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Let’s teach mathematics creatively | Ivan Zelich | TEDxYouth@Sydney


[Music]

[Music] [Applause]

you know it’s not longer since I

you know it’s not longer since I finished high school I have many great

finished high school I have many great

finished high school I have many great memories socializing competing

memories socializing competing

memories socializing competing publishing and presenting at

publishing and presenting at

publishing and presenting at international conferences but all of

international conferences but all of

international conferences but all of which happened outside the classroom I’m

which happened outside the classroom I’m

which happened outside the classroom I’m sure you all have great memories of your

sure you all have great memories of your

sure you all have great memories of your high school some of us might even

high school some of us might even

high school some of us might even remember our teachers reflecting back I

remember our teachers reflecting back I

remember our teachers reflecting back I realize that teachers in Queensland

realize that teachers in Queensland

realize that teachers in Queensland needed to teach a certain curriculum in

needed to teach a certain curriculum in

needed to teach a certain curriculum in a certain way there wasn’t much room for

a certain way there wasn’t much room for

a certain way there wasn’t much room for manoeuvre which in a way made everybody

manoeuvre which in a way made everybody

manoeuvre which in a way made everybody the same so I guess it is fair to say

the same so I guess it is fair to say

the same so I guess it is fair to say that your typical classroom environment

that your typical classroom environment

that your typical classroom environment will consist of desks whiteboards a

will consist of desks whiteboards a

will consist of desks whiteboards a pre-programmed teacher and a group of

pre-programmed teacher and a group of

pre-programmed teacher and a group of students robotically copying down

students robotically copying down

students robotically copying down word-for-word everything the teacher was

word-for-word everything the teacher was

word-for-word everything the teacher was narrating there’s only one way to put an

