The "Why" of Math | Po-Shen Loh | TEDxCMU

Summary

Highlights

• Po-Shen Loh views math as an 'epidemic' affecting millions globally, needing a new educational approach. ✨
• Emphasizing the importance of asking 'why' in education, rather than just teaching content. 🧐
• The potential of using smartphones to make math as engaging as sports is revolutionary! ⚡
• Math enhances intuition and problem-solving, making it a vital life skill. 💡
• Collaboration across different educational organizations can powerfully shift math learning. 🚀
• Instilling a love for math involves showing its real-life applications and exciting challenges. 🌟

Key Takeaways

• Math isn't just an academic hurdle; it's a global phenomenon that requires innovative teaching methods. 🌍
• The key to learning math may lie in making it as fun and accessible as sports like basketball. 🏀
• By utilizing digital platforms like smartphones, math can become more personalized and engaging. 📱
• Math provides a unique framework for developing strong reasoning skills and problem-solving capabilities. 🧠
• Collaboration and diversity in teaching methods can significantly enhance math education. 🤝
• Understanding math transcends memorization; it's about grasping concepts and recognizing patterns. 🔍

Overview

Chapters

• 00:00 - 01:00: Introduction and Problem Statement The chapter introduces a global issue likened to an epidemic: the widespread aversion and intimidation many people feel towards math. It humorously suggests that this 'ailment' affects billions, causes headaches, and lasts for decades. While the speaker offers no medical credentials to cure the discomfort people experience with math, they set the stage for addressing this pervasive problem.
• 01:00 - 02:00: Inspiration and Founding of XP The chapter titled 'Inspiration and Founding of XP' begins with a math professor from Carnegie Mellon University discussing his experience and perspective as the national coach of the United States International Math Olympiad team. This role inspired him to think about methods to improve how math is approached and learned, both nationally and internationally.
• 02:00 - 03:00: Examining Approaches to Learning Math In this chapter, the focus is on the exploration of different methodologies and approaches to learning mathematics. It begins by acknowledging the limitations of an individual working alone, emphasizing the need for diverse perspectives and skills. This realization led to the founding of a social enterprise, XP, aimed at enhancing the learning and understanding of math through collaborative efforts. The chapter sets the stage for discussing how collaborative and social approaches can innovate traditional math education.
• 03:00 - 04:00: The Contrast with Sports The chapter titled 'The Contrast with Sports' explores the societal and educational efforts to enhance mathematics learning. The narrative begins with the author's attendance at a conference at Oxford University, discussing national programs aimed at improving math education. A critical reflection occurs when the author considers the financial investments made by governments and society in promoting mathematical education, paralleling it with investments in sports and other public initiatives. This reflection is intended to provoke thought about the value placed on mathematics and the strategies employed to foster mathematical understanding across the public sphere.
• 04:00 - 05:00: Reimagining Math Education The chapter "Reimagining Math Education" challenges the traditional approach to teaching mathematics by drawing parallels with how sports are learned. It questions the substantial investment in math education despite its lack of effectiveness, and contrasts this with the informal, yet successful, learning of sports like basketball. It suggests that by understanding the broader motivations and contexts of why and how people engage in learning activities, educational methods can be improved.
• 05:00 - 06:00: Math in Entertainment The chapter "Math in Entertainment" discusses the contrast between the promotion of sports, like basketball, and math. It brings into question why there is a significant amount of money spent on advertising sports to the public compared to math. The speaker encourages reflection on why math isn't advertised as frequently and suggests reevaluating the perception of math beyond the typical argument of its benefits.
• 06:00 - 07:00: Real-Life Math Example and Teen Engagement This chapter explores how real-life examples of math can engage teenagers. It compares the advertising strategies of popular soda brands, which often use appealing imagery to attract consumers, to how math can be marketed more engagingly to young people. The chapter suggests that just as soda ads go beyond mere nutritional facts by appealing to emotions, math education also needs to tap into motivations that operate below the conscious level. It proposes taking inspiration from the bold tactics used in entertainment to make math more appealing and engaging for teens.
• 07:00 - 08:00: Collaboration and Production The chapter 'Collaboration and Production' features an engaging start with music that sets the tone, before diving into a discussion about a challenging situation – possibly a bomb – implying tension or urgency.
• 08:00 - 09:00: Math's Relevance and A Sixth Sense The chapter titled 'Math's Relevance and A Sixth Sense' likely explores the practical application of mathematical concepts in everyday life. The excerpt illustrates this by depicting a scenario where a person uses the Pythagorean theorem to strategize beating a bus in an alleyway scenario, suggesting an instinctive use of mathematics in real-world situations. Furthermore, it hints at the idea of involving teenagers in the developmental processes of things intended for them by suggesting that teenagers could play a crucial role in creating solutions targeted at their age group.
• 09:00 - 10:00: Human Intuition and Misconceptions In the chapter titled 'Human Intuition and Misconceptions,' the focus is on exploring the secret elements of design and conversation. The segment briefly skips over a math lesson, emphasizing a result where adding certain components leads to 25, and the square root of 25 yields 5, suggesting a deeper insight into problem-solving or understanding through intuitive leaps.
• 10:00 - 11:00: Concepts and Memorization The chapter titled "Concepts and Memorization" discusses various strategies and techniques to enhance learning and retention through collaboration and effective methods. It highlights the importance of working together with others, possibly indicating a collaborative study approach or group activities as a means to reinforce understanding and memorization. Although the transcript only offers a brief glimpse, it suggests an interactive setting that encourages quick learning and adaptation.
• 11:00 - 12:00: Making Math Accessible Through Technology The chapter discusses the importance of collaboration and acknowledges the contributions of individuals and groups, such as Christian Brown and Steel Town's teen film crew, in making math accessible through technology. It introduces a preview of a series that combines math, real-life, and entertainment, emphasizing the collaborative efforts with various partners to produce these educational materials.
• 12:00 - 13:00: Solving Math Education's Challenges The chapter discusses how math education can solve various challenges by engaging both the subconscious and conscious minds. It highlights the usefulness and relevance of math, suggesting that math provides valuable skills and insights akin to a 'sixth sense.' The chapter aims to promote the idea that math is not only beneficial for intellectual growth but also for practical and everyday applications.
• 13:00 - 14:00: The Importance of a Thoughtful World The chapter explores the concept of perception and intuition through a relatable scenario. It begins with the scene of an audience being quizzed about the level of fullness in cone-shaped cups. The aim is to challenge the listeners' intuition on gauging volume, prompting them to think deeper about how they perceive everyday situations. This sets the stage for a broader discussion on the importance of thoughtful perception in life.

