[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:10.37,0:00:14.37,Default,,0000,0000,0000,,A friend of mine told me recently\Nthat her six-year-old son
Dialogue: 0,0:00:14.37,0:00:17.60,Default,,0000,0000,0000,,had come from school\Nand said he hated math.
Dialogue: 0,0:00:18.31,0:00:21.88,Default,,0000,0000,0000,,And this is hard for me to hear\Nbecause I actually love math.
Dialogue: 0,0:00:22.37,0:00:26.68,Default,,0000,0000,0000,,The beauty and power of mathematical\Nthinking have changed my life.
Dialogue: 0,0:00:26.68,0:00:29.84,Default,,0000,0000,0000,,But I know that many people\Nlived a very different story.
Dialogue: 0,0:00:30.00,0:00:33.28,Default,,0000,0000,0000,,Math can be the best of times\Nor the worst of times,
Dialogue: 0,0:00:33.51,0:00:36.61,Default,,0000,0000,0000,,an exhilarating journey of discovery
Dialogue: 0,0:00:36.61,0:00:41.80,Default,,0000,0000,0000,,or descent into tedium,\Nfrustration, and despair.
Dialogue: 0,0:00:43.52,0:00:47.80,Default,,0000,0000,0000,,Mathematical miseducation\Nis so common we can hardly see it.
Dialogue: 0,0:00:48.09,0:00:50.14,Default,,0000,0000,0000,,We practically expect math class
Dialogue: 0,0:00:50.14,0:00:55.29,Default,,0000,0000,0000,,to be repetition and memorization\Nof disjointed technical facts.
Dialogue: 0,0:00:55.60,0:00:58.20,Default,,0000,0000,0000,,And we're not surprised\Nwhen students aren't motivated,
Dialogue: 0,0:00:58.20,0:01:00.33,Default,,0000,0000,0000,,when they leave school disliking math,
Dialogue: 0,0:01:00.33,0:01:03.33,Default,,0000,0000,0000,,even committed to avoiding it\Nfor the rest of their lives.
Dialogue: 0,0:01:04.18,0:01:08.71,Default,,0000,0000,0000,,Without mathematical literacy,\Ntheir career opportunities shrink.
Dialogue: 0,0:01:09.03,0:01:12.74,Default,,0000,0000,0000,,And they become easy prey\Nfor credit card companies,
Dialogue: 0,0:01:12.74,0:01:15.18,Default,,0000,0000,0000,,payday lenders, the lottery,
Dialogue: 0,0:01:16.10,0:01:17.37,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:01:17.67,0:01:21.41,Default,,0000,0000,0000,,and anyone, really, who wants\Nto dazzle them with a statistic.
Dialogue: 0,0:01:21.70,0:01:25.50,Default,,0000,0000,0000,,Did you know that if you insert\Na single statistic into an assertion,
Dialogue: 0,0:01:25.50,0:01:29.95,Default,,0000,0000,0000,,people are 92 percent more likely\Nto accept it without question?
Dialogue: 0,0:01:29.95,0:01:32.66,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:01:33.74,0:01:36.21,Default,,0000,0000,0000,,Yeah, I totally made that up.
Dialogue: 0,0:01:36.21,0:01:37.34,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:01:37.36,0:01:43.04,Default,,0000,0000,0000,,And 92 percent is - it has weight\Neven though it's completely fabricated.
Dialogue: 0,0:01:43.04,0:01:44.50,Default,,0000,0000,0000,,And that's how it works.
Dialogue: 0,0:01:44.50,0:01:46.35,Default,,0000,0000,0000,,When we're not comfortable with math,
Dialogue: 0,0:01:46.35,0:01:49.10,Default,,0000,0000,0000,,we don't question\Nthe authority of numbers.
Dialogue: 0,0:01:51.53,0:01:56.01,Default,,0000,0000,0000,,But what's happening\Nwith mathematical alienation
Dialogue: 0,0:01:56.01,0:01:58.10,Default,,0000,0000,0000,,is only half the story.
Dialogue: 0,0:01:58.10,0:02:02.60,Default,,0000,0000,0000,,Right now, we're squandering\Nour chance to touch life after life
Dialogue: 0,0:02:02.60,0:02:06.34,Default,,0000,0000,0000,,with the beauty and power\Nof mathematical thinking.
