what I’m going to talk to you about today is a math education in fact I’m
today is a math education in fact I’m
today is a math education in fact I’m going to start with math education and
going to start with math education and
going to start with math education and I’m going to end my talk without math
I’m going to end my talk without math
I’m going to end my talk without math education and it’s really important to
education and it’s really important to
education and it’s really important to understand why I chose this title seeing
understand why I chose this title seeing
understand why I chose this title seeing the way to succeed in school mathematics
the way to succeed in school mathematics
the way to succeed in school mathematics because the key word here is seeing
because the key word here is seeing
because the key word here is seeing because currently in our math classrooms
because currently in our math classrooms
because currently in our math classrooms we do a lot of watching have you seen
we do a lot of watching have you seen
we do a lot of watching have you seen the movie arrival yes if you haven’t you
the movie arrival yes if you haven’t you
the movie arrival yes if you haven’t you should go see it and you’re probably
should go see it and you’re probably
should go see it and you’re probably wondering why I’m asking you if you’ve
wondering why I’m asking you if you’ve
wondering why I’m asking you if you’ve seen the movie arrival if you sit in a
seen the movie arrival if you sit in a
seen the movie arrival if you sit in a theater and you watch a movie and you
theater and you watch a movie and you
theater and you watch a movie and you really like it sometimes you go see it a
really like it sometimes you go see it a
really like it sometimes you go see it a second time at third time in four times
second time at third time in four times
second time at third time in four times some of us go see it 20 times does that
some of us go see it 20 times does that
some of us go see it 20 times does that make me capable of making that movie not
make me capable of making that movie not
make me capable of making that movie not at all I can sit in that movie over and
at all I can sit in that movie over and
at all I can sit in that movie over and over and over again watch it very
over and over again watch it very
over and over again watch it very carefully and really at best all I can
carefully and really at best all I can
carefully and really at best all I can do is learn the script by heart but I
do is learn the script by heart but I
do is learn the script by heart but I will never be able to see how to make
will never be able to see how to make
will never be able to see how to make that movie and that’s exactly what we do
that movie and that’s exactly what we do
that movie and that’s exactly what we do in mathematics classrooms is that we sit
in mathematics classrooms is that we sit
in mathematics classrooms is that we sit children in mathematics theatres and ask
children in mathematics theatres and ask
children in mathematics theatres and ask them to watch mathematics movies for
them to watch mathematics movies for
them to watch mathematics movies for example the multiplication table over
example the multiplication table over
example the multiplication table over and over and over again and then expect
and over and over again and then expect
and over and over again and then expect them to know multiplication or know how
them to know multiplication or know how
them to know multiplication or know how we built that table in the first place
we built that table in the first place
we built that table in the first place so what they do in effect for those who
so what they do in effect for those who
so what they do in effect for those who succeed in memorizing the multiplication
succeed in memorizing the multiplication
succeed in memorizing the multiplication facts is that they’ve learned the script
facts is that they’ve learned the script
facts is that they’ve learned the script at best they haven’t been behind the
at best they haven’t been behind the
at best they haven’t been behind the scenes to know how to make a
scenes to know how to make a
scenes to know how to make a multiplication table so that’s the
multiplication table so that’s the
multiplication table so that’s the problem that’s the main problem with our
problem that’s the main problem with our
problem that’s the main problem with our education right now in mathematics is
education right now in mathematics is
education right now in mathematics is that we get the children to watch and so
that we get the children to watch and so
that we get the children to watch and so they don’t see behind the scenes so
they don’t see behind the scenes so
they don’t see behind the scenes so let’s see how that works what’s this
let’s see how that works what’s this
let’s see how that works what’s this number I can’t hear you thank you what
number I can’t hear you thank you what
