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