Dialogue: 0,0:02:06.60,0:02:10.86,Default,,0000,0000,0000,,I led a workshop on this topic recently,\Nand at the end, a woman raised her hand
Dialogue: 0,0:02:10.86,0:02:13.99,Default,,0000,0000,0000,,and said that the experience\Nmade her feel - and this is a quote -
Dialogue: 0,0:02:14.29,0:02:16.00,Default,,0000,0000,0000,,"like a God."
Dialogue: 0,0:02:16.27,0:02:19.19,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:02:19.19,0:02:21.77,Default,,0000,0000,0000,,That's maybe the best\Ndescription I've ever heard
Dialogue: 0,0:02:21.77,0:02:24.76,Default,,0000,0000,0000,,for what mathematical\Nthinking can feel like,
Dialogue: 0,0:02:25.88,0:02:28.53,Default,,0000,0000,0000,,so we should examine what it looks like.
Dialogue: 0,0:02:28.53,0:02:29.55,Default,,0000,0000,0000,,A good place to start
Dialogue: 0,0:02:29.55,0:02:33.09,Default,,0000,0000,0000,,is with the words of the philosopher\Nand mathematician René Descartes,
Dialogue: 0,0:02:33.09,0:02:37.11,Default,,0000,0000,0000,,who famously proclaimed,\N"I think, therefore I am."
Dialogue: 0,0:02:37.59,0:02:41.06,Default,,0000,0000,0000,,But Descartes looked deeper\Ninto the nature of thinking.
Dialogue: 0,0:02:41.06,0:02:44.03,Default,,0000,0000,0000,,Once he established himself\Nas a thing that thinks,
Dialogue: 0,0:02:44.03,0:02:47.16,Default,,0000,0000,0000,,he continued, "What is a thinking thing?"
Dialogue: 0,0:02:47.89,0:02:52.12,Default,,0000,0000,0000,,It is the thing that doubts,\Nunderstands, conceives,
Dialogue: 0,0:02:52.12,0:02:55.83,Default,,0000,0000,0000,,that affirms and denies,\Nwills and refuses,
Dialogue: 0,0:02:55.83,0:02:57.76,Default,,0000,0000,0000,,that imagines also,
Dialogue: 0,0:02:57.76,0:02:59.30,Default,,0000,0000,0000,,and perceives.
Dialogue: 0,0:03:00.46,0:03:05.70,Default,,0000,0000,0000,,This is the kind of thinking we need\Nin every math class every day.
Dialogue: 0,0:03:06.37,0:03:11.32,Default,,0000,0000,0000,,So, if you are a teacher or a parent\Nor anyone with a stake in education,
Dialogue: 0,0:03:11.32,0:03:13.38,Default,,0000,0000,0000,,I offer these five principles
Dialogue: 0,0:03:13.38,0:03:18.58,Default,,0000,0000,0000,,to invite thinking into the math\Nwe do at home and at school.
Dialogue: 0,0:03:21.38,0:03:24.21,Default,,0000,0000,0000,,Principle one: start with a question.
Dialogue: 0,0:03:24.86,0:03:28.28,Default,,0000,0000,0000,,The ordinary math class\Nbegins with answers
Dialogue: 0,0:03:28.28,0:03:30.37,Default,,0000,0000,0000,,and never arrives at a real question.
Dialogue: 0,0:03:30.37,0:03:32.42,Default,,0000,0000,0000,,"Here are the steps\Nto multiply. You repeat.
Dialogue: 0,0:03:32.42,0:03:34.37,Default,,0000,0000,0000,,Here are the steps to divide. You repeat.
Dialogue: 0,0:03:34.37,0:03:36.47,Default,,0000,0000,0000,,We've covered the material.\NWe're moving on."
Dialogue: 0,0:03:36.47,0:03:39.31,Default,,0000,0000,0000,,What matters in the model\Nis memorizing the steps.
Dialogue: 0,0:03:39.31,0:03:44.37,Default,,0000,0000,0000,,There's no room to doubt\Nor imagine or refuse,
Dialogue: 0,0:03:44.89,0:03:46.87,Default,,0000,0000,0000,,so there's no real thinking here.
Dialogue: 0,0:03:48.23,0:03:50.84,Default,,0000,0000,0000,,What would it look like\Nif we started with a question?
