Lec 10 | MIT 5.95J Teaching College-Level Science and Engineering, Spring 2009

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Now, what I want to do now, is basically summarize all the themes —

Basically, summarize all the themes of each of the sessions we've had.

Partly as a way of reminding you of all the things we did

and also of jogging your memory of any questions you might have about that.

and then it will be your chance to ask questions

so I'll think aloud here. I'll do it in a way

that I can leave them up the whole time. So let me let me do it here.

I'll do it on these two guys.

Yea, do it here. Ok, so our sessions and the summaries of them

So session number one was

the introduction, so I'll start with session two, which was

So teaching equations, ah now the fundamental idea I wanted people to learn on this one was to help students

learn equations in big chunks.

So, doing derivations is generally antithetical to that, because students will just see the little symbols

and they'll see a ton, and ton, and ton of symbols. And their chunk size is much smaller than you.

So, you will overload their short-term memory and they won't really be understanding. They'll be just

trying to remember and trying to write as fast as they can.

So, is that visible, the orange? Yea? Great. Oh yea good, your a good test.

Ok chunks, so teaching equations: you want to try to chunk the equations.

Because that gives meaning for the student. For example, what does each term mean, well how would you

expect that term to show up in the equation. Those are the kinds of things that a book generally does

not do very well. And that's something that you as a teacher, actually have a lot of value to add.. Uh

now I, just learned about a book. Uh, that does try to do this. Uh, which is called "The Student's Guide

to Maxwell's Equations" Which is, does anybody know that book?

Yea? You know? Ok, so it looks fantastic. I'm like number 7 or something in the queue to get a copy from the MIT libraries - which shows how popular it is.

But the way it's organized - first of all it's sold an immense number of copies for a technical textbook. Something like 7000 or something like that.

So it's sort of a physics bestseller. Uh, ok it's not an Agatha Christie novel, but it's really well done.

Uh and each chapter talks about one of the equations. So there's four -roughly - of Maxwell's equations and there's four chapters - one per equation.

So, it's helping the students chunk just by the very structure of the books. But most books don't do that - aren't that well - that interestingly constructed - not thoughtfully constructed.

So, it's something that you as a teacher really should do. Ok, the next one.

Misconceptions. So, why do we spend a whole session on misconceptions?

Well it's fundamentally important - uh, misconceptions - because if you don't know where your students are, you have no chance of bringing them to where you want them to go.

The example that's classic, that's probably started this whole line of research about misconceptions was students understanding of force and motion.

And basically what you'd find is most peoples intuitive understanding of force and motion is F = MV.

If you have an object, you stop pushing it, it stops moving. Force and velocity are connected. If you have a heavier object, you have to push it harder. If you have a lighter object, you push it less.

So, force and mass are connected. So it looks like F = MV. Whereas, we would like to teach them F = MA - Newton's second law: force equals mass times acceleration.

So, there's a fundamental difference there. And if you don't take account of that, you'll end up producing just rote knowledge.

They'll say, ok, well whenever I happen to be in physics class I'll use F = MA and I'll just solve problems symbolically using that procedure you told me.

But I don't really believe it or understand it or use it in my own reasoning. So, my intuition is no longer available for reasoning.

So, by taking account of students' misconceptions - helping them come to a intuitive understanding of how things really work, you're actually making them much smarter.

So, this is, uh -

So that's knowing how students think.

So this is, pretty much opposite to behaviorism. And this whole line of - ah - 'cause your saying well I really want to peer into how people are reflecting and how their cognition works.

So, what's going on under the hood.

And behaviorism says well no, ah, all you need to do is look at the behavior. If they're solving problems correctly, that's fine.

Whereas, actually, you want to know, well, why did they solve it that way. Is it because they really understood it, or not.

Did they just say 3 times 6 is 18 because they were told or they memorized it? Or, was it because they really understood it, in which case they can make a word problem related to it.

So, knowing how students think, then you're actually part of the cognitive revolution and you are connecting to students directly - and making them much smarter.

Ok, homework and exam questions.

Ok, so, constructing homework and exam questions. The main theme of that was Bloom's Taxonomy.

Ok, so this was a hierarchy of goals that you could have. So, the full name is, "A Taxonomy of Educational Objectives."

And the ones we're talking about, if you look at the full title, it's the Cognitive Domain. There's the cognitive and affective - affective means related to feelings and emotion.

Uh, this is the cognitive domain ones I am talking about here. So, are you asking for just comprehension, are you asking for students to analyze, are you asking them to synthesize knowledge? What is the level of cognitive activity that you are asking for.

And generally, you want to mix levels. Uh, so you don't want to just push the students off a cliff.

And say, ok, uh, discuss how - you know the first day in thermodynamics class - discuss how the second law of thermodynamics applies to the entropy of the universe.

You know, that's just too hard. You've pushed them way off the cliff and you've jumped way too high in the taxonomy.

You also don't want to just give them pure comprehension problems - do they remember the rule that you're trying to teach.

Rather you want to mix them. And Bloom's Taxonomy gives you a structured way of seeing what level your questions are at and making sure you mix them.

So that you prepare students with comprehension questions so that they can later do evaluation questions.

Ok, course design.

So, for course design, the big idea is big ideas.

So you want to organize your course around some kind of large ideas. Ideally, those large ideas will transfer outside of the course, too.

And if a whole curriculum is organized around a few large ideas, for example, waves, and offlitory motion

you could also organize a whole bunch of a physics major around ideas like that. Or conservation.

By giving structure to the curriculum, you turn it away from just a series of unconnected facts.

Like ok, this topic, that topic, that topic, that topic. You actually - you give it form and organization

and then it's much more likely to be built into long lasting chunks in the students' minds.

Ok, so next one was [inaudible]

The sixth session was "Interactive Teaching." And the main theme is that questioning and reflecting lead to long lasting learning.

So, I showed you four different - three or four different - timescales on which you could be interactive.

When you ask questions - a short one is when you wait 5 seconds - or actually some of you suggested 7

which is probably better. It's just harder to do, ah, but it's probably better.

So, you wait a certain amount of time to allow people to actually formulate questions.

