so up until about third grade math class
is great students usually have this
carefree intuition with math and they
are confidence happy even they like math
who does that but then at some point
everything changes ever wonder why pammi
I noticed that you’re still struggling
at your long division fluency but I’ve
made the process so simple even you
could do it
just remember the steps divide multiply
under subtract remainder but if you’re
having a hard time remembering that just
remember the letters of the acronym DM
us are but if you’re having a hard time
remembering that just remember our
clever pneumonic doughnuts make us saggy
rotunda’s DM us are divided multiply
under subtract remainder see this is
simple just follow the steps I’m gonna
send you home with lots of extra
worksheets so you can gain proficiency
yep pretty sure that’s when math class
started to suck
did you ever wonder why we had to learn
long division I mean when I was a kid
adults tried to get away with telling me
it would be very important to know when
I became an adult you know like if I had
to balance a checkbook or work a cash
register or something now I realized
that all my deep-rooted trust issues
come from the fact that I was lied to
nobody uses the long division algorithm
as an adult he perhaps 30 40 years ago
accurate pen and paper calculations
might have been handy but let’s just be
honest who’s really gonna bust out long
division on paper anymore even my old
fashioned push-button phone can do
division imagine what a 10 year olds
fancy smartphone can do and they’ve all
got him so last September after years of
constantly searching for ways to make
math relevant to teenagers by stroke of
Providence I found myself teaching
fourth grade math for part of the day it
was a crazy change because fourth
graders haven’t been disillusioned by
life yet they have this wonderfully
curious nature and they love to explore
new ideas and they don’t have to be
bribed or threatened to participate in
class well inevitably we made it to the
long division unit and of course I
started teaching it the same way I
learned as a child and saying this is
simple just follow the steps one day I
watched my students as they worked in
that creepy way that teachers do hands
there was this sad heavy silence in the
room and they weren’t even necessarily
doing the long division wrong they just
hated life at that moment I felt this
twinge of guilt deep in my bowels but I
thought to myself how else will they
ever be proficient at division they must
be able to keep up with the demands of
our modern technology driven job market
and proficiency in mathematics is the
only way that will happen
so I collected the assignments and I
found this little note written in the
margin of Carly’s paper which really
wasn’t that surprising since Carly was
constantly writing me notes like I love
math or you are so pretty and funny and
I love you who could blame her but this
time it said mrs. Warren I’m sorry that
I’m bad at math and that twinge of guilt
started to feel more like a very painful
cramp
I wanted to write her note of my own
that said Carly this is not math at
least it shouldn’t be
am I the only one that has ever wondered
at the ridiculousness of this thing we
call math how many times must a child’s
natural curiosity and confidence be
sacrificed on the altar of proficiency
before we realize that something needs
to change it was there in that
fourth-grade classroom where I came face
to face with the reality of math
education in our country it’s kind of
pointless don’t get me wrong
math is not pointless mathematics as
Galileo said is the language with which
God has written the universe math is
everywhere and of course is extremely
useful for countless applications I’m
talking about what is taught in the
classroom and why it is being taught I
mean are we being honest when we tell
our kids the years of laboring over
algorithms and formulas will all be
useful for a job someday really when was
the last time you found the volume of an
ellipsoid or the imaginary roots of a
quadratic equation at your job I’ll
never forget the first smartypants high
school student who challenged me with
the questions you know the questions
that every high school math student ever
asks what is the point of all this when
will I ever use it well Alex I’ve got
news for you you
you probably won’t in fact studies show
that very few Americans will ever need
to use anything more than basic
arithmetic or fractions in the workplace
and whether it’s basic arithmetic or
basic derivative calculus it’s all
available in the blink of an eye on your
smartphone or computer so there really
wasn’t any need to spend thousands of
hours struggling in the classroom
because it’s all right there in the palm
of your hands so it would seem that the
radical development of technology has
made math education your relevant and
unnecessary if getting the answer rights
if being proficient is really the goal
of our education then couldn’t we save
ourselves a lot of hassle if we just
left math to the most proficient ones of
all computers I mean who better to
follow rules and algorithms is there no
place in mathematics for the human
elements for the carly’s and the Alexes
and the everyday people like me that
struggle to find any connection between
the classroom and real life quite the
contrary
I believe the need for math education
has never been greater never been more
necessary than in this modern technology