number I can’t hear you thank you what about this one 123 what about this big
about this one 123 what about this big
about this one 123 what about this big one
one
one and in fact I can keep throwing numbers
and in fact I can keep throwing numbers
and in fact I can keep throwing numbers are you and you will know them or at
are you and you will know them or at
are you and you will know them or at least I hope so and that’s because
least I hope so and that’s because
least I hope so and that’s because you’ve learnt or you’ve sat in that
you’ve learnt or you’ve sat in that
you’ve learnt or you’ve sat in that mathematics theatre and you’ve learned
mathematics theatre and you’ve learned
mathematics theatre and you’ve learned what we call the whole number decimal
what we call the whole number decimal
what we call the whole number decimal enumeration chart that’s the script so
enumeration chart that’s the script so
enumeration chart that’s the script so they put the script in front of you
they put the script in front of you
they put the script in front of you you’ve memorized this so the first
you’ve memorized this so the first
you’ve memorized this so the first number on the right is going to be your
number on the right is going to be your
number on the right is going to be your your ones and then the tens and then the
your ones and then the tens and then the
your ones and then the tens and then the hundreds and then the thousands and so
hundreds and then the thousands and so
hundreds and then the thousands and so forth and you’ve learnt this quite well
forth and you’ve learnt this quite well
forth and you’ve learnt this quite well but you didn’t learn how this chart was
but you didn’t learn how this chart was
but you didn’t learn how this chart was created again this is the movie and not
created again this is the movie and not
created again this is the movie and not the behind the scenes so what we’ll do
the behind the scenes so what we’ll do
the behind the scenes so what we’ll do is we will go behind the scenes to see
is we will go behind the scenes to see
is we will go behind the scenes to see why that is not working in fact that’s
why that is not working in fact that’s
why that is not working in fact that’s what’s making a math education not
what’s making a math education not
what’s making a math education not working so we’re going to write a script
working so we’re going to write a script
working so we’re going to write a script because when you ghost watch a movie the
because when you ghost watch a movie the
because when you ghost watch a movie the script is not just didn’t just appear
script is not just didn’t just appear
script is not just didn’t just appear there somebody actually wrote the script
there somebody actually wrote the script
there somebody actually wrote the script so I’m going to do a little activity my
so I’m going to do a little activity my
so I’m going to do a little activity my earrings are clicking and take a lot
earrings are clicking and take a lot
earrings are clicking and take a lot okay it’s also a strip show so we’re
okay it’s also a strip show so we’re
okay it’s also a strip show so we’re going to use the numbers you know i’m
going to use the numbers you know i’m
going to use the numbers you know i’m not going to do something crazy because
not going to do something crazy because
not going to do something crazy because most people I know are not comfortable
most people I know are not comfortable
most people I know are not comfortable with mathematics so we’re going to
with mathematics so we’re going to
with mathematics so we’re going to choose the numbers one two three four
choose the numbers one two three four
choose the numbers one two three four five six seven eight nine and we’ll use
five six seven eight nine and we’ll use
five six seven eight nine and we’ll use t410 and notice there’s no zero right
t410 and notice there’s no zero right
t410 and notice there’s no zero right we’ll get rid of 0 in fact historically
we’ll get rid of 0 in fact historically
we’ll get rid of 0 in fact historically zero came really late late 16th century
zero came really late late 16th century
zero came really late late 16th century so we’re just going to use these
so we’re just going to use these
so we’re just going to use these numerals now and I want you to write or
numerals now and I want you to write or
numerals now and I want you to write or think in your head how you would write
think in your head how you would write
think in your head how you would write the numbers 8 2 22 with these numerals
the numbers 8 2 22 with these numerals
the numbers 8 2 22 with these numerals all I’ve changes to remove is 0 and put
all I’ve changes to remove is 0 and put
all I’ve changes to remove is 0 and put in a t410 well you’re probably thinking
in a t410 well you’re probably thinking
in a t410 well you’re probably thinking this is how we write eight this is how
this is how we write eight this is how
this is how we write eight this is how we write nine this is how we write ten
