1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:03,970 Commons license. 3 00:00:03,970 --> 00:00:06,910 Your support will help MIT OpenCourseWare continue to 4 00:00:06,910 --> 00:00:10,660 offer high-quality educational resources for free. 5 00:00:10,660 --> 00:00:13,460 To make a donation or view additional materials from 6 00:00:13,460 --> 00:00:17,390 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,390 --> 00:00:18,640 ocw.mit.edu. 8 00:00:21,140 --> 00:00:25,180 Due to technical difficulties, only a portion of lecture one 9 00:00:25,180 --> 00:00:27,100 is available for viewing. 10 00:00:27,100 --> 00:00:29,380 PROFESSOR: Welcome to Teaching College-Level Science and 11 00:00:29,380 --> 00:00:31,340 engineering. 12 00:00:31,340 --> 00:00:35,530 The title contains the word teaching, which may spark some 13 00:00:35,530 --> 00:00:36,460 questions in your mind. 14 00:00:36,460 --> 00:00:40,270 For example, is teaching just an art? 15 00:00:40,270 --> 00:00:44,240 Or is it something that's just something you're born with? 16 00:00:44,240 --> 00:00:47,970 In which case, either you have it or you don't have it. 17 00:00:47,970 --> 00:00:50,630 Well, obviously, I don't believe that, or I wouldn't be 18 00:00:50,630 --> 00:00:51,820 teaching a course on it. 19 00:00:51,820 --> 00:00:53,210 What would be the point? 20 00:00:53,210 --> 00:00:56,770 Or is it purely a science where there's a set of 21 00:00:56,770 --> 00:00:59,790 equations and procedures to learn, and then all of a 22 00:00:59,790 --> 00:01:02,260 sudden, you'll be an excellent teacher? 23 00:01:02,260 --> 00:01:04,599 Well, actually, it's neither. 24 00:01:04,599 --> 00:01:05,670 And it's both. 25 00:01:05,670 --> 00:01:09,910 It's things that we're all born with, on the one hand. 26 00:01:09,910 --> 00:01:13,290 And there're also procedures and techniques and ways of 27 00:01:13,290 --> 00:01:16,020 thinking that will improve how you teach and 28 00:01:16,020 --> 00:01:17,260 that we can all learn. 29 00:01:17,260 --> 00:01:20,540 So it's a happy mix, my favorite mix, 30 00:01:20,540 --> 00:01:23,140 an art and a science. 31 00:01:23,140 --> 00:01:26,160 So another example that's an art and the 32 00:01:26,160 --> 00:01:29,500 science is book design. 33 00:01:29,500 --> 00:01:33,110 So compared to, for example, just pure art-- 34 00:01:33,110 --> 00:01:34,940 painting, say modern painting-- 35 00:01:34,940 --> 00:01:39,770 very unconstrained, versus say biology procedures in the 36 00:01:39,770 --> 00:01:44,930 laboratory, very, very closely specified. 37 00:01:44,930 --> 00:01:46,410 It's somewhere in between. 38 00:01:46,410 --> 00:01:48,900 There's an art-- 39 00:01:48,900 --> 00:01:52,740 all the arts of color, space-- 40 00:01:52,740 --> 00:01:56,310 but they all have to be used together to achieve a 41 00:01:56,310 --> 00:01:57,740 particular purpose. 42 00:01:57,740 --> 00:02:00,800 So again, in there, there's some beautifully designed 43 00:02:00,800 --> 00:02:03,270 books and some not so beautifully designed books. 44 00:02:03,270 --> 00:02:06,740 And there're principles behind that that we can use to design 45 00:02:06,740 --> 00:02:07,250 good books. 46 00:02:07,250 --> 00:02:10,060 And similarly, there are principles we can use to 47 00:02:10,060 --> 00:02:11,840 design good teaching. 