narrating there’s only one way to put an

narrating there’s only one way to put an end to this automated learning

end to this automated learning

end to this automated learning environment and that was someone to ask

environment and that was someone to ask

environment and that was someone to ask but that all was necessary for the exam

but that all was necessary for the exam

but that all was necessary for the exam and that was the key to high school

and that was the key to high school

and that was the key to high school knowing what you didn’t need to know I

knowing what you didn’t need to know I

knowing what you didn’t need to know I spent most of my high school learning

spent most of my high school learning

spent most of my high school learning about things I didn’t need to know for

about things I didn’t need to know for

about things I didn’t need to know for me maths is a journey and the most

me maths is a journey and the most

me maths is a journey and the most interesting journeys are the ones in

interesting journeys are the ones in

interesting journeys are the ones in which you explore and gain experience so

which you explore and gain experience so

which you explore and gain experience so I believe math should be taught as a

I believe math should be taught as a

I believe math should be taught as a journey not a set of equations to be

journey not a set of equations to be

journey not a set of equations to be applied to something as if maths is a

applied to something as if maths is a

applied to something as if maths is a set of dusty tools in the shed of

set of dusty tools in the shed of

set of dusty tools in the shed of science for me my maths journey Sawa is

science for me my maths journey Sawa is

science for me my maths journey Sawa is really young

really young

really young I’ve always loved numbers and my parents

I’ve always loved numbers and my parents

I’ve always loved numbers and my parents realized that early on when I started

realized that early on when I started

realized that early on when I started doing Negra number addition at 3 years

doing Negra number addition at 3 years

doing Negra number addition at 3 years old

old

old I also loved squaring numbers and at one

I also loved squaring numbers and at one

I also loved squaring numbers and at one stage I could do five digit

stage I could do five digit

stage I could do five digit multiplication

multiplication

multiplication my head actually had a book where I’d

my head actually had a book where I’d

my head actually had a book where I’d write down little tricks and formula

write down little tricks and formula

write down little tricks and formula used to solve such equations quicker

used to solve such equations quicker

used to solve such equations quicker part of the writing I was only 5 years

part of the writing I was only 5 years

part of the writing I was only 5 years old so yes I love maths and my very

old so yes I love maths and my very

old so yes I love maths and my very school’s public in competitions at age

school’s public in competitions at age

school’s public in competitions at age of 13 I was spotted by the national

of 13 I was spotted by the national

of 13 I was spotted by the national director of the Australian mathematical

director of the Australian mathematical

director of the Australian mathematical trust who put me in training for the

trust who put me in training for the

trust who put me in training for the Australian limpia team and it was there

Australian limpia team and it was there

Australian limpia team and it was there that I discover that actually wasn’t

that I discover that actually wasn’t

that I discover that actually wasn’t that a good at geometry I was and still

that a good at geometry I was and still

that a good at geometry I was and still am bad at drawing and this made me

am bad at drawing and this made me

am bad at drawing and this made me scared of the subject how could I

scared of the subject how could I

scared of the subject how could I possibly prove that three points line a

possibly prove that three points line a

possibly prove that three points line a line when my lines look like circles so

line when my lines look like circles so

line when my lines look like circles so I worked on geometry problems to

I worked on geometry problems to

I worked on geometry problems to maximize my chances of winning and it

maximize my chances of winning and it

maximize my chances of winning and it was there that discovered the unexpected

was there that discovered the unexpected

was there that discovered the unexpected beauty in geometry not in the drawing

beauty in geometry not in the drawing

beauty in geometry not in the drawing part of course but in the way certain

part of course but in the way certain

part of course but in the way certain mathematically challenging concepts

mathematically challenging concepts

mathematically challenging concepts could be explained simply through

could be explained simply through

could be explained simply through visualization what is the infinite sum

visualization what is the infinite sum

visualization what is the infinite sum of 1/2 plus 1/4 plus 1/8 plus 1/16 etc

of 1/2 plus 1/4 plus 1/8 plus 1/16 etc

of 1/2 plus 1/4 plus 1/8 plus 1/16 etc well to some of you this met this some

well to some of you this met this some

well to some of you this met this some may seem daunting if you look at this

may seem daunting if you look at this

may seem daunting if you look at this animation where each time we’re adding

animation where each time we’re adding

animation where each time we’re adding half the previous rectangle it does make

half the previous rectangle it does make

half the previous rectangle it does make sense that these rectangles will

sense that these rectangles will

sense that these rectangles will eventually add up to a square that has

eventually add up to a square that has

eventually add up to a square that has area 1 but if I now ask you where the

area 1 but if I now ask you where the

area 1 but if I now ask you where the parallel lines do meet well parent lines

parallel lines do meet well parent lines

parallel lines do meet well parent lines are defined not to meet if you look at

are defined not to meet if you look at

are defined not to meet if you look at it in a certain angle it does appear

it in a certain angle it does appear

it in a certain angle it does appear that these lines will eventually meet at

that these lines will eventually meet at

that these lines will eventually meet at a point at infinity and it turns out

a point at infinity and it turns out

a point at infinity and it turns out this point is used extensively in

this point is used extensively in

this point is used extensively in mathematics nowadays I was learning all

mathematics nowadays I was learning all

mathematics nowadays I was learning all this outside the classroom