Dialogue: 0,0:03:51.50,0:03:55.02,Default,,0000,0000,0000,,For example, here\Nare the numbers from 1 to 20.
Dialogue: 0,0:03:55.02,0:03:57.60,Default,,0000,0000,0000,,Now, there's a question\Nlurking in this picture,
Dialogue: 0,0:03:58.28,0:04:00.18,Default,,0000,0000,0000,,hiding in plain sight.
Dialogue: 0,0:04:00.86,0:04:03.07,Default,,0000,0000,0000,,What's going on with the colors?
Dialogue: 0,0:04:04.59,0:04:07.14,Default,,0000,0000,0000,,Now, intuitively it feels like\Nthere's some connection
Dialogue: 0,0:04:07.14,0:04:09.62,Default,,0000,0000,0000,,between the numbers and the colors.
Dialogue: 0,0:04:09.62,0:04:13.83,Default,,0000,0000,0000,,I mean, maybe it's even possible to extend\Nthe coloring to more numbers.
Dialogue: 0,0:04:15.14,0:04:18.89,Default,,0000,0000,0000,,At the same time, the meaning\Nof the colors is not clear.
Dialogue: 0,0:04:19.54,0:04:20.89,Default,,0000,0000,0000,,It's a real mystery.
Dialogue: 0,0:04:21.47,0:04:25.70,Default,,0000,0000,0000,,And so, the question\Nfeels authentic and compelling.
Dialogue: 0,0:04:26.90,0:04:31.41,Default,,0000,0000,0000,,And like so many authentic\Nmathematical questions,
Dialogue: 0,0:04:31.42,0:04:36.84,Default,,0000,0000,0000,,this one has an answer that is\Nboth beautiful and profoundly satisfying.
Dialogue: 0,0:04:38.66,0:04:41.45,Default,,0000,0000,0000,,And of course, I'm not going\Nto tell you what it is.
Dialogue: 0,0:04:41.45,0:04:43.70,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:04:44.69,0:04:47.16,Default,,0000,0000,0000,,I don't think of myself as a mean person,
Dialogue: 0,0:04:47.16,0:04:50.54,Default,,0000,0000,0000,,but I am willing to deny you\Nwhat you want.
Dialogue: 0,0:04:50.54,0:04:52.07,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:04:52.07,0:04:55.65,Default,,0000,0000,0000,,Because I know if I rush to an answer,
Dialogue: 0,0:04:55.65,0:04:58.86,Default,,0000,0000,0000,,I would've robbed you\Nof the opportunity to learn.
Dialogue: 0,0:04:59.70,0:05:03.48,Default,,0000,0000,0000,,Thinking happens only\Nwhen we have time to struggle.
Dialogue: 0,0:05:04.74,0:05:06.68,Default,,0000,0000,0000,,And that is principle two.
Dialogue: 0,0:05:07.74,0:05:10.87,Default,,0000,0000,0000,,It's not uncommon for students\Nto graduate from high school
Dialogue: 0,0:05:10.87,0:05:16.16,Default,,0000,0000,0000,,believing that every math problem\Ncan be solved in 30 seconds or less,
Dialogue: 0,0:05:16.16,0:05:19.26,Default,,0000,0000,0000,,and if they don't know the answer,\Nthey're just not a math person.
Dialogue: 0,0:05:19.51,0:05:21.79,Default,,0000,0000,0000,,This is a failure of education.
Dialogue: 0,0:05:21.79,0:05:25.66,Default,,0000,0000,0000,,We need to teach kids\Nto be tenacious and courageous,
Dialogue: 0,0:05:25.66,0:05:28.31,Default,,0000,0000,0000,,to persevere in the face of difficulty.
Dialogue: 0,0:05:28.65,0:05:30.91,Default,,0000,0000,0000,,The only way to teach perseverance
Dialogue: 0,0:05:30.91,0:05:36.52,Default,,0000,0000,0000,,is to give students time\Nto think and grapple with real problems.
Dialogue: 0,0:05:37.20,0:05:40.68,Default,,0000,0000,0000,,I brought this image\Ninto a classroom recently,
Dialogue: 0,0:05:40.68,0:05:42.90,Default,,0000,0000,0000,,and we took the time to struggle.