48 00:02:11,840 --> 00:02:14,600 So the whole point of this semester is to design good 49 00:02:14,600 --> 00:02:16,350 teaching and how you do that. 50 00:02:16,350 --> 00:02:20,000 And rather than me give you a big long theory about it, 51 00:02:20,000 --> 00:02:23,570 because actually there isn't really theory so much in the 52 00:02:23,570 --> 00:02:26,960 equivalent to, say, Einstein's theory of relativity. 53 00:02:26,960 --> 00:02:29,120 But there's principles to learn. 54 00:02:29,120 --> 00:02:33,620 The best way to learn those principles is with an example. 55 00:02:33,620 --> 00:02:37,930 So what we're going to do today is I'm going to do an 56 00:02:37,930 --> 00:02:40,750 example of teaching with you. 57 00:02:40,750 --> 00:02:43,850 We're going to do a sort of maybe slightly sped-up version 58 00:02:43,850 --> 00:02:47,420 of what we would normally do, say, if we were actually using 59 00:02:47,420 --> 00:02:49,050 this example in a class. 60 00:02:49,050 --> 00:02:51,770 Then we're going to analyze why it was done that way. 61 00:02:51,770 --> 00:02:54,990 And from that analysis, general principles of teaching 62 00:02:54,990 --> 00:02:57,390 will come out that will be addressed 63 00:02:57,390 --> 00:02:58,670 throughout the semester. 64 00:02:58,670 --> 00:03:01,530 And they'll be addressed in the context 65 00:03:01,530 --> 00:03:03,050 of particular tasks. 66 00:03:03,050 --> 00:03:07,180 Like for example, how to make slides that are useful for 67 00:03:07,180 --> 00:03:10,920 teaching, how to use a blackboard, how to teach 68 00:03:10,920 --> 00:03:13,660 equations, how to design a whole 69 00:03:13,660 --> 00:03:15,830 course, how to make problems. 70 00:03:15,830 --> 00:03:19,960 So all of those tasks will be the week by week subjects. 71 00:03:19,960 --> 00:03:22,720 And in each task, all of the principles that we're going to 72 00:03:22,720 --> 00:03:26,670 talk about now will show up in those tasks. 73 00:03:26,670 --> 00:03:30,060 And you'll see the principles illustrated repeatedly. 74 00:03:30,060 --> 00:03:34,290 OK, so the problem-- 75 00:03:34,290 --> 00:03:36,420 one of my favorites. 76 00:03:36,420 --> 00:03:39,300 So these are two cones. 77 00:03:39,300 --> 00:03:42,560 One has twice the dimensions of the other cone. 78 00:03:42,560 --> 00:03:44,310 So let me show you how I made the cones. 79 00:03:50,460 --> 00:03:55,960 So I printed out a circle and just cut out one quarter of 80 00:03:55,960 --> 00:03:58,240 the circle. 81 00:03:58,240 --> 00:04:00,846 And then I taped this edge to that edge. 82 00:04:05,410 --> 00:04:10,520 Or in mathematician speak, I identified the edges, which 83 00:04:10,520 --> 00:04:13,220 now I know means I taped the edges together. 84 00:04:13,220 --> 00:04:16,200 And then you get a cone, like that. 85 00:04:16,200 --> 00:04:19,850 So this cone and the other cone were cut out of the same 86 00:04:19,850 --> 00:04:22,440 sheet of paper except this one has twice the linear 87 00:04:22,440 --> 00:04:24,280 dimensions in its circle. 88 00:04:24,280 --> 00:04:28,990 So I think this circle was 7 centimeters in radius, and 89 00:04:28,990 --> 00:04:32,820 this is 3 and 1/2 centimeters in radius. 90 00:04:32,820 --> 00:04:35,280 So other than that, they're the same. 91 00:04:35,280 --> 00:04:38,870 And the question is, which one has the 92 00:04:38,870 --> 00:04:40,230 higher terminal velocity? 93 00:04:40,230 --> 00:04:41,860 Or are they about comparable? 94 00:04:41,860 --> 00:04:44,640 So in particular, the question is this. 95 00:04:44,640 --> 00:04:45,960 So I'm going to drop them. 96 00:04:45,960 --> 00:04:48,980 And the question is, what's their ratio of their terminal 97 00:04:48,980 --> 00:04:50,230 velocities? 