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  • GIL STRANG: Typically, the first few days of class,

  • these guys ask what's the class average going to be?

  • How are we going to be graded?

  • I don't have any answers for that stuff.

  • So I say what is totally true, that I don't feel

  • my main job is to grade them.

  • My job is to teach them or learn with them.

  • That's what I continue to do, and gradually, they

  • begin to believe.

  • SARAH HANSEN: Today in the podcast,

  • we're talking with teaching legend Professor Gil Strang.

  • GIL STRANG: Maybe the key point is that make it human.

  • You're a person like the student is a person.

  • The book isn't quite a person, but it was written by a person.

  • SARAH HANSEN: Welcome to Chalk Radio,

  • a podcast about inspired teaching at MIT.

  • I'm your host, Sarah Hansen, from MIT OpenCourseWare.

  • One of OCW's most popular courses

  • is Professor Strang's 18.06 Linear Algebra,

  • a key foundation for his new course on machine learning,

  • in which he's teaching students to teach computers.

  • Professor Strang is known for inspiring students

  • through his teaching.

  • One YouTube commenter sums it up well.

  • Quote: "This is not lecture.

  • This is art."

  • We wanted to talk with Professor Strang

  • to see how he's been able to make complex math concepts

  • engaging and accessible.

  • We'll pick up our conversation with his explanation

  • of what his new course, 18.065 Matrix Methods in Data

  • Analysis, Signal Processing, and Machine Learning is all about.

  • GIL STRANG: So this is my adventure

  • into the subject of deep learning.

  • For example, recognizing an image,

  • recognizing a zip code, a bunch of numbers,

  • translating languages, or playing chess,

  • so that's what the course is about.

  • How does the machine learn?

  • Essentially, the idea is say take an image,

  • then the deep learning system leads the machine

  • to look at the examples.

  • We all learn from examples.

  • The machine learns from examples,

  • and from many examples, or many chess games

  • or many pages of Chinese, you learn what's happening.

  • And what the math part is is that the machine ultimately

  • tries to assign a certain weight to a certain number,

  • big or small, to each part of the image.

  • So perhaps, if you're drawing a three,

  • the computer recognizes a three, of course, by the curves

  • and gives less weight, or zero weight sometimes,

  • to the empty space around the three but picks out that three.

  • So that's the idea of deep learning.

  • SARAH HANSEN: Traditionally, math courses

  • have been defined by testing, which honestly makes sense.

  • There's typically a right and a wrong answer in math.

  • If you know the operation, if you do it right,

  • you should get the answer.

  • Tests can be a great vehicle for strengthening and measuring

  • students' skills, but Professor Strang's approach is different.

  • GIL STRANG: So I ask everybody to do a project.

  • There is no final exam.

  • Actually, there is no exam at all.

  • I shouldn't like say this, but that's

  • really what the subject is is having an idea of how--

  • OK, I'll use deep learning for some thing.

  • Like the recent proposed project was can you identify

  • what makes an image or a picture attractive?

  • SARAH HANSEN: Hmm.

  • GIL STRANG: So somebody has to say,

  • these pictures are attractive.

  • These are not.

  • We have to tell the computer something.

  • SARAH HANSEN: What did that feel like to try

  • something new, pedagogically?

  • GIL STRANG: Oh, it's fun.

  • I like teaching, and this is a subject where students

  • just come from everywhere.

  • Because they know what stuff to learn,

  • and they've heard about it.

  • And some of them know more than me,

  • and then those students write even better projects.

  • Yeah.

  • So I do the lectures for the first three quarters

  • of the course, and then I try to get them to present which

  • is a great experience for them.

  • So it takes a little urging to get them,

  • but yeah, it's really just wonderful.

  • SARAH HANSEN: What insights have you

  • gained about having more of a student-led course

  • and a project-based course?

  • GIL STRANG: You realize, slowly but finally,

  • that that's how people learn, by doing.

  • You couldn't give them a better way to learn

  • than create a project.

  • Usually it's on some topic they know about

  • or they they're interested in.

  • Like how do you find a criminal in a bunch of people?

  • Yeah.

  • It's a very effective way to learn,

  • and it's something that gets remembered.

