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Due to technical difficulties, only a portion of lecture 1 is available for viewing

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Welcome to Teaching College-Level Science and Engineering.

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Now, the title contains the word "teaching," which may spark some questions in your mind.

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For example, is teaching just an art? Or is it something that's just - something you're born with.

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In which case, either you have it or you don't have it. Well, obviously I don't believe that

0:00:49.465,0:00:51.985
or I wouldn't be teaching a course on it.

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What would be the point?

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Or is it purely a science, where there's a set of equations and procedures to learn,

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and then all of a sudden you'll be an excellent teacher?

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Well, actually, it's neither and it's both. It's things that we're all born with,

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on the one hand, and they're also procedures and techniques, and ways of thinking

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that will improve how you teach, and that we can all learn.

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So it's a happy mix, my favorite mix,

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an art and a science. So, for example, another example that's an art and a science is book design.

0:01:29.274,0:01:36.316
So compared for example to just pure art, painting, say modern painting, very unconstrained

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vs. say, biology procedures in the laboratory

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you know, very very closely specified. It's somewhere in between there is an art but there is, of all

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of the arts, of colors, of space, but they all have to

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be used together to achieve a particular purpose. So, again, there are some beautifully designed books and

0:02:01.955,0:02:05.859
some not so beautifully designed books. And there are principles behind that that we can use to design good books.

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Simiilarly, there are principles we can use to design good teaching.

0:02:11.932,0:02:15.817
So this is the whole point of this semester is to design good teaching and how you do that.

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And rather than give you a big long theory about it,

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because actually there isn't really theory

0:02:22.505,0:02:26.425
so much in the equivalent to say Einstein's theory of relativity,

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but there's principles to learn.

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The best way to learn those principles is

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with an example.

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So what we're gonna do today is

0:02:35.989,0:02:40.636
I'm going to do an example of teaching with you.

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We're gonna do it slightly sped-up version of what we'd normally do

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say if we were actually using this example in a class.

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Then we're gonna analyze why it was done that way.

0:02:52.181,0:02:56.010
and from an analysis, general principles of teaching will come out

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that will be address throughout the semester

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and they'll be addressed in the context of particular tasks,

0:03:03.650,0:03:08.124
for example, how to make slides that are useful for teaching.

0:03:08.124,0:03:10.822
How to use a blackboard.

0:03:10.822,0:03:12.608
How to teach equations.

0:03:12.655,0:03:14.700
How to design a whole course.

0:03:14.700,0:03:16.059
How to make problems.

0:03:16.059,0:03:20.481
So all of those tasks will be the week-by-week subjects

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and in each task, all the principles that we're gonna talk about now

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will show up in those tasks and you'll see the principles illustrated repeatedly.

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So, the problem. One of my favorites,

0:03:36.737,0:03:38.751
so these are two cones

0:03:39.874,0:03:42.693
one is -- has twice the dimensions of the other cones.

0:03:42.693,0:03:46.634
So let me show you how I made the cones.

0:03:50.388,0:03:55.183
So I printed out a circle and just cut out

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one quarter of the circle

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and then I taped this edge to that edge.

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Or in mathematician speak, I identified the edges

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which I now know means I taped the edges together.

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and then you get a cone like that.

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So this cone and the other cone were cut out of the same sheet of paper

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except this one has twice the linear dimensions in its circle.

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This circle was seven centimeters in radius and this is three and a half centimeters in radius.

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Other than that, they're the same.

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The question is which one has the higher terminal of velocity or are they more comparable.

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So the question is this.

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I'm gonna drop them and the question is

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what is the ratio of their terminal velocities?

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So the ratio of the big cone's terminal velocity to the small cone's terminal velocity

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is equals to what and you get choices along this axis

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So here is...

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Okay, so those are the five regions to choose from.

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So you have five choices for the ratio

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roughly one quarter

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some range here, because nothing's exact

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and we're definitely not gonna do an exact experiment.

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Roughly one half, roughly one, roughly two, or roughly four.

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So does everyone understand the question?

0:06:04.675,0:06:06.234
You're gonna get to try it yourself.

0:06:08.541,0:06:10.237
Question about the question

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I don't know if you could restate the question... actually there was a signing sheet going around... and I sorta lost it.

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So, uh, yeah, can I restate the question, no problem.