driven culture where presidential
debates are no longer built on solid
logical arguments but rather twenty
second sound bites meant to placate an
ignorant voting populace where a hateful
political climate is driven by impulse
and emotion instead of wisdom and
discourse where our children are driven
to and fro by the winds of confusion in
a battle for their own identities oh yes
we need mathematics but not the math
that you and I were taught we need
something that reaches outside the
boundaries of the class
and touches real life we need a
Renaissance so there was this dude his
name was Isaac Newton he was kind of
famous I guess I think he like invented
gravity or something well he wrote a lot
about where he got his inspiration
he said if I have seen further it is by
standing upon the shoulders of giants in
this man’s discoveries anchored the
Scientific Revolution and yet he of all
people recognized that his great
accomplishments were made possible only
because he stood upon the shoulders of
the Ancients Aristotle Euclid Archimedes
Plato and other classical scholars men
who studied math for a much different
purpose than we do today
you see ancient scholars were less
interested in what math could help you
do and they were more concerned with how
math could affect who you are as a
person they presented math as an
exploration of the mind a personal quest
for truth it was this desire to uncover
truth that motivated Newton and other
Renaissance Sciences to make their
world-changing discoveries but when I
find most intriguing is that classical
mathematics wasn’t aimed primarily at
professional mathematicians or people
who would use it in the workplace one of
the most influential works of ancient
philosophy is Plato’s Republic in it
Plato argued that mathematical training
was the number one priority for anyone
in a position of authority in matters of
the States
and not because of its utility in daily
living but rather in the spirit of a
philosopher
math should be studied because its
ultimate aim is to lead the mind to
truth you see what Plato and other
philosophers knew and what we seem to
have forgotten is that math is
hands-down the greatest tool for
training the minds to reason well think
well argue well to seek out truth and
staunchly defended these men knew that
in order for democracy to succeed
citizens would need a kind of wisdom
that only mathematical training could
develop doesn’t this mean something
coming from the civilization that
introduced democracy to the rest of the
worlds the mathematical philosophy of
the ancient Greeks reached far beyond
their borders and their time influencing
not just mathematicians and scientists
for millennia to come but also political
leaders like surprise Abraham Lincoln
Lincoln wrote that when he wished to
demonstrate the truth of a proposition
when he really wanted to prove something
beyond the shadow of a doubt he could
only do so thanks to his persistent
study of classical Greek mathematics in
that ancient ideal of seeking out and
defending truth was showcased for all
the world to see when Lincoln boldly
argued the proposition that all men are
created equal how skillfully did he
argue that truth and how staunchly did
he defend it we cannot underestimate the
power of math education to change the
course of history and thanks to the
democratic ideals handed down to us from
ancient Greek civilization we all as
citizens have positions of authority in
matters of the state do we not need
citizens and rulers who
like Abraham Lincoln seek out truth and
defendants what could be a more relevant
connection between the classroom and
real life than this but the wisdom
ancient scholars had in mind wasn’t
cultivated by this is simple just follow
the steps and unlike today learning
wasn’t seen as just a transfer of
information from a teacher to the
students no in the ancient tradition
learning was seen as an exchange it was
full of questions not from the students
but from the teacher by asking
purposeful and well-timed questions the
teacher would guide the student to
discover the answers for himself it’s no
wonder that so much of ancient Greek
philosophy was written in the form of a
dialogue because to them education was a
two-way street more like a discussion
than a lecture it was this process this
dialogue that developed the critical
thinking skills required to reason well
think well are you well to seek out
truth and defend it no acronyms or
clever mnemonics required just dialogue
trying to remember when math class ever
resembled anything close to a dialogue
all I remember is a one-way street where
the teacher gave me the steps to get the
answer rights and I wrote them down in
my notes no dialogue no discovery just
write this down so you can be proficient
as an educator I have spent so much time
focused on how to teach math when all
along I really should have been focused
on why we teach math the ancient Greeks
knew the why and from that the how
flowed naturally as the results of
course if personal discovery of truth is
our goal if cultivating discern
and wise citizens is our goal then we
must train every student to think for
himself but this can never be
accomplished with the DM us our kind of
education that we experience growing up
padayatra I read Carly’s note I marched
into that fourth-grade classroom and I
swore to them that as long as I was
their teacher they would never do the
long division algorithm ever again
Carly raised her hand and said but mrs.