So that promotes interaction on a short scale. You can ask short questions one or two minutes - two or

three minutes with a multiple choice right in the middle of a lecture. It gives you feedback.so it's

related to the misconceptions one. You're learning how students think just as they answer the questions.

Or you could do longer, or, on the same time scale you could ask feedback questions from this sheet

at the end of the lecture so that's also promoting a space for questions

and you can actually see how successful that is.

There's so many questions actually, we could spend two more sessions answering all the questions, which

I'm glad about.

Because questioning and reflecting, that's how people make knowledge their own.

So, the formal name for that is Constructivism. What you're doing is you're helping people construct knowledge.

And you can do this on a long scale - like for example for a whole lecture - you can use a question like "the wood blocks" - ah - which I showed you earlier.

You can actually do that for an entire lecture. And, actually, we just did that for an entire lecture in my artoproximation class.

Because the wood blocks leads to xylophones - and I brought in the xylophone - and we could talk about how the pitches of the thick and thin wood blocks relate to the pitches shorter and longer xylophone slots.

So, there's lots - so rich examples like that - one doesn't have that many of them. But, when you do have them, you can actually build an entire session around them.

And it produces all of these good things.

Ok, 7.

So lecture planning and performing. So for the planning of a lecture - just like for the course - the planning of a course - you want to organize it around some kind of big idea.

Some kind of thing that gives it structure. The whole lecture, you want an objective.

So, an example of: by the end of a lecture I want students to be able to explain the origin of the terms in the Navier–Stokes equation.

So, then you would choose your activities in lecture around this goal. But that goal - just like the longer scale one for the whole course - gives structure to the lecture.

And you know what to put in, and what not to put in. And the lecture planning blank sheets - or the templates I gave you - I posted - you can use those to that end.

Ok, that's for the planning part. And for the performing - the - let's say the main thing in performing that people don't normally think about - when they think about teaching - is timing.

Ok so, you want to create little bits of suspense and interest which are then - you know - little bits of tension that are then released.

And you want to do it on multiple scales: short and long. You know, the interactive teaching questions from here help do that. Especially if you have a demonstration, because people want to know.

Hmm, is the thick wood block going to be higher pitch or is it going to be lower pitch? Hmm. And you'll find that when you do things like that the entire room is dead silent because people really want to know.

And the way you structure the questions can promote that - by having people vote they've now made a public commitment which then activates the cognitive dissonance part of people's minds.

They don't - they have a - by making a public commitment they've now made their internal state more towards the public state, which is "All I want to know is what's going on".

And they really do want to know what's going on.

So, timing - you can use - get a lot of timing ideas from the interactive teaching methods. The timing is really important for performing. Imagine jokes where people tell you the punch line first, and then they tell you the rest of the joke.

Right? They don't go over too well. And most comics - at least most successful comics - don't do that.

But, we usually do that with our teaching.

Ok. Blackboards and slides for teaching.

So, the main concepts to think about there are the chunk size that students have and how many spots they have in short-term memory.

Ok, so with a blackboard you have many advantages for free. Which is that - on the blackboard - you don't have to use too many short-term memory slots.

Uh, you can put the entire session all on one giant set of blackboards in the front. And you can offload a lot of the work onto something that is individual field and present for everyone all the time.

Because remember, their chunk size is much smaller than yours. Uh, so you might see the entire lecture as one chunk, but obviously they don't see it that way or they wouldn't be in that lecture.

They're the learners. Uh, and then, when you're doing the slides - if you're going to use slides for teaching - to mitigate some of this problem of not having enough short-term memory slots: generally not enough space.

Well, you could try to get four black - four slide projectors - or three slide projectors, but it's pretty hard to do. And it sort of triples or, quintuples, nuntuples the time to prepare the slides.

Because you have to synchronize three different slide presentations. Uh, so at least use assertions at the title, and then visual evidence.

Visual evidence is much easier to remember and the assertions help people to know what to look for.

So, they're not spending all their cycles - which they don't have that many of because their short term memory has been filled up - uh, they're expending their cycles trying to understand the visual evidence.

[Inaudible] I posted a set of example slides with the tech source. There was a request for the tech source, so I posted that, as well.

Uh, showing this method of presentation for the factorial - the logarithm of the factorial.

Ok, and then, the last one was [inaudible]. So, maybe the summary could be one - the comment that was on one of the sheets was: is there any hope? [laughter]

Alright, and I think, well that question is - it's coupled to another question. So the main theme for that is that social and educational... Social and educational change are coupled.

So, if there's no hope for education there's no hope for society. Uh, or alternatively, if there's hope for education there's hope for society and vice versa.

But the main positive lesson from this is that by improving society you improve education, and also by improving education, you improve society.

So, that's one really good reason to want to be a teacher, and to make teaching a part of your career, as I'm sure many of you are thinking about doing.

Ok, so those are the short summaries of the nine sessions. What I'd like to do now is give you a chance to ask any questions you have.

Well, of course, have our - in - let's see - in 10 minutes - at 10:10 - 10:00 - we'll take a 10 minute break. Ah, but before that I want to start the question session.

So, the way we'll do that is if everyone could just look at your index card that you brought with a question. Or it doesn't have to be an index card - it could be a sheet of paper.

Ah, and spend one minute thinking about something that puzzles you, you wonder about, you're interested in, you'd like to know more about. About anything related to teaching.

And check-in with a neighbor or two. And we'll just start doing questions.

Ok, and then we'll have our break at 10:00.

So, I'll leave all these guys up here, and then I'll mark here: your questions.

Ok, so take another 10 or 20 seconds to formulate a question. Ah, or formulate your thoughts and we'll start.

So, uh, kind of implicitly throughout this semester,

we've kind of been thinking that our audience is, like,

a college-aged audience. So if you're teaching older

people, what are the things that you have to do differently?

Good question. So, let me repeat the question,

and then also that'll give me a chance to bring in

one of the other comments from the question

sheets, which is, so the question was,

what about teaching older learners, so

people who aren't college aged, so middle-aged people.

Do you have to do things differently?

