title

Jo Boaler: How to Learn Math | Lex Fridman Podcast #226

description

Jo Boaler is a professor of mathematics education at Stanford and the co-founder of youcubed. Please support this podcast by checking out our sponsors:
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EPISODE LINKS:
Jo's Twitter: https://twitter.com/joboaler
youcubed: https://www.youcubed.org/
Jo's Books: https://amzn.to/2Y3S2xW
Elastic by Leonard Mlodinow: https://amz.run/4tCk
Deep Work by Cal Newport: https://amz.run/4tCl
3Blue1Brown: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
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PODCAST INFO:
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Full episodes playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Clips playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41
OUTLINE:
0:00 - Introduction
0:23 - What is beautiful about mathematics?
9:12 - How difficult should math really be?
17:31 - Students giving up on math
28:52 - Improving math education in schools
38:49 - Inspiring mathematical creativity
56:35 - youcubed
1:00:55 - Best methods for studying math
1:21:29 - Advice for young people
SOCIAL:
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detail

{'title': 'Jo Boaler: How to Learn Math | Lex Fridman Podcast #226', 'heatmap': [{'end': 2395.112, 'start': 2334.897, 'weight': 0.769}], 'summary': "Jo boaler explores the beauty of mathematics, visual learning, and creative problem-solving, emphasizing the significance of visual learning in mathematics and its impact on brain function and problem-solving abilities. she also discusses the importance of intuition in math, the soviet education system's emphasis on excellence, the transformative impact of multidimensional math education, parental influence on children's math achievement, and the need for a new approach to teaching math, advocating for a shift from performance-based grading to more informative measures. furthermore, she emphasizes the importance of balancing math education with creativity, flexibility, and collaboration, discusses the impact of textbooks on modern education, and the profound impact of teaching approaches on student engagement. lastly, she emphasizes the need for perseverance in learning mathematics and the transformative effects of the online class 'how to learn math'.", 'chapters': [{'end': 397.175, 'segs': [{'end': 22.193, 'src': 'embed', 'start': 0.029, 'weight': 0, 'content': [{'end': 8.09, 'text': 'The following is a conversation with Joe Bowler, a mathematics educator at Stanford and co-founder of ucubed.org,', 'start': 0.029, 'duration': 8.061}, {'end': 11.611, 'text': 'that seeks to inspire young minds with the beauty of mathematics.', 'start': 8.09, 'duration': 3.521}, {'end': 16.132, 'text': 'To support this podcast, please check out our sponsors in the description.', 'start': 12.531, 'duration': 3.601}, {'end': 22.193, 'text': 'This is the Lex Friedman Podcast, and here is my conversation with Joe Bowler.', 'start': 17.152, 'duration': 5.041}], 'summary': 'Podcast featuring joe bowler, a stanford math educator and co-founder of ucubed.org, inspiring young minds with math.', 'duration': 22.164, 'max_score': 0.029, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU29.jpg'}, {'end': 171.117, 'src': 'embed', 'start': 141.966, 'weight': 1, 'content': [{'end': 146.669, 'text': 'but it turns out what the neuroscience is telling us is that when we think about maths,', 'start': 141.966, 'duration': 4.703}, {'end': 151.932, 'text': 'there are two visual pathways in the brain and we should all be thinking about it visually.', 'start': 146.669, 'duration': 5.263}, {'end': 160.034, 'text': "Some approaches have been say, well, you're a visual learner, so we'll give you visuals and you're not a visual learner.", 'start': 152.852, 'duration': 7.182}, {'end': 165.175, 'text': "But actually, if you think you're not a visual learner,", 'start': 160.674, 'duration': 4.501}, {'end': 171.117, 'text': "it's probably more important that you have a visual approach so you can develop that part of your brain.", 'start': 165.175, 'duration': 5.942}], 'summary': 'Neuroscience suggests visual thinking is crucial for math, regardless of perceived learning style.', 'duration': 29.151, 'max_score': 141.966, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU141966.jpg'}, {'end': 245.29, 'src': 'embed', 'start': 203.463, 'weight': 2, 'content': [{'end': 207.767, 'text': 'Or maybe you build it with something physical that would cause a different connection.', 'start': 203.463, 'duration': 4.304}, {'end': 217.155, 'text': 'And what we want for kids is we call it a multidimensional experience of math, seeing it in different ways, experiencing it in different ways.', 'start': 207.787, 'duration': 9.368}, {'end': 220.418, 'text': 'That will cause that great connected brain function.', 'start': 217.896, 'duration': 2.522}, {'end': 223.214, 'text': "You know, there's these stories of physicists doing the same.", 'start': 220.632, 'duration': 2.582}, {'end': 230.58, 'text': 'I find physicists are often better at building that part of their brain of using visualization for intuition building,', 'start': 223.314, 'duration': 7.266}, {'end': 237.046, 'text': 'because you ultimately want to understand the like, the deepest secret underneath this problem.', 'start': 230.58, 'duration': 6.466}, {'end': 239.328, 'text': 'And for that, you have to intuit your way there.', 'start': 237.066, 'duration': 2.262}, {'end': 245.29, 'text': 'And you mentioned offline that one of the ways you might approach a problem is to try to tell a story about it.', 'start': 239.708, 'duration': 5.582}], 'summary': 'Encouraging multidimensional math experiences for kids to enhance brain function and intuition building.', 'duration': 41.827, 'max_score': 203.463, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU203463.jpg'}, {'end': 381.189, 'src': 'embed', 'start': 351.677, 'weight': 4, 'content': [{'end': 353.119, 'text': 'Like reasoning is really hard.', 'start': 351.677, 'duration': 1.442}, {'end': 355.392, 'text': "Yeah, it's hard.", 'start': 353.55, 'duration': 1.842}, {'end': 360.497, 'text': "I love to value what's hard in maths instead of being afraid of it.", 'start': 355.412, 'duration': 5.085}, {'end': 364.02, 'text': "We know that when you struggle, that's actually a really good time for your brain.", 'start': 360.597, 'duration': 3.423}, {'end': 367.183, 'text': "You want to be struggling when you're thinking about things.", 'start': 364.54, 'duration': 2.643}, {'end': 372.825, 'text': "So if it's hard to think intuitively about something, that's probably a really good time for your brain.", 'start': 367.263, 'duration': 5.562}, {'end': 381.189, 'text': 'I used to work with somebody called Sebastian Thrun, who is a great sort of mathematician, you might think of him, AI person.', 'start': 372.845, 'duration': 8.344}], 'summary': 'Struggling with math is beneficial for brain; sebastian thrun, ai expert mentioned.', 'duration': 29.512, 'max_score': 351.677, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU351677.jpg'}], 'start': 0.029, 'title': 'Mathematics and visual learning', 'summary': 'Delves into the beauty of mathematics with joe bowler, emphasizing visualizing, creative problem-solving, and multiple methods in math education. it also discusses the significance of visual learning in mathematics, revealing that it leads to better brain function and problem-solving abilities.', 'chapters': [{'end': 120.508, 'start': 0.029, 'title': 'Beauty of mathematics with joe bowler', 'summary': 'Explores the beauty of mathematics with joe bowler, emphasizing the importance of visualizing, creative problem-solving, and multiple methods in mathematics education, challenging the conventional notion of math being solely about numbers.', 'duration': 120.479, 'highlights': ['Joe Bowler emphasizes the beauty of mathematics lies in its creativity, visualization, and the multiple methods and solutions available, challenging the conventional notion of math with only one method and answer.', 'He advocates for making any mathematics area visual, interesting, and creative, highlighting the importance of visualizing math problems and thinking about math in other ways besides numbers.', "It's a disservice that mathematics has primarily been associated with numbers, as there are various ways to approach and solve math problems, including visual, algebraic, and geometric methods."]}, {'end': 397.175, 'start': 121.032, 'title': 'Visual learning in mathematics', 'summary': 'Discusses the importance of visual learning in mathematics, emphasizing that all individuals should develop a visual approach, as it has been revealed by neuroscience that there are two visual pathways in the brain and that a multidimensional experience of math leads to better brain function and problem-solving abilities.', 'duration': 276.143, 'highlights': ['Neuroscience reveals two visual pathways in the brain and emphasizes the importance of a visual approach in mathematics for all individuals. It has been revealed by neuroscience that when thinking about math, there are two visual pathways in the brain, and it is important for all individuals to have a visual approach, even if they do not consider themselves visual learners.', 'A multidimensional experience of math, including visual, physical, and verbal approaches, leads to better connected brain function and problem-solving abilities. It is important for children to have a multidimensional experience of math, seeing it in different ways and experiencing it in different ways, as this leads to better connected brain function and problem-solving abilities.', 'Physicists are often better at using visualization for intuition building, and intuition plays a crucial role in solving math problems. Physicists are often better at using visualization for intuition building, and intuition plays a crucial role in solving math problems. It is important to task oneself with building an intuition about a problem and utilizing visualization to understand patterns.', "Struggling and reasoning in math are valuable and beneficial for brain development, as they lead to better problem-solving abilities. Struggling and reasoning in math are valuable and beneficial for brain development, as they lead to better problem-solving abilities. It is important to value what's hard in math instead of being afraid of it, as struggling is a good time for brain development."]