Dialogue: 0,0:05:42.90,0:05:47.40,Default,,0000,0000,0000,,And the longer we spent, the more\Nthe class came alive with thinking.
Dialogue: 0,0:05:47.72,0:05:49.38,Default,,0000,0000,0000,,The students made observations.
Dialogue: 0,0:05:49.38,0:05:51.00,Default,,0000,0000,0000,,They had questions.
Dialogue: 0,0:05:51.00,0:05:52.14,Default,,0000,0000,0000,,Like,
Dialogue: 0,0:05:52.14,0:05:55.89,Default,,0000,0000,0000,,"Why do the numbers in that last column\Nalways have orange and blue in them?"
Dialogue: 0,0:05:56.30,0:06:00.80,Default,,0000,0000,0000,,and "Does it mean anything that the green\Nspots are always going diagonally?"
Dialogue: 0,0:06:01.20,0:06:03.66,Default,,0000,0000,0000,,and "What's going on\Nwith those little white numbers
Dialogue: 0,0:06:03.66,0:06:05.18,Default,,0000,0000,0000,,in the red segments?
Dialogue: 0,0:06:05.18,0:06:07.92,Default,,0000,0000,0000,,Is it important that those\Nare always odd numbers?"
Dialogue: 0,0:06:09.15,0:06:11.65,Default,,0000,0000,0000,,Struggling with a genuine question,
Dialogue: 0,0:06:11.65,0:06:16.48,Default,,0000,0000,0000,,students deepen their curiosity\Nand their powers of observation.
Dialogue: 0,0:06:17.14,0:06:23.43,Default,,0000,0000,0000,,They also develop\Nthe ability to take a risk.
Dialogue: 0,0:06:25.26,0:06:28.30,Default,,0000,0000,0000,,Some students noticed\Nthat every even number has orange in it,
Dialogue: 0,0:06:28.30,0:06:30.16,Default,,0000,0000,0000,,and they were willing to stake a claim.
Dialogue: 0,0:06:30.16,0:06:32.47,Default,,0000,0000,0000,,"Orange must mean even."
Dialogue: 0,0:06:33.01,0:06:35.83,Default,,0000,0000,0000,,And then they asked, "Is that right?"
Dialogue: 0,0:06:35.83,0:06:37.24,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:06:37.64,0:06:41.16,Default,,0000,0000,0000,,This can be a scary place as a teacher.
Dialogue: 0,0:06:41.16,0:06:44.41,Default,,0000,0000,0000,,A student comes to you\Nwith an original thought.
Dialogue: 0,0:06:45.39,0:06:47.39,Default,,0000,0000,0000,,What if you don't know the answer?
Dialogue: 0,0:06:49.34,0:06:53.80,Default,,0000,0000,0000,,Well, that is principle three:\Nyou are not the answer key.
Dialogue: 0,0:06:55.40,0:06:59.78,Default,,0000,0000,0000,,Teachers, students may ask you questions\Nyou don't know how to answer.
Dialogue: 0,0:06:59.78,0:07:02.15,Default,,0000,0000,0000,,And this can feel like a threat.
Dialogue: 0,0:07:02.15,0:07:04.38,Default,,0000,0000,0000,,But you are not the answer key.
Dialogue: 0,0:07:05.54,0:07:07.94,Default,,0000,0000,0000,,Students who are inquisitive
Dialogue: 0,0:07:07.94,0:07:10.21,Default,,0000,0000,0000,,is a wonderful thing\Nto have in your classroom.
Dialogue: 0,0:07:10.21,0:07:12.29,Default,,0000,0000,0000,,And if you can respond by saying,
Dialogue: 0,0:07:12.90,0:07:15.78,Default,,0000,0000,0000,,"I don't know. Let's find out,"
Dialogue: 0,0:07:16.26,0:07:18.46,Default,,0000,0000,0000,,math becomes an adventure.
Dialogue: 0,0:07:19.88,0:07:22.65,Default,,0000,0000,0000,,And parents, this goes for you too.
Dialogue: 0,0:07:22.65,0:07:25.64,Default,,0000,0000,0000,,When you sit down to do math\Nwith your children,
Dialogue: 0,0:07:25.64,0:07:28.24,Default,,0000,0000,0000,,you don't have to know all the answers.