Warren how will we do the division is
there any other way and honestly I had
no idea I was totally just making it up
as I went but I just started asking them
questions
what is division how does it relate to
the other operations what are we even
trying to do and that was when a bunch
of fourth graders conjectured and
debated and discussed ideas until they
came up with a division algorithm of
their own which probably isn’t really
that inspiring because who cares a
calculator will do division for you but
it’s not the halving of knowledge that
makes math relevant it’s the discovery
we will restore meaning to mathematics
when we embrace the same time honored
tradition that raised up some of the
greatest minds in history but we must
make education a two-way street when we
ask our children questions to lead them
to solve problems themselves instead of
just giving the steps to get the right
answer I experienced a beautiful
renaissance in my math classes when I
started having real purposeful dialogue
with my students dialogue that I hope
will equip them to be citizens who
discover and defend truth in our worlds
I am confident that when we teach math
for the right reasons we will never
again have to ask what is the point of
all this
[Applause]
is great students usually have this
carefree intuition with math and they
are confidence happy even they like math
who does that but then at some point
everything changes ever wonder why pammi
I noticed that you’re still struggling
at your long division fluency but I’ve
made the process so simple even you
could do it
just remember the steps divide multiply
under subtract remainder but if you’re
having a hard time remembering that just
remember the letters of the acronym DM
us are but if you’re having a hard time
remembering that just remember our
clever pneumonic doughnuts make us saggy
rotunda’s DM us are divided multiply
under subtract remainder see this is
simple just follow the steps I’m gonna
send you home with lots of extra
worksheets so you can gain proficiency
yep pretty sure that’s when math class
started to suck
did you ever wonder why we had to learn
long division I mean when I was a kid
adults tried to get away with telling me
it would be very important to know when
I became an adult you know like if I had
to balance a checkbook or work a cash
register or something now I realized
that all my deep-rooted trust issues
come from the fact that I was lied to
nobody uses the long division algorithm
as an adult he perhaps 30 40 years ago
accurate pen and paper calculations
might have been handy but let’s just be
honest who’s really gonna bust out long
division on paper anymore even my old
fashioned push-button phone can do
division imagine what a 10 year olds
fancy smartphone can do and they’ve all
got him so last September after years of
constantly searching for ways to make
math relevant to teenagers by stroke of
Providence I found myself teaching
fourth grade math for part of the day it
was a crazy change because fourth
graders haven’t been disillusioned by
life yet they have this wonderfully
curious nature and they love to explore
new ideas and they don’t have to be
bribed or threatened to participate in
class well inevitably we made it to the
long division unit and of course I
started teaching it the same way I
learned as a child and saying this is
simple just follow the steps one day I
watched my students as they worked in
that creepy way that teachers do hands
there was this sad heavy silence in the
room and they weren’t even necessarily
doing the long division wrong they just
hated life at that moment I felt this
twinge of guilt deep in my bowels but I
thought to myself how else will they
ever be proficient at division they must
be able to keep up with the demands of
our modern technology driven job market
and proficiency in mathematics is the
only way that will happen
so I collected the assignments and I
found this little note written in the
margin of Carly’s paper which really
wasn’t that surprising since Carly was
constantly writing me notes like I love
math or you are so pretty and funny and
I love you who could blame her but this
time it said mrs. Warren I’m sorry that
I’m bad at math and that twinge of guilt
started to feel more like a very painful
cramp
I wanted to write her note of my own
that said Carly this is not math at
least it shouldn’t be
am I the only one that has ever wondered
at the ridiculousness of this thing we
call math how many times must a child’s
natural curiosity and confidence be
sacrificed on the altar of proficiency
before we realize that something needs
to change it was there in that
fourth-grade classroom where I came face
to face with the reality of math
education in our country it’s kind of
pointless don’t get me wrong
math is not pointless mathematics as
Galileo said is the language with which
God has written the universe math is
everywhere and of course is extremely
useful for countless applications I’m
talking about what is taught in the
classroom and why it is being taught I
mean are we being honest when we tell
our kids the years of laboring over
algorithms and formulas will all be
useful for a job someday really when was
the last time you found the volume of an
ellipsoid or the imaginary roots of a
quadratic equation at your job I’ll
never forget the first smartypants high
school student who challenged me with
the questions you know the questions
that every high school math student ever
asks what is the point of all this when
will I ever use it well Alex I’ve got
news for you you
you probably won’t in fact studies show
that very few Americans will ever need
to use anything more than basic
arithmetic or fractions in the workplace
and whether it’s basic arithmetic or
basic derivative calculus it’s all
available in the blink of an eye on your
smartphone or computer so there really
wasn’t any need to spend thousands of
hours struggling in the classroom
because it’s all right there in the palm
of your hands so it would seem that the
radical development of technology has
made math education your relevant and
unnecessary if getting the answer rights
if being proficient is really the goal
of our education then couldn’t we save
ourselves a lot of hassle if we just
left math to the most proficient ones of
all computers I mean who better to
follow rules and algorithms is there no
place in mathematics for the human
elements for the carly’s and the Alexes
and the everyday people like me that
struggle to find any connection between
the classroom and real life quite the
contrary
I believe the need for math education
has never been greater never been more
necessary than in this modern technology
driven culture where presidential