}], 'duration': 397.146, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU29.jpg', 'highlights': ['Joe Bowler emphasizes the beauty of mathematics lies in its creativity, visualization, and the multiple methods and solutions available, challenging the conventional notion of math with only one method and answer.', 'Neuroscience reveals two visual pathways in the brain and emphasizes the importance of a visual approach in mathematics for all individuals.', 'A multidimensional experience of math, including visual, physical, and verbal approaches, leads to better connected brain function and problem-solving abilities.', 'Physicists are often better at using visualization for intuition building, and intuition plays a crucial role in solving math problems.', 'Struggling and reasoning in math are valuable and beneficial for brain development, as they lead to better problem-solving abilities.']}, {'end': 995.255, 'segs': [{'end': 521.407, 'src': 'embed', 'start': 497.214, 'weight': 0, 'content': [{'end': 504.158, 'text': "And then there's the tools of visualization, like color, all of those things that you're absolutely right.", 'start': 497.214, 'duration': 6.944}, {'end': 508.68, 'text': "They're actually not taught very much, like the art of visualization.", 'start': 504.238, 'duration': 4.442}, {'end': 510.401, 'text': 'Not taught.', 'start': 508.88, 'duration': 1.521}, {'end': 513.203, 'text': 'We love as well color coding.', 'start': 511.322, 'duration': 1.881}, {'end': 521.407, 'text': 'When you represent something mathematically, you can show color to show the growth and code that.', 'start': 513.903, 'duration': 7.504}], 'summary': 'Visualization tools like color and coding are under-taught in mathematical representation.', 'duration': 24.193, 'max_score': 497.214, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU497214.jpg'}, {'end': 598.397, 'src': 'embed', 'start': 573.54, 'weight': 1, 'content': [{'end': 582.947, 'text': "I think it's great when things are challenging, but there's something that's really key to being able to deal with challenging maths,", 'start': 573.54, 'duration': 9.407}, {'end': 586.289, 'text': 'and that is knowing that you can do it.', 'start': 582.947, 'duration': 3.342}, {'end': 593.334, 'text': "And I think the problem in education is a lot of people have got this idea that you're either born with a maths brain or you're not.", 'start': 586.85, 'duration': 6.484}, {'end': 598.397, 'text': "So when they start to struggle, they think, oh, I don't have that maths brain.", 'start': 594.114, 'duration': 4.283}], 'summary': "Belief in ability crucial for tackling challenging math, dispelling 'maths brain' myth in education.", 'duration': 24.857, 'max_score': 573.54, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU573540.jpg'}, {'end': 721.861, 'src': 'embed', 'start': 699.127, 'weight': 2, 'content': [{'end': 709.995, 'text': 'But when you open up maths and you let kids experience it in different ways, maybe visually, with numbers, with words, What happens is kids.', 'start': 699.127, 'duration': 10.868}, {'end': 711.696, 'text': 'there are many more kids who can access it.', 'start': 709.995, 'duration': 1.701}, {'end': 720.28, 'text': "So those different brain wirings you're talking about, where some people are just more able to do something in a particular way.", 'start': 712.556, 'duration': 7.724}, {'end': 721.861, 'text': "that's why we want to.", 'start': 720.28, 'duration': 1.581}], 'summary': 'Diverse math experiences help more kids access it.', 'duration': 22.734, 'max_score': 699.127, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU699127.jpg'}, {'end': 969.597, 'src': 'embed', 'start': 898.69, 'weight': 3, 'content': [{'end': 904.496, 'text': 'So math, but also science and literature, by the way, was also hit very hard.', 'start': 898.69, 'duration': 5.806}, {'end': 907.739, 'text': 'Like we read a lot of serious adult stuff.', 'start': 904.676, 'duration': 3.063}, {'end': 909.781, 'text': 'America does that a little bit too.', 'start': 908.299, 'duration': 1.482}, {'end': 915.486, 'text': "They challenge young adults with good literature, but they don't challenge adults very much with math.", 'start': 909.961, 'duration': 5.525}, {'end': 923.509, 'text': 'So those two things, valuing excellence and just a lot of math in the curriculum.', 'start': 916.227, 'duration': 7.282}, {'end': 928.55, 'text': 'Do you find that interesting? Because it seems to have been successful.', 'start': 923.709, 'duration': 4.841}, {'end': 930.151, 'text': "Yeah, I think that's very interesting.", 'start': 928.59, 'duration': 1.561}, {'end': 934.092, 'text': 'And there is a lot of success of people coming through the Soviet system.', 'start': 930.231, 'duration': 3.861}, {'end': 943.855, 'text': "I think something that's very different to the US and other countries in the world is that idea that excellence is important and you can get there if you work hard.", 'start': 934.152, 'duration': 9.703}, {'end': 948.719, 'text': "In the US there's an idea that excellence is important,", 'start': 945.075, 'duration': 3.644}, {'end': 955.206, 'text': "but then kids are given the idea in many ways that you can either do it or you're one of the people who can't.", 'start': 948.719, 'duration': 6.487}, {'end': 959.671, 'text': "So many students in the school system think they're one of the kids who can't.", 'start': 956.289, 'duration': 3.382}, {'end': 963.854, 'text': "So there's no point in trying hard because you're never going to get there.", 'start': 959.771, 'duration': 4.083}, {'end': 969.597, 'text': 'So if you can switch that idea, it would be huge.', 'start': 964.834, 'duration': 4.763}], 'summary': 'Soviet education system prioritizes excellence and math, leading to successful outcomes, while us system lacks emphasis on challenging adults with math and promoting a belief in achieving excellence through hard work.', 'duration': 70.907, 'max_score': 898.69, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU898690.jpg'}], 'start': 397.175, 'title': 'The role of intuition and soviet education system', 'summary': "Discusses the importance of intuition in math, accommodating different learning styles, and the soviet education system's emphasis on excellence, hard work, and rigorous education, contrasting it with the us system.", 'chapters': [{'end': 749.184, 'start': 397.175, 'title': 'The power of intuition in math', 'summary': 'Discusses the importance of intuition and visualization in mathematics, the value of struggling with challenging math, and the need for a multidimensional approach to teaching math to accommodate different learning styles and brain wirings.', 'duration': 352.009, 'highlights': ['The importance of intuition and visualization in mathematics is emphasized, highlighting the role of intuition in problem-solving and the value of visualization tools and color coding for understanding mathematical concepts. Role of intuition in problem-solving, use of visualization tools and color coding for understanding math', "The value of struggling with challenging math is discussed, emphasizing the importance of knowing that one can overcome struggles in math and the detrimental impact of the belief that one is not born with a 'maths brain'. Importance of knowing one can overcome struggles in math, impact of belief in not having a 'maths brain'", 'The need for a multidimensional approach to teaching math to accommodate different learning styles and brain wirings is highlighted, discussing the limitations of the traditional method of teaching math and the benefits of opening up math to different ways of learning. Limitations of traditional method of teaching math, benefits of opening up math to different ways of learning']}, {'end': 995.255, 'start': 750.925, 'title': 'Soviet system: valuing excellence & hard work', 'summary': "Discusses the soviet education system's focus on valuing excellence, hard work, and the belief that anyone can achieve greatness through rigorous math and literature education, contrasting it with the us system.", 'duration': 244.33, 'highlights': ['The Soviet education system valued excellence and emphasized the belief that anyone can achieve greatness through hard work, resulting in a lot of success for people coming through the system. Valuing excellence, belief in achieving greatness through hard work, success of people from the Soviet system.', "The Soviet system focused on rigorous math and literature education, with a heavy emphasis on geometry and a belief that math is fundamental to the development of the human mind. Rigorous math and literature education, heavy emphasis on geometry, belief in math's importance to human mind development.", "Contrasting with the US system, the chapter highlights the difference in beliefs regarding achieving excellence, where the Soviet system emphasizes that anyone can achieve greatness with hard work, while the US system may lead kids to believe that they are unable to achieve excellence. Contrast with US system, belief in achieving excellence through hard work, US system's impact on kids' belief in achieving excellence."]}], 'duration': 598.08, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU397175.jpg', 'highlights': ['Role of intuition in problem-solving, use of visualization tools and color coding for understanding math', "Importance of knowing one can overcome struggles in math, impact of belief in not having a 'maths brain'", 'Limitations of traditional method of teaching math, benefits of opening up math to different ways of learning', 'Valuing excellence, belief in achieving greatness through hard work, success of people from the Soviet system', "Rigorous math and literature education, heavy emphasis on geometry, belief in math's importance to human mind development", "Contrast with US system, belief in achieving excellence through hard work, US system's impact on kids' belief in achieving excellence"]}, {'end': 1656.89, 'segs': [{'end': 1051.573, 'src': 'embed', 'start': 1022.148, 'weight': 0, 'content': [{'end': 1024.288, 'text': 'In our camp classrooms, they were three hours long.', 'start': 1022.148, 'duration': 2.14}, {'end': 1029.226, 'text': 'When we were planning, the teachers were like, three hours.', 'start': 1026.484, 'duration': 2.742}, {'end': 1035.887, 'text': "Are we going to be able to keep the kids excited for three hours? Turned out they didn't want to go to break or lunch.", 'start': 1029.246, 'duration': 6.641}, {'end': 1038.828, 'text': "They'd be so into these mathematical patterns.", 'start': 1035.968, 'duration': 2.86}, {'end': 1040.868, 'text': "We couldn't stop them.", 'start': 1039.488, 'duration': 1.38}, {'end': 1042.769, 'text': 'It was amazing.', 'start': 1041.189, 'duration': 1.58}, {'end': 1048.691, 'text': 'So yeah, if maths was more like that, then I think having more of it would be a really good thing.', 'start': 1042.848, 'duration': 5.843}, {'end': 1051.573, 'text': 'So what age are you talking about?', 'start': 1049.071, 'duration': 2.502}], 'summary': 'In camp