we write nine this is how we write ten
we write nine this is how we write ten now because we have a symbol for that
now because we have a symbol for that
now because we have a symbol for that which is called T and then you probably
which is called T and then you probably
which is called T and then you probably sell it goes pretty easy let’s go on t1
sell it goes pretty easy let’s go on t1
sell it goes pretty easy let’s go on t1 because 10 plus one makes 11 t 2 for 12
because 10 plus one makes 11 t 2 for 12
because 10 plus one makes 11 t 2 for 12 t 3 for 13 all the way to 19 which you
t 3 for 13 all the way to 19 which you
t 3 for 13 all the way to 19 which you probably think of t nine
probably think of t nine
probably think of t nine team makes sense then you get to 20 then
team makes sense then you get to 20 then
team makes sense then you get to 20 then it’s TG 1010 you know that makes 2010 10
it’s TG 1010 you know that makes 2010 10
it’s TG 1010 you know that makes 2010 10 14 21 10 10 24 22 when I asked this
14 21 10 10 24 22 when I asked this
14 21 10 10 24 22 when I asked this question to my student teachers they
question to my student teachers they
question to my student teachers they always give me these answers because
always give me these answers because
always give me these answers because that’s what they learnt is that they
that’s what they learnt is that they
that’s what they learnt is that they learned the script but they don’t really
learned the script but they don’t really
learned the script but they don’t really learn how to write a script in effect
learn how to write a script in effect
learn how to write a script in effect this is what is truly what we should be
this is what is truly what we should be
this is what is truly what we should be writing so 848 949 t410 11 now why is it
writing so 848 949 t410 11 now why is it
writing so 848 949 t410 11 now why is it I’m writing 11 this way not with a tee
I’m writing 11 this way not with a tee
I’m writing 11 this way not with a tee well if you look at the T in the t1 the
well if you look at the T in the t1 the
well if you look at the T in the t1 the t is in which column is in the tens
t is in which column is in the tens
t is in which column is in the tens column so in effect that t1 represents a
column so in effect that t1 represents a
column so in effect that t1 represents a hundred and one not 11 when you look at
hundred and one not 11 when you look at
hundred and one not 11 when you look at 11 with just 11 you don’t say 1+1 you’re
11 with just 11 you don’t say 1+1 you’re
11 with just 11 you don’t say 1+1 you’re not adding the digits together you
not adding the digits together you
not adding the digits together you realize that the first one on your left
realize that the first one on your left
realize that the first one on your left is telling you how many tens so I have
is telling you how many tens so I have
is telling you how many tens so I have 110 and then I have a 11 so that makes
110 and then I have a 11 so that makes
110 and then I have a 11 so that makes 11 so 12 13 14 all the way to 19 so how
11 so 12 13 14 all the way to 19 so how
11 so 12 13 14 all the way to 19 so how do we represent 20 without a zero well
do we represent 20 without a zero well
do we represent 20 without a zero well it’s simply won t because i can put 10
it’s simply won t because i can put 10
it’s simply won t because i can put 10 ones in one column and then after that i
ones in one column and then after that i
ones in one column and then after that i put sorry I’m going backwards 10 ones
put sorry I’m going backwards 10 ones
put sorry I’m going backwards 10 ones and one column and then I simply need
and one column and then I simply need
and one column and then I simply need one more 10 to account for the 20
one more 10 to account for the 20
one more 10 to account for the 20 objects and then 21 would simply be 21
objects and then 21 would simply be 21
objects and then 21 would simply be 21 to tens and 11 and 22 will be 2 to the
to tens and 11 and 22 will be 2 to the
to tens and 11 and 22 will be 2 to the bottom line here is how we write a
bottom line here is how we write a
bottom line here is how we write a script we learn what’s what’s the system
script we learn what’s what’s the system
script we learn what’s what’s the system behind it and in fact we should be
behind it and in fact we should be
behind it and in fact we should be creating those systems so how do we
creating those systems so how do we
creating those systems so how do we write a hundred have two zeros to
write a hundred have two zeros to
write a hundred have two zeros to contend with here so all I’m going to do
contend with here so all I’m going to do
contend with here so all I’m going to do then is simply use my t410 so if I have
then is simply use my t410 so if I have
then is simply use my t410 so if I have 10 in my ones column how many more do I
10 in my ones column how many more do I
10 in my ones column how many more do I need I need nine more tends to make a