this outside the classroom

this outside the classroom luckily nowadays you have the internet

luckily nowadays you have the internet

luckily nowadays you have the internet where we can learn things in our own

where we can learn things in our own

where we can learn things in our own time in fact I didn’t need school

time in fact I didn’t need school

time in fact I didn’t need school classes at all because participating in

classes at all because participating in

classes at all because participating in mathematical forums was like a class of

mathematical forums was like a class of

mathematical forums was like a class of its own I was so involved in online

its own I was so involved in online

its own I was so involved in online communities that I actually start

communities that I actually start

communities that I actually start Blagh were post solutions to problems

Blagh were post solutions to problems

Blagh were post solutions to problems that I found beautiful especially ones

that I found beautiful especially ones

that I found beautiful especially ones people can solve and it was there that I

people can solve and it was there that I

people can solve and it was there that I met zooming Liang who lives in America

met zooming Liang who lives in America

met zooming Liang who lives in America at the time we were both 16 and loved

at the time we were both 16 and loved

at the time we were both 16 and loved geometry is and solving mathematical

geometry is and solving mathematical

geometry is and solving mathematical problems in general coincidentally

problems in general coincidentally

problems in general coincidentally zooming in our boat stuck on the same

zooming in our boat stuck on the same

zooming in our boat stuck on the same open problem and it took us five days to

open problem and it took us five days to

open problem and it took us five days to solve this problem a cycle where I

solve this problem a cycle where I

solve this problem a cycle where I worked through the night and zooming

worked through the night and zooming

worked through the night and zooming we’ll continue our left off swimming

we’ll continue our left off swimming

we’ll continue our left off swimming would do the same

would do the same

would do the same repeat the time zone difference actually

repeat the time zone difference actually

repeat the time zone difference actually worked quite well

worked quite well

worked quite well we had eyes on the prom for 120 hours

we had eyes on the prom for 120 hours

we had eyes on the prom for 120 hours straight now reflect on your high school

straight now reflect on your high school

straight now reflect on your high school experience we had to solve 30 problems

experience we had to solve 30 problems

experience we had to solve 30 problems in one and a half hours is it really

in one and a half hours is it really

in one and a half hours is it really testing our ability to think creatively

unlike in high school where you could

unlike in high school where you could submit your solutions to be marked

submit your solutions to be marked

submit your solutions to be marked assuming and I weren’t even done we

assuming and I weren’t even done we

assuming and I weren’t even done we stumbled upon a new theorem in

stumbled upon a new theorem in

stumbled upon a new theorem in mathematics extending the one we had

mathematics extending the one we had

mathematics extending the one we had just solved what a theorem stated was

just solved what a theorem stated was

just solved what a theorem stated was that a point in the Triangle plane lies

that a point in the Triangle plane lies

that a point in the Triangle plane lies an isomorphic equivalent to I superior

an isomorphic equivalent to I superior

an isomorphic equivalent to I superior cubics in its petal triangles but here’s

cubics in its petal triangles but here’s

cubics in its petal triangles but here’s a diagram for the theorem it’s bit

a diagram for the theorem it’s bit

a diagram for the theorem it’s bit simplified unfortunately we too had no

simplified unfortunately we too had no

simplified unfortunately we too had no idea how to prove this problem and it

idea how to prove this problem and it

idea how to prove this problem and it took us six months to finally figure out

took us six months to finally figure out

took us six months to finally figure out a way just to start the proof and

a way just to start the proof and

a way just to start the proof and another week to solve it let alone nine

another week to solve it let alone nine

another week to solve it let alone nine months for it to be published who could

months for it to be published who could

months for it to be published who could have thought by the end of it that our

have thought by the end of it that our

have thought by the end of it that our diagram would look like this what a

diagram would look like this what a

diagram would look like this what a theorem did was that it made the complex

theorem did was that it made the complex

theorem did was that it made the complex field of I so people cubics easier to

field of I so people cubics easier to

field of I so people cubics easier to deal with and allows difficult

deal with and allows difficult

deal with and allows difficult geometrical problems to be solved by

geometrical problems to be solved by

geometrical problems to be solved by people with only high school level

people with only high school level

people with only high school level understanding of geometry it avoids

understanding of geometry it avoids

understanding of geometry it avoids pages of calculation – more elegant and

pages of calculation – more elegant and

pages of calculation – more elegant and quicker approaches in fact

quicker approaches in fact

quicker approaches in fact when I tried to solve the equations of

when I tried to solve the equations of

when I tried to solve the equations of our theorem my computer timed out so

our theorem my computer timed out so

our theorem my computer timed out so clearly maths isn’t just a set of

clearly maths isn’t just a set of

clearly maths isn’t just a set of equations but more like a crime thriller

equations but more like a crime thriller

equations but more like a crime thriller where the build build up to the ending

where the build build up to the ending

where the build build up to the ending is far more important than the ending

is far more important than the ending

is far more important than the ending itself something I had to create new

itself something I had to create new

itself something I had to create new theory in the field of AI spooler cubics

theory in the field of AI spooler cubics

theory in the field of AI spooler cubics in order to solve our new theorem and it

in order to solve our new theorem and it

in order to solve our new theorem and it turned out that these subsidiary results