classrooms, 3-hour math lessons kept kids engaged, wanting more.', 'duration': 29.425, 'max_score': 1022.148, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1022148.jpg'}, {'end': 1130.346, 'src': 'embed', 'start': 1103.346, 'weight': 1, 'content': [{'end': 1106.528, 'text': 'So middle school years, our camps are middle school students.', 'start': 1103.346, 'duration': 3.182}, {'end': 1108.89, 'text': 'We think of those years as really pivotal.', 'start': 1107.049, 'duration': 1.841}, {'end': 1117.577, 'text': "Many kids in those years are deciding, yes, I'm going to keep going with STEM subjects or no, I'm not, that this isn't for me.", 'start': 1109.23, 'duration': 8.347}, {'end': 1125.581, 'text': 'So, I mean, all years are important and in all years you can kind of switch kids and get them on a different pathway.', 'start': 1118.437, 'duration': 7.144}, {'end': 1127.983, 'text': 'But I think those middle school years are really important.', 'start': 1125.641, 'duration': 2.342}, {'end': 1130.346, 'text': "So what's the role of the teacher in this??", 'start': 1128.464, 'duration': 1.882}], 'summary': 'Middle school camps are pivotal for stem interest. teachers play a crucial role.', 'duration': 27, 'max_score': 1103.346, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1103346.jpg'}, {'end': 1393.476, 'src': 'embed', 'start': 1369.788, 'weight': 2, 'content': [{'end': 1377.091, 'text': 'The textbooks have a lot to answer for in producing this very uninspiring mathematics.', 'start': 1369.788, 'duration': 7.303}, {'end': 1384.833, 'text': 'But yeah, if you open up the subject and have people see and solve it in different ways and value those different ways.', 'start': 1378.391, 'duration': 6.442}, {'end': 1389.595, 'text': 'Somebody I appreciated a lot is a mathematician called Maryam Mizakhani.', 'start': 1385.454, 'duration': 4.141}, {'end': 1390.595, 'text': "I don't know if you've heard of her.", 'start': 1389.615, 'duration': 0.98}, {'end': 1392.476, 'text': 'She won the Fields Medal.', 'start': 1390.675, 'duration': 1.801}, {'end': 1393.476, 'text': 'She was from Iran.', 'start': 1392.556, 'duration': 0.92}], 'summary': "Textbooks' limitations in inspiring math; diverse approaches valued. maryam mizakhani, fields medal winner from iran, appreciated.", 'duration': 23.688, 'max_score': 1369.788, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1369788.jpg'}], 'start': 995.255, 'title': 'Transformative math education', 'summary': "Emphasizes the impact of multidimensional math education through stanford summer camps, stresses the pivotal role of middle school years, and discusses the power of visual mathematics exemplified by maryam mizakhani's fields medal-winning work.", 'chapters': [{'end': 1042.769, 'start': 995.255, 'title': 'Transforming math education for kids', 'summary': "Highlights the impact of engaging and multidimensional math education, as evidenced by the success of stanford summer camps, where kids were engrossed in three-hour math sessions and didn't want breaks or lunch, showcasing the potential for a transformative change in math education.", 'duration': 47.514, 'highlights': ["The success of Stanford summer camps' engaging math education is evidenced by kids being engrossed in three-hour math sessions and not wanting breaks or lunch, demonstrating the potential for transformative change in math education.", "The impact of engaging and multidimensional math education is highlighted through the success of Stanford summer camps, where kids were so engrossed in mathematical patterns that they didn't want breaks or lunch, showcasing the potential for transformative change in math education.", "The enthusiasm of kids for engaging and multidimensional math education is evident from the success of Stanford summer camps, where kids were so engrossed in mathematical patterns during three-hour sessions that they didn't want breaks or lunch, indicating the potential for transformative change in math education."]}, {'end': 1369.768, 'start': 1042.848, 'title': 'Importance of middle school years in math education', 'summary': 'Highlights the pivotal role of middle school years in math education, specifically emphasizing the impact of fifth grade and the need for teachers to provide belief and encouragement to students, as well as support for nonstandard learners and creative thinkers.', 'duration': 326.92, 'highlights': ["The pivotal role of fifth grade and middle school years in influencing students' attitudes towards math and STEM subjects, with many students deciding to continue or disengage during this period.", "The significant impact of teachers' belief and encouragement on students' academic performance, as evidenced by a study where an additional sentence expressing belief led to improved English performance a year later.", 'The importance of supporting nonstandard learners and creative thinkers in the education system, as exemplified by mathematicians and physicists who have succeeded despite facing challenges in the traditional education system.']}, {'end': 1656.89, 'start': 1369.788, 'title': 'Inspiring mathematics: the power of visualization', 'summary': "Discusses the power of visual mathematics, exemplified by maryam mizakhani's fields medal-winning work, the impact of a teacher's belief in a student's ability, and the influence of parents' math anxiety on children's achievement in school.", 'duration': 287.102, 'highlights': ["Maryam Mizakhani's visual approach to mathematics and her groundbreaking work that connected previously unconnected areas of maths, winning her the Fields Medal, the first woman to achieve this in mathematics. Maryam Mizakhani's visual and unconventional approach to mathematics, which connected previously unconnected areas of maths, winning her the prestigious Fields Medal, making her the first woman to achieve this in mathematics.", "The influence of a teacher's belief in a student's ability, exemplified by Maryam Mizakhani's experience of being told she couldn't do maths at the age of 13, yet she went on to win the Fields Medal. The significant impact of a teacher's belief in a student's ability, as seen in Maryam Mizakhani's experience of being told she couldn't do maths at the age of 13, but eventually winning the prestigious Fields Medal.", "The study's finding that the amount of maths anxiety parents had predicted their child's achievement in school, especially when they helped with homework, signaling the importance of parents' attitudes towards mathematics. The study's finding that parents' maths anxiety predicted their child's achievement in school, particularly when they helped with homework, emphasizing the significance of parents' attitudes towards mathematics."]}], 'duration': 661.635, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU995255.jpg', 'highlights': ["The success of Stanford summer camps' engaging math education is evidenced by kids being engrossed in three-hour math sessions and not wanting breaks or lunch, demonstrating the potential for transformative change in math education.", "The pivotal role of fifth grade and middle school years in influencing students' attitudes towards math and STEM subjects, with many students deciding to continue or disengage during this period.", "Maryam Mizakhani's visual approach to mathematics and her groundbreaking work that connected previously unconnected areas of maths, winning her the Fields Medal, the first woman to achieve this in mathematics."]}, {'end': 2321.124, 'segs': [{'end': 1687.986, 'src': 'embed', 'start': 1656.91, 'weight': 0, 'content': [{'end': 1659.872, 'text': "I haven't experienced parents worrying that their kids will be better than them.", 'start': 1656.91, 'duration': 2.962}, {'end': 1673.199, 'text': 'I have experienced parents Just having a really bad relationship with maths and, you know, not wanting to help, not knowing how to help saying things.', 'start': 1660.913, 'duration': 12.286}, {'end': 1681.584, 'text': "Another study showed that when mothers say to their daughters, I was bad at maths in school, their daughter's achievement goes down.", 'start': 1674.562, 'duration': 7.022}, {'end': 1687.986, 'text': 'So we know that kids pick up on these messages, which is why I say you should fake it.', 'start': 1682.564, 'duration': 5.422}], 'summary': "Negative parental attitudes towards math impact children's achievement, as evidenced by a decrease in daughters' achievement when mothers express their own struggles with math.", 'duration': 31.076, 'max_score': 1656.91, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1656910.jpg'}, {'end': 1787.98, 'src': 'embed', 'start': 1761.767, 'weight': 1, 'content': [{'end': 1768.534, 'text': "So I'm one of five writers of a new framework for the state of California, a new maths framework that's coming out next year.", 'start': 1761.767, 'duration': 6.767}, {'end': 1773.498, 'text': 'And we are recommending through this maths framework that people teach in this way.', 'start': 1769.474, 'duration': 4.024}, {'end': 1777.101, 'text': "It's called Teaching to Big Ideas.", 'start': 1773.979, 'duration': 3.122}, {'end': 1787.98, 'text': 'So at the moment, people have standards that have been written and then textbooks have taken these standards and made not very good questions.', 'start': 1778.695, 'duration': 9.285}], 'summary': 'Developed new maths framework for california, promoting teaching to big ideas.', 'duration': 26.213, 'max_score': 1761.767, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1761767.jpg'}, {'end': 1886.615, 'src': 'embed', 'start': 1861.053, 'weight': 2, 'content': [{'end': 1865.837, 'text': "and so teachers don't see the connections between ideas, nor do the kids.", 'start': 1861.053, 'duration': 4.784}, {'end': 1877.787, 'text': "Anyway, this is a bit of a long way of saying that what we've done in this new initiative is we have set out maths as a set of big ideas and connections between them.", 'start': 1866.577, 'duration': 11.21}, {'end': 1880.109, 'text': 'This is grade three.', 'start': 1877.827, 'duration': 2.282}, {'end': 1886.615, 'text': "Instead of there being 60 standards, we've said well,", 'start': 1881.11, 'duration': 5.505}], 'summary': 'New initiative sets out math as big ideas and connections, reducing 60 standards.', 'duration': 25.562, 'max_score': 1861.053, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1861053.jpg'}, {'end': 2073.804, 'src': 'embed', 'start': 2048.827, 'weight': 3, 'content': [{'end': 2055.513, 'text': 'And yes, have a great at the end of the year, but during the year, you can assess kids in much better ways.', 'start': 2048.827, 'duration': 6.686}, {'end': 2065.141, 'text': "A great way of assessing kids is to give them a rubric that kind of outlines what they're learning over