Dialogue: 0,0:07:28.65,0:07:31.52,Default,,0000,0000,0000,,You can ask your child\Nto explain the math to you
Dialogue: 0,0:07:31.52,0:07:33.74,Default,,0000,0000,0000,,or try to figure it out together.
Dialogue: 0,0:07:35.55,0:07:39.78,Default,,0000,0000,0000,,Teach them that not knowing\Nis not failure.
Dialogue: 0,0:07:40.41,0:07:42.98,Default,,0000,0000,0000,,It's the first step to understanding.
Dialogue: 0,0:07:44.24,0:07:49.89,Default,,0000,0000,0000,,So, when this group of students\Nasked me if orange means even,
Dialogue: 0,0:07:49.89,0:07:51.97,Default,,0000,0000,0000,,I don't have to tell them the answer.
Dialogue: 0,0:07:52.24,0:07:54.56,Default,,0000,0000,0000,,I don't even need to know the answer.
Dialogue: 0,0:07:54.91,0:07:58.72,Default,,0000,0000,0000,,I can ask one of them to explain to me\Nwhy she thinks it's true.
Dialogue: 0,0:07:59.34,0:08:02.03,Default,,0000,0000,0000,,Or we can throw the idea out to the class.
Dialogue: 0,0:08:02.95,0:08:05.73,Default,,0000,0000,0000,,Because they know the answers\Nwon't come from me,
Dialogue: 0,0:08:05.73,0:08:09.19,Default,,0000,0000,0000,,they need to convince themselves\Nand argue with each other
Dialogue: 0,0:08:09.19,0:08:10.91,Default,,0000,0000,0000,,to determine what's true.
Dialogue: 0,0:08:10.91,0:08:14.30,Default,,0000,0000,0000,,And so, one student says,\N"Look, 2, 4, 6, 8, 10, 12.
Dialogue: 0,0:08:14.30,0:08:15.92,Default,,0000,0000,0000,,I checked all of the even numbers.
Dialogue: 0,0:08:15.92,0:08:17.31,Default,,0000,0000,0000,,They all have orange in them.
Dialogue: 0,0:08:17.31,0:08:18.78,Default,,0000,0000,0000,,What more do you want?"
Dialogue: 0,0:08:18.78,0:08:21.13,Default,,0000,0000,0000,,And another student says,\N"Well, wait a minute,
Dialogue: 0,0:08:21.13,0:08:22.37,Default,,0000,0000,0000,,I see what you're saying,
Dialogue: 0,0:08:22.37,0:08:24.93,Default,,0000,0000,0000,,but some of those numbers\Nhave one orange piece,
Dialogue: 0,0:08:24.93,0:08:27.09,Default,,0000,0000,0000,,some have two or three.
Dialogue: 0,0:08:27.09,0:08:28.91,Default,,0000,0000,0000,,Like, look at 48.
Dialogue: 0,0:08:29.49,0:08:31.63,Default,,0000,0000,0000,,It's got four orange pieces.
Dialogue: 0,0:08:31.63,0:08:35.76,Default,,0000,0000,0000,,Are you telling me that 48\Nis four times as even as 46?
Dialogue: 0,0:08:36.23,0:08:38.38,Default,,0000,0000,0000,,There must be more to the story."
Dialogue: 0,0:08:39.48,0:08:41.52,Default,,0000,0000,0000,,By refusing to be the answer key,
Dialogue: 0,0:08:41.52,0:08:45.98,Default,,0000,0000,0000,,you create space for this kind\Nof mathematical conversation and debate.
Dialogue: 0,0:08:45.98,0:08:51.50,Default,,0000,0000,0000,,And this draws everyone in\Nbecause we love to see people disagree.
Dialogue: 0,0:08:52.27,0:08:57.09,Default,,0000,0000,0000,,After all, where else can you see\Nreal thinking out loud?
Dialogue: 0,0:08:57.09,0:09:00.97,Default,,0000,0000,0000,,Students doubt, affirm, deny, understand.
Dialogue: 0,0:09:02.18,0:09:06.24,Default,,0000,0000,0000,,And all you have to do as the teacher\Nis not be the answer key
Dialogue: 0,0:09:06.24,0:09:08.91,Default,,0000,0000,0000,,and say "yes" to their ideas.
Dialogue: 0,0:09:11.05,0:09:12.92,Default,,0000,0000,0000,,And that is principle four.
