Let’s teach mathematics creatively Ivan Zelich TEDxYouthSydney

[Music] [Applause] you know it's not longer since I finished high school I have many great memories socializing competing publishing and presenting at international conferences but all of which happened outside the classroom I'm sure you all have great memories of your high school some of us might even remember our teachers reflecting back I realize that teachers in Queensland needed to teach a certain curriculum in a certain way there wasn't much room for manoeuvre which in a way made everybody the same so I guess it is fair to say that your typical classroom environment will consist of desks whiteboards a pre-programmed teacher and a group of students robotically copying down word-for-word everything the teacher was narrating there's only one way to put an end to this automated learning environment and that was someone to ask but that all was necessary for the exam and that was the key to high school knowing what you didn't need to know I spent most of my high school learning about things I didn't need to know for me maths is a journey and the most interesting journeys are the ones in which you explore and gain experience so I believe math should be taught as a journey not a set of equations to be applied to something as if maths is a set of dusty tools in the shed of science for me my maths journey Sawa is really young I've always loved numbers and my parents realized that early on when I started doing Negra number addition at 3 years old I also loved squaring numbers and at one stage I could do five digit multiplication my head actually had a book where I'd write down little tricks and formula used to solve such equations quicker part of the writing I was only 5 years old so yes I love maths and my very school's public in competitions at age of 13 I was spotted by the national director of the Australian mathematical trust who put me in training for the Australian limpia team and it was there that I discover that actually wasn't that a good at geometry I was and still am bad at drawing and this made me scared of the subject how could I possibly prove that three points line a line when my lines look like circles so I worked on geometry problems to maximize my chances of winning and it was there that discovered the unexpected beauty in geometry not in the drawing part of course but in the way certain mathematically challenging concepts could be explained simply through visualization what is the infinite sum of 1/2 plus 1/4 plus 1/8 plus 1/16 etc well to some of you this met this some may seem daunting if you look at this animation where each time we're adding half the previous rectangle it does make sense that these rectangles will eventually add up to a square that has area 1 but if I now ask you where the parallel lines do meet well parent lines are defined not to meet if you look at it in a certain angle it does appear that these lines will eventually meet at a point at infinity and it turns out this point is used extensively in mathematics nowadays I was learning all this outside the classroom luckily nowadays you have the internet where we can learn things in our own time in fact I didn't need school classes at all because participating in mathematical forums was like a class of its own I was so involved in online communities that I actually start Blagh were post solutions to problems that I found beautiful especially ones people can solve and it was there that I met zooming Liang who lives in America at the time we were both 16 and loved geometry is and solving mathematical problems in general coincidentally zooming in our boat stuck on the same open problem and it took us five days to solve this problem a cycle where I worked through the night and zooming we'll continue our left off swimming would do the same repeat the time zone difference actually worked quite well we had eyes on the prom for 120 hours straight now reflect on your high school experience we had to solve 30 problems in one and a half hours is it really testing our ability to think creatively unlike in high school where you could submit your solutions to be marked assuming and I weren't even done we stumbled upon a new theorem in mathematics extending the one we had just solved what a theorem stated was that a point in the Triangle plane lies an isomorphic equivalent to I superior cubics in its petal triangles but here's a diagram for the theorem it's bit simplified unfortunately we too had no idea how to prove this problem and it took us six months to finally figure out a way just to start the proof and another week to solve it let alone nine months for it to be published who could have thought by the end of it that our diagram would look like this what a theorem did was that it made the complex field of I so people cubics easier to deal with and allows difficult geometrical problems to be solved by people with only high school level understanding of geometry it avoids pages of calculation - more elegant and quicker approaches in fact when I tried to solve the equations of our theorem my computer timed out so clearly maths isn't just a set of equations but more like a crime thriller where the build build up to the ending is far more important than the ending itself something I had to create new theory in the field of AI spooler cubics in order to solve our new theorem and it turned out that these subsidiary results end up being the most important and widely applicable part of our article for mass loss theorem is a perfect example of this back in the 1700s one was formulated people had no idea how to prove the simple looking problem but fast forward to the 20th century with whole new fields of analytical number theory and an algebraic number theory had to be invented in order to solve the problem it was finally resolved Andrew Wiles but in contribution were hundreds of mathematicians worldwide so just imagine learning the result a to the X plus PDV x equals c DX what are you actually learning the whole concept of thinking of mathematics of the journey follows from the idea that the ability to think creatively is far more important than the ability to know and to apply in 2015 alphago was placed in competition with lee solo in the game go while the computer did win four out of five times is where the computer lost which begs the question how could a computer that could compute a surplus of a hundred moves ahead lose to a mere human and it was there that I realized that we have an edge over computers to visualize geometrically to think abstractly and out of the box and to use these qualities to create innovation what this means is our human imagination and creativity cannot be replicated by a computer so the question is are we as the younger generation being given the best opportunities to use our talents in qualities in the best possible way and currently I don't believe our education system understands the importance of creativity in schools we're taught to set a follow of rules procedures we're taught to accept rather than question to test rather than experiment what is the point of 12 years of teaching if a simple computer program could do the exact same thing billions of times faster but being told that wrong is bad and in the process we're losing the fundamental property that makes us human creativity just imagine the world with complex numbers didn't exist and now imagine a poor inquisitive child asking his teacher why aren't there solutions to x squared equals negative 1 we have solutions for x squared equals 1 1 4 2 9 3 but why not negative numbers and just imagine a response such as just accept that there isn't or even worse being ridiculed for claiming such numbers should exist then the whole field of complex analysis and it's ubiquitous applications in engineering wouldn't have been invented we won't be able to fly planes or even watch movies in our cinemas so comfortably today so just imagine what kinds of innovations you might be losing nowadays to encourage creativity I believe we need to introduce real mathematics from an earlier age that is true we need to understand the concept of logical thinking and proof writing earlier for example instead of homework being to repeatedly apply the same technique for 50 differently worded problems why can't it be think of this theorem or problem and how would you prove it and then in the next class discuss strategies or what the students thought and show them how the proof would work out and instead of losing half of the students during class I believe we need to incorporate methods of active learning where students will read content in advance and the teacher would go over what they do not understand lastly I believe we need to make it clear that being wrong is okay because in my experience I've learnt the most out of being wrong and knowing where I've gone wrong coincidentally has given me a better understanding of mathematics as a whole similar ideas - I'll just be mentioning have been employed in Finland and look what that's got them that the best education system in the world they understand that our human imagination and creativity should be praised is more important to visualize them to know and to follow a procedure just like you cannot appreciate a story by reading its ending you cannot appreciate maths physics art or any subject by set of rules and ways to apply them we need to teach these subjects what they are a journey [Applause] [Music]

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