the course of a unit or a few weeks.", 'start': 2056.554, 'duration': 8.587}, {'end': 2070.583, 'text': "So kids can actually see the journey they're on, like, this is what we're doing mathematically.", 'start': 2065.862, 'duration': 4.721}, {'end': 2073.804, 'text': 'Sometimes they self-assess on those units.', 'start': 2071.224, 'duration': 2.58}], 'summary': 'Assess kids with rubrics to track learning progress and enable self-assessment.', 'duration': 24.977, 'max_score': 2048.827, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2048827.jpg'}], 'start': 1656.91, 'title': 'Transforming math education', 'summary': "Explores the impact of parental influence on children's math achievement, the need for a new approach to teaching math, and the development of a new framework for math education in california, emphasizing 'teaching to big ideas'. it also discusses the initiative of reorganizing mathematics k10 into big ideas and connections, reducing 60 standards to a small number of interconnected concepts, while advocating for a shift from performance-based grading to more informative measures during the year.", 'chapters': [{'end': 1835.879, 'start': 1656.91, 'title': 'Transforming math education', 'summary': "Explores the impact of parental influence on children's math achievement, the need for a new approach to teaching math, and the development of a new framework for math education in california, emphasizing 'teaching to big ideas'.", 'duration': 178.969, 'highlights': ["The influence of parental attitudes towards math has an impact on children's achievement, with a study showing that when mothers express negativity towards math, their daughters' achievement in math decreases. This highlights the negative impact of parental attitudes on children's math achievement, supported by a study that demonstrates how mothers' negative statements about their own math abilities lead to a decrease in their daughters' math achievement.", 'Many individuals, including successful people and students at Stanford, have a negative relationship with math, perceiving it as a set of methods to memorize rather than a different subject altogether. This emphasizes the prevalence of negative perceptions of math among successful individuals and even students at Stanford, who view math as a set of memorization methods rather than a distinct subject, indicating the need for a shift in perspective.', "The development of a new framework for math education in California, known as 'Teaching to Big Ideas', aims to transform the teaching approach by deviating from traditional standards and uninspiring textbooks. This highlights the effort to revolutionize math education in California through the introduction of a new framework, 'Teaching to Big Ideas', which aims to break away from traditional standards and uninspiring textbooks, offering a more engaging and effective teaching approach."]}, {'end': 2321.124, 'start': 1836.98, 'title': 'Rethinking mathematics education', 'summary': 'Discusses the initiative of reorganizing mathematics k10 into big ideas and connections, reducing 60 standards to a small number of interconnected concepts, while advocating for a shift from performance-based grading to more informative measures during the year.', 'duration': 484.144, 'highlights': ['The initiative of reorganizing mathematics K10 into big ideas and connections The chapter introduces the initiative to set out mathematics K10 as a set of big ideas and connections, reducing the number of standards and emphasizing interconnected concepts.', "Advocating for a shift from performance-based grading to more informative measures during the year The chapter discusses the drawbacks of performance-based grading and advocates for a shift towards more informative measures during the year, such as using rubrics to assess students' progress and self-assessment.", 'Encouraging extension of tasks for students excelling in specific areas The chapter highlights the importance of encouraging students to extend tasks further, providing an example of a student excelling in an activity and being encouraged to explore the concept further.', "Challenges in teaching and the need for sensitivity to students' individual needs The chapter emphasizes the challenges in teaching and the need for sensitivity to students' individual needs, highlighting the importance of tailoring feedback and challenges to each student's unique characteristics."]}], 'duration': 664.214, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU1656910.jpg', 'highlights': ["The influence of parental attitudes towards math has an impact on children's achievement, with a study showing that when mothers express negativity towards math, their daughters' achievement in math decreases.", "The development of a new framework for math education in California, known as 'Teaching to Big Ideas', aims to transform the teaching approach by deviating from traditional standards and uninspiring textbooks.", 'The initiative of reorganizing mathematics K10 into big ideas and connections, reducing the number of standards and emphasizing interconnected concepts.', "Advocating for a shift from performance-based grading to more informative measures during the year, such as using rubrics to assess students' progress and self-assessment."]}, {'end': 2929.702, 'segs': [{'end': 2395.112, 'src': 'heatmap', 'start': 2334.897, 'weight': 0.769, 'content': [{'end': 2342.371, 'text': "actually there's a video of me doing this on our website that I love when I first meet students.", 'start': 2334.897, 'duration': 7.474}, {'end': 2344.194, 'text': 'And this is what I do.', 'start': 2343.212, 'duration': 0.982}, {'end': 2346.037, 'text': 'I show them a picture.', 'start': 2344.214, 'duration': 1.823}, {'end': 2347.559, 'text': 'This is the picture I show them.', 'start': 2346.077, 'duration': 1.482}, {'end': 2350.684, 'text': "And it's a picture of seven dots like this.", 'start': 2348.32, 'duration': 2.364}, {'end': 2358.786, 'text': "And I show it for just a few seconds, and I say to them, I'd like you to tell me how many dots there are, but I don't want you to count them.", 'start': 2353.204, 'duration': 5.582}, {'end': 2360.267, 'text': 'I want you to group the dots.', 'start': 2359.206, 'duration': 1.061}, {'end': 2366.489, 'text': "And I show it them, and then I take it away before they've even had enough time to count them.", 'start': 2360.867, 'duration': 5.622}, {'end': 2372.171, 'text': 'And then I ask them, so how did you see it? And I go around the room, and..', 'start': 2367.129, 'duration': 5.042}, {'end': 2378.114, 'text': "Amazingly enough, there's probably 18 different ways of seeing these seven dots.", 'start': 2373.551, 'duration': 4.563}, {'end': 2382.357, 'text': 'So I asked people, tell me how you grouped it.', 'start': 2379.535, 'duration': 2.822}, {'end': 2385.28, 'text': 'Some people see it as like an outside hole with a center dot.', 'start': 2382.418, 'duration': 2.862}, {'end': 2388.642, 'text': 'Some people see like stripes of lines.', 'start': 2385.78, 'duration': 2.862}, {'end': 2390.823, 'text': 'Some people see segments.', 'start': 2389.362, 'duration': 1.461}, {'end': 2393.691, 'text': 'And I collect them all and I put them on the board.', 'start': 2391.969, 'duration': 1.722}, {'end': 2395.112, 'text': 'And at the end, I say, look at this.', 'start': 2393.831, 'duration': 1.281}], 'summary': 'Using a picture of 7 dots, students are shown to group them in various ways, revealing 18 different perspectives.', 'duration': 60.215, 'max_score': 2334.897, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2334897.jpg'}, {'end': 2428.129, 'src': 'embed', 'start': 2395.492, 'weight': 0, 'content': [{'end': 2399.896, 'text': 'We are a class of 30 kids and we saw these seven dots in 18 different ways.', 'start': 2395.492, 'duration': 4.404}, {'end': 2401.858, 'text': "There's actually a mathematical term for this.", 'start': 2400.236, 'duration': 1.622}, {'end': 2403.199, 'text': "It's called groupitizing.", 'start': 2401.918, 'duration': 1.281}, {'end': 2404.96, 'text': 'Groupitizing? Yeah.', 'start': 2403.94, 'duration': 1.02}, {'end': 2406.762, 'text': 'I like it.', 'start': 2406.141, 'duration': 0.621}, {'end': 2407.483, 'text': "It's kind of cool.", 'start': 2406.802, 'duration': 0.681}, {'end': 2414.549, 'text': 'So turns out, though, that how well you groupitize predicts how well you do in maths.', 'start': 2407.683, 'duration': 6.866}, {'end': 2419.927, 'text': 'Is it raw talent or is it just something that you can develop??', 'start': 2415.586, 'duration': 4.341}, {'end': 2428.129, 'text': "I don't think you're born groupitizing, I think, but some kids have developed that ability, if you like, and you can learn it.", 'start': 2420.207, 'duration': 7.922}], 'summary': '30 kids saw 7 dots in 18 ways, groupitizing predicts math success', 'duration': 32.637, 'max_score': 2395.492, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2395492.jpg'}, {'end': 2512.067, 'src': 'embed', 'start': 2485.663, 'weight': 1, 'content': [{'end': 2490.925, 'text': 'So what would you say is the role of creativity and flexibility in the learning of math?', 'start': 2485.663, 'duration': 5.262}, {'end': 2500.237, 'text': 'I think what we know now is that what we need for this 21st century world we live in is a flexible mind.', 'start': 2491.345, 'duration': 8.892}, {'end': 2508.964, 'text': 'Schools should not really be about teaching kids particular methods, but teaching them to approach problems with flexibility.', 'start': 2502.159, 'duration': 6.805}, {'end': 2512.067, 'text': 'Being creative, thinking creatively is really important.', 'start': 2509.525, 'duration': 2.542}], 'summary': 'Creativity and flexibility are essential for learning math in the 21st century world.', 'duration': 26.404, 'max_score': 2485.663, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2485663.jpg'}, {'end': 2793.216, 'src': 'embed', 'start': 2764.066, 'weight': 3, 'content': [{'end': 2766.888, 'text': 'And the ones who collaborated did better on the problem.', 'start': 2764.066, 'duration': 2.822}, {'end': 2770.11, 'text': 'Collaboration is important.', 'start': 2767.868, 'duration': 2.242}, {'end': 2779.457, 'text': "What was so eye-opening for these undergrads, and they talked about it in lovely ways, was I learned to value other people's thinking on a problem.", 'start': 2770.55, 'duration': 8.907}, {'end': 2783.42, 'text': 'I learned to value that other people saw it in different ways.', 'start': 2780.157, 'duration': 3.263}, {'end': 2793.216, 'text': 'And it was quite a big experience for them that they came out thinking, you know, I can do maths with other people.', 'start': 2784.512, 'duration': 8.704}], 'summary': 'Collaboration improved problem solving