Now, before I answer that, let me say why

I repeat the question. So, the comment was that it

is a good idea to repeat the question, because

OCW asked that I repeat the question, so it's

because of the pickup, the microphone pickup

I guess is here, and it picks up me much better

than the audience. So it's good for that. But it's

also good, as the commenter pointed out, it's

good because it makes, it shows the students

who are asking the question that I actually value

their questions, because I'm telling everybody,

look this is something we should all be thinking

about, so it brings the whole class together

around it, and it also gives me time to think

about the question. Although in this case, I didn't

actually use any of that time to think about the

question, so let me think about the question now.

So I'm not sure it actually gives you that much time.

It actually gives you one or two seconds. But,

actually, if you just want one or two seconds,

it's best to just sit there still and think for one or two seconds,

so that's what I'm going to do now.

Okay, so now I waited actually four seconds, just

to show that it's possible to do that, though difficult.

So, there are some things that are different, and

I'd say that one of the main differences is not just

the misconceptions, but the conceptions of

learning that people have. So, for example,

you might be teaching people who just failed

out of math in school, never did math again.

And now you want to help them learn math.

Or you want to help them learn reading

and they always thought of themselves as

terrible readers. So now they've been, they've

imbibed the lesson of the blue-eyed, brown-eyed

experiment, which is that they are bad at this. They,

you know, for whatever reason, it's their fault.

You know, and we're very good at that. We're very

good at passing blame. Sort of, why didn't people

learn physics? Oh, well, physics is a very hard

subject. It's not that we teach it terribly, it's a very

hard subject. So basically we're saying, blame the

victim. It's very convenient. So after a while of that,

the victim actually starts to get

Stockholm Syndrome, so they start to identify with

their captors, and they agree, yes, physics is a

very hard subject, I never had a head for physics.

So, as an experiment for that, next time you go to

a party, ask people "What do you do?"

I mean, obviously not a party of other graduate

students in science and engineering, because it

wouldn't work, that test wouldn't work here.

But just, for example, so my officemate when I was

a graduate student, he used to live in Hollywood,

in Hollywood itself. So he used to go to parties,

and his roommate was a script rewriter. So his roommate

would actually, scripts that were considered too

bad even to make movies out of, but they really

thought they should make a movie out of it,

because they thought they could make a lot of

money if they just rewrote the script in bits, sort of

like D-grade scripts that needed to be made

C-grade, his roommate rewrote them. So he

had a lot of Hollywood connections. So they had a

lot of parties, he had a lot of parties with people

who weren't from CalTech, which was good.

So go to a pary like that, and when people say what do you do?

Say, oh I'm a chemistry guy; I teach physics, or I'm a TA for this class or I'm working on a PHD in mathematics

And just watch how fast people run [laughter] Alright. You know so if they're more polite - if they're

not very polite they'll say, "Oh, what do YOU do." If they are more polite, they'll say, "Oh, I was always

terrible with that."

"That was never my thing" Ok, so now - and this is so prevalent - ah, so now what do you have to do in

that case, Well you have to - so that's their misconception.

And so number three up there. You really take account of that.

They're way of thinking about math and physics - the way that it was taught to them completely did not

work. And now you have to just go around that.

And so one of the ways, actually Brian Butterworth, uh, who actually studies this.

He's a professor of neurophisiology in London.

I've mentioned his book a couple times. I think it's called "The Mathmatical Brain" or "What Counts".

Depending upon whether it is the American or English title.

So, math phobia is caused by people having a fear that there is only one way to get the right aswer.

Right, so they think that they are walking across a tightrope.

And if you make one misstep, then you fall into the abyss.

Right, and so if you have that conception of mathematical reasoning and problem-solving then you are going to have a lot

of fear. Right, so what you have to do is you have to show people, "No, actually," - ah

Write it up here.

So, if this was their model. That's the one way to get to the solution and actually you have to show

them, not that, but... And show them even dead-ends.

You know. Not every method or solution will work out.

Some might just end up there, some might end up there, some connect to other methods and get to a solution.

And even maybe - that's one solution, but maybe there's two.

So, you want to show them that there's robust paths across the river.

You're not trying to - for example - jump Niagara Falls, where one misstep and down you go.

So that's the way of reducing the math phobia.

Now that's a particular example, but it's an example of how you have to think slightly differently for

the adult learner. The reason is that they have had longer time to internalize the misconception.

The high school student, they haven't necessarily formed their own view of themselves.

It's less true of the college level where people are forming their view of self.

More and more. But it's still changable. Especially in America. And that's one really excellent part

of the American university system.

So, you may not realize it - if you come from America - but in almost every other country in the

world, when you go to university, You pick your subject and that's what you do.

For the rest of your university time.

So, England for example, it's even before that.

If you want to do physics at Cambridge, you would have to have done, for the last two years of high school

- basically everyone who did physics at Cambridge did physics, math, chemistry, and further math.

For their maths, I should say.

So, further math is just more math - basically like

DC - DE calculus.

So they, for the last four years - two years - of school, only math, and physics, and chemistry courses.

And then, they go on to university and do just physics.

And Cambridge had a radical innovation on that, which is

in the first year, you didn't do just physics, you did physics math, chemistry, and maybe a fourth subject.

Ah, so that was considered very progressive, and it was compared to the rest of the educational system.

In Europe, in general, there isn't that freedom.

So, in America, you still have it. So, students in colleges are still going to be quite different from

the people that basically fixed their view of themself as bad at math, or bad at whatever.

And that's one of the things that you change when you think about adult learners.

Ok, I'll take one question back there and then we'll have our break.

Student: Towards the beginning of the class we talked about

the experiment in math teaching in New Hampshire

Professor: Benezet, the experiment? Student: Yea, the the Benezet experiment.

I don't think we ever really got to figure out what happened to that [inaudible]

Professor: Ok, So what happened to the Benezet experiment in New Hampshire.

So this was in the Louis Benezet was superintendent of schools

in Manchester, New Hampshire from 1924 to 1938

And so what happened. You know, if it was so great, where is it now?

Uh, so, I might have mentioned that I actually went and did research

on what happened to it. And I went to the Manchester

New Hampshire school board, and just spent a whold day in their archives reading all the minutes of all

the school board discussions about it. And all the votes about Benezet.

