Math class needs a makeover | Dan Meyer | TEDxNYED

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.

Can I ask you to please recall a time

when you really loved something -

a movie, an album, a song or a book -

and you recommended it wholeheartedly

to someone you also really liked,

and you anticipated
that reaction, you waited for it,

and it came back, and the person hated it?

So, by way of introduction,

that is the exact same state

in which I spent every working day
of the last six years. (Laughter)

I teach high school math.

I sell a product to a market

that doesn't want it,
but is forced by law to buy it.

I mean, it's just a losing proposition.

So there's a useful stereotype
about students that I see,

a useful stereotype about you all.

I could give you guys

an algebra-two final exam,

and I would expect no higher

than a 25 percent pass rate.

And both of these facts say
less about you or my students

than they do about what we call
math education

in the U.S. today.

So, I'd like to talk about some problems
that we're having with this.

To start with, I'd like to break
math down into two categories.

One is computation;
this is the stuff you've forgotten.

For example, factoring quadratics

with leading coefficients
greater than one.

This stuff is also really easy to relearn,

provided you have
a really strong grounding in reasoning.

Math reasoning -

we'll call it the application

of math processes
to the world around us -

this is hard to teach.

This is what we would love
students to retain,

even if they don't go
into mathematical fields.

This is also something that,
the way we teach it in the U.S.

all but ensures they won't retain it.

So, I'd like to talk about why that is,

why that's such a calamity
for society, what we can do about it

and, to close with,
why this is an amazing time

to be a math teacher.

So first, five symptoms

that you're doing math reasoning wrong

in your classroom.

One is a lack of initiative;
your students don't self-start.

You finish your lecture block

and immediately you have
five hands going up

asking you to re-explain
the entire thing at their desks.

Students lack perseverance.

They lack retention; you find yourself

re-explaining concepts
three months later, wholesale.

There's an aversion to word problems,

which describes 99 percent of my students.

And then the other one percent

is eagerly looking for the formula

to apply in that situation.

This is really destructive.

David Milch, creator of "Deadwood"
and other amazing TV shows,

has a really good description for this.

He swore off creating

contemporary drama,

shows set in the present day,

because he saw
that when people fill their mind

with four hours a day of, for example,
"Two and a Half Men," no disrespect,

it shapes the neural pathways, he said,

in such a way that they expect
simple problems.

He called it, "an impatience
with irresolution."

You're impatient with things
that don't resolve quickly.

You expect sitcom-sized problems
that wrap up in 22 minutes,

three commercial breaks and a laugh track.

And I'll put it to all of you,

what you already know, that no problem
worth solving is that simple.

I am very concerned about this

because I'm going to retire
in a world that my students will run.

I'm doing bad things

to my own future and well-being

when I teach this way.

I'm here to tell you that the way
our textbooks -

particularly mass-adopted textbooks -
teach math reasoning

and patient problem solving,

it's functionally equivalent
to turning on

"Two and a Half Men"
and calling it a day.

(Laughter)

In all seriousness.

Here's an example
from a physics textbook.

It applies equally to math.

Notice, first of all here,

that you have exactly three pieces
of information there,

each of which will figure into a formula

somewhere, eventually,

which the student will then compute.

This conditions students to expect this,
I believe, in real life.

And ask yourself, what problem
have you solved, ever,

that was worth solving

where you knew
all of the given information in advance;

where you didn't have
a surplus of information

and you had to filter it out,

or you didn't have
insufficient information

and had to go find some.

I'm sure we all agree that
no problem worth solving is like that.

And the textbook, I think,
knows how it's hamstringing students

because, watch this,
this is the practice problem set.

When it comes time
to the actual problem set,

we have problems like this right here

where we're just swapping out numbers
and tweaking the context a little bit.

And if the student still doesn't recognize
the stamp this was molded from,

it helpfully explains to you

what sample problem you can return to
to find the formula.

You could literally, I mean this,

pass this particular unit
without knowing any physics,

just knowing how to decode a textbook.

That's a shame.

So I can diagnose the problem
a little more specifically in math.

Here's a really cool problem. I like this.

It's about defining steepness and slope

using a ski lift.

But what you have here is actually
four separate layers,

and I'm curious which of you can see
the four separate layers

and, particularly, how when
they're compressed together

and presented to the student all at once,

how that creates this
impatient problem solving.

I'll define them here:
You have the visual.

You also have the mathematical structure,

talking about grids, measurements, labels,

points, axes, that sort of thing.

You have substeps, which all lead
to what we really want to talk about:

which section is the steepest.

So I hope you can see.

I really hope you can see
how what we're doing here

is taking a compelling
question, a compelling answer,

but we're paving a smooth, straight path

from one to the other

and congratulating
our students for how well

they can step over the small cracks
in the way.

That's all we're doing here.

So I want to put to you that if we can
separate these in a different way

and build them up with students,

we can have everything we're looking for
in terms of patient problem solving.

So right here I start with the visual,

and I immediately ask the question:

Which section is the steepest?

And this starts conversation

because the visual is created in such
a way where you can defend two answers.

So you get people arguing
against each other,

friend versus friend,

in pairs, journaling, whatever.

And then eventually we realize

it's getting annoying to talk about

the skier in the lower
left-hand side of the screen

or the skier just above the mid line.