debates are no longer built on solid
logical arguments but rather twenty
second sound bites meant to placate an
ignorant voting populace where a hateful
political climate is driven by impulse
and emotion instead of wisdom and
discourse where our children are driven
to and fro by the winds of confusion in
a battle for their own identities oh yes
we need mathematics but not the math
that you and I were taught we need
something that reaches outside the
boundaries of the class
and touches real life we need a
Renaissance so there was this dude his
name was Isaac Newton he was kind of
famous I guess I think he like invented
gravity or something well he wrote a lot
about where he got his inspiration
he said if I have seen further it is by
standing upon the shoulders of giants in
this man’s discoveries anchored the
Scientific Revolution and yet he of all
people recognized that his great
accomplishments were made possible only
because he stood upon the shoulders of
the Ancients Aristotle Euclid Archimedes
Plato and other classical scholars men
who studied math for a much different
purpose than we do today
you see ancient scholars were less
interested in what math could help you
do and they were more concerned with how
math could affect who you are as a
person they presented math as an
exploration of the mind a personal quest
for truth it was this desire to uncover
truth that motivated Newton and other
Renaissance Sciences to make their
world-changing discoveries but when I
find most intriguing is that classical
mathematics wasn’t aimed primarily at
professional mathematicians or people
who would use it in the workplace one of
the most influential works of ancient
philosophy is Plato’s Republic in it
Plato argued that mathematical training
was the number one priority for anyone
in a position of authority in matters of
the States
and not because of its utility in daily
living but rather in the spirit of a
philosopher
math should be studied because its
ultimate aim is to lead the mind to
truth you see what Plato and other
philosophers knew and what we seem to
have forgotten is that math is
hands-down the greatest tool for
training the minds to reason well think
well argue well to seek out truth and
staunchly defended these men knew that
in order for democracy to succeed
citizens would need a kind of wisdom
that only mathematical training could
develop doesn’t this mean something
coming from the civilization that
introduced democracy to the rest of the
worlds the mathematical philosophy of
the ancient Greeks reached far beyond
their borders and their time influencing
not just mathematicians and scientists
for millennia to come but also political
leaders like surprise Abraham Lincoln
Lincoln wrote that when he wished to
demonstrate the truth of a proposition
when he really wanted to prove something
beyond the shadow of a doubt he could
only do so thanks to his persistent
study of classical Greek mathematics in
that ancient ideal of seeking out and
defending truth was showcased for all
the world to see when Lincoln boldly
argued the proposition that all men are
created equal how skillfully did he
argue that truth and how staunchly did
he defend it we cannot underestimate the
power of math education to change the
course of history and thanks to the
democratic ideals handed down to us from
ancient Greek civilization we all as
citizens have positions of authority in
matters of the state do we not need
citizens and rulers who
like Abraham Lincoln seek out truth and
defendants what could be a more relevant
connection between the classroom and
real life than this but the wisdom
ancient scholars had in mind wasn’t
cultivated by this is simple just follow
the steps and unlike today learning
wasn’t seen as just a transfer of
information from a teacher to the
students no in the ancient tradition
learning was seen as an exchange it was
full of questions not from the students
but from the teacher by asking
purposeful and well-timed questions the
teacher would guide the student to
discover the answers for himself it’s no
wonder that so much of ancient Greek
philosophy was written in the form of a
dialogue because to them education was a
two-way street more like a discussion
than a lecture it was this process this
dialogue that developed the critical
thinking skills required to reason well
think well are you well to seek out
truth and defend it no acronyms or
clever mnemonics required just dialogue
trying to remember when math class ever
resembled anything close to a dialogue
all I remember is a one-way street where
the teacher gave me the steps to get the
answer rights and I wrote them down in
my notes no dialogue no discovery just
write this down so you can be proficient
as an educator I have spent so much time
focused on how to teach math when all
along I really should have been focused
on why we teach math the ancient Greeks
knew the why and from that the how
flowed naturally as the results of
course if personal discovery of truth is
our goal if cultivating discern
and wise citizens is our goal then we
must train every student to think for
himself but this can never be
accomplished with the DM us our kind of
education that we experience growing up
padayatra I read Carly’s note I marched
into that fourth-grade classroom and I
swore to them that as long as I was
their teacher they would never do the
long division algorithm ever again
Carly raised her hand and said but mrs.
Warren how will we do the division is
there any other way and honestly I had
no idea I was totally just making it up
as I went but I just started asking them
questions
what is division how does it relate to
the other operations what are we even
trying to do and that was when a bunch
of fourth graders conjectured and
debated and discussed ideas until they
came up with a division algorithm of
their own which probably isn’t really
that inspiring because who cares a
calculator will do division for you but
it’s not the halving of knowledge that
makes math relevant it’s the discovery
we will restore meaning to mathematics
when we embrace the same time honored
tradition that raised up some of the
greatest minds in history but we must
make education a two-way street when we
ask our children questions to lead them
to solve problems themselves instead of
just giving the steps to get the right
answer I experienced a beautiful
renaissance in my math classes when I
started having real purposeful dialogue
with my students dialogue that I hope
will equip them to be citizens who
discover and defend truth in our worlds
I am confident that when we teach math
for the right reasons we will never
again have to ask what is the point of
all this
[Applause]
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