And whether to reappoint him as superintendant

or what to do about the curriculum. And basically, what happened was two things:

First of all, there was extensive studies done showing that the curriculum was very successful

Uh, so one study was by

So, Eta Burman. She was a teacher in Manchester

in the program. And then she did her masters in education - I'm pretty sure - at Boston University.

Uh, yes, I'm sure it is. Because you can find her thesis in the Boston University library.

So, she did her education thesis - was an assessment of how the students did

in that experimental program versus the reqular program.

And the students in the experimental program were just much better.

Ah, it was just totally clear. So now, what happened?

Well, what happened partly was that -

I think a lot of it is what Alfie Kohn article about "Not for my kid"

How priviledged parents undermine school reform.

So, there was huge opposition from the priveledged parents.

And so I interviewed some of the people who had those priveledged parents

who had taken that curriculum 50 or 60 years ago.

And one of them was later mayor of Manchester.

And he said his parents just hated the curriculum.

So generally, ah, the people whose parents were foreign

for example, French Quebeca, who'd come to

New Hampshire to work in the mills.

Ah, the non-English speakers, the lower-middle class, it was ok it was fine.

And the ones I talked to from that background loved the curriculum.

And the few who really hated it were actually socially quite powerful.

Ah, and they came from the predominantly English-speaking families.

And they hated that he wasn't, for example, giving homework.

Because he said, if you have 8 hours of school, what more homework do you need?

Which, I think is actually true.

Ah, if you can't teach people in 8 hours a day - um, that's rediculous - that's 40 hours a week.

So, why are you giving them still more homework?

Ah, so he didn't have homework, he actually had them learn in school

which is one of the benefits of interactive teaching.

If you're lecture is no longer dictation and you're actually learning, you don't have to do a lot of

stuff out of school

So, there was opposition there. So - and - what happened was the

votes in the school board went to something like this:

uh... see how this is T... so this is 1938... and 1924

And this is the votes "in favor" and "against." They went roughly like this:

So, the school board, I think, had about, ah, I think had about 15 people on it.

14 people depending, I mean, sometimes, one person wasn't on the school board.

Ah, so the first votes were something like 13-1

So, in other words, +12

And then - uh so, over here 1924 - when he was first appointed...

And then, the votes went like this and then started going down

like that, and by 1938 - so there was votes taken every 3 or 4 years or 2 years -

uh, whether to renew the appointment. Cause that was just the term.

And by here, this was - the vote was 6 to 6, uh, right here.

Uh, that's right. It was 6 to 6 in 1937,

And then, what happened in 1938, was they didn't vote to not take him on,

But what they did is they voted to use a standard textbook.

So they voted to use a standard textbook in the curriculum

and then the curriculum was declared incompatible with the standard textbook

And of course, the standard textbook was pretty terrible - I haven't read the textbook personally

but I'm sure that - given the state of standard textbooks - then and now.

Alright so, and it certainly wasn't the progressive - kind of - understanding algorithms

approach that Benezet had.

So, then the textbook was instituted and the curriculum was basically killed off like that.

So then Benezet left for a professorship of education at Dartmouth

And then they - after Benezet left - so this is Benezet...

Benezet left, The new superintendant put in a - basically - drill and kill curriculum

with lots of testing and uh, sort of the standard now.

No child left behind 60 years - 70 years before it's time.

Ok, but the curriculum was very successful

and it was basically killed off by opposition

from - ah - wealthy parents AND - to be fair - Benezet didn't help his case

- ah - so a couple of the students told me that

- actually when the students wouldn't answer things in class

he would sometimes make fun of them. Now that's terrible.

I mean, it's terrible just on moral grounds, but also

it's terrible political strategy.

Because now the parents are going to go - I mean the kids will tell their parents

and if the parents needed any ammunition, at all.

There they have it.

So, Benezet was just arming the enemy, too.

Yea?

[student mostly inaudible]

Yea. Good question.

Eh, well. Yes, good question.

So is there a comparable force in college education? The parents with previledge?

Ah, yea, Unfortunately it's ones colleagues on the faculty.

Ah, The reason is because they were the ones who did well by the old system.

And so now, a change is likely to be misinterpreted - or maybe rightly interpreted -

as, well, this isn't for the benefit of the top 5%. So, we can't do it.

Ah, so, for example

interactive teaching is often criticized as, "Well that's really useful for the people that aren't learning

anything. But the top 5% - it'll just slow them down."

So, we can't possibly do it.

So, the wars about interactive teaching turn on - a lot - of that question.

And that is a very similar force.

Uh, because people are saying, "Well, it's those people who are just like me, because their the ones

that will become future faculty. And those ones aren't given the benefit of the system."

Imperically, that's not true. I think the - they are actually benefitted, as well.

Ah, and Benezet found that too.

It wasn't that some people did worse, they were all doing better.

Ah, but it's the intensity of the response that you get to things sometimes

in that vein, shows that it's an underlying social force.

And not just purely a cognitive reason.

Is that, ah, what you were thinking about?

Ok, so 10:08 - at 10:18 we'll start again with more questions.

Ok

So, I know there's sevreal more questions.

Because I already have 2 in the queue

Uh, go ahead.

[student] My question is what do you do when you are confronted

with a question you don't know the answer to

[professor] Ok, what do you... I don't know. No. Sorry.

[laughter]

The question was what do you do when you are confronted

with a question that you don't know the answer to.

And my answer was I have no idea.

There's good answers to that question.

And hopefully I will give you one of them.

Ah. So, I would say the number one thing is not to bullshit.

That can only end - at best - it won't end in disaster. But, it can end in disaster.

Ah, so the first thing - so if you don't know the answer to it, but you have to think

what's going to get triggered in you.

So, if it's something - for example - really related to the material

you're more likely to to get triggered and say - Oh I should have known the answer to that,

I must be a lousy teacher, ah how will they ever respect me again

So, if you remember the discussion we had last time about political barriers -

about the 3 levels at which conversations are carried on.

So, this is from difficult conversations: there's the factual level,

the emotional level, and the meaning level.

So, the fact is someone just asked you a question.

And you don't know the answer right away.