And we realize how great would it be

if we just had some A, B, C and D labels

to talk about them more easily.

And then as we start to define
what does steepness mean,

we realize it would be nice
to have some measurements

to really narrow it down,
specifically what that means.

And then and only then,

we throw down that mathematical structure.

The math serves the conversation,

the conversation doesn't serve the math.

And at that point, I'll put it to you
that nine out of 10 classes

are good to go on the whole
slope, steepness thing.

But if you need to,

your students can then develop
those substeps together.

Do you guys see how this, right here,
compared to that -

which one creates that patient problem
solving, that math reasoning?

It's been obvious in my practice, to me.

And I'll yield the floor here
for a second to Einstein,

who, I believe, has paid his dues.

He talked about the formulation
of a problem being so incredibly important

and yet in my practice, in the U.S. here,

we just give problems to students;

we don't involve them
in the formulation of the problem.

So 90 percent of what I do

with my five hours of prep time per week

is to take fairly compelling elements

of problems like this from my textbook

and rebuild them in a way that supports

math reasoning
and patient problem solving.

And here's how it works.

I like this question.
It's about a water tank.

The question is: How long
will it take you to fill it up?

First things first,
we eliminate all the substeps.

Students have to develop those,

they have to formulate those.

And then notice that all the information
written on there is stuff you'll need.

None of it's a distractor,
so we lose that.

Students need to decide,

"All right, well, does the height matter?

Does the side length matter?

Does the color of the valve matter?
What matters here?"

Such an underrepresented
question in math curriculum.

So now we have a water tank.

How long will it take you to fill it up?
And that's it.

And because this is the 21st century

and we would love to talk
about the real world on its own terms,

not in terms of line art or clip art

that you so often see in textbooks,

we go out and we take a picture of it.

So now we have the real deal.

How long will it take it to fill it up?

And then even better is we take a video,

a video of someone filling it up.

And it's filling up slowly,
agonizingly slowly.

It's tedious.

Students are looking at their watches,
rolling their eyes,

and they're all wondering
at some point or another,

"Man, how long is it going to take
to fill up?"

(Laughter)

That's how you know
you've baited the hook, right?

And that question, off this right here,
is really fun for me

because, like the intro,

I teach kids -
because of my inexperience -

I teach the kids
that are the most remedial, all right?

And I've got kids who will not
join a conversation about math

because someone else has the formula;

someone else knows how to work
the formula better than me,

so I won't talk about it.

But here, every student
is on a level playing field of intuition.

Everyone's filled something
up with water before,

so I get kids answering the question,
"How long will it take?"

I've got kids who are mathematically
and conversationally intimidated

joining the conversation.

We put names on the board,
attach them to guesses,

and kids have bought in here.

And then we follow
the process I've described.

And the best part here,
or one of the better parts

is that we don't get our answer
from the answer key

in the back of the teacher's edition.

We, instead, just watch
the end of the movie.

(Laughter)

And that's terrifying,

because the theoretical
models that always work out

in the answer key in the back
of a teacher's edition,

that's great,

but it's scary to talk
about sources of error

when the theoretical does not
match up with the practical.

But those conversations
have been so valuable,

among the most valuable.

So, compare all that to your textbook.

So I'm here to report
some really fun games

with students who come pre-installed

with these viruses day one of the class.

These are the kids
who now, one semester in,

I can put something on the board,

totally new, totally foreign,

and they'll have a conversation
about it for three or four minutes more

than they would have
at the start of the year,

which is just so fun.

We're no longer averse to word problems,

because we've redefined
what a word problem is.

We're no longer intimidated by math,

because we're slowly
redefining what math is.

This has been a lot of fun.

I encourage math teachers
I talk to to use multimedia,

because it brings the real world
into your classroom

in high resolution and full color;

to encourage student intuition
for that level playing field;

to ask the shortest question
you possibly can

and let those more specific questions
come out in conversation;

to let students build the problem,

because Einstein said so;

and to finally, in total,
just be less helpful,

because the textbook is helping you
in all the wrong ways:

It's buying you out of your obligation,

for patient problem solving
and math reasoning, to be less helpful.

And why this is an amazing time
to be a math teacher right now

is because we have the tools to create

this high-quality curriculum
in our front pocket.

It's ubiquitous and fairly cheap,

and the tools to distribute it

freely under open licenses

has also never been cheaper
or more ubiquitous.

I put a video series
on my blog not so long ago

and it got 6,000 views in two weeks.

I get emails still from teachers
in countries I've never visited

saying, "Wow, yeah.
We had a good conversation about that.

Oh, and by the way, here's how I made
your stuff better,"

which, wow.

I put this problem on my blog recently:

In a grocery store,
which line do you get into,

the one that has one cart and 19 items

or the line with four carts
and three, five, two and one items.

And the linear modeling involved in that
was some good stuff for my classroom,

but it eventually got me

on "Good Morning America"
a few weeks later,

which is just bizarre, right?

And from all of this, I can only conclude

that people, not just students,

are really hungry for this.

Math makes sense of the world.

Math is the vocabulary

for your own intuition.

So I just really encourage you,
whatever your stake is in education -

whether you're a student, parent,
teacher, policy maker, whatever -

insist on better math curriculum.

We need more patient problem solvers.

Thank you. (Applause)