for undergrads, changing their perspective on math.', 'duration': 29.15, 'max_score': 2764.066, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2764066.jpg'}, {'end': 2909.988, 'src': 'embed', 'start': 2875.809, 'weight': 6, 'content': [{'end': 2879.93, 'text': 'And the other thing you have to put aside is this social comparison thinking.', 'start': 2875.809, 'duration': 4.121}, {'end': 2884.872, 'text': 'If you are sitting there thinking wow, that was an amazing idea.', 'start': 2880.89, 'duration': 3.982}, {'end': 2886.632, 'text': "he's so much better than I am.", 'start': 2884.872, 'duration': 1.76}, {'end': 2891.213, 'text': "that's really gonna stop you taking on the value of that idea.", 'start': 2886.632, 'duration': 4.581}, {'end': 2901.196, 'text': "And so there's a lot of that going on between these Stanford students when they came and trying to help them let go of that.", 'start': 2892.314, 'duration': 8.882}, {'end': 2909.988, 'text': "One of the things I've discovered just because being a little bit more in the public eye, how rewarding it is to celebrate others.", 'start': 2901.943, 'duration': 8.045}], 'summary': 'Avoid social comparison and celebrate others for a more rewarding experience.', 'duration': 34.179, 'max_score': 2875.809, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2875809.jpg'}], 'start': 2321.184, 'title': 'Balancing math education', 'summary': "Emphasizes the importance of balancing math education with creativity, flexibility, and collaboration, showcasing 'groupitizing' as a predictor of math ability and the positive impact on students' performance.", 'chapters': [{'end': 2540.627, 'start': 2321.184, 'title': 'Teaching math with creativity', 'summary': "Emphasizes the importance of teaching math with creativity and flexibility, highlighting the concept of 'groupitizing' as a predictor of mathematical ability, and advocating for a shift towards valuing creative problem-solving approaches in math education.", 'duration': 219.443, 'highlights': ["The concept of 'groupitizing' is highlighted as a predictor of mathematical ability, with the speaker emphasizing that how well a person can groupitize predicts how well they will do in math.", 'The role of creativity and flexibility in learning math is emphasized, with the focus on developing a flexible mind for the 21st century world, rather than just teaching specific methods.', 'The speaker uses an engaging approach to teaching math by showing a picture of seven dots and asking students to group them in different ways, demonstrating that there are 18 different ways to perceive the dots, promoting creativity and flexibility in problem-solving.']}, {'end': 2929.702, 'start': 2541.647, 'title': 'Balancing education for creative thinking', 'summary': "Emphasizes the importance of shifting the balance in education towards developing creative, flexible thinking and collaboration, as demonstrated by the positive impact on students' math performance and the insights gained from collaboration with daniel kahneman.", 'duration': 388.055, 'highlights': ["Collaboration in education leads to improved problem-solving and achievement, as seen in the positive impact on students' math performance after being taught to collaborate, with the ones who collaborated doing better on the problem.", "The value of collaboration and the importance of learning to appreciate other people's perspectives and ways of thinking, as demonstrated by the undergrads who learned to collaborate and saw the benefits of building on each other's ideas.", "The significance of developing collaborative skills, such as active listening and genuine curiosity about others' perspectives, exemplified through the experience of interacting with Daniel Kahneman and his expertise in collaboration.", 'The detrimental effects of social comparison thinking and the need to let go of it to fully benefit from collaboration and value the ideas of others, as highlighted in the challenges faced by the Stanford students and the importance of putting aside social comparison thinking.']}], 'duration': 608.518, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2321184.jpg', 'highlights': ["The concept of 'groupitizing' as a predictor of mathematical ability is emphasized.", 'Emphasis on developing a flexible mind for the 21st century world in math education.', 'Engaging approach to teaching math by promoting creativity and flexibility in problem-solving.', 'Collaboration in education leads to improved problem-solving and achievement.', "Importance of learning to appreciate other people's perspectives and ways of thinking.", "Significance of developing collaborative skills, such as active listening and genuine curiosity about others' perspectives.", 'Detrimental effects of social comparison thinking and the need to let go of it to fully benefit from collaboration.']}, {'end': 3875.555, 'segs': [{'end': 2993.01, 'src': 'embed', 'start': 2967.322, 'weight': 6, 'content': [{'end': 2975.957, 'text': "When we're talking about basic, like high school calculus, biology, chemistry, those are like, those are incredible.", 'start': 2967.322, 'duration': 8.635}, {'end': 2983.943, 'text': "It's like Wikipedia, but with color and nice little- You must have seen some good textbooks if they had pretty pictures in color.", 'start': 2976.897, 'duration': 7.046}, {'end': 2993.01, 'text': 'Yeah, I mean, I remember, I guess it was very, very standard, like AP Calculus, AP Biology, AP Chemistry.', 'start': 2984.603, 'duration': 8.407}], 'summary': 'High school courses like calculus, biology, and chemistry were standard, including ap level.', 'duration': 25.688, 'max_score': 2967.322, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2967322.jpg'}, {'end': 3069.177, 'src': 'embed', 'start': 3042.091, 'weight': 3, 'content': [{'end': 3049.818, 'text': "And like in this more modern digital age, what's the best materials with which to do these kinds of educations?", 'start': 3042.091, 'duration': 7.727}, {'end': 3053.382, 'text': "Well, I'm intrigued that you had such a good experience with textbooks.", 'start': 3050.158, 'duration': 3.224}, {'end': 3054.202, 'text': 'I mean, I can..', 'start': 3053.642, 'duration': 0.56}, {'end': 3059.367, 'text': 'remember loving some textbooks I had when I was learning and I love books.', 'start': 3055.083, 'duration': 4.284}, {'end': 3062.13, 'text': 'I love to pick up books and look through them.', 'start': 3059.527, 'duration': 2.603}, {'end': 3069.177, 'text': 'But a lot of maths textbooks are not good experiences for kids.', 'start': 3063.111, 'duration': 6.066}], 'summary': 'Math textbooks can be a poor learning experience for kids.', 'duration': 27.086, 'max_score': 3042.091, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3042091.jpg'}, {'end': 3162.652, 'src': 'embed', 'start': 3127.466, 'weight': 5, 'content': [{'end': 3129.227, 'text': 'yeah, point three, two point.', 'start': 3127.466, 'duration': 1.761}, {'end': 3132.689, 'text': "it feels like you're making progress and like it's little celebrations,", 'start': 3129.227, 'duration': 3.462}, {'end': 3137.312, 'text': "because you do the problem and it seems really hard and you don't know how to do it.", 'start': 3132.689, 'duration': 4.623}, {'end': 3140.936, 'text': 'and then you try and try and then eventually succeed.', 'start': 3137.312, 'duration': 3.624}, {'end': 3147.943, 'text': "then you make that little step and yeah, further progress, and then you get to the end of a chapter and you get to like it's closure.", 'start': 3140.936, 'duration': 7.007}, {'end': 3151.287, 'text': "you're like, yeah, all right, i got that figured out, and then you go on to the next chapter.", 'start': 3147.943, 'duration': 3.344}, {'end': 3152.288, 'text': 'i can see that.', 'start': 3151.287, 'duration': 1.001}, {'end': 3154.951, 'text': 'i mean i think it could be in a textbook.', 'start': 3152.288, 'duration': 2.663}, {'end': 3162.652, 'text': "you can have a good experience with a textbook, but what's really important is what is in that textbook.", 'start': 3154.951, 'duration': 7.701}], 'summary': 'Students feel a sense of progress and accomplishment solving challenging problems, leading to motivation and further progress in learning.', 'duration': 35.186, 'max_score': 3127.466, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3127466.jpg'}, {'end': 3201.07, 'src': 'embed', 'start': 3170.494, 'weight': 4, 'content': [{'end': 3173.555, 'text': "We don't have this separation of algebra and geometry.", 'start': 3170.494, 'duration': 3.061}, {'end': 3177.457, 'text': "And I don't think any other country apart from the US has that.", 'start': 3174.515, 'duration': 2.942}, {'end': 3185.681, 'text': "But I look at kids in algebra classes where they're doing algebra for a year, and I think I would have been pretty bored doing that.", 'start': 3178.237, 'duration': 7.444}, {'end': 3192.605, 'text': 'By the way, can we analyze your upbringing real quick?', 'start': 3188.483, 'duration': 4.122}, {'end': 3199.089, 'text': 'Why do British folks call mathematics maths??', 'start': 3193.486, 'duration': 5.603}, {'end': 3201.07, 'text': 'Why is it the plural??', 'start': 3200.029, 'duration': 1.041}], 'summary': "Algebra and geometry not separated, british call math 'maths'. no country except us separates algebra and geometry.", 'duration': 30.576, 'max_score': 3170.494, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3170494.jpg'}, {'end': 3316.946, 'src': 'embed', 'start': 3280.993, 'weight': 7, 'content': [{'end': 3281.633, 'text': 'I mean, online..', 'start': 3280.993, 'duration': 0.64}, {'end': 3289.485, 'text': "Having great teachers online obviously extends those teachers to many more people, and that's a wonderful thing.", 'start': 3283.078, 'duration': 6.407}, {'end': 3294.19, 'text': 'I have quite a few online courses myself.', 'start': 3289.505, 'duration': 4.685}, {'end': 3305.181, 'text': "I got the bug working with Sebastian when he had released his first MOOC and I thought maybe I could do one in maths education and I didn't know if anybody would take it.", 'start': 3294.33, 'duration': 10.851}, {'end': 3316.946, 'text': 'I remember releasing it that first summer and it was a free online class and 30,000 maths teachers took it that first summer and they were all talking about it with each other and sharing it,', 'start': 3306.482, 'duration': 10.464}], 'summary': 'Online education expands access to great teachers, with 30,000 maths teachers taking a free online class in the first summer.', 'duration': 35.953, 'max_score': 3280.993, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3280993.jpg'}, {'end': 3428.584, 'src': 'embed', 'start': 3392.374, 'weight': 0, 'content': [{'end': 3395.338, 'text': "Yeah, that's really effective.", 