The emotional reaction - the emotional transmission is

Oh my god, I feel worried and nervous.

and then, the meaning level is oh, what does that mean for me

oh, it means that I'm a bad teacher - they found me out.

I'm really not supposed to be here.

Right, and so, the same thing happens with students

when you ask them a question that they don't know.

So, you want to create structures where that meaning -

that bad meaning isn't triggered.

Uh, so you want to just pause, first of all. The reason is if you don't pause

then you are more likely to act out based on the emotion

So, I've seen this happen several times

when I was a graduate student

Uh, which is that whether the -

So, this is - sometimes when the person

didn't know, but in general when they were somehow challenged

by the question. So, either way, whether it's because you don't know the answer

or because the student's tone has some kind of cheekiness to it

and you feel a bit of insolance and you think

I'm the teacher, Goddammit

How dare you talk to me like that

So, that emotional reaction - whether it's - or that challenge,

that worry, that anxiety about your authority

will produce a bad response, in general

Ok, so if you just right away respond

you are likely to do bad things

and this is something I've seen happen a few times

where you put the student down or you compete with the student

You say things like, how could you not know that?

And then you dismiss the question

So, if you pause for just one or two seconds - even an instant -

after you practice it - just the pausing to realize

Oh, wait a minute. Uh, I just had an emotional reaction happen

Uh, I felt it in my body. I got a bit sweaty. Ah, my palms sweated

Whatever it may be, that your particular reaction is -

I feel it often in my face, my face gets warm

Uh, if you remember - ah - way back

When we were doing the, what is it the wood blocks, or the cones?

No, it was the cones.

When I was dropping the cones.

And there was a question - when it was time for question and discussion -

one person said, Oh, the answer is block and I've seen you do it before

And I just remember, just feeling flushed.

I was like, Ok this is not the time to answer that question.

Ah, so it's the same thing. So, that's lesson number one, is to pause.

And then you can think and regroup and have a relective response.

The reflective response is maybe, oh, you know that's a really interesting question

I'd never thought about that

but I'm going to think about that and I'll tell you the next time.

That's perfectly fine.

Another one is you can try to figure out the answer together

You say, Well, I'm not sure, but let's see

if we can find out the answer in the next minute or two

if not, I'll work on it in the eavening, or work on it tomorrow and tell you.

And then you can try it together.

And then students have

the advantage of seeing how you would reason about a question

And it helps, if you do that intentionally

because there's sort of a general rule of thumb

which is that one's facility with equations declines with distance to the blackboard

So, the closer to the blackboard, the lower the facility of the equation.

So, if you just leap to the blackboard and start writing,

you're likely to feel too nervous and actually just mess it up just because of that

So, if you say ok, let's actually think about doing this together

think about what you might do. Think about some approaches

then go to the blackboard and maybe start working

Then, you know you have your out.

If it doesn't work in 2 minutes, say

Ok look, it's a good question, I'll really need to think about this some more

Ah, and I'll do that, and I'll come back to you.

Ok, does that help answer your question?

[student] Yes, cause we were just talking about how the discussions with our students

and I'd be like, perhaps there'd be somebody who'd point out a different way of doing something

and you're not prepared to talk about, you know, that with them

[professor] Right, so what if somebody produces - yea

if you're going to do interactive teaching you're going to have lots of discussions.

So, people think Oh, interactive teaching means you just let the students do everything

and just kick back. No, it's actually much harder.

Ah, because you have - it's - your now - you've changed it back from

basically, playing prerecorded tape - which is what a lot of lecturing is

you just get out and read the book.

That's what one of my lecturers did.

Ah, to - it's now a stage performance - a stage performance in the old days -

in the Elizabethan Theatre - where the audience interacted with the stage

Ah, so that's much harder.

You have to have to really know - you have to "know your lines"

Not that you're going to say the same lines no matter what

you have to really feel the lines, you have to really understand the feel - so it is harder

You're going to be producing lots of

discussions and at a place like MIT the students -

who are very curious and their gonna think

Well, oh what about this

Well, that's fine so you want to use

Ah, sort of Ikedo - so if someone suggests something

you hadn't thought of don't dismiss it.

You say Oh, I hadn't thought of that - that's a really good suggestion

Which and usually - maybe - I'll use that next year.

Ah, when I teach the course.

Thank you.

So, if you just think about the students as your allies.

Then your reaction - that you'll intrinsicly produce -

will be much less confrontational and much less worried.

Ok, uh.

So, I'll give you one example of where I was very, very nervous

and - ok - what I did.

So this was - I was lecturing thermodynamics and there were 200 students

and I was doing the Carnot Cycle

So this was the last lecture - so we were doing the Carnot Cycle -

and I drew it up on the board

and you know I'd encouraged questions

throughout the whole lecture and throughout the whole lecture course

So, of course someone raised their hand and said

Oh, excuse me, I think that this box should be - is not right

They didn't know what was wrong with it - they said

Oh, that box isn't right

So, I looked at it, and I thought

Oh my god, they're right.. So, I have now just drawn rubbish

on the board in front of 200 people and

I had a buch of my colleages that day who happened to decided

that was the day to come visit my lecture

[laughter]

Ah, so I think that was probably why I was a bit nervous to begin with.

And then, that probably contributed to me writing down the wrong diagram.

So, I realized, I needed some time to actually think.

So, I said, You know, you're right.

Let me just think. And I just turned my back,

and - for a whole minute - I sorted out what was wrong.

And then, everything was fine after that. But I still remember that.

I still remember the feeling in my body, just that sinking feeling of

Oh, my god, disaster has happened. Right, I have just been exposed.

Really I should have been one of the students in the class.

Ah, so pausing is immensely valuable.

[calls student's name][inaudible answer]

Oh, right, so when you - often when you want to do something more interactive

in your teaching the counter arguments are, well you're going to harm the top 5%.

Well, one counter argument - so, first of all

it doesn't often help to counter argue

cognitive reasons if there is an emotional underpinning.

So, generally I try to step aside from those arguments.

Because, they - unless the people have a sense of humor, I find.

If the people have a sense of humor then you can actually say

you can present things in a humorous way that challenge their view.

And they can take it on board.