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So I'm gonna drop them

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just like this no tricks,

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I'm not gonna flip this one around or anything.

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And the question is, what's the ratio of their terminal speeds.

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So right away, as soon as you let go of them,

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they come to a steady speed,

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which is their terminal velocity.

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And the question is how do the terminal speeds of the big one and the small one differ.

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So in particular, the question is what's the ratio?

0:06:46.136,0:06:47.975
And there's five choices for them.

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Okay.

0:06:49.925,0:06:51.272
That help?

0:06:51.272,0:06:53.981
-Yes, and what were the dimensions of them again.

0:06:53.981,0:07:00.328
-So this guy is -- he was cut out of a circle who was 7 centimeters in radius.

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And this guy was cut out of a circle who was 3.5 centimeters in radius.

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And then I was also very careful to use-- do this right?--

0:07:09.997,0:07:15.247
I used half the width of tape on the small guy as I did on the big guy

0:07:15.247,0:07:21.086
just to get it really very perfect scale.

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Any questions about the question?

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Okay, so think for yourself for about 30 seconds or so

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just to induct yourself into the problem

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and then we'll take a vote.

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And then you'll have a chance to discuss it with each other.

0:08:18.739,0:08:20.396
Okay, let's just take a vote

0:08:20.396,0:08:29.289
so I understand I haven't given all of you enough time to come up with an exact answer or calculate anything.

0:08:29.320,0:08:34.786
So let's just get a straw poll and then you'll have a chance to argue about it with your neighbor.

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So who votes for 1/4 which is--

0:08:38.443,0:08:42.124
so let's see-- 1, 2, 3, 4, 5, 6.

0:08:44.139,0:08:47.955
Who votes for 1/2?

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[counts] 12

0:08:54.468,0:08:57.804
Who votes for C?

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About 22.

0:09:01.489,0:09:04.276
Who votes for D?

0:09:04.276,0:09:05.622
No takers.

0:09:05.622,0:09:06.914
No takers for D.

0:09:06.914,0:09:11.133
How about E?

0:09:11.133,0:09:13.362
Okay, so

0:09:13.362,0:09:15.378
now find a neighbor or two,

0:09:15.378,0:09:16.723
one or two neighbors,

0:09:16.723,0:09:18.519
introduce yourself to your neighbor,

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and also by the way, unless you're taking notes on your laptop,

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if you could close your laptop, that would be very helpful for the purpose of discussion in this whole

0:09:27.303,0:09:28.041
course.

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So find a neighbor or two, introduce yourself,

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you'll be given a chance to meet graduate students from across te institute,

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and try to convince them about your answer.

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Especially if you have a different answer.

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Or if you happen to share an answer, try to figure out why you're sure of it

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or if you're not sure of it, settle...

0:09:48.161,0:09:50.691
So, discussion time.

0:09:50.691,0:09:54.361
And if you have any questions that come up as you're discussing,

0:09:54.361,0:09:56.474
raise your hand and I'll come and wonder over.

0:09:58.519,0:10:01.456
Okay, so meanwhile I also handed out

0:10:01.456,0:10:04.323
feedback sheets for the end of the session

0:10:04.323,0:10:07.404
which I'll ask you to spend a minute on at the end.

0:10:07.404,0:10:11.476
You'll notice one of the question is what's the most confusing thing?

0:10:11.476,0:10:14.515
So if anything really confusing comes up during the whole session,

0:10:14.515,0:10:17.317
you can just put it right there, you don't have to wait until the end,

0:10:17.317,0:10:19.648
or if there's something you really liked or hated,

0:10:19.648,0:10:22.456
that's question 2, you can put whenever to come up.

0:10:22.733,0:10:26.756
But, vote #2 and then we'll take some reasons...

0:10:26.756,0:10:29.435
so...

0:10:29.435,0:10:32.499
One quarter.

0:10:32.499,0:10:36.366
One, two, three.

0:10:36.366,0:10:39.363
Okay, four.

0:10:39.363,0:10:41.942
One half.

0:10:41.942,0:10:44.234
Halves don't have it.

0:10:44.234,0:10:48.374
There's one... okay great. 4, 5, 6.

0:10:49.250,0:10:50.902
Equall.

0:10:51.764,0:10:54.153
Let's call it 30.

0:10:54.153,0:10:58.180
Two

0:10:58.180,0:11:00.830
and four.