need I need nine more tends to make a
need I need nine more tends to make a hundred and so it writes 90 so what is
hundred and so it writes 90 so what is
hundred and so it writes 90 so what is going on here is that I’m working behind
going on here is that I’m working behind
going on here is that I’m working behind the scenes so instead of telling them
the scenes so instead of telling them
the scenes so instead of telling them here’s the chart
here’s the chart
here’s the chart results how it’s built and this is how
results how it’s built and this is how
results how it’s built and this is how you place numbers in it we need to
you place numbers in it we need to
you place numbers in it we need to engage the students in building that
engage the students in building that
engage the students in building that chart so understanding how we build that
chart so understanding how we build that
chart so understanding how we build that charge so we start with ones so let’s
charge so we start with ones so let’s
charge so we start with ones so let’s say we use popsicle sticks then after I
say we use popsicle sticks then after I
say we use popsicle sticks then after I have one’s counting by one is very
have one’s counting by one is very
have one’s counting by one is very tedious especially that have a large
tedious especially that have a large
tedious especially that have a large amount of things and so I’m going to
amount of things and so I’m going to
amount of things and so I’m going to group them and then count the group’s so
group them and then count the group’s so
group them and then count the group’s so I’m gonna make a bunch of popsicle
I’m gonna make a bunch of popsicle
I’m gonna make a bunch of popsicle sticks here I chose five so I bunch my
sticks here I chose five so I bunch my
sticks here I chose five so I bunch my five popsicle stick then I can simply
five popsicle stick then I can simply
five popsicle stick then I can simply count bunches of five because it’s much
count bunches of five because it’s much
count bunches of five because it’s much more quick to do that and then I will
more quick to do that and then I will
more quick to do that and then I will regroup because even if I have a large
regroup because even if I have a large
regroup because even if I have a large amount of popsicle sticks grouping them
amount of popsicle sticks grouping them
amount of popsicle sticks grouping them by 5 i’m going to end up with the same
by 5 i’m going to end up with the same
by 5 i’m going to end up with the same problem of having many groups of five to
problem of having many groups of five to
problem of having many groups of five to call 22 count and so therefore it’s not
call 22 count and so therefore it’s not
call 22 count and so therefore it’s not efficient so I’m so k so when I have
efficient so I’m so k so when I have
efficient so I’m so k so when I have five bunches of five popsicle sticks
five bunches of five popsicle sticks
five bunches of five popsicle sticks I’ll stick up in a bag and they can just
I’ll stick up in a bag and they can just
I’ll stick up in a bag and they can just count the bags so what we’ve done
count the bags so what we’ve done
count the bags so what we’ve done cleverly is develop this system of
cleverly is develop this system of
cleverly is develop this system of counting that is so efficient it’s
counting that is so efficient it’s
counting that is so efficient it’s become so efficient that we don’t
become so efficient that we don’t
become so efficient that we don’t remember how we created that system then
remember how we created that system then
remember how we created that system then we have to use symbols to code it either
we have to use symbols to code it either
we have to use symbols to code it either verbally or in writing so if I’m
verbally or in writing so if I’m
verbally or in writing so if I’m counting popsicle sticks by bunches of
counting popsicle sticks by bunches of
counting popsicle sticks by bunches of five only 0 1 2 3 4 i’ll never see a 5
five only 0 1 2 3 4 i’ll never see a 5
five only 0 1 2 3 4 i’ll never see a 5 because the minute i have five things it
because the minute i have five things it
because the minute i have five things it becomes one bigger object and then we’ve
becomes one bigger object and then we’ve
becomes one bigger object and then we’ve introduced place value so in here we
introduced place value so in here we
introduced place value so in here we have sticks then we have bunches then we
have sticks then we have bunches then we
have sticks then we have bunches then we have bags and then we’d have boxes
have bags and then we’d have boxes
have bags and then we’d have boxes crates and so forth right so this is
crates and so forth right so this is
crates and so forth right so this is what our system is built on this idea of
what our system is built on this idea of
what our system is built on this idea of these these points here this is how
these these points here this is how