But if they don't have a sense of humor or you don't have a good way of presenting it

that way, I find it's just wiser to step aside and see if you can find some way

around it maybe try half of what you wanted to do

or say, well yea, you know I worry about that too, a bit.

So lets leave the main course alone that way.

Let's try an experiment and see how it goes.

Uh, we can agree on some questions that all the students should be able to do.

Your trying to make it cooperative. So that's one thing.

But, if you can, if you do want to sort of go directly into cognitive discussions and reasons

one is - and this has scope for making humor - is that

What's a top student? I mean the tops student is the top 5%

when the top 5% by the current system of testing and homeworks

So, they're often the top 5% in regurgitating canned formulas or

by the time they get higher and higher and more selections happen

they're good at pattern matching and solving problems they don't even understand

I mean certainly, the final exam in Cambridge - ah, that people took in their final year

- if I just sat down, I would not have passed it in the physics department.

And so, there are students who did really really well on it

but I'm sure I understood more physics then them

Ah, and it's because if you train for those kinds of questions

- even if you don't understand what you are doing -

you can actually answer them.

So, now, the top 5% at that. Well, is that so valuable to preserve?

Maybe I should [inaudible] change the rules of the game

So, now if you just say it as directly as I've said it

then you'll trigger the meaning of - cause alot of the times you'll - those 5% became the people you

are talking to

Ah, so you have to - ah, maybe do it slightly differently

and say, look what is the thing you are most concerned about?

About the students not knowing. Whether they are the top 5% or not

And a lot of times people - they'll just give you a big long list

They'll say oh - on their own before you can say it - they'll say oh

we can never use anything outside of the class.

So, people will just outright conceded that

- not even conceed - they'll say, yea it's so terrible,

and people will talk about this all the time

say look, we all agree to that, but look is there a way that we can make people really good at that

Cause, even the top 5% I find are not like that

So, now you've opened the door and now you can

have a shared discussion

based on something like that.

Ok, so that's how you can reach, sort of the 80% who are not sure, but are willing to listen.

Yea

[student] I was wondering what you think of the serveys that they have at MIT

by which the students evaluate the professors and teachers

And also how to interpret the results of those?

[professor] Oh [inaudible] I'm glad you said that

for several reasons, one of the other reasons

is that - heh, this course has one too [laughter] - So, it's - the way that I'll put it on the course

website - ah, just after class. Ah, so it's 595 is one of the course numbers.

but it's also 6.92 or something, so all core 6 point classes have an online evaluation system

So, for everybody we-re doing it that way.

So, everybody who is registered for the class is listed as a possible

servey filler-outer. So, I encourage everyone to -

I'll put the link on the website, just click on the link

and if you have your MIT certificates installed, it'll just

take you to the online servey

So, I think the serveys are very useful.

Now, the numbers, the numbers are sort of a ballpark of whether things are working or not.

But I think the most useful part of the serveys are the comments that people make.

So, again, I encourage you to make comments in the comment boxes

whereever they are. Ah, for example there is one that says,

"What would you suggest for people next year."

Ah, so part of that, I'm going to learn by reading these.

Ah, so I'll [inaudible] good ideas from how you would do this course.

from your homeworks. But the servey should actually help with that.

So, I think the serveys are really useful if used properly.

I don't think they are very useful for say, ok, you get tenure

you don't get tenure. Ah, because the numbers - and people just use the numbers -

for that. I don't think the numbers are super-reliable.

I mean 7 is probably significantly better than 4 or 5.

But, there are a lot of ways to get 6 and a half from 7, say, 6 or 5.

How did that happen? Well, you want to really look into the course and see that

and the course servey doesn't really address that super-well.

But, the comments give you space - if you really listen closely - to understand them.

So, I think they are quite useful. But what I really like to see is

- cause those are surveys right after the class.

And you know my goal - what I've been trying to stress this whole time is -

how can you construct teaching for long-lasting learning

You know, questioning and reflecting, ideally, for long-lasting learning.

Well, if it really lasts long, people should remember something a year later

So, I think actually a policy should be changed to do feedback sheets

at the end of each lecture - so you get the quick feedback you need as the lecturer

and then by the end of the course you have a lot of feedback

and you can really improve things next time and then do the servey a year after the course is finished

And if people don't remember anything from the course - right away

that's a pretty important peice of feedback

So, I fear that the results from that kind of servey would be quite distressing

'Cause people would - you'd ask thinkgs like which of the ideas from the course do you really use?

And, people have done serveys like that.

Ah, in physics majors - so there's serveys of physics majors in the job

whether they're in research, or in industry, finance - well before that ended

Ah, what do you use from your physics degree?

And very rarely do you find people saying - if you just average across all the jobs -

Maxwell's Equations. It's just not on the list, it's very low on the list.

Ah, it's things like general problem solving, quantitative skills, working in groups...

Now, it's not necessarily true that therefore we should just dump all of our classes

and teach people how to work in groups - that's not what I'm saying

But, it's useful to know that you can take that into account

So, that would be my ideal: serveys 1 year, 5 years, 10 years later.

And there are a few of those at MIT - alumni serveys.

Meckie - I know - has done a few of them.

Ok, other questions? Yes?

[student] Ah, [inaudible] [professor] Yea, 2-3 years. [student] You got [a course] down pretty well.

Does it become boring?

[professor] Good question.

Yea, so, so the question is: you make a new course, 2 or 3 years, you have refined it

ah, after 5 years, does it become boring?

My guess is probably yea. Ah, unless you keep changing it.

So, I've taught Art of Approximation for almost 9 years now.

And every 3 or 4 years I figure out a completely new way of doing it.

And now it's finally converging, I would say.

Finally, realized the main thing - because I didn't know this when I first started.

Ah, because I was a new teacher. Ah, so organize it around large ideas

main themes, transferable techniques.

So, I finally converged to that - now, I'm changing the examples

And so, it's probably converging, but I could probably keep doing that for another 3 or 4 years

but if you just do it - so you refine it for 2 or 3 years - and just keep doing it

I would say, yea, for another couple years

maybe just thinking about other courses.