'start': 3392.374, 'duration': 2.964}, {'end': 3396.959, 'text': 'You mentioned YouCubed.', 'start': 3395.939, 'duration': 1.02}, {'end': 3402.962, 'text': "So what's the mission? What's the goal? You mentioned how it started, but what's..", 'start': 3397.06, 'duration': 5.902}, {'end': 3406.404, 'text': "Yeah, where are you at now and what's your dream with it?", 'start': 3402.962, 'duration': 3.442}, {'end': 3409.665, 'text': 'What are the kind of things that people should go and check out on there?', 'start': 3406.744, 'duration': 2.921}, {'end': 3412.427, 'text': 'Yeah, we started YouCubed.', 'start': 3410.446, 'duration': 1.981}, {'end': 3417.289, 'text': "I guess it was about five years ago now, and we've had over 52 million visitors to the site.", 'start': 3412.427, 'duration': 4.862}, {'end': 3418.83, 'text': "So I'm very happy about that.", 'start': 3417.329, 'duration': 1.501}, {'end': 3428.584, 'text': 'And our goal is to share good ideas for teaching with teachers, students, parents in maths and to help.', 'start': 3419.49, 'duration': 9.094}], 'summary': 'Youcubed has had over 52 million visitors in 5 years, sharing math teaching ideas.', 'duration': 36.21, 'max_score': 3392.374, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3392374.jpg'}, {'end': 3518.738, 'src': 'embed', 'start': 3490.523, 'weight': 1, 'content': [{'end': 3497.905, 'text': 'So lessons, there were videos to show kids, and there were tips for parents, there were all sorts of things on the site.', 'start': 3490.523, 'duration': 7.382}, {'end': 3499.985, 'text': "And it's been amazing.", 'start': 3498.025, 'duration': 1.96}, {'end': 3509.376, 'text': 'We took inspiration from the Week of Code, which got teachers to focus on coding for a week.', 'start': 3501.206, 'duration': 8.17}, {'end': 3512.976, 'text': 'And we have this thing called the Week of Inspirational Maths.', 'start': 3509.716, 'duration': 3.26}, {'end': 3515.717, 'text': 'And we say, just try it for a week.', 'start': 3513.957, 'duration': 1.76}, {'end': 3518.738, 'text': 'Just give us one week and try it and see what happens.', 'start': 3516.257, 'duration': 2.481}], 'summary': 'Inspired by week of code, launched week of inspirational maths, urging to try for a week.', 'duration': 28.215, 'max_score': 3490.523, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3490523.jpg'}], 'start': 2929.702, 'title': 'Textbooks and math education', 'summary': 'Discusses the impact of textbooks on modern education, the differences in math education between countries, and the mission and impact of youcubed, which has had over 52 million visitors, aiming to inspire math education.', 'chapters': [{'end': 3127.466, 'start': 2929.702, 'title': 'Role of textbooks in modern education', 'summary': "Discusses the role of textbooks in modern education, highlighting the impact of textbooks on students' learning experiences, and contrasting traditional textbook-based learning with a more flexible and engaging approach, as demonstrated in a camp setting.", 'duration': 197.764, 'highlights': ["The traditional use of textbooks in education is being questioned, with some students feeling restricted by the rigid structure of textbooks, as exemplified by the comparison to the 'Bible' and the monotony of following specific exercises daily.", 'The speaker and the interviewer reminisce about their positive experiences with textbooks in high school, particularly in subjects like calculus and biology, emphasizing the visual appeal and accessible nature of these textbooks.', 'The chapter explores a modern approach to education by discussing a camp where students were provided with a more flexible and engaging learning environment, free from the constraints of traditional textbooks, resulting in a more positive and empowering learning experience.']}, {'end': 3392.314, 'start': 3127.466, 'title': 'The power of mathematics education', 'summary': 'Highlights the joy of progress in learning mathematics, the differences between math education in england and the us, the effectiveness of online education in mathematics, and the importance of pedagogy in online learning.', 'duration': 264.848, 'highlights': ["The joy of progress in learning mathematics is emphasized, with the speaker discussing the sense of achievement and closure when completing a chapter or problem, highlighting the importance of the learning experience (e.g., 'little celebrations' and 'closure').", "The differences between math education in England and the US are explored, with the speaker expressing boredom at the idea of focusing solely on algebra for a year and discussing the multidimensional nature of 'maths' as opposed to the singular 'math' in the US.", "The effectiveness of online education in mathematics is discussed, with the speaker sharing their positive experience of reaching a wide audience through MOOCs, highlighting the impact of engaging pedagogy and the need for active learning (e.g., 'never to talk more than five minutes' and 'ask people to do something')."]}, {'end': 3875.555, 'start': 3392.374, 'title': 'Youcubed: inspiring math education', 'summary': 'Discusses the mission and impact of youcubed, which has had over 52 million visitors in its 5-year history, aiming to erase math anxiety, share math as a creative subject, and provide accessible teaching resources. it also highlights the success of the week of inspirational maths and the creation of k-8 math books, with a desire to extend inspiration throughout the year.', 'duration': 483.181, 'highlights': ["YouCubed has had over 52 million visitors in its 5-year history. The significant number of visitors indicates the widespread impact and reach of YouCubed's mission in sharing good ideas for teaching math.", 'The Week of Inspirational Maths has been downloaded millions of times, with teachers using it at the beginning of each school year. The high download count and annual usage by teachers demonstrate the success and positive reception of this program as an effective teaching tool.', 'Creation of K-8 math books with big ideas and rich activities, although not designed for daily use. The development and completion of K-8 math books provide valuable resources for teachers, albeit with a desire to produce daily creative visual math tasks for every year group.', 'Desire to extend the inspiration of the Week of Inspirational Maths throughout the entire year. The aspiration to maintain the positive impact of the Week of Inspirational Maths for the entire school year reflects a commitment to continuous inspiration in math education.']}], 'duration': 945.853, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU2929702.jpg', 'highlights': ['YouCubed has had over 52 million visitors in its 5-year history, indicating widespread impact and reach.', 'The Week of Inspirational Maths has been downloaded millions of times, with teachers using it at the beginning of each school year, demonstrating its success as an effective teaching tool.', 'Desire to extend the inspiration of the Week of Inspirational Maths throughout the entire year, reflecting a commitment to continuous inspiration in math education.', "The traditional use of textbooks in education is being questioned, with some students feeling restricted by the rigid structure, exemplified by the comparison to the 'Bible' and the monotony of following specific exercises daily.", "The differences between math education in England and the US are explored, with the speaker expressing boredom at the idea of focusing solely on algebra for a year and discussing the multidimensional nature of 'maths' as opposed to the singular 'math' in the US.", 'The joy of progress in learning mathematics is emphasized, with the speaker discussing the sense of achievement and closure when completing a chapter or problem, highlighting the importance of the learning experience.', 'The speaker and the interviewer reminisce about their positive experiences with textbooks in high school, particularly in subjects like calculus and biology, emphasizing the visual appeal and accessible nature of these textbooks.', 'The effectiveness of online education in mathematics is discussed, with the speaker sharing their positive experience of reaching a wide audience through MOOCs, highlighting the impact of engaging pedagogy and the need for active learning.']}, {'end': 4415.694, 'segs': [{'end': 3956.252, 'src': 'embed', 'start': 3898.999, 'weight': 0, 'content': [{'end': 3909.646, 'text': "I probably didn't do very much of that for most of my education, asking why, except for later, much later in the subjects on, like grad school,", 'start': 3898.999, 'duration': 10.647}, {'end': 3911.647, 'text': "when you're doing research on them?", 'start': 3909.646, 'duration': 2.001}, {'end': 3919.612, 'text': 'When your first task of doing something novel using this, or solving a problem really outside the classroom.', 'start': 3912.307, 'duration': 7.305}, {'end': 3920.912, 'text': 'They have to publish on it.', 'start': 3919.972, 'duration': 0.94}, {'end': 3926.915, 'text': "It's the first time you think wait, why are these things interesting, useful?", 'start': 3920.952, 'duration': 5.963}, {'end': 3928.576, 'text': 'Which are the things that are useful?', 'start': 3927.176, 'duration': 1.4}, {'end': 3935.06, 'text': 'And yeah, I guess that would be nice if we did that much earlier that the quest of invention.', 'start': 3928.596, 'duration': 6.464}, {'end': 3936.22, 'text': 'Yeah, yeah.', 'start': 3935.08, 'duration': 1.14}, {'end': 3942.304, 'text': 'I mean, one of the sad pieces of research data I think about is the questions kids ask.', 'start': 3937.001, 'duration': 5.303}, {'end': 3949.667, 'text': 'in school goes down in a linear progression.', 'start': 3943.862, 'duration': 5.805}, {'end': 3956.252, 'text': "In the early years, you can't stop kids asking those questions, but they learn not to ask the questions.", 'start': 3950.367, 'duration': 5.885}], 'summary': 'Research shows decline in kids asking questions in school, emphasizing need for earlier focus on invention and inquiry.', 'duration': 57.253, 'max_score': 3898.999, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3898999.jpg'}, {'end': 4058.73, 'src': 'embed', 'start': 4028.647, 'weight': 3, 'content': [{'end': 4032.048, 'text': 'I was, yeah, he was the chair of the maths department.', 'start': 4028.647, 'duration': 3.401}, {'end': 4033.268, 'text': 'I remember that really well.', 'start': 4032.068, 'duration': 1.2}, {'end': 4041.53, 'text': 'So, maybe because of that experience, one of the things we encourage when we teach kids is asking questions,', 'start': 4033.848, 'duration': 7.682}, {'end': 4045.531, 'text': 'and we value it when they ask questions and we put them up on walls and celebrate.', 'start': 