The "Why" of Math | Po-Shen Loh | TEDxCMU Transcription

• 00:00 - 00:30 [Applause] thank you there's a pain that affects millions billions of people around the world it causes heads to hurt some people say they're allergic to it it affects them for over a decade of their lives it's math such an epidemic surely needs a doctor I'm afraid I'm not a real doctor
• 00:30 - 01:00 but I can doctor some math I'm a math professor here at Carnegie Mellon University a few years ago when I became the national coach of the United States International math Olympiad team it inspired me to think about what I could do to try to help everyone with the way they approach and learn math on a national and international scale there
• 01:00 - 01:30 was only one problem one is the loneliest number as they say and one person cannot possibly have the diversity of thought diversity of skills to achieve this and so I founded the social enterprise XP to help me achieve these goals around this time I really started to think about what might be
• 01:30 - 02:00 behind people's thinking about mathematics and also what we could do to try to help everyone learn math I attended a conference at Oxford University and I remember this very distinctly not at the end of the first day when we were all talking about different ways that we could run national programs to help more people learn math suddenly occurred to me you know how much money are we spending as a public society from the government's and
• 02:00 - 02:30 education departments to teach people how to do math we're spending a lot actually but how much money are we spending as a government to teach people how to play basketball but how come people can still play basketball or any of your other favorite sports actually maybe we should start asking the question of why people do what they do because actually here's
• 02:30 - 03:00 another interesting stat how much money is spent to try to convince people to play basketball whether through advertisements or media have you ever seen an advertisement for math ah so maybe maybe we actually need to ask the question of why but not the usual kind of question of why is this good for you I mean when was the last time you remember seeing an advertisement for
• 03:00 - 03:30 your favorite soda telling you you should drink it because of how nutritious it is actually usually you see somebody that you might want to be like taking a drink and being happy you see human motivation starts even below the conscious so maybe if we want to move the needle on mass we need to be bold and take a page from entertainment
• 03:30 - 04:00 [Music] dude that's a bomb that's the bus I know he's not gonna make I promise you this is actually a nice video now I'm gonna cut ahead to a part in the middle where you can see how the math and real life intersect and since the street in the
• 04:00 - 04:30 alleyway create a right triangle I can use the Pythagorean theorem to beat the bus I [Music] know there are four spaces between the telephone poles on the street the bus is currently on and the street the bus and I were just on has three spaces so actually maybe the secret if you're trying to build something that will help teenagers maybe teenagers should be a key
• 04:30 - 05:00 component of that design and that conversation that's the secret here maybe let me jump to the end just so you can see how this works yes there is a math lesson in between we're jumping over it right now and if I add them together it makes 25 and the square root of 25 is 5 [Music]
• 05:00 - 05:30 all right how did you get here so fast hop back here Theron man I gotta learn that so collaboration by the way is a
• 05:30 - 06:00 beautiful thing remember I said one person can't possibly do what is needed to move the needle credits to Christian Brown for his crazy parkour skills engaged rusalka and also the steel town steel towns teen film crew which were all behind this particular production in fact what you've just seen here is a preview in some sense is the first of a series of math real-life and entertainment that we're producing we're working actually with a variety of different partners in
• 06:00 - 06:30 the film and entertainment space so that hits the first part of the Y which is the subconscious the good thing though is that actually this is worth it math actually is useful so there's the next level and that's star Park talking into the conscious because I also want to share that we're not just doing math because it makes us feel good actually math can give you a sense a sixth sense so to speak and I like to give this example to show this will be relevant to
• 06:30 - 07:00 you in your life the next time that you may be facing a beverage served in a cone-shaped cup I just want to do a quick quiz of the audience just this is not a math quiz this is an intuition quiz which one of these is half-full in terms of how full of the volume who thinks it's the first one who thinks it's the second one third one fourth one
• 07:00 - 07:30 and indeed the majority of the audience agrees with what I thought too which is I thought the answer was the third one and it's wrong actually there was about one or two hands that went for the fourth option believe it or not if you're looking at that fourth option that is actually half-full by volume this is an example of how human intuition is actually chronically wrong across