And I already have a sign that tha's happening, cause I'm now thinking

hum, you know I would like to make a physics of music class

You know and they may be related to the other class

cause we just did the wood blocks and the xylaphone in my approximation class

and I'm thinking oh, you know, a whole class in the physics and music would be

a lot of fun to make. Organize it around demonstrations

and you could bring in the physics as needed for the demonstrations

and choose all the denomstrations

so all the main physical ideas in acoustics and electromagnetism, mechanics, and sound

are all combined. Oh, well that would be a really nice design problem.

So, maybe I am converging with the art of approximation one after 9 years.

So, it depends how often you keep changing things.

Yea, and that's OK. Because you'll find that that's the natural life cycle.

So, for example, if you are a faculty member, say, in almost any university in the country

Every - after 6 years you get a sabattical.

So, in the sabattical, you would be very well advised - I mean you could teach if you want -

but you would be very well advised to not show up on any committees,

not teach - and generally, you are pretty much required not to - and just leave

Because otherwise you will be dealing with all of the normal run of the mill things

You won't be able to have a block of time to really think.

So, if you've developed this course - after 5 or 6 years - it's automatically going to have to be

given to somebody else.

And that's fine. Cause that's around the time that you''ll be thinking about other stuff

and a sabbattical is the time to reorient yourself towards other stuff.

So, looking ahead towards that. What you want to do is write up what you do.

So the first year, it's pretty hard, you're just barely scrambling - your trying to breathe - it's like

having four children - as having quadruplets. Ah, well maybe - I don't know - I haven't had that happen

But, ah, the first year you do a course - a brand new course - especially a three days week one -

it's pretty hard. So I can tell you, this is two hours a week, but it's the first time I have taught

this course, so it's a lot of work.

Ah, and that will be true. So the first year, yea, you just want to survive.

The second year, you start to figure out what to do, what to write, and just

start writing stuff up bit by bit. Ah, you know lecture notes

problem sets that are, you know type set.

Things that other people can reuse pretty easily.

So then, when the course is handed off to somebody else, they can continue

that and refine it based on what you've done.

And everything you did doesn't just vanish.

Yea

[student] So, you've mentioned [inaudible] about teaching [inaudible]

[professor] The grunge? [student][inaudible]

[professor] Yea, so the question is - so I like to use lecture time

for the larger ideas, concepts, for the chunks - for example the teaching equation one

and leave the derivations, the detail manipulations, the mechanics of stuff.

The mecha-grunge, let's say, for the textbook.

Ah, do I have any suggestions for how to choose a good textbook?

Well, ah, it becomes less - it is important to choose a good textbook

But it becomes less important if the classroom is focusing on concepts and chunks.

Because that's the differentiator generally between the good and the bad textbooks

Is that the good textbooks do more of that.

So, if your focusing on that in the classroom

then you have more freedom - not freedom to use bad textbooks - but the bad textbooks don't do you as

much harm. Because the students don't need so much out of the textbook

They need to basically have a place where the derivations are correct

and that's an important part. And it has the derivations you need, sure.

Ah, so right away you can relax about choosing a textbook slightly

Ah, but how do you find good ones?

Now, I look at the reviews online and see what students say about them.

Ah, so I do a web search for books and I see what books people are using, what people are commenting

on. I look at - on the online book stores - the various reviews of books. Ah, that helps a lot.

Nowadays, often people put the first chapter and the table of contents online. The publisher's do.

And ideally they would put the whole book online - some are doing that, too.

Ah, so have a look at that. From the table of contents, you can really tell alot about a textbook.

You say, hmm, is this organized right? Does it have the right philosphy that I'm looking for?

So, look right away at the preface, where the author talks about why this book - and if they have no

good reason for why this book? It's probably not the book for you.

Uh, sometimes you don't have a choice about the book.

People will just say, well this is the book that we always use.

Or, it's the first time that you have taught the course.

For example, you're hired in July - you're hired, say, in March - you start your job in July.

And in August they come to you and say, oh, professor blah is on sabbatical teaching X,

you're up. The course book is already there, so you can't do much about that.

So, someday you don't have freedom, but then when you do want to do it.

So look at the preface and the online reviews are quite helpful.

But, don't worry as much if your classroom is interactive, that mitigates a lot of

textbook problems.

Yea?

[student][inaudible]

[professor] Uh huh?

[student][inaudible]

[professor] Right.

[student][inaudible]

[professor] Ok, so let me unpack those. So, there were several questions in there.

First, is there a difference between - are there any studies on the difference between results

produced by the European - say - educational system versus the American.

The European where people just do their one subject.

To first order. Where the American one where you take many different courses across many different subjects.

Ah, I'm not sure about that. But, ah, also the notion of effectiveness is not clear.

So, the goal - what's the goal?

I think the historical reasons why it's different is that education in America

- early on - back in colonial times - [inaudible] - just post-colonial times.

Er, early 1800's was seen as a democratic thing. The idea was that this is a democracy and all the

citizens are expected to participate in that and so ok they had a narrow definition of citizens.

Just white males - but within that definition - the idea was that everybody had to participate, or was

going to participate. So, to that end, they needed a broad education.

They couldn't just specialize in one thing, because it would be too narrow to actually

help govern society. Because society is multi-farious and multi-disciplinary intrinsically.

Whereas, in Europe that idea of democracy came hundreds of years later, if at all.

Maybe at the end of Wolrld War 1.

So, the European educational system is much more trained for producing people in a -

much more oriented towards producing people that would fit into a particular slot in society.

Ah, so now - if you want to measure how effect each was at it's historical goals.

I mean, that's a fair question.

To measure how effective each is at producing people who are trained for a particular slot in society.

I don't think that's a very useful analysis, the historical origins of the two systems are different.

Ah, it's much more fruitful, I would say, to think about the goals. Which goals do we agree with?

Can we get the benefits of the American goal with some of the benefits of the specialization in Europe?

And I think at places like MIT you do that. I mean, students will come out of MIT they have a broader

education than the students that come out of European universities, and they actually know a lot.

Now, I would like it to be much more conceptual and long-lasting, but that's true of the European ones,

too.

So, I would take the question back from just studying the end results to

think carefully as a society about the purposes.