Dialogue: 0,0:09:13.95,0:09:15.99,Default,,0000,0000,0000,,Now, this one is difficult.
Dialogue: 0,0:09:16.14,0:09:19.36,Default,,0000,0000,0000,,What if a student comes to you\Nand says 2 plus 2 equals 12?
Dialogue: 0,0:09:20.18,0:09:21.85,Default,,0000,0000,0000,,You've got to correct them, right?
Dialogue: 0,0:09:21.85,0:09:25.20,Default,,0000,0000,0000,,And it's true, we want students\Nto understand certain basic facts
Dialogue: 0,0:09:25.20,0:09:26.73,Default,,0000,0000,0000,,and how to use them.
Dialogue: 0,0:09:27.14,0:09:31.42,Default,,0000,0000,0000,,But saying "yes" is not the same thing\Nas saying "You're right."
Dialogue: 0,0:09:31.91,0:09:35.70,Default,,0000,0000,0000,,You can accept ideas,\Neven wrong ideas, into the debate
Dialogue: 0,0:09:35.70,0:09:37.96,Default,,0000,0000,0000,,and say "yes" to your students' right
Dialogue: 0,0:09:37.96,0:09:41.74,Default,,0000,0000,0000,,to participate in the act\Nof thinking mathematically.
Dialogue: 0,0:09:42.84,0:09:48.59,Default,,0000,0000,0000,,To have your idea dismissed\Nout of hand is disempowering.
Dialogue: 0,0:09:48.59,0:09:53.24,Default,,0000,0000,0000,,To have it accepted, studied,\Nand disproven is a mark of respect.
Dialogue: 0,0:09:53.85,0:09:57.67,Default,,0000,0000,0000,,It's also far more convincing to be shown\Nyou're wrong by your peers
Dialogue: 0,0:09:57.67,0:10:00.02,Default,,0000,0000,0000,,than told you're wrong by the teacher.
Dialogue: 0,0:10:01.29,0:10:03.93,Default,,0000,0000,0000,,But allow me to take this a step further.
Dialogue: 0,0:10:04.87,0:10:08.35,Default,,0000,0000,0000,,How do you actually know\Nthat 2 plus 2 doesn't equal 12?
Dialogue: 0,0:10:09.26,0:10:11.57,Default,,0000,0000,0000,,What would happen\Nif we said "yes" to that idea?
Dialogue: 0,0:10:12.70,0:10:13.94,Default,,0000,0000,0000,,I don't know.
Dialogue: 0,0:10:14.21,0:10:15.64,Default,,0000,0000,0000,,Let's find out.
Dialogue: 0,0:10:17.64,0:10:20.26,Default,,0000,0000,0000,,So, if 2 plus 2 equaled 12,
Dialogue: 0,0:10:20.58,0:10:25.14,Default,,0000,0000,0000,,then 2 plus 1 would be one less,\Nso that would be 11.
Dialogue: 0,0:10:25.59,0:10:29.38,Default,,0000,0000,0000,,And that would mean that 2 plus 0,\Nwhich is just 2, would be 10.
Dialogue: 0,0:10:29.100,0:10:32.88,Default,,0000,0000,0000,,But if 2 is 10, then 1 would be 9,
Dialogue: 0,0:10:32.88,0:10:34.60,Default,,0000,0000,0000,,and 0 would be 8.
Dialogue: 0,0:10:35.18,0:10:37.48,Default,,0000,0000,0000,,And I have to admit this looks bad.
Dialogue: 0,0:10:38.52,0:10:40.82,Default,,0000,0000,0000,,It looks like we broke mathematics.
Dialogue: 0,0:10:41.58,0:10:45.04,Default,,0000,0000,0000,,But I actually understand\Nwhy this can't be true now.
Dialogue: 0,0:10:45.56,0:10:47.34,Default,,0000,0000,0000,,Just from thinking about it,
Dialogue: 0,0:10:47.34,0:10:50.84,Default,,0000,0000,0000,,if we were on a number line,
Dialogue: 0,0:10:51.50,0:10:54.04,Default,,0000,0000,0000,,and if I'm at 0,\N8 is eight steps that way,
Dialogue: 0,0:10:54.04,0:10:56.48,Default,,0000,0000,0000,,and there's no way\NI could take eight steps
Dialogue: 0,0:10:56.48,0:10:58.56,Default,,0000,0000,0000,,and wind up back where I started.