4041.53, 'duration': 4.001}, {'end': 4048.772, 'text': "And, um, it's funny cause.", 'start': 4045.711, 'duration': 3.061}, {'end': 4055.149, 'text': 'I wish there was a feedback signal because he probably to put a positive spin on it.', 'start': 4049.827, 'duration': 5.322}, {'end': 4058.73, 'text': "he probably didn't realize the negative impact he's had in that moment, right?", 'start': 4055.149, 'duration': 3.581}], 'summary': 'Encouraging kids to ask questions is a key teaching strategy.', 'duration': 30.083, 'max_score': 4028.647, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4028647.jpg'}, {'end': 4251.319, 'src': 'embed', 'start': 4225.586, 'weight': 4, 'content': [{'end': 4230.993, 'text': 'It was more like she, uh, she was the catalyst for that collaborative experience.', 'start': 4225.586, 'duration': 5.407}, {'end': 4234.857, 'text': 'I mean, yeah, the many ways teachers can inspire kids.', 'start': 4232.054, 'duration': 2.803}, {'end': 4241.765, 'text': "I mean, sometimes it's a personal message, but it can be your teaching approach that changes maths for kids.", 'start': 4234.997, 'duration': 6.768}, {'end': 4247.157, 'text': 'You know, Cal Newport, he wrote a book called Deep Work.', 'start': 4242.455, 'duration': 4.702}, {'end': 4251.319, 'text': "And he's a mathematician, a theoretical computer scientist.", 'start': 4248.698, 'duration': 2.621}], 'summary': 'Teachers have various ways to inspire kids, such as through personal messages or teaching approaches. cal newport, a mathematician and theoretical computer scientist, wrote a book called deep work.', 'duration': 25.733, 'max_score': 4225.586, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4225586.jpg'}, {'end': 4352.813, 'src': 'embed', 'start': 4322.124, 'weight': 5, 'content': [{'end': 4327.465, 'text': 'And so everybody needs those rich, deep problems.', 'start': 4322.124, 'duration': 5.341}, {'end': 4337.127, 'text': 'Most kids go through their whole maths experience of however many years, never once working on a problem in that kind of deep way.', 'start': 4328.385, 'duration': 8.742}, {'end': 4342.689, 'text': 'So the undergrad class I teach at Stanford, we do that.', 'start': 4338.147, 'duration': 4.542}, {'end': 4345.77, 'text': 'We work on these deep problems every session.', 'start': 4342.749, 'duration': 3.021}, {'end': 4352.813, 'text': 'And the students come away going, OK, I never want to go back to that maths relationship I had where it was just all about quick answers.', 'start': 4346.39, 'duration': 6.423}], 'summary': 'Teaching undergrads to solve deep math problems at stanford to change their perspective on math.', 'duration': 30.689, 'max_score': 4322.124, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4322124.jpg'}], 'start': 3875.555, 'title': 'Importance of asking why and impact of teaching approaches', 'summary': "Emphasizes the significance of encouraging students to ask 'why' in education, citing the decline in question-asking behavior among students. it also discusses the profound impact of teaching approaches on student engagement, emphasizing the importance of encouraging questions, fostering collaborative problem-solving, and promoting deep work in mathematics education.", 'chapters': [{'end': 3956.252, 'start': 3875.555, 'title': 'Importance of asking why in education', 'summary': "Emphasizes the importance of encouraging students to ask 'why' in education, starting from math class, to foster curiosity and innovation, as evidenced by the decline in question-asking behavior among students over the years.", 'duration': 80.697, 'highlights': ["Encouraging students to ask 'why' in education fosters curiosity and innovation, as evidenced by the decline in question-asking behavior among students over the years. The chapter emphasizes the importance of encouraging students to ask 'why' in education, starting from math class, to foster curiosity and innovation, as evidenced by the decline in question-asking behavior among students over the years.", 'Research data indicates a decline in question-asking behavior among students in school over the years. One of the sad pieces of research data is the decline in question-asking behavior among students in school, which goes down in a linear progression, indicating a decrease in curiosity and questioning as students progress through the education system.', "The author reflects on the lack of emphasis on asking 'why' during earlier education and the potential benefits of introducing the quest for invention at an earlier stage. The author reflects on the lack of emphasis on asking 'why' during earlier education and the potential benefits of introducing the quest for invention at an earlier stage, such as in math class, to encourage students to explore the reasons behind concepts and foster a mindset of curiosity and innovation."]}, {'end': 4415.694, 'start': 3956.792, 'title': 'Impact of teaching approaches on student engagement', 'summary': 'Discusses the profound impact of teaching approaches on student engagement, citing personal experiences and highlighting the importance of encouraging questions, fostering collaborative problem-solving, and promoting deep work in mathematics education.', 'duration': 458.902, 'highlights': ["Encouraging questions and valuing them is crucial for student engagement, as negative responses to questions can have a lasting impact, as demonstrated by the speaker's personal experience in a high school maths class. Negative responses to student questions can discourage further engagement; the speaker's own experience led to a reluctance to ask questions in that class.", "The positive impact of a teacher fostering collaborative problem-solving among students is emphasized, with the speaker recounting how this approach transformed their experience in mathematics education. Encouraging collaborative problem-solving can change students' perception of a subject; the speaker's personal experience of discussing and solving math problems with peers was transformative.", 'The importance of providing students with deep, inspiring problems in mathematics education is underscored, as it cultivates the ability to work slowly and deeply, promoting a shift away from quick-answer-focused learning. Deep, inspiring problems encourage slow and deep thinking; students benefit from experiences that allow them to work on problems in a deep way, moving away from rapid question-answering approaches.']}], 'duration': 540.139, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU3875555.jpg', 'highlights': ["Encouraging students to ask 'why' in education fosters curiosity and innovation, as evidenced by the decline in question-asking behavior among students over the years.", 'Research data indicates a decline in question-asking behavior among students in school over the years, indicating a decrease in curiosity and questioning as students progress through the education system.', "The author reflects on the lack of emphasis on asking 'why' during earlier education and the potential benefits of introducing the quest for invention at an earlier stage, such as in math class, to encourage students to explore the reasons behind concepts and foster a mindset of curiosity and innovation.", "Encouraging questions and valuing them is crucial for student engagement, as negative responses to questions can have a lasting impact, as demonstrated by the speaker's personal experience in a high school maths class.", 'The positive impact of a teacher fostering collaborative problem-solving among students is emphasized, with the speaker recounting how this approach transformed their experience in mathematics education.', 'The importance of providing students with deep, inspiring problems in mathematics education is underscored, as it cultivates the ability to work slowly and deeply, promoting a shift away from quick-answer-focused learning.']}, {'end': 5431.277, 'segs': [{'end': 4504.253, 'src': 'embed', 'start': 4416.854, 'weight': 1, 'content': [{'end': 4422.477, 'text': 'And to be successful, I think in certain subjects like mathematics, you wanna be able to develop that skill.', 'start': 4416.854, 'duration': 5.623}, {'end': 4431.181, 'text': "Otherwise you're not going to get to the really rewarding experience of solving these problems.", 'start': 4422.617, 'duration': 8.564}, {'end': 4442.085, 'text': "Definitely. There was a survey done of kids in school where they were asked how long will you work on a maths problem before you give up and decide it's not possible to solve it?", 'start': 4432.481, 'duration': 9.604}, {'end': 4446.486, 'text': 'And the result on average across the kids was two minutes.', 'start': 4442.625, 'duration': 3.861}, {'end': 4458.831, 'text': "Yeah, that's a bad sign, but that was a powerful sign that they need to learn to not give up so quickly.", 'start': 4451.448, 'duration': 7.383}, {'end': 4468.605, 'text': "Yeah We mentioned offline, because we've been talking so much about visualization, Grant Sanderson, 3LU1Brown.", 'start': 4459.571, 'duration': 9.034}, {'end': 4476.615, 'text': "So he's inspired millions of people with exactly the kind of way of thinking that you've been talking about.", 'start': 4469.326, 'duration': 7.289}, {'end': 4477.656, 'text': 'Yeah, I love his..', 'start': 4476.655, 'duration': 1.001}, {'end': 4491.03, 'text': 'work converting sort of mathematical concepts into visual, like visually representing them, exploring them in ways that help you illuminate,', 'start': 4478.527, 'duration': 12.503}, {'end': 4491.87, 'text': 'like the concepts.', 'start': 4491.03, 'duration': 0.84}, {'end': 4497.991, 'text': 'What do you think is the role of that? So he uses mostly programmatic visualizations.', 'start': 4493.37, 'duration': 4.621}, {'end': 4504.253, 'text': "So it's the thing I mentioned where there's like animations created by writing computer programs.", 'start': 4498.071, 'duration': 6.182}], 'summary': 'Encouraging perseverance in math; kids give up after 2 min. visualization aids learning.', 'duration': 87.399, 'max_score': 4416.854, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4416854.jpg'}, {'end': 4609.879, 'src': 'embed', 'start': 4581.618, 'weight': 6, 'content': [{'end': 4585.951, 'text': 'And maybe they could go on to take some other mathematical idea and make it that beautiful.', 'start': 4581.618, 'duration': 4.333}, {'end': 4587.063, 'text': 'Well, he does that.', 'start': 4586.343, 'duration': 0.72}, {'end': 4592.967, 'text': 'He created a library called Manum and he open sourced it.', 'start': 4589.085, 'duration': 3.882}, {'end': 4596.35, 'text': 'And that library is the, people should check it out.', 'start': 4593.007, 'duration': 3.343}, {'end': 4601.693, 'text': "It's written in Python and it uses some of those