0:11:00.830,0:11:03.258
Okay, so

0:11:03.258,0:11:04.943
thanks for the votes.

0:11:04.943,0:11:07.037
Let's take reasons for any of them.

0:11:07.037,0:11:09.736
I'll take reasons for any of them, I'll put them up here.

0:11:09.736,0:11:11.501
You don't even have to agree with the reasons,

0:11:11.501,0:11:14.482
just something you guys discussed and something that was plausible.

0:11:14.482,0:11:17.473
-C...

0:11:17.473,0:11:20.039
-Oh....

0:11:21.287,0:11:23.846
-When you do these activities,

0:11:23.846,0:11:27.652
there's always some... [indistinct]

0:11:27.652,0:11:30.283
I want to know what you would do in that kind of situation.

0:11:30.283,0:11:33.580
-So, you're hmm...

0:11:33.580,0:11:35.388
[laughter] I'm not sure how to phrase this.

0:11:35.388,0:11:37.764
Uh...

0:11:37.764,0:11:39.587
Let me just take other comments.

0:11:39.587,0:11:41.802
[laughter]

0:11:41.802,0:11:43.613
I'll come to it afterwards.

0:11:43.613,0:11:45.264
Other comments

0:11:45.264,0:11:46.960
for any of the reasons.

0:11:46.960,0:11:48.475
So again, it doesn't have to be anything you necessarily believe

0:11:48.475,0:11:50.277
but things that are plausible

0:11:50.277,0:11:54.130
and that's actually more instructive than what you think is for sure right,

0:11:54.130,0:11:58.124
because you're trying to figure out what might be true and you're expanding

0:11:58.124,0:11:59.686
the ways you're thinking.

0:11:59.686,0:12:06.159
-C, because they have identical mass to certain...

0:12:06.159,0:12:11.769
-C, so mass-to-area ratio is the same.

0:12:13.707,0:12:19.028
Okay, can people think of plausible reasons against that argument?

0:12:20.736,0:12:21.690
Yes.

0:12:21.690,0:12:23.847
-I have no idea what the actual formula is.

0:12:23.847,0:12:24.644
-Right.

0:12:24.644,0:12:29.645
-There was a square there...

0:12:29.645,0:12:32.619
-Right, so I'll call this not C.

0:12:32.619,0:12:36.888
So supposedly, formual actually depended on the square root of A

0:12:36.888,0:12:39.565
or something like that.

0:12:39.565,0:12:44.198
You know maybe---- say, one chance out of three that it has A to the first power here.

0:12:44.198,0:12:48.058
It could have A to the 1/2 or 8 to the 2.

0:12:48.628,0:12:50.902
So, could be...

0:12:57.410,0:12:58.787
A to the k

0:12:58.787,0:13:03.010
M over A to the K for K not equal to one.

0:13:03.010,0:13:05.021
Okay, others.

0:13:05.021,0:13:12.074
4 against C, intuitive reasons, or for any of the others.

0:13:17.766,0:13:20.642
Okay, so hopefully that's...

0:13:20.688,0:13:23.596
-[indistinct]

0:13:23.596,0:13:27.683
...that air resistance goes with the area

0:13:27.683,0:13:31.278
and the gravitational force...

0:13:31.278,0:13:33.999
-Okay, so let's see.

0:13:33.999,0:13:42.395
F drag partial to area and weight.

0:13:42.395,0:13:44.073
So that's the argument for which choice?

0:13:44.073,0:13:46.683
For C, okay.

0:13:47.961,0:13:51.131
How do you know that the drab scales are the area.

0:13:51.131,0:13:54.941
Maybe the scales with the square root of area.

0:13:57.818,0:14:02.669
Any argument pro or con?

0:14:05.115,0:14:07.681
Okay, yeah.

0:14:07.681,0:14:14.655
-scales with the area...you can just break it up...

0:14:14.655,0:14:18.525
-Okay, so there's a ....

0:14:18.525,0:14:22.993
So for this, let's say there's a ... for subdividing

0:14:22.993,0:14:26.291
I'll just know that is subdividing.

0:14:31.552,0:14:34.432
Okay, yeah.

0:14:34.432,0:14:38.405
-Some weird shape... and then go to the rest of the pieces so...

0:14:38.405,0:14:42.950
-So it may depend on the division--I mean, the geometry,

0:14:42.950,0:14:45.719
so I'll put that here as geometry.