turned out that these subsidiary results

turned out that these subsidiary results end up being the most important and

end up being the most important and

end up being the most important and widely applicable part of our article

widely applicable part of our article

widely applicable part of our article for mass loss theorem is a perfect

for mass loss theorem is a perfect

for mass loss theorem is a perfect example of this back in the 1700s one

example of this back in the 1700s one

example of this back in the 1700s one was formulated people had no idea how to

was formulated people had no idea how to

was formulated people had no idea how to prove the simple looking problem but

prove the simple looking problem but

prove the simple looking problem but fast forward to the 20th century with

fast forward to the 20th century with

fast forward to the 20th century with whole new fields of analytical number

whole new fields of analytical number

whole new fields of analytical number theory and an algebraic number theory

theory and an algebraic number theory

theory and an algebraic number theory had to be invented in order to solve the

had to be invented in order to solve the

had to be invented in order to solve the problem it was finally resolved Andrew

problem it was finally resolved Andrew

problem it was finally resolved Andrew Wiles but in contribution were hundreds

Wiles but in contribution were hundreds

Wiles but in contribution were hundreds of mathematicians worldwide so just

of mathematicians worldwide so just

of mathematicians worldwide so just imagine learning the result a to the X

imagine learning the result a to the X

imagine learning the result a to the X plus PDV x equals c DX what are you

plus PDV x equals c DX what are you

plus PDV x equals c DX what are you actually learning the whole concept of

actually learning the whole concept of

actually learning the whole concept of thinking of mathematics of the journey

thinking of mathematics of the journey

thinking of mathematics of the journey follows from the idea that the ability

follows from the idea that the ability

follows from the idea that the ability to think creatively is far more

to think creatively is far more

to think creatively is far more important than the ability to know and

important than the ability to know and

important than the ability to know and to apply in 2015 alphago was placed in

to apply in 2015 alphago was placed in

to apply in 2015 alphago was placed in competition with lee solo in the game go

competition with lee solo in the game go

competition with lee solo in the game go while the computer did win four out of

while the computer did win four out of

while the computer did win four out of five times is where the computer lost

five times is where the computer lost

five times is where the computer lost which begs the question how could a

which begs the question how could a

which begs the question how could a computer that could compute a surplus of

computer that could compute a surplus of

computer that could compute a surplus of a hundred moves ahead lose to a mere

a hundred moves ahead lose to a mere

a hundred moves ahead lose to a mere human and it was there that I realized

human and it was there that I realized

human and it was there that I realized that we have an edge over computers to

that we have an edge over computers to

that we have an edge over computers to visualize geometrically to think

visualize geometrically to think

visualize geometrically to think abstractly and out of the box and to use

abstractly and out of the box and to use

abstractly and out of the box and to use these qualities to create innovation

these qualities to create innovation

these qualities to create innovation what this means is our human imagination

what this means is our human imagination

what this means is our human imagination and creativity cannot be replicated by a

