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Talkabout Tuesday 01: Newton's Method and Self-Directed Learning

ai-in-the-air_tt-ep-01
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Summary

Exploration of how Sudbury education works through the lens of Newton's Method - iterative failure leading to rapid improvement. Discusses the value of failure, play, and laughter versus stress in learning.

Transcript

0:00 Welcome to Talk About Tuesday of Arts and Ideas in the Air, Under the Tent, and Around Baltimore.
0:09 This is not the daily news podcasting. That comes in a separate, smaller bit.
0:17 Instead, this is a segment where I, and perhaps others in the future, talk about some topic of the school.
0:28 For those who are interested in hearing about that.
0:32 I thought today I would just start with sort of my thoughts as to how this education kind of really works.
0:42 It's something I've been thinking about for years, of course.
0:45 The past year or so I've had a pretty clear idea of something I want to convey,
0:52 but I've always found it very hard to convey it whenever I tried to write it.
0:57 So maybe talking about it will help.
1:00 So one of the key differences between our school and conventional schooling,
1:07 I mean there are many differences, but one of them is that we really cherish not only exploration, but failure.
1:17 And even failure to do, right?
1:21 We really want to let our students explore the full range of experiences, emotions, success, failure, negotiations,
1:35 you know, emotions, every emotion under the sun, right?
1:39 All of that is, you know, we consider to be extremely valuable in the importance of this schooling.
1:47 We don't view knowledge, you know, like a particular set of knowledge as that valuable.
1:57 Instead, what we think of is this is the time for our students' brains to fully form
2:05 and so that they can model the world and they can navigate it.
2:10 They can make choices and decisions and really figure out, you know, what they want,
2:16 how to get it, and then actually doing it.
2:20 You know, these things seem like they're fairly simple ideas.
2:27 You know, like, doesn't everybody get this as they grow up?
2:32 But it really takes a lot of experience of trying all these things out to acquire it.
2:43 It's not natural. It's a lot easier to just sit and listen to somebody talk about some stuff,
2:49 remember it for a little bit, and then, you know, write it and then forget about it.
2:55 What's much harder is coming up with that stuff, right?
3:01 And that's something that we allow our students to really do here fully.
3:07 And that really means, you know, taking a step back.
3:13 Now, I think that's all fairly standard.
3:20 My contribution to this is inspired by a mathematical technique called Newton's Method.
3:28 In Newton's Method, it's basically trying to answer a question, a hard question.
3:34 For those in the know, it's trying to find out when a function is zero, but it doesn't matter.
3:40 That's a hard question.
3:42 And instead of answering the hard question, you answer a simple question.
3:50 And so, you know, that simple question, you get the wrong answer to the original question,
3:59 no question about it, but then you get a new kind of starting point from that simpler question.
4:04 You get closer, right?
4:06 And then you do it again.
4:08 So now you've got a better starting point because you answered a simple question that gave you the wrong answer,
4:13 but it's a better answer than the one you started with.
4:16 And you just keep doing that.
4:20 With Newton's Method, it's basically approximate the function with the line.
4:24 We can do stuff with lines because lines are easy.
4:27 You find the, you know, where the line crosses the x-axis, that's easy.
4:33 And then you take that as a new guessing point.
4:35 That's the business of calculus.
4:37 That's fine.
4:38 Now, what happens with Newton's Method is the precision, it doesn't like just slowly get to the answer, right?
4:46 It could have, right?
4:48 And in fact, sometimes it does if you have a really bad guess or you're in a particular weird situation
4:55 that leads to poor convergence, as they say.
4:59 But typically what happens is you start with a not great guess.
5:04 And then every time you iterate, you double the amount of precision.
5:09 So when trying to teach this method, and I've been teaching it for decades,
5:15 it's really hard because you can't get enough steps.
5:18 I mean, oftentimes three or four steps, you're done.
5:21 You've got like 16 digits.
5:23 You're just done, right?
5:24 It's amazingly effective.
5:26 So what is that process?
5:27 It's try something stupid, get a wrong answer, use that answer to do something a little less stupid,
5:35 but still pretty stupid, and get a much better answer.
5:39 And like a few times with that, you're done.
5:42 And that really feels to me like what we see happening with our students here.
5:47 You know, they have no idea about something.
5:50 They try something, it fails miserably, but they get a little feedback,
5:55 just a little feedback from that failure.
5:58 And now if they choose to pursue it some more,
6:02 they've got a much better starting point than they did before,
6:05 and now they do a much better job, still not great.
6:09 And by the third or fourth time, if they're still pursuing it, you know, boom, they're experts.
6:16 You know, that is fantastic to see that, and for them to experience that.
6:23 You know, and that's, I also think what's behind laughter, which we hear all the time here, of course.
6:31 Laughter is this notion that you're saying, "I'm going to fail at this.
6:38 I don't know what I'm doing, but I'm figuring it out."
6:41 So don't be, you know, mucking about.
6:46 And so it's an invitation for people to kind of stay out unless they want to join in that goofiness,
6:51 which also means, like, don't tell me the answer, right?
6:55 If you don't know how to do something, you want to join in and have some fun, great.
6:59 But if you know how to do something, don't spoil the fun, right?
7:02 That's the key of laughter.
7:04 It's also an opportunity, I think there's a difference between, you know, laughing and stressing.
7:11 Stressing has, you know, generally the conventional education.
7:18 Students often experience a lot of stress.
7:21 Stress also allows for some kind of learning, but it's a very focused, tight learning that has no depth, right?
7:31 Or generally has no depth.
7:34 It's just like I am walking this very narrow beam across this vast chasm and I got to get one foot in front of the other.
7:43 I can't be jumping around. I can't be dancing. I'm just doing that.
7:46 So there's, like, very focused, very tunnel vision.
7:49 It's an effective, you know, really great tool to have when you really need to get something right.
7:56 But when you're trying to really get a broad perspective and get a broad set of skills, you know, stress is the wrong thing.
8:05 So I think, you know, laughter is like this expansive, failure-driven mode and then stress is no failure, right?
8:14 Do not fail. If you fail, you will fall.
8:18 And so it's very focused, it's very limiting, and it has its uses.
8:24 And in fact, to really get mastery over something, you know, you'll see somebody when they're, you know,
8:31 like, you see it with students, like, who've really mastered something.
8:36 I'm not going to say that they're, like, stress stressed, but they're, you know, they're really focused.
8:42 They're, you know, they're right on that, they're tight on the target of their interest, right?
8:51 So they're, you know, I kind of like call out good stress.
8:57 It's self-driven stress, but it's like trying for that perfection, right?
9:02 That comes much later after the whole laughter and silliness and, you know, doing whatever.
9:09 So, I don't know, I hope this makes some sense to people.
9:14 Bottom line for me is that one of the greatest benefits of a Sudbury education or, you know,
9:22 really self-directed education is just that ability to really embrace, well, failing, goofing around,
9:34 being silly, and learning how things really work and what to do and how to achieve it.
9:45 So, I hope this was enlightening and, look, I look forward to future Tuesdays with you
9:54 where I will talk about some other topics hopefully and hopefully some other people will join.
10:00 If you have questions about the model, please let me know and I will answer some of the questions here.
10:07 This is an attempt to fill in the gap of not having to talk about Tuesdays
10:14 where we would gather and talk about the model.
10:19 So, maybe this will fill in just a little bit about that.
10:24 Thank you, have a nice day, and see you later.