0:14:52.134,0:14:54.506
What else might it depend on?

0:14:54.521,0:15:00.108
For example, is air resistance say always proportional to area?

0:15:02.108,0:15:03.293
Hmm.

0:15:04.667,0:15:05.712
Yeah?

0:15:07.045,0:15:09.045
-...Depend on the material of the surface.

0:15:09.045,0:15:12.338
-Okay, so it might depend on the material

0:15:12.338,0:15:16.828
and it certainly does, which is actually why I was careful

0:15:16.828,0:15:18.883
to construct them out of the same piece of paper,

0:15:18.883,0:15:21.735
so let me put this.

0:15:21.735,0:15:24.840
Material...

0:15:24.840,0:15:28.079
So the surface roughness.

0:15:28.079,0:15:30.964
[indisctinct question]

0:15:33.564,0:15:36.005
-Okay, so whether they fall vertically or downward.

0:15:36.005,0:15:37.367
Yeah, that's true.

0:15:37.367,0:15:40.045
So it might depend on the way I drop them.

0:15:40.045,0:15:42.228
So to make us not have to worry about that,

0:15:42.228,0:15:46.812
I'll just drop them simultaniously, pointing downward.

0:15:46.827,0:15:52.540
So the fall configuration.

0:15:52.601,0:15:57.024
So there's all these other variables.

0:15:57.024,0:15:59.362
Okay, so let's do the experiment and then I'll come back to your question.

0:15:59.362,0:16:05.950
Okay, so let's do the experiement this way

0:16:09.970,0:16:14.408
so I'll stand on the table

0:16:14.408,0:16:23.104
and pray that I have matching socks on with is sort of 80% these days.

0:16:23.104,0:16:26.363
It's increased.

0:16:26.363,0:16:28.155
And I will drop them on the count of 3.

0:16:28.155,0:16:29.336
1--

0:16:29.336,0:16:33.861
Are they both, the points, about the same level?

0:16:33.861,0:16:35.775
They look sort of to me but

0:16:35.775,0:16:40.906
my depth perception is actually quite bad

0:16:40.906,0:16:43.312
so is that about equal?

0:16:43.312,0:16:46.978
Okay, so 1, 2, 3.

0:16:46.978,0:16:48.709
Simulateous.

0:16:48.709,0:16:52.895
Okay, so there you have choice C.

0:16:52.956,0:16:55.246
Interesting consequence of that.

0:16:55.246,0:16:58.300
So what that shows is that

0:16:58.300,0:17:01.837
drag in this case is proportional to area.

0:17:01.837,0:17:05.512
It turns out, that that's not always the case.

0:17:05.512,0:17:08.421
So drag very often,

0:17:08.421,0:17:10.260
well, not very often in everyday life,

0:17:10.260,0:17:16.178
but very easily can be proportional to...

0:17:20.835,0:17:23.125
proportional to size.

0:17:23.125,0:17:26.644
And you don't know ahead of time which one it's gonna be.

0:17:26.644,0:17:30.851
So it vari--- so it turns out at slow speeds,

0:17:30.851,0:17:31.687
low Reynold's number

0:17:31.687,0:17:32.679
this is true.

0:17:32.679,0:17:34.953
Turns out at high Reynold's number, this is true.

0:17:34.969,0:17:37.409
And this is the simplest experiment to show that.

0:17:37.409,0:17:40.526
So what this shows is that drag is proportional to area

0:17:40.526,0:17:42.895
so with the same velocity,

0:17:42.895,0:17:50.055
the extra weight is balanced by the extra drag force.

0:17:50.055,0:17:52.445
Exactly, four to one.

0:17:52.445,0:18:00.349
And what that shows now--the consequence--is that

0:18:02.918,0:18:07.663
I'm gonna replace the proportional with a twittle.

0:18:07.663,0:18:09.286
So it has an area in it,

0:18:09.286,0:18:12.057
so I'm gonna get something with the correct units in it.

0:18:12.057,0:18:13.988
So it has an area in it

0:18:13.988,0:18:16.440
and now you have left the play with

0:18:16.440,0:18:20.156
density, speed, and viscosity.

0:18:20.156,0:18:23.814
So now let's actually construct the drag force as a result of that.

0:18:23.814,0:18:27.499
So we know from the experiment, it's proportional to area.