these these points here this is how we’ve developed this whole chart in the
we’ve developed this whole chart in the
we’ve developed this whole chart in the first place so when we present children
first place so when we present children
first place so when we present children with simply this chart already made up
with simply this chart already made up
with simply this chart already made up they don’t get to see behind the scenes
they don’t get to see behind the scenes
they don’t get to see behind the scenes they get to watch so it is a time for
they get to watch so it is a time for
they get to watch so it is a time for change we know for over a hundred years
change we know for over a hundred years
change we know for over a hundred years now that we’re not we’re failing to
now that we’re not we’re failing to
now that we’re not we’re failing to children in school in mathematics and in
children in school in mathematics and in
children in school in mathematics and in fact a lot of adults end up not liking
fact a lot of adults end up not liking
fact a lot of adults end up not liking mathematics and choosing careers that
mathematics and choosing careers that
mathematics and choosing careers that EGNOS make sure that they don’t have to
EGNOS make sure that they don’t have to
EGNOS make sure that they don’t have to have any
have any
have any Madison so it has a large impact and
Madison so it has a large impact and
Madison so it has a large impact and really it’s just a change in the way we
really it’s just a change in the way we
really it’s just a change in the way we do things are the way we approach the
do things are the way we approach the
do things are the way we approach the teaching of mathematics now the results
teaching of mathematics now the results
teaching of mathematics now the results and methods of mathematics or its
and methods of mathematics or its
and methods of mathematics or its artifacts there the movie that we that
artifacts there the movie that we that
artifacts there the movie that we that we go sit to watch in the theater the
we go sit to watch in the theater the
we go sit to watch in the theater the actual mathematics lies in the thinking
actual mathematics lies in the thinking
actual mathematics lies in the thinking that creates those artifacts so again
that creates those artifacts so again
that creates those artifacts so again it’s behind the scenes of the movie that
it’s behind the scenes of the movie that
it’s behind the scenes of the movie that the mathematics is actually occurring
the mathematics is actually occurring
the mathematics is actually occurring and those artifacts are indeed
and those artifacts are indeed
and those artifacts are indeed surprising just like arrival is a
surprising just like arrival is a
surprising just like arrival is a beautiful movie to watch but that’s not
beautiful movie to watch but that’s not
beautiful movie to watch but that’s not we want we don’t want kids to be become
we want we don’t want kids to be become
we want we don’t want kids to be become really good at watching movies or
really good at watching movies or
really good at watching movies or watching mathematical results we want
watching mathematical results we want
watching mathematical results we want them to become mathematical thinkers so
them to become mathematical thinkers so
them to become mathematical thinkers so some of those artifacts are surprising
some of those artifacts are surprising
some of those artifacts are surprising sometimes we discovered with our
sometimes we discovered with our
sometimes we discovered with our creative thinking that there are
creative thinking that there are
creative thinking that there are irrational numbers now those numbers
irrational numbers now those numbers
irrational numbers now those numbers were accepted only about 150 years ago
were accepted only about 150 years ago
were accepted only about 150 years ago so it’s not unusual for learners to have
so it’s not unusual for learners to have
so it’s not unusual for learners to have struggles to understand these particular
struggles to understand these particular
struggles to understand these particular kinds of numbers no one here doubts that
kinds of numbers no one here doubts that
kinds of numbers no one here doubts that even if they hate math it is practical
even if they hate math it is practical
even if they hate math it is practical it serves practical purposes for example
it serves practical purposes for example
it serves practical purposes for example the Pythagorean theorem is used in
the Pythagorean theorem is used in
the Pythagorean theorem is used in construction to paint your wall in your
construction to paint your wall in your
construction to paint your wall in your room you need to take some measurements
room you need to take some measurements
room you need to take some measurements and know how much paint you’re going to
and know how much paint you’re going to
and know how much paint you’re going to need so mathematics is practical but if