• 07:30 - 08:00 seven billion people now most people don't believe that that could possibly be half the good thing is that math gives you a framework to go from something you don't believe to something that you might believe and the idea is that when you think about volume if you start shrinking the dimension of an object on all three dimensions the volume of the object changes by the
• 08:00 - 08:30 product of how much you change on each direction if you have it this way half of this way in half of this way you just 1/8 of the whole thing and so actually 80% 0.8 times 0.8 times 0.8 that's 0.512 that's about 50% to me as somebody who loves math I feel that if you start to use this aspect of math then you can see the whole world with some sort of heightened sensitivity you see patterns you understand and that's one of the
• 08:30 - 09:00 most pleasurable feelings actually to understand what's going on around you and to be able to change everything well but it wouldn't be very nice for me just to do a tease and say oh this is all great stuff but you know as everyone knows people are born either able to do math or not let me debunk that right now I don't think that's the truth actually there are certain aspects to math that if you learn it the right way actually everyone on earth could
• 09:00 - 09:30 actually do math and have this sixth sense you see the best analogy I would give is this I'm gonna put something on the board I will give you two seconds it's a pattern of lines on a dark background memorize as much of it as you can in two seconds are you ready one two okay so now most of you probably can memorize a part of it instantly and for most of you there are parts of it that
• 09:30 - 10:00 if you had 20 seconds you wouldn't be able to have memorized and what I'm referring to here is a car there's a notion of concepts and structure a lot of times when we learn math we're used to thinking of trying to memorize as many pieces as possible I will say if I'm trying to memorize this just by the little marks on the screen I will also fail miserably but at the same time the fact that many of you have different parts of it that you immediately recognize just show the power you have when you understand concepts and so
• 10:00 - 10:30 actually pulling back to the basketball analogy one other reason why so many people can play basketball it's because of accessibility it's not just a tease saying basketball is fun but good luck you won't find a hoop anywhere there's a hoop in every neighborhood so clearly what we need to do is to do the same for math but won't that cost another billion dollars to put the equivalent in front of everyone well we are at a unique
• 10:30 - 11:00 moment in human history very unique moment where it doesn't cost another billion dollars because there is a portal through which everyone can access which might be in your pocket right now in fact there are no two billion smartphones in the world and this opens up another way to let everyone learn math through maybe what should be the best possible ways which are one-on-one because actually I can even give an analysis of why math is so hard to learn
• 11:00 - 11:30 every subject has concepts I claim math has less concepts to learn than history but there's one fundamental difference if you look at how the concepts of math are arranged the quadratic formula needs square roots it also needs fractions these addition subtraction there are very very long chains of dependencies links between the concepts where I say in history it is
• 11:30 - 12:00 not quite so linear and so if you might have happened to get sick for a week or had something else on your mind in middle school when you were anyway transitioning into adolescence and adulthood and missed some things missed some links then you might suddenly wonder why things aren't making sense honestly it's just because some of the links in the middle are missing but then that gives a recipe to try to fix this if only we could find
• 12:00 - 12:30 a way to identify everybody's missing links and patch them one at a time then everything would make sense I mean personally I'll share I liked math because for me I couldn't remember anything and so it was the easiest subject you just had to know how to problem solve away from link to link and the beauty with computers the fact that everyone has access to a smartphone and the fact that the computer servers that you build can process a billion
• 12:30 - 13:00 calculations a second which by the way is doing math as fast as the entire world working together at the same time the fact that these have all converged at the same time makes a way that we could actually give that access to every single person I've just described a strategy in abstract of course it's great that there are lots of different groups all trying to achieve through this strategy with what we do actually we decided that we even wanted to
• 13:00 - 13:30 combine that with something else going back to that diversity going back to that idea that there are different things that move you maybe there should even be different ways to learn every lesson how about that if we work together on this all of the different education organizations in the world we will achieve everybody being able to do math but now there's a deepest deepest why why in the world should we even
• 13:30 - 14:00 bother doing this and I'll share that what is really a strong motivation for why I get up every day to work on this project because actually thinking is what makes us human math the way we are advocating is actually the art of thinking and reasoning we want to build a more thoughtful world thank you [Applause]