0:18:28.392,0:18:29.763
And now among these,

0:18:29.763,0:18:34.152
so this here is the kinematic viscosity,

0:18:34.152,0:18:39.887
which is the one you may be more familiar with divided by row, the density.

0:18:39.887,0:18:44.214
So, we got to put some of these guys in, some of these guys in,

0:18:44.214,0:18:46.022
and some of these guys in.

0:18:46.022,0:18:49.091
And let the units come in as a force.

0:18:49.091,0:18:51.842
Well, one of them we can do right away.

0:18:51.842,0:18:57.004
There's how many powers of mass over on this side?

0:18:57.004,0:18:58.842
In a force, just one.

0:18:58.842,0:19:00.142
Right, and there's one here.

0:19:00.142,0:19:02.694
So we need to get one over on this side.

0:19:02.694,0:19:04.924
Now, among all these guys, which of them have mass in them?

0:19:05.017,0:19:07.600
Not this one, 'cause you divided them all out.

0:19:07.600,0:19:09.284
Not velocity,

0:19:09.284,0:19:10.984
only density.

0:19:10.984,0:19:12.095
And density is one power of mass,

0:19:12.095,0:19:15.564
so you have to put one density.

0:19:15.564,0:19:17.759
Question?

0:19:17.759,0:19:19.244
[indistinct question]

0:19:19.244,0:19:21.555
So this is a force.

0:19:21.555,0:19:22.602
Good question.

0:19:22.602,0:19:24.474
So drag is a force.

0:19:24.474,0:19:32.583
So this is just newtons or uh, mass legth per time square.

0:19:32.583,0:19:34.705
Does it help?

0:19:34.705,0:19:38.250
So it's just newtons.

0:19:38.250,0:19:41.720
In SI Newtons or in general, mass length per time squared.

0:19:41.720,0:19:46.224
So mass times an acceleration.

0:19:46.224,0:19:50.441
Okay, so now, we've matched the units of mass

0:19:50.441,0:19:54.428
and there's-- but we haven't matched the units of time yet.

0:19:54.428,0:19:56.165
So let's sort out the time.

0:19:56.165,0:19:58.515
There's no time here, there's not time there.

0:20:00.190,0:20:01.865
There's T to the minus 2 there.

9:59:59.000,9:59:59.000
Well -- what can we do about that?

9:59:59.000,9:59:59.000
We have to match -- We have to throw in some v and some nu (viscosity)

9:59:59.000,9:59:59.000
And the problem is we don't know how much

9:59:59.000,9:59:59.000
So the time doesn't helps us enough

9:59:59.000,9:59:59.000
Turns out, to make the time and the length work

9:59:59.000,9:59:59.000
The simultaneous constraint

9:59:59.000,9:59:59.000
The only way we can do it is that

9:59:59.000,9:59:59.000
Okay, making the same argument

9:59:59.000,9:59:59.000
Just to get the masses to match, the legths to match and the times to match

9:59:59.000,9:59:59.000
This is the only way to do it

9:59:59.000,9:59:59.000
So you don't have any viscosity

9:59:59.000,9:59:59.000
So actually that's the simplest experiment I know

9:59:59.000,9:59:59.000
To show that the drag at high speed, most flows are actually high speed,

9:59:59.000,9:59:59.000
High Reynolds number

9:59:59.000,9:59:59.000
Is independent from viscosity

9:59:59.000,9:59:59.000
So it's ro, A, v squared

9:59:59.000,9:59:59.000
And that is a great result because it tells you a lot of stuff

9:59:59.000,9:59:59.000
About everyday flows and everyday life

9:59:59.000,9:59:59.000
Like for example, why did people reduced speed

9:59:59.000,9:59:59.000
Speed limit on the highway back in the 70's,

9:59:59.000,9:59:59.000
To conserve gas

9:59:59.000,9:59:59.000
Well, on the highway

9:59:59.000,9:59:59.000
You're burning gasoline to fight drag

9:59:59.000,9:59:59.000
So if you reduce the speed

9:59:59.000,9:59:59.000
You reduce the drag,

9:59:59.000,9:59:59.000
You reduce the amount of gasoline

9:59:59.000,9:59:59.000
In particular, if reduce speed by 20%,

9:59:59.000,9:59:59.000
You reduce v squared by 40%

9:59:59.000,9:59:59.000
Which reduces drag by 40%

9:59:59.000,9:59:59.000
Decreased gas consumption by 40%

9:59:59.000,9:59:59.000
So you can these things right way, just by a simple formula

9:59:59.000,9:59:59.000
Which is a imediate consequence of this experiment

9:59:59.000,9:59:59.000
Now, turns out, this -- how do you get that to work?