need so mathematics is practical but if
need so mathematics is practical but if you speak to most mathematicians they’ll
you speak to most mathematicians they’ll
you speak to most mathematicians they’ll tell you mathematics is beautiful how
tell you mathematics is beautiful how
tell you mathematics is beautiful how many of you think mathematics is
many of you think mathematics is
many of you think mathematics is beautiful very good well I do I find it
beautiful very good well I do I find it
beautiful very good well I do I find it surprising and it’s practical but it’s
surprising and it’s practical but it’s
surprising and it’s practical but it’s also beautiful here’s my favorite
also beautiful here’s my favorite
also beautiful here’s my favorite formulas that a Laplace transform how
formulas that a Laplace transform how
formulas that a Laplace transform how many of you are familiar with this one
many of you are familiar with this one
many of you are familiar with this one how are you okay the level of class
how are you okay the level of class
how are you okay the level of class transform is is a formula that takes a
transform is is a formula that takes a
transform is is a formula that takes a very complex problem and converts it
very complex problem and converts it
very complex problem and converts it into a simple problem to solve so very
into a simple problem to solve so very
into a simple problem to solve so very powerful it’s a very powerful formula
powerful it’s a very powerful formula
powerful it’s a very powerful formula and that’s what makes it beautiful so
and that’s what makes it beautiful so
and that’s what makes it beautiful so I’m talking about mathematical thinking
I’m talking about mathematical thinking
I’m talking about mathematical thinking so well how do we do that and what is it
so well how do we do that and what is it
so well how do we do that and what is it so mathematical thinking is a whole way
so mathematical thinking is a whole way
so mathematical thinking is a whole way of looking at things of stripping them
of looking at things of stripping them
of looking at things of stripping them down to their numerical structural or
down to their numerical structural or
down to their numerical structural or logical essentials and of analyzing the
logical essentials and of analyzing the
logical essentials and of analyzing the underlying patterns it’s a way of
underlying patterns it’s a way of
underlying patterns it’s a way of looking at the world seeing the world in
looking at the world seeing the world in
looking at the world seeing the world in ways that you can size things you can
ways that you can size things you can
ways that you can size things you can time things you can measure things you
time things you can measure things you
time things you can measure things you can see the patterns what’s the same
can see the patterns what’s the same
can see the patterns what’s the same what’s not the same the relationships
what’s not the same the relationships
what’s not the same the relationships among things that’s what mathematical
among things that’s what mathematical
among things that’s what mathematical thinking is all about but if we teach a
thinking is all about but if we teach a
thinking is all about but if we teach a script in other words we keep plopping
script in other words we keep plopping
script in other words we keep plopping these kids in the mathematics theater
these kids in the mathematics theater
these kids in the mathematics theater instead of having them work behind the
instead of having them work behind the
instead of having them work behind the scenes then we get the results we get
scenes then we get the results we get
scenes then we get the results we get for that right I was in grade one
for that right I was in grade one
for that right I was in grade one working with grade 1 kids this year and
working with grade 1 kids this year and
working with grade 1 kids this year and I asked him a very simple problem 3 I
I asked him a very simple problem 3 I
I asked him a very simple problem 3 I gave him sequences of numbers 3 4 what
gave him sequences of numbers 3 4 what
gave him sequences of numbers 3 4 what number six seven eight I also put the
number six seven eight I also put the
number six seven eight I also put the box at the beginning what number comes
box at the beginning what number comes
box at the beginning what number comes before four five six seven and I even
before four five six seven and I even
before four five six seven and I even put the box at the end through two three
put the box at the end through two three
put the box at the end through two three four or five what number comes after
four or five what number comes after
four or five what number comes after that well I wasn’t surprised with the
that well I wasn’t surprised with the
that well I wasn’t surprised with the teacher surgery was this is what they
teacher surgery was this is what they
teacher surgery was this is what they answered they put one in all the boxes
