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How long will it take you to fill it up? And that's it.
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And because this is the 21st century
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and we would love to talk about the real world on its own terms,
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not in terms of line art or clip art
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that you so often see in textbooks,
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we go out and we take a picture of it.
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So now we have the real deal.
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How long will it take it to fill it up?
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And then even better is we take a video,
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a video of someone filling it up.
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And it's filling up slowly, agonizingly slowly.
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It's tedious.
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Students are looking at their watches, rolling their eyes,
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and they're all wondering at some point or another,
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"Man, how long is it going to take to fill up?"
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(Laughter)
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That's how you know you've baited the hook, right?
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And that question, off this right here, is really fun for me
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because, like the intro,
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I teach kids -- because of my inexperience --
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I teach the kids that are the most remedial, all right?
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And I've got kids who will not join a conversation about math
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because someone else has the formula;
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someone else knows how to work the formula better than me,
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so I won't talk about it.
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But here, every student is on a level playing field of intuition.
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Everyone's filled something up with water before,
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so I get kids answering the question, "How long will it take?"
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I've got kids who are mathematically and conversationally intimidated
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joining the conversation.
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We put names on the board, attach them to guesses,
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and kids have bought in here.
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And then we follow the process I've described.
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And the best part here, or one of the better parts
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is that we don't get our answer from the answer key
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in the back of the teacher's edition.
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We, instead, just watch the end of the movie.
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09:01
(Laughter)
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And that's terrifying,
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because the theoretical models that always work out
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in the answer key in the back of a teacher's edition,
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that's great, but
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it's scary to talk about sources of error
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when the theoretical does not match up with the practical.
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But those conversations have been so valuable,
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among the most valuable.
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So I'm here to report some really fun games
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with students who come pre-installed
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with these viruses day one of the class.
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These are the kids who now, one semester in,
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I can put something on the board,
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totally new, totally foreign,
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and they'll have a conversation about it for three or four minutes more
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than they would have at the start of the year,
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which is just so fun.
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We're no longer averse to word problems,
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because we've redefined what a word problem is.
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We're no longer intimidated by math,
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because we're slowly redefining what math is.
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This has been a lot of fun.
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I encourage math teachers I talk to to use multimedia,
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because it brings the real world into your classroom
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in high resolution and full color;
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to encourage student intuition for that level playing field;
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to ask the shortest question you possibly can
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and let those more specific questions come out in conversation;
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to let students build the problem,
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because Einstein said so;
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and to finally, in total, just be less helpful,
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because the textbook is helping you in all the wrong ways:
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It's buying you out of your obligation,
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for patient problem solving and math reasoning, to be less helpful.
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And why this is an amazing time to be a math teacher right now
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is because we have the tools to create
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this high-quality curriculum in our front pocket.
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It's ubiquitous and fairly cheap,
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and the tools to distribute it
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freely under open licenses
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has also never been cheaper or more ubiquitous.
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I put a video series on my blog not so long ago
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and it got 6,000 views in two weeks.
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I get emails still from teachers in countries I've never visited
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saying, "Wow, yeah. We had a good conversation about that.
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Oh, and by the way, here's how I made your stuff better,"
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which, wow.
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I put this problem on my blog recently:
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In a grocery store, which line do you get into,
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the one that has one cart and 19 items
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or the line with four carts and three, five, two and one items.
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And the linear modeling involved in that was some good stuff for my classroom,
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but it eventually got me on "Good Morning America" a few weeks later,
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which is just bizarre, right?
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And from all of this, I can only conclude
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that people, not just students,
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are really hungry for this.
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Math makes sense of the world.
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Math is the vocabulary
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for your own intuition.
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So I just really encourage you, whatever your stake is in education --
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whether you're a student, parent, teacher, policy maker, whatever --
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insist on better math curriculum.
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We need more patient problem solvers. Thank you. (Applause)
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ABOUT THE SPEAKER
Dan Meyer - EducatorDan Meyer is exploring the way we teach teachers to teach kids.
Why you should listen
Dan Meyer asks, "How can we design the ideal learning experience for students?" As a part-time Googler, a provocative blogger and a full-time high-school math teacher, his perspective on curriculum design, teacher education and teacher retention is informed by tech trends and online discourse as much as front-line experience with students.
Meyer has spun off his enlightening message -- that teachers "be less helpful" and push their students to formulate the steps to solve math problems -- into a nationwide tour-of-duty on the speaking circuit.
Dan Meyer | Speaker | TED.com