and creativity cannot be replicated by a

and creativity cannot be replicated by a computer

computer

computer so the question is are we as the younger

so the question is are we as the younger

so the question is are we as the younger generation being given the best

generation being given the best

generation being given the best opportunities to use our talents in

opportunities to use our talents in

opportunities to use our talents in qualities in the best possible way and

qualities in the best possible way and

qualities in the best possible way and currently I don’t believe our education

currently I don’t believe our education

currently I don’t believe our education system understands the importance of

system understands the importance of

system understands the importance of creativity in schools we’re taught to

creativity in schools we’re taught to

creativity in schools we’re taught to set a follow of rules procedures we’re

set a follow of rules procedures we’re

set a follow of rules procedures we’re taught to accept rather than question to

taught to accept rather than question to

taught to accept rather than question to test rather than experiment what is the

test rather than experiment what is the

test rather than experiment what is the point of 12 years of teaching if a

point of 12 years of teaching if a

point of 12 years of teaching if a simple computer program could do the

simple computer program could do the

simple computer program could do the exact same thing billions of times

exact same thing billions of times

exact same thing billions of times faster but being told that wrong is bad

faster but being told that wrong is bad

faster but being told that wrong is bad and in the process we’re losing the

and in the process we’re losing the

and in the process we’re losing the fundamental property that makes us human

fundamental property that makes us human

fundamental property that makes us human creativity just imagine the world with

creativity just imagine the world with

creativity just imagine the world with complex numbers didn’t exist and now

complex numbers didn’t exist and now

complex numbers didn’t exist and now imagine a poor inquisitive child asking

imagine a poor inquisitive child asking

imagine a poor inquisitive child asking his teacher why aren’t there solutions

his teacher why aren’t there solutions

his teacher why aren’t there solutions to x squared equals negative 1 we have

to x squared equals negative 1 we have

to x squared equals negative 1 we have solutions for x squared equals 1 1 4 2 9

solutions for x squared equals 1 1 4 2 9

solutions for x squared equals 1 1 4 2 9 3 but why not negative numbers and just

3 but why not negative numbers and just

3 but why not negative numbers and just imagine a response such as just accept

imagine a response such as just accept

imagine a response such as just accept that there isn’t or even worse being

that there isn’t or even worse being

that there isn’t or even worse being ridiculed for claiming such numbers

ridiculed for claiming such numbers

ridiculed for claiming such numbers should exist then the whole field of

should exist then the whole field of

should exist then the whole field of complex analysis and it’s ubiquitous

complex analysis and it’s ubiquitous

complex analysis and it’s ubiquitous applications in engineering wouldn’t

applications in engineering wouldn’t

applications in engineering wouldn’t have been invented we won’t be able to

have been invented we won’t be able to

have been invented we won’t be able to fly planes or even watch movies in our

fly planes or even watch movies in our

fly planes or even watch movies in our cinemas so comfortably today so just

cinemas so comfortably today so just

cinemas so comfortably today so just imagine what kinds of innovations you

imagine what kinds of innovations you

imagine what kinds of innovations you might be losing nowadays to encourage

might be losing nowadays to encourage

might be losing nowadays to encourage creativity I believe we need to

creativity I believe we need to

creativity I believe we need to introduce real mathematics from an

introduce real mathematics from an

introduce real mathematics from an earlier age that is true we need to

earlier age that is true we need to

earlier age that is true we need to understand the concept of logical

understand the concept of logical

understand the concept of logical thinking and proof writing earlier for

thinking and proof writing earlier for

thinking and proof writing earlier for example instead of homework being to

example instead of homework being to

example instead of homework being to repeatedly apply the same technique for

repeatedly apply the same technique for

repeatedly apply the same technique for 50 differently worded problems why can’t

50 differently worded problems why can’t

50 differently worded problems why can’t it be think of this theorem or problem

it be think of this theorem or problem

it be think of this theorem or problem and how would you prove it and then in

and how would you prove it and then in

and how would you prove it and then in the next class discuss strategies or

the next class discuss strategies or

the next class discuss strategies or what the students thought and show them

what the students thought and show them

what the students thought and show them how the proof would work out and instead

how the proof would work out and instead

how the proof would work out and instead of losing half of the students during

of losing half of the students during

of losing half of the students during class I believe we need to incorporate

class I believe we need to incorporate

class I believe we need to incorporate methods of active learning where

methods of active learning where

methods of active learning where students will read content in advance

students will read content in advance

students will read content in advance and the teacher would go over what they

and the teacher would go over what they

and the teacher would go over what they do not understand lastly I believe we

do not understand lastly I believe we

do not understand lastly I believe we need to make it clear that being wrong

need to make it clear that being wrong

need to make it clear that being wrong is okay because in my experience I’ve

is okay because in my experience I’ve

is okay because in my experience I’ve learnt the most out of being wrong and

learnt the most out of being wrong and

learnt the most out of being wrong and knowing where I’ve gone wrong

knowing where I’ve gone wrong

knowing where I’ve gone wrong coincidentally has given me a better

coincidentally has given me a better

coincidentally has given me a better understanding of mathematics as a whole

understanding of mathematics as a whole

understanding of mathematics as a whole similar ideas – I’ll just be mentioning

similar ideas – I’ll just be mentioning

similar ideas – I’ll just be mentioning have been employed in Finland and look

have been employed in Finland and look

have been employed in Finland and look what that’s got them that the best

what that’s got them that the best

what that’s got them that the best education system in the world they

education system in the world they

education system in the world they understand that our human imagination

understand that our human imagination

understand that our human imagination and creativity should be praised is more

and creativity should be praised is more

and creativity should be praised is more important to visualize them to know and

important to visualize them to know and

important to visualize them to know and to follow a procedure just like you

to follow a procedure just like you

to follow a procedure just like you cannot appreciate a story by reading its

cannot appreciate a story by reading its

cannot appreciate a story by reading its ending you cannot appreciate maths

ending you cannot appreciate maths

ending you cannot appreciate maths physics art or any subject by set of

physics art or any subject by set of

physics art or any subject by set of rules and ways to apply them we need to

rules and ways to apply them we need to

rules and ways to apply them we need to teach these subjects what they are a

teach these subjects what they are a

teach these subjects what they are a journey

journey

journey [Applause]

[Applause]

[Applause] [Music]

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