answered they put one in all the boxes
answered they put one in all the boxes and that’s because the script is you
and that’s because the script is you
and that’s because the script is you count one two three four five six so for
count one two three four five six so for
count one two three four five six so for them no matter where it was you have to
them no matter where it was you have to
them no matter where it was you have to start the script at one and I have lots
start the script at one and I have lots
start the script at one and I have lots and lots of examples of this of children
and lots of examples of this of children
and lots of examples of this of children who watch mathematics instead of being
who watch mathematics instead of being
who watch mathematics instead of being interactive with the mathematics they
interactive with the mathematics they
interactive with the mathematics they give you these kinds of results but can
give you these kinds of results but can
give you these kinds of results but can we get kids to think that’s a good
we get kids to think that’s a good
we get kids to think that’s a good question there’s a lot of debate right
question there’s a lot of debate right
question there’s a lot of debate right now about thinking skills cognitive
now about thinking skills cognitive
now about thinking skills cognitive ability executive functions and so forth
ability executive functions and so forth
ability executive functions and so forth and I’ve been working closely with
and I’ve been working closely with
and I’ve been working closely with children all my career and I can tell
children all my career and I can tell
children all my career and I can tell you that yes it’s actually easier to get
you that yes it’s actually easier to get
you that yes it’s actually easier to get them to think than my adults so
them to think than my adults so
them to think than my adults so absolutely we can get them to learn to
absolutely we can get them to learn to
absolutely we can get them to learn to think and once we get them to learn to
think and once we get them to learn to
think and once we get them to learn to think then we know that they can develop
think then we know that they can develop
think then we know that they can develop mathematical thinking so we need to get
mathematical thinking so we need to get
mathematical thinking so we need to get sure to be sure that they can think
sure to be sure that they can think
sure to be sure that they can think first I’ll give you an example at the
first I’ll give you an example at the
first I’ll give you an example at the beginning of
beginning of
beginning of year I gave them these figures very
year I gave them these figures very
year I gave them these figures very simple shaped squares circles and
simple shaped squares circles and
simple shaped squares circles and triangles and I asked them to look
triangles and I asked them to look
triangles and I asked them to look carefully with their eyes to see what is
carefully with their eyes to see what is
carefully with their eyes to see what is different one of them is very different
different one of them is very different
different one of them is very different from the others and they responded
from the others and they responded
from the others and they responded immediately some of them said a some of
immediately some of them said a some of
immediately some of them said a some of them said these some of them said see
them said these some of them said see
them said these some of them said see and then when I asked them why they
and then when I asked them why they
and then when I asked them why they chose I want they said why not I said
chose I want they said why not I said
chose I want they said why not I said but look just look very carefully with
but look just look very carefully with
but look just look very carefully with you guys see what’s the same what’s not
you guys see what’s the same what’s not
you guys see what’s the same what’s not the same you know they just looked at me
the same you know they just looked at me
the same you know they just looked at me with blank looks ok well let’s be then
with blank looks ok well let’s be then
with blank looks ok well let’s be then no no no I don’t want you just to give
no no no I don’t want you just to give
no no no I don’t want you just to give me an answer I want you to look
me an answer I want you to look
me an answer I want you to look carefully at this and there was they
carefully at this and there was they
carefully at this and there was they didn’t seem to understand what I was
didn’t seem to understand what I was
didn’t seem to understand what I was asking them to do so we did some more
asking them to do so we did some more
asking them to do so we did some more activities where they had to observe and
activities where they had to observe and
activities where they had to observe and discern what’s the same and what’s not
discern what’s the same and what’s not