Dialogue: 0,0:11:01.20,0:11:02.74,Default,,0000,0000,0000,,Unless ...
Dialogue: 0,0:11:03.19,0:11:04.42,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:11:04.92,0:11:07.39,Default,,0000,0000,0000,,well, what if it wasn't a number line?
Dialogue: 0,0:11:08.41,0:11:10.75,Default,,0000,0000,0000,,What if it was a number circle?
Dialogue: 0,0:11:11.88,0:11:14.70,Default,,0000,0000,0000,,Then I could take eight steps\Nand wind back where I started.
Dialogue: 0,0:11:14.70,0:11:15.73,Default,,0000,0000,0000,,8 would be 0.
Dialogue: 0,0:11:15.73,0:11:19.79,Default,,0000,0000,0000,,In fact, all of the infinite numbers\Non the real line would be stacked up
Dialogue: 0,0:11:19.79,0:11:22.15,Default,,0000,0000,0000,,in those eight spots.
Dialogue: 0,0:11:22.97,0:11:24.93,Default,,0000,0000,0000,,And we're in a new world.
Dialogue: 0,0:11:27.35,0:11:29.52,Default,,0000,0000,0000,,And we're just playing here, right?
Dialogue: 0,0:11:31.74,0:11:34.44,Default,,0000,0000,0000,,But this is how new math gets invented.
Dialogue: 0,0:11:36.34,0:11:40.47,Default,,0000,0000,0000,,Mathematicians have actually been studying\Nnumber circles for a long time.
Dialogue: 0,0:11:40.47,0:11:42.74,Default,,0000,0000,0000,,They've got a fancy name and everything:
Dialogue: 0,0:11:42.74,0:11:44.71,Default,,0000,0000,0000,,modular arithmetic.
Dialogue: 0,0:11:45.15,0:11:47.34,Default,,0000,0000,0000,,And not only does the math work out,
Dialogue: 0,0:11:47.34,0:11:49.49,Default,,0000,0000,0000,,it turns out to be ridiculously useful
Dialogue: 0,0:11:49.49,0:11:52.53,Default,,0000,0000,0000,,in fields like cryptography\Nand computer science.
Dialogue: 0,0:11:52.53,0:11:54.60,Default,,0000,0000,0000,,It's actually no exaggeration to say
Dialogue: 0,0:11:54.60,0:11:58.38,Default,,0000,0000,0000,,that your credit card number\Nis safe online
Dialogue: 0,0:11:58.38,0:12:00.23,Default,,0000,0000,0000,,because someone was willing to ask,
Dialogue: 0,0:12:00.23,0:12:03.78,Default,,0000,0000,0000,,"What if it was a number circle\Ninstead of a number line?"
Dialogue: 0,0:12:05.08,0:12:09.48,Default,,0000,0000,0000,,So, yes, we need to teach students\Nthat 2 plus 2 equals 4.
Dialogue: 0,0:12:10.31,0:12:14.25,Default,,0000,0000,0000,,But also we need to say "yes"\Nto their ideas and their questions
Dialogue: 0,0:12:14.55,0:12:17.70,Default,,0000,0000,0000,,and model the courage\Nwe want them to have.
Dialogue: 0,0:12:18.24,0:12:21.33,Default,,0000,0000,0000,,It takes courage to say,\N"What if 2 plus 2 equals 12?"
Dialogue: 0,0:12:21.33,0:12:24.02,Default,,0000,0000,0000,,and actually explore the consequences.
Dialogue: 0,0:12:25.06,0:12:27.13,Default,,0000,0000,0000,,It takes courage to say,
Dialogue: 0,0:12:27.13,0:12:30.90,Default,,0000,0000,0000,,"What if the angles in a triangle\Ndidn't add up to 180 degrees?"
Dialogue: 0,0:12:31.47,0:12:34.45,Default,,0000,0000,0000,,or "What if there were\Na square root of negative 1?"
Dialogue: 0,0:12:34.71,0:12:38.25,Default,,0000,0000,0000,,or "What if there were\Ndifferent sizes of infinity?"