9:59:59.000,9:59:59.000
This is the low Reynolds number limit

9:59:59.000,9:59:59.000
You can't deduce it from this experiment, but, if you know that this is true, you can make the same argument

9:59:59.000,9:59:59.000
And figure out, how the drag force varies for low Reynolds number

9:59:59.000,9:59:59.000
Okay, now let's just check wheter this formula here

9:59:59.000,9:59:59.000
That we deduced, works at all

9:59:59.000,9:59:59.000
So the folow up question is the following

9:59:59.000,9:59:59.000
Which is that I have -- 1, 2, 3, 4

9:59:59.000,9:59:59.000
Here on this side, I have 4 small cones

9:59:59.000,9:59:59.000
They're all identical to this small cone

9:59:59.000,9:59:59.000
So 1 small cone, 2 small cones, 3 small cones, 4 small cones

9:59:59.000,9:59:59.000
So I'm gonna stack all 4 small cones, into a thick small cone

9:59:59.000,9:59:59.000
And I'm gonna race it against one small cone

9:59:59.000,9:59:59.000
So the question is: what is the ratio of these guys' terminal speeds?

9:59:59.000,9:59:59.000
So let's call v4 and v1

9:59:59.000,9:59:59.000
So, 4...

9:59:59.000,9:59:59.000
Okay, so, what is the ratio of their terminal speeds?

9:59:59.000,9:59:59.000
1/4, 1/2, 1, 2 or 4?

9:59:59.000,9:59:59.000
So, talk to your neighboor for just a minute, we'll take a quick vote and we'll do the experiment

9:59:59.000,9:59:59.000
Okay, so let's take a vote and then we'll do the experiment

9:59:59.000,9:59:59.000
1/4?

9:59:59.000,9:59:59.000
Who votes for 1/4 ratio?

9:59:59.000,9:59:59.000
Who votes for 1/2?

9:59:59.000,9:59:59.000
1?

9:59:59.000,9:59:59.000
2?

9:59:59.000,9:59:59.000
It's about 35...

9:59:59.000,9:59:59.000
4?

9:59:59.000,9:59:59.000
Oh, 10

9:59:59.000,9:59:59.000
Okay, so, let's do the experiment

9:59:59.000,9:59:59.000
1, 2, 3, 4 of them

9:59:59.000,9:59:59.000
Okay so now let me drop them like --- that

9:59:59.000,9:59:59.000
Well it's kinda of hard to tell isn't it?

9:59:59.000,9:59:59.000
So that was actually not well designed experiment, right?

9:59:59.000,9:59:59.000
Because you actually have to get it out of timer and decide wich one is going faster

9:59:59.000,9:59:59.000
And measure how long it took

9:59:59.000,9:59:59.000
It would be nice if had a way that was just like the other experiment

9:59:59.000,9:59:59.000
What was nice about the other experiment is when I drop them,

9:59:59.000,9:59:59.000
You got the answer, by the fact that they hit simultaneously

9:59:59.000,9:59:59.000
So if we can make them hit simultaneously

9:59:59.000,9:59:59.000
Then that would be nice, now what do I have to do to do that?

9:59:59.000,9:59:59.000
Well I either have to -- Yeah -- I either have to switch their heights

9:59:59.000,9:59:59.000
4 to 1 or 2 to 1

9:59:59.000,9:59:59.000
So, let's try 4 to 1

9:59:59.000,9:59:59.000
Okay -- [laughter] -- Is that sort of 4 to 1?

9:59:59.000,9:59:59.000
No? What do I have to do?

9:59:59.000,9:59:59.000
This guy got go down

9:59:59.000,9:59:59.000
This is where my depth perception really fails me

9:59:59.000,9:59:59.000
So I only have a monocular vision. I can see with both eyes, but I don't binocular fuse

9:59:59.000,9:59:59.000
So I can't tell depth

9:59:59.000,9:59:59.000
[Indistinguishable suggestion from aluminum]

9:59:59.000,9:59:59.000
Oh that's true