discern what’s the same and what’s not the same and so for then they got better
the same and so for then they got better
the same and so for then they got better at it they got so good at it that they
at it they got so good at it that they
at it they got so good at it that they surprised me after about four sessions I
surprised me after about four sessions I
surprised me after about four sessions I gave them another similar problem but
gave them another similar problem but
gave them another similar problem but this time I threw in some noise in grade
this time I threw in some noise in grade
this time I threw in some noise in grade one there’s they’re learning language so
one there’s they’re learning language so
one there’s they’re learning language so they’re learning how to read and how to
they’re learning how to read and how to
they’re learning how to read and how to write so I presented them with letters
write so I presented them with letters
write so I presented them with letters which had nothing to do with the the the
which had nothing to do with the the the
which had nothing to do with the the the task but it was just to add some noise
task but it was just to add some noise
task but it was just to add some noise to see how well they would do and I
to see how well they would do and I
to see how well they would do and I asked them which one of these doesn’t
asked them which one of these doesn’t
asked them which one of these doesn’t belong I’m math person so I know it’s w
belong I’m math person so I know it’s w
belong I’m math person so I know it’s w because W has four lines and all of the
because W has four lines and all of the
because W has four lines and all of the other letters have three lines most of
other letters have three lines most of
other letters have three lines most of the children pick 2w and I was quite
the children pick 2w and I was quite
the children pick 2w and I was quite happy but then I asked of wine and they
happy but then I asked of wine and they
happy but then I asked of wine and they said because it starts with adi and i
said because it starts with adi and i
said because it starts with adi and i went ok can you explain that to me go
went ok can you explain that to me go
went ok can you explain that to me go Wow a F and H wd4 w of it oh my goodness
Wow a F and H wd4 w of it oh my goodness
Wow a F and H wd4 w of it oh my goodness that is so smart I was thinking dude
that is so smart I was thinking dude
that is so smart I was thinking dude simple numbers of lines and instead they
simple numbers of lines and instead they
simple numbers of lines and instead they came up with something a lot deeper
came up with something a lot deeper
came up with something a lot deeper using their language knowledge in order
using their language knowledge in order
using their language knowledge in order to look and see what’s going on with
to look and see what’s going on with
to look and see what’s going on with these letters so absolute
these letters so absolute
these letters so absolute we can change from not having a clue
we can change from not having a clue
we can change from not having a clue what to do with the task to actually
what to do with the task to actually
what to do with the task to actually coming up with something that surprised
coming up with something that surprised
coming up with something that surprised me as a researcher and that brings me to
me as a researcher and that brings me to
me as a researcher and that brings me to my conclusion and the idea that I’m
my conclusion and the idea that I’m
my conclusion and the idea that I’m trying to push that I’ve been trying to
trying to push that I’ve been trying to
trying to push that I’ve been trying to push for great many number of years is
push for great many number of years is
push for great many number of years is that instead of teaching mathematics
that instead of teaching mathematics
that instead of teaching mathematics what we should be doing is teaching
what we should be doing is teaching
what we should be doing is teaching mathematical thinking which in of course
mathematical thinking which in of course
mathematical thinking which in of course it requires thinking so we need to go
it requires thinking so we need to go
it requires thinking so we need to go away walk away from mathematics
away walk away from mathematics
away walk away from mathematics education and start looking at
education and start looking at
education and start looking at educational mathematics so that the kids
educational mathematics so that the kids
educational mathematics so that the kids are using mathematics really to learn
are using mathematics really to learn
are using mathematics really to learn about seeing the world and we’re back to
about seeing the world and we’re back to
about seeing the world and we’re back to my movie arrival so I thank you very
my movie arrival so I thank you very
my movie arrival so I thank you very much
much
much [Applause]
”
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