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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
more ubiquitous I put a video series on
my blog not so long ago and I got a six
thousand views in two weeks I get emails
still from from teachers and 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 you're in a
grocery store which which line do you
get into the one that has one car in 19
items with line width with four carts
and three five two and one items and the
linear modeling involved in that was
some good stuff in 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 policymaker
whatever it's insist on better math
curriculum we need more patient problem
solvers thank you
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