Dialogue: 0,0:12:39.31,0:12:41.100,Default,,0000,0000,0000,,But that courage and those questions
Dialogue: 0,0:12:42.67,0:12:46.20,Default,,0000,0000,0000,,led to some of the greatest\Nbreakthroughs in history.
Dialogue: 0,0:12:46.100,0:12:49.78,Default,,0000,0000,0000,,All it takes is willingness to play.
Dialogue: 0,0:12:51.41,0:12:53.65,Default,,0000,0000,0000,,And that is principle five.
Dialogue: 0,0:12:55.27,0:12:58.04,Default,,0000,0000,0000,,Mathematics is not about following rules.
Dialogue: 0,0:12:58.49,0:12:59.89,Default,,0000,0000,0000,,It's about playing
Dialogue: 0,0:13:00.33,0:13:03.11,Default,,0000,0000,0000,,and exploring and fighting\Nand looking for clues
Dialogue: 0,0:13:03.11,0:13:05.07,Default,,0000,0000,0000,,and sometimes breaking things.
Dialogue: 0,0:13:05.64,0:13:09.19,Default,,0000,0000,0000,,Einstein called play\Nthe highest form of research.
Dialogue: 0,0:13:09.58,0:13:14.41,Default,,0000,0000,0000,,And a math teacher who lets\Ntheir students play with math
Dialogue: 0,0:13:14.41,0:13:17.61,Default,,0000,0000,0000,,gives them the gift of ownership.
Dialogue: 0,0:13:18.89,0:13:20.33,Default,,0000,0000,0000,,Playing with math can feel
Dialogue: 0,0:13:20.33,0:13:22.97,Default,,0000,0000,0000,,like running through the woods\Nwhen you were a kid.
Dialogue: 0,0:13:22.97,0:13:26.84,Default,,0000,0000,0000,,And even if you were on a path,\Nit felt like it all belonged to you.
Dialogue: 0,0:13:27.91,0:13:30.56,Default,,0000,0000,0000,,Parents, if you want to know
Dialogue: 0,0:13:30.56,0:13:33.52,Default,,0000,0000,0000,,how to nurture the mathematical\Ninstincts of your children,
Dialogue: 0,0:13:33.52,0:13:35.23,Default,,0000,0000,0000,,play is the answer.
Dialogue: 0,0:13:36.00,0:13:39.55,Default,,0000,0000,0000,,What books are to reading,\Nplay is to mathematics.
Dialogue: 0,0:13:39.55,0:13:43.35,Default,,0000,0000,0000,,And a home filled with blocks\Nand puzzles and games and play
Dialogue: 0,0:13:43.84,0:13:47.16,Default,,0000,0000,0000,,is a home where mathematical\Nthinking can flourish.
Dialogue: 0,0:13:48.82,0:13:54.62,Default,,0000,0000,0000,,I believe we have the power to help\Nmathematical thinking flourish everywhere.
Dialogue: 0,0:13:55.75,0:14:00.74,Default,,0000,0000,0000,,We can't afford to misuse math\Nto create passive rule-followers.
Dialogue: 0,0:14:01.16,0:14:04.19,Default,,0000,0000,0000,,Math has the potential\Nto be our greatest asset
Dialogue: 0,0:14:04.19,0:14:07.59,Default,,0000,0000,0000,,in teaching the next generation\Nto meet the future
Dialogue: 0,0:14:07.59,0:14:11.63,Default,,0000,0000,0000,,with courage, curiosity, and creativity.
Dialogue: 0,0:14:12.52,0:14:15.48,Default,,0000,0000,0000,,And if all students get a chance
Dialogue: 0,0:14:15.48,0:14:19.64,Default,,0000,0000,0000,,to experience the beauty and power\Nof authentic mathematical thinking,
Dialogue: 0,0:14:20.86,0:14:24.88,Default,,0000,0000,0000,,maybe it won't sound\Nso strange when they say,
Dialogue: 0,0:14:25.87,0:14:27.26,Default,,0000,0000,0000,,"Math?
Dialogue: 0,0:14:28.24,0:14:30.71,Default,,0000,0000,0000,,I actually love math."
Dialogue: 0,0:14:31.78,0:14:32.97,Default,,0000,0000,0000,,Thank you.
Dialogue: 0,0:14:32.97,0:14:35.63,Default,,0000,0000,0000,,(Applause)