Math class needs a makeover Dan Meyer

[Music]

can I ask you to please recall a time

when you really love something a movie

an album a song or a book and you

recommended it wholeheartedly to someone

you also really liked and you anticipate

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 spend every

working day of last six years I teach

high school math I I sell a product to a

market that doesn’t want it but is

forced by law to buy it I mean that’s

kind of it it’s just a losing

proposition so there’s there’s a useful

stereotype about students that I see a

useful stereotype about you all I could

give you guys algebra 2 final exam and

I’d expect no higher than a 25 percent

pass rate and both of these facts say

say less about you or my students than

they do about what we call math

education in the u.s. today to start

with I’d like a break math down into two

categories one is computation this is

the stuff you’ve forgotten for example

factoring quadratics with leading

coefficient greater than one

okay this stuff is also really easy to

relearn provided that you have a really

strong grounding in reasoning math

reasoning we’ll call it the the

application of math processes to the

world around us this is hard to teach

there’s 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 US all but ensures they won’t retain

it so I like talk about why that is why

that’s such a calamity for society what

can do about it and to close with why

this is an amazing time to be a math

teacher

okay so first five five symptoms that

you’re doing math reasoning wrong in

your classroom okay one is a lack of

initiative your students don’t self

start you finish your lecture block and

immediately have five hands going up

asking you to re-explain an entire thing

at their desks students lack

perseverance they lack retention you

find yourself reacquainting concepts

three months later wholesale there’s an

aversion to word problems which

describes 99% of my students and then

the other 1% are eagerly looking for the

formula to apply in that situation okay

this is really destructive David Milt a

creator of dead wood

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 a

resolution you’re impatient with things

that don’t resolve quickly you expect

sitcom size problems that wrap up in 22

minutes three commercial breaks in US

and a laugh track and I’ll put it to all

of you what you already know that no

problem we’re solving is that simple I

am very concerned about this because the

I’m gonna retire in a world that my

students will run I’m doing I’m doing

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

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 okay I believe in real life and

ask yourselves what problem have you

solved ever

that was worth solving where you knew

all of the given information in advance

or 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 we’re

solving just 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 you have

problems like this right here where

we’re just swapping out numbers and

tweaking the context a little bit and

the student still doesn’t recognize the

stamp this is molded from it helpfully

explains to you like what what sample

proud you can return to you to find the

formula you literally I mean this past

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

actually four separate layers I’m

curious which of you can see the four

separate layers and particularly how

when they’re compressed together and

presented a student all at once how that

creates that this impatient

problem-solving I’ll define them here

you have the visual okay you also have

the mathematical structure talking about

grids measurements labels points axes

that sort of thing you have sub steps

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 congratulate 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 it 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 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 we get people

arguing against each other friend versus

friend impairs journaling whatever and

then eventually we realize it’s it’s

getting annoying to talk about the skier

in the lower left hand side of the

screen or the the skier just above the

midline and we realized how great would

it be if we just had some a B C and D

labels to talk about them more easily

and then and then as we start to define

like what what does steepness mean we

realized it’d be nice to have some

measurements so 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 ten

classes are good to go on the whole

slope steepness thing but if you need to

your students can then develop those sub

steps 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 is paid his dues he talked

about the formulation of prom being so

incredibly important and yet in my

practice in the u.s. here we just give

problems of student we don’t involve

them in the formulation of the problem

so 90% of what I do with my five hours

of prep time per week

it’d 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 ok first things

first we eliminate all the sub steps

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 is such an underrepresented

question 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 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 going to take to

fill up

that’s how you know you baited the hook

right and and that question off this

right here is really fun for me because

like I like the intro I teach I teach

kids because of my inexperience I teach

the kids that are the most remedial

alright and I got kids who will not join

a conversation about math because

there’s like someone else has the

formula someone else knows how to work

the formula better than me so I won’t I

won’t talk about it but here every

student is on the level playing field of

intuition like everyone spilled

something up with water before so I get

kids answering the question how long

will it take I got kids who are who are

mathematically and conversationally

intimidated joining the conversation

when you put 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 a teacher’s edition

we instead just watch the end of the

movie and that’s terrifying all right

because the theoretical models that

always work out in the answer key the

back of a teacher’s edition like that’s

great but it’s scary to talk about

sources of error when the theoretical

does not match up at the practical but

those conversations have been so

valuable among the most valuable so I’m

here to report some really fun games

with students who come pre-installed

with these viruses day one of the class

okay

these are kids who 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 started the year which is 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 I math cuz we’re slowly

redefining what math is this has been a

lot of fun I encourage Matthews as I

talked to to use multimedia because it

brings the real world into your

classroom and high resolution in 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 it finally in total just be less

helpful because the textbook is helping

you in all the wrong ways as helping you

it’s buying you out of your

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 it’s 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