same elements.", 'start': 4596.51, 'duration': 5.183}, {'end': 4605.276, 'text': 'Like it allows you to animate equations and animate little shapes.', 'start': 4602.053, 'duration': 3.223}, {'end': 4609.879, 'text': 'Like people that, you know, he has a very distinct style in his videos.', 'start': 4605.716, 'duration': 4.163}], 'summary': 'Mathematical library manum, open sourced in python, features animated equations and shapes.', 'duration': 28.261, 'max_score': 4581.618, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4581618.jpg'}, {'end': 4879.405, 'src': 'embed', 'start': 4853.314, 'weight': 0, 'content': [{'end': 4861.42, 'text': "controlled trials and given it to middle school kids and other middle school kids who don't take it but are taught by the same teachers,", 'start': 4853.314, 'duration': 8.106}, {'end': 4862.581, 'text': 'so their teachers are the same.', 'start': 4861.42, 'duration': 1.161}, {'end': 4870.603, 'text': 'And the kids who take the online class end up 68% more engaged in their maths class and do better at the end of the year.', 'start': 4863.121, 'duration': 7.482}, {'end': 4879.405, 'text': "So that's a little six session, 15 minute class, and it changes kids' maths relationships.", 'start': 4870.683, 'duration': 8.722}], 'summary': 'Middle school kids taking online class show 68% more engagement and improved math performance.', 'duration': 26.091, 'max_score': 4853.314, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4853314.jpg'}, {'end': 5052.905, 'src': 'embed', 'start': 5025.148, 'weight': 5, 'content': [{'end': 5030.953, 'text': 'as opposed to believing in that you can do something else, something big, whatever your heart says to do.', 'start': 5025.148, 'duration': 5.805}, {'end': 5043.96, 'text': "And one of the things that I realized the value of this quite recently, which is sad to say, is how important it is to seek out when you're younger,", 'start': 5031.793, 'duration': 12.167}, {'end': 5050.243, 'text': 'to seek out mentors, to seek out the people like surround yourself with people that will believe in you.', 'start': 5043.96, 'duration': 6.283}, {'end': 5052.905, 'text': "It's like a little bit is on you.", 'start': 5050.884, 'duration': 2.021}], 'summary': 'Seek out mentors and surround yourself with believers to achieve your goals.', 'duration': 27.757, 'max_score': 5025.148, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU5025148.jpg'}, {'end': 5232.003, 'src': 'embed', 'start': 5205.359, 'weight': 3, 'content': [{'end': 5212.282, 'text': "you've got to think that 100 years from now, education will be totally different to the way it is now.", 'start': 5205.359, 'duration': 6.923}, {'end': 5218.545, 'text': "Maybe we won't have subject boundaries anymore because those don't really make much sense.", 'start': 5212.662, 'duration': 5.883}, {'end': 5225.938, 'text': "It's interesting to think how certain tools like programming, maybe they'll be deeply integrated in everything we do.", 'start': 5219.091, 'duration': 6.847}, {'end': 5226.938, 'text': 'You would think, yeah.', 'start': 5225.958, 'duration': 0.98}, {'end': 5232.003, 'text': 'You would think that all kids are growing up learning to program and create.', 'start': 5227.119, 'duration': 4.884}], 'summary': 'Education in 100 years: no subject boundaries, programming integrated into learning for all kids.', 'duration': 26.644, 'max_score': 5205.359, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU5205359.jpg'}], 'start': 4416.854, 'title': 'Perseverance and visualizing math', 'summary': "Emphasizes the need for perseverance in learning mathematics, revealing that kids give up after two minutes on average. it also discusses the impact of visually representing mathematical concepts and the transformative effects of the online class 'how to learn math', which led to a 68% increase in engagement and performance in math class.", 'chapters': [{'end': 4476.615, 'start': 4416.854, 'title': 'Importance of perseverance in learning mathematics', 'summary': 'Emphasizes the need for perseverance in learning mathematics, citing a survey that revealed on average kids give up on solving a math problem after two minutes, highlighting the importance of developing perseverance skills in mathematics.', 'duration': 59.761, 'highlights': ['A survey found that on average kids give up on solving a math problem after two minutes, indicating the need to develop perseverance skills in mathematics.', 'Grant Sanderson, 3LU1Brown, has inspired millions with his approach to thinking and visualization, aligning with the discussion on the importance of perseverance in learning mathematics.']}, {'end': 4831.798, 'start': 4476.655, 'title': 'Visualizing mathematical concepts', 'summary': 'Discusses the impact of visually representing mathematical concepts through programmatic visualizations, the role of storytelling in creating visuals, and the potential for democratizing education through online platforms such as moocs.', 'duration': 355.143, 'highlights': ['The impact of visually representing mathematical concepts through programmatic visualizations and storytelling in creating visuals. The role of programmatic visualizations in illuminating mathematical concepts, the use of storytelling in weaving a narrative with visuals, and the transformative effect of experiencing mathematical ideas in this way.', 'The potential for democratizing education through online platforms such as MOOCs. The initial excitement around MOOCs democratizing education, the need to address the accessibility and equality of online learning, and the positive impact of making educational resources available to people all over the world.', 'The impact of programmatic visualizations and the creation of a library called Manim. The creation of the Manim library, its open-source nature, and its use of programmatic visualizations to animate equations and shapes, as well as its influence on other educators.']}, {'end': 5431.277, 'start': 4832.018, 'title': 'Transforming education with how to learn math', 'summary': "Discusses the impact of an online class 'how to learn math' on students, revealing a 68% increase in engagement and performance in math class, the importance of believing in oneself, and the potential evolution of the education system over the next 100 years.", 'duration': 599.259, 'highlights': ["The class 'How to Learn Math' resulted in a 68% increase in engagement and performance in math class based on randomized controlled trials with middle school students. The online class 'How to Learn Math' demonstrated a significant 68% increase in student engagement and performance in math class, as observed in randomized controlled trials with middle school students.", 'The importance of believing in oneself is emphasized, as many individuals, including students and adults, have been discouraged from pursuing certain paths and need to be reminded that they can achieve anything. The chapter highlights the significance of believing in oneself, addressing how individuals, including students and adults, have been discouraged from pursuing certain paths, emphasizing the need to remind them that they can achieve anything.', 'The potential evolution of the education system over the next 100 years is discussed, envisioning a future with a transformed system that integrates technology, removes subject boundaries, and fosters creativity. The transcript delves into the potential evolution of the education system over the next 100 years, envisioning a transformed system that integrates technology, removes subject boundaries, and fosters creativity.']}], 'duration': 1014.423, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KZnGSVwIpeU/pics/KZnGSVwIpeU4416854.jpg', 'highlights': ["The class 'How to Learn Math' resulted in a 68% increase in engagement and performance in math class based on randomized controlled trials with middle school students.", 'A survey found that on average kids give up on solving a math problem after two minutes, indicating the need to develop perseverance skills in mathematics.', 'Grant Sanderson, 3LU1Brown, has inspired millions with his approach to thinking and visualization, aligning with the discussion on the importance of perseverance in learning mathematics.', 'The potential evolution of the education system over the next 100 years is discussed, envisioning a future with a transformed system that integrates technology, removes subject boundaries, and fosters creativity.', 'The impact of visually representing mathematical concepts through programmatic visualizations and storytelling in creating visuals.', 'The importance of believing in oneself is emphasized, as many individuals, including students and adults, have been discouraged from pursuing certain paths and need to be reminded that they can achieve anything.', 'The impact of programmatic visualizations and the creation of a library called Manim.']}], 'highlights': ["The class 'How to Learn Math' resulted in a 68% increase in engagement and performance in math class based on randomized controlled trials with middle school students.", "The success of Stanford summer camps' engaging math education is evidenced by kids being engrossed in three-hour math sessions and not wanting breaks or lunch, demonstrating the potential for transformative change in math education.", "The pivotal role of fifth grade and middle school years in influencing students' attitudes towards math and STEM subjects, with many students deciding to continue or disengage during this period.", "The influence of parental attitudes towards math has an impact on children's achievement, with a study showing that when mothers express negativity towards math, their daughters' achievement in math decreases.", 'A multidimensional experience of math, including visual, physical, and verbal approaches, leads to better connected brain function and problem-solving abilities.', "The concept of 'groupitizing' as a predictor of mathematical ability is emphasized.", 'The importance of believing in oneself is emphasized, as many individuals, including students and adults, have been discouraged from pursuing certain paths and need to be reminded that they can achieve anything.', 'The potential evolution of the education system over the next 100 years is discussed, envisioning a future with a transformed system that integrates technology, removes subject boundaries, and fosters creativity.', 'The impact of visually representing mathematical concepts through programmatic visualizations and storytelling in creating visuals.', "The traditional use of textbooks in education is being questioned, with some students feeling restricted by the rigid structure, exemplified by the comparison to the 'Bible' and the monotony of following specific exercises daily."]}