  • Where doing exam questions that I might make up,

  • sort of mathy questions, I don't know

  • if that's remembered 10 years later,

  • but I think people's projects are.

  • SARAH HANSEN: Along with this new approach

  • comes a new paradigm for measuring student learning.

  • Projects involve more than right and wrong answers.

  • Projects are subjective, and bringing the subjectivity

  • into a math course comes with some initial skepticism,

  • especially from students who are so used to the typical

  • "learn the subject, perform on the test" way of doing things.

  • One of the things that makes Professor

  • Strang and his courses so special

  • is that he's not attached to these paradigms.

  • In 18.065, in one of the videos, you

  • talk about grading students' work.

  • GIL STRANG: Yeah.

  • SARAH HANSEN: And you tell them that, although this

  • is important, to grade their work,

  • it's not your main concern.

  • That your main concern is actually learning with them.

  • GIL STRANG: Right.

  • SARAH HANSEN: Could you talk a little bit about that?

  • GIL STRANG: Yeah.

  • That's right.

  • So typically, the first few days of class, these guys

  • ask, what's the class average going to be?

  • How are we going to be graded?

  • I don't have any answers for that stuff.

  • So I say what is totally true, that I don't feel

  • my main job is to grade them.

  • My job is to teach them or learn with them,

  • and that's what I continue to do,

  • and gradually they begin to believe.

  • At the beginning, they still think,

  • OK, but he's got to give me a B or C or an A,

  • but really that's not what 18.065 is about, a grade.

  • It's just not.

  • Math is something you do.

  • You don't just read.

  • You have to do it.

  • You have to think about it.

  • The way to learn math is to get into it

  • and work on a thing which takes some thought.

  • You don't see it immediately, but you see it eventually.

  • SARAH HANSEN: One of my favorite takeaways

  • from Professor Strang's approach is that he centers his lessons

  • around the humans in his class.

  • For him, it's about engaging with the students in his course

  • as people, and the learning is done by everyone.

  • GIL STRANG: Well, first, I like students, and I want to help.

  • And maybe the key point is to think with them,

  • not to just say, OK, here it is.

  • Listen.

  • Listen up.

  • I think through the question all over again, as they do,

  • and you have to give time.

  • You can't zip through a proof, because the class

  • has to be thinking with you.

  • And it happens that I lose the thread,

  • or I come up to a dead end, where I don't know

  • what I'm supposed to do next.

  • But well, that's OK, because students

  • are going to hit dead ends.

  • So it seems to me it's OK for me to get stuck too and then given

  • they see, oh, OK, maybe this is the way

  • to get out of that corner.

  • I suppose, I try to think it through once again,

  • and then you automatically see the word.

  • You recognize what words you need to use

  • and what the steps are.

  • Yeah.

  • If you're not thinking it yourself,

  • then you're probably going too fast

  • and not connecting with the thinking of the class.

  • And of course, you don't know what everybody

  • is thinking in that class, but overall,

  • if you stay conscious of the class,

  • conscious of where they are.

  • That's I think the same for any speaker

  • is to be conscious of the audience,

  • and it's maybe the key point is to make it human.

  • You're a person, like the student is a person.

  • The book isn't quite a person, but it

  • was written by a person, and to see that it's just

  • like a natural thing to do.

  • Yeah.

  • So essentially, I think the thing is, I like students,

  • I like math, and putting them together is just

  • the best job in the world.

  • [MUSIC PLAYING]

  • SARAH HANSEN: Professor Strang shares additional thoughts

  • on teaching linear algebra and matrix methods and data

  • analysis, signal processing and machine learning

  • in videos within the Instructor Insights sections

  • of his OCW courses.

  • You can find them at ocw.mit.edu.

  • While you're there, download the teaching resources

  • from his courses, and watch his lecture videos.

  • Discover the magic of his teaching for yourself.

  • We're so happy to bring you conversations with MIT faculty

  • who are passionate about impacting

  • the world in positive ways.

  • Write to us to share your story of how

  • you're using OCW materials to shape your world or those

  • of others.

  • Until next time, I'm Sarah Hansen from MIT OpenCourseWare.

  • [MUSIC PLAYING]

GIL STRANG: Typically, the first few days of class,

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