Now about the physics of music, I would say, actually I could imagine

teaching and intro to physics course that's physics of music

where students would learn all the fundamental ideas of, say, first semester physics, but through the

physics of music. And I don't think it would be - So they wouldn't actually be deprived of

the essential knowledge of physics. They would actually be contextualized.

So, they might actually learn it for longer lasting - might have a longer lasting value.

Ok, other quest --- Yea?

[student][inaudible]

[professor] Yea, the're in the math phobic mode or phobic mode.

So, this is a really interesting question, so the comment was that a lot of people at MIT

- a lot of students - one of the emotional barriers they have is that they feel - I would call that a

meaning barrier. If you, let me rephrase it in the three levels of conversation

So, their emotion is that they are very tense and anxious.

And the meaning is that they are feeling - when something doesn't go right for them:

they get something wrong on a problem, or in class. They feel like, they think that's exposing how they

really don't`belong here. Ah, and that creates a lot of anxiety and tension, and misery.

So, at CalTech there was a saying that, oh yea, CalTech is a terrible place for the bottom half of the

99th percentile. You know, which captures that pretty well.

Like, all of these people who - all the undergrads who went to CalTech

Right? They were probably validictorians in their high school and [inaudible] above and doing science

fair projects then everyone else around them. And now they come to CalTech, and they feel terrible.

Like, what are we doing that produces that? It's crazy.

Uh, so how can your teaching, can you take account of that?

You know, so that, I would say also relates partly to the misconceptions

You know, they have this misconception, or this conception about themselves

And what can you do, well, ah, phobias are very difficult, ah you have to work around them

So, one thing is you don't want to trigger them

Ah, so every time you trigger them you reinforce them.

Because [inaudible] so, any neurobiology people in here?

I forget, PCS?

A fundamental rule of neurobiololgy - ah brain - neurons -

so this is of course - I teach the art of approximation, so forgive me for approximating the

whole brain with one sentance: is neurons that fire together, wire together

Ok, so if wiring together, that means, ah, they activate - they increase their coupling

And so increasing that - so when they fire together - so for example, they

you, create classroom environment - or something happened in the classroom

that, they get something wrong.

And now that is still wired somewhat to the bad feeling, and their thoughts

of oh my god, I don't belong here.

So, now you've reinforced that, they are going to wire together more

reinforces that pathway. So, what you have to do is actually prevent those guys from wiring together.

Ah, and one thing is, create an environment where, whenever people get things wrong, it's actually great!

Right, so, that wasn't right, great! Now think of how much you are actually going to learn!

Or, when you get things wrong - you want to model that, too.

You say, oh, you're right! Thanks! Oh, I've learned something from you.

Ah. You know, so try not to be defensive - because that will help

- because if you are defensive then that triggers them wiring - that wiring -

and that firing together builds up the wiring together.

So, creating a classroom environment where feeling bad and competing against other people

isn't the goal, is one way to minimize it.

So, minimize the importance of, like, defined destinctions of homework

Did I get a 95 - oh this person is getting a 95, I'm only getting a 90.

So, that's one reason MIT was PASS/FAIL - er for a whole year it was pass/fail.

Ah, and that was to mitigate the pressure that students were coming in feeling like

oh my god, now I don't belong here.

We said, look, we don't care about your grades in the first year

you are really here to adjust to university - to a different way of learning

And now, it was actually done in a way that

somehow the competition was partly the students reinforcing the culture of the upperclassmen

as well

If you could actually try to mitigate that, you would go a long way towards

mitigating the wiring together. But you can do it in your own classroom, too.

Deemphasizing the things that trigger that.

And so when you call on people, I - so for example, for that reason MIT - I almost never

what's called cold calling - if you've ever seen that old movie, what's called the Paper Chase

So, the paper chase is what's called the - is about the - what's called the -

what we could call today the terroristic socratic method.

Ah, so the law schools all use the socratic method

where you ask people - you read a case, and you ask them about things.

Things about it.

Ok, Mr Jones, what do you think - what were the findings of law?

Mr Smith, ah, or Mrs Dartmouth, what do you think about that?

Ah, do you agree with that? Or is that pure rubbish?

Ah, so people were just put on the spot repeatedly.

And it just produced terror in the students.

And that was considered part of the hazing ritual basically.

So, at MIT, I just don't do that at all.

Because I think, it just triggeres that.

I'd rather, just create a structure where my students feel ready to participate.

Ah, by interactive teaching giving them time to think to each other, and then say something.

So, you can do stuff and it's hard it's an important problem.

Uh, yea? Sure.

[student][inaudible]

[professor] Yes. So really good point. So the point was that it's worthwhile making it explicit for the students.

Ah, and realy naming the feeling that they're going through.

Like look, you may be feeling really terrible, and feeling like you are an impostor.

Well, let it be known that I've felt the same way too for a long time.

And describe it to them, and talk to them about why they may be feeling that.

Say look, we have a competitive - this is - there is a culture of competition in the society and the

university and it's actually harmful for your learning. And share with them some readings about that.

Ah, help them see that yea, this is something that they are going to have to struggle with, but there

is help to do that, and they are not alone. And that. So yea, definitely, be explicit about things like that.

Ok, so one more question. Yea?

[student][inaudible]

[professor] Good question! Do I think contextualizing the course is a way to fight that?

I think it is, because - ah

When the course is not contextualized it generally tends to be really abstractly focused.

And the - the interest and the orientation towards doing things first abstractly is very rare.

I don't have it, and I've gone really far in math and physics.

My office mate had it - in graduate school. He was the only person that I've ever met who

would rather have a proof than a picture.

Ah, and now he's a professor at Cal Tech and he's also doing well.

Ah, but, it's pretty rare. So, by contextualizing the course, for almost everybody -

I would say even for my friend and office-mate.

You are actually connecting to a much larger part of their mind and their experience.

So you are actually making people much more intelligent and much more equal in that way.

So, that's one more reason I would actually like to teach the physics of music class.

[student][inaudible]

[professor] Interesting, yea. So if someone gets around the phobia you might have -

pardon?

Interesting, so that wasn't - so I was there 10 years ago and that wasn't true then.