98 00:05:01,710 --> 00:05:05,110 So the ratio of the big cone's terminal velocity to the small 99 00:05:05,110 --> 00:05:07,430 cone's terminal velocity is equal to what. 100 00:05:07,430 --> 00:05:13,095 And you get choices along this axis. 101 00:05:13,095 --> 00:05:14,419 So here is-- 102 00:05:37,900 --> 00:05:40,450 OK, so those are the five regions to choose from. 103 00:05:46,350 --> 00:05:48,070 So you have five choices for the ratio, 104 00:05:48,070 --> 00:05:49,780 basically roughly 1/4. 105 00:05:49,780 --> 00:05:53,415 This is some range here, because nothing's exact. 106 00:05:53,415 --> 00:05:56,880 And we're certainly not going to do an exact experiment. 107 00:05:56,880 --> 00:06:01,890 Roughly 1/2, roughly 1, roughly 2, or roughly 4. 108 00:06:01,890 --> 00:06:04,100 So does everyone understand the question? 109 00:06:04,100 --> 00:06:05,920 Because you're going to get to try it yourself. 110 00:06:08,500 --> 00:06:10,072 Question about the question? 111 00:06:10,072 --> 00:06:11,758 AUDIENCE: If you could restate it-- actually, there was a 112 00:06:11,758 --> 00:06:12,964 sign-up sheet going around which distracted me. 113 00:06:12,964 --> 00:06:15,940 So I sort of lost the-- 114 00:06:15,940 --> 00:06:17,840 PROFESSOR: Sure. 115 00:06:17,840 --> 00:06:18,840 Could I restate the question? 116 00:06:18,840 --> 00:06:20,390 No problem. 117 00:06:20,390 --> 00:06:23,480 So I'm going to drop them, just like this. 118 00:06:23,480 --> 00:06:24,050 No tricks-- 119 00:06:24,050 --> 00:06:27,280 I'm not going to flip this one around or anything. 120 00:06:27,280 --> 00:06:29,710 And the question is, what's the ratio of 121 00:06:29,710 --> 00:06:30,910 their terminal speed? 122 00:06:30,910 --> 00:06:34,770 So right away, as soon as you let go of them, they come to a 123 00:06:34,770 --> 00:06:37,390 steady speed, which is their terminal velocity. 124 00:06:37,390 --> 00:06:40,470 And the question is, how do the terminal speeds of the big 125 00:06:40,470 --> 00:06:42,700 one and the small one differ? 126 00:06:42,700 --> 00:06:46,090 OK, so in particular, the question is, what's the ratio? 127 00:06:46,090 --> 00:06:49,482 And there's five choices for them. 128 00:06:49,482 --> 00:06:51,384 Does that help? 129 00:06:51,384 --> 00:06:51,866 AUDIENCE: Yeah. 130 00:06:51,866 --> 00:06:54,280 So what were the dimension of them again? 131 00:06:54,280 --> 00:06:56,440 PROFESSOR: So this guy is-- 132 00:06:56,440 --> 00:07:00,230 he was cut out of a circle who was 7 centimeters in radius. 133 00:07:00,230 --> 00:07:02,710 And this guy was cut out of a circle who was 3 and 1/2 134 00:07:02,710 --> 00:07:05,640 centimeters in radius. 135 00:07:05,640 --> 00:07:08,530 And then I was also very careful to use-- 136 00:07:08,530 --> 00:07:08,983 let's see. 137 00:07:08,983 --> 00:07:09,550 Did I do this right? 138 00:07:09,550 --> 00:07:14,510 Yeah, I used to half the with of tape on the small guy as I 139 00:07:14,510 --> 00:07:18,950 did on the big guy, just to get it really very perfectly 140 00:07:18,950 --> 00:07:20,650 scale invariant. 141 00:07:20,650 --> 00:07:22,430 OK any questions about the question? 142 00:07:27,170 --> 00:07:31,220 OK, so think to yourself for about 30 seconds or so, just 143 00:07:31,220 --> 00:07:34,340 to induct yourself into the problem. 144 00:07:34,340 --> 00:07:36,430 And then we'll take a vote. 145 00:07:36,430 --> 00:07:38,870 And then you'll have a chance to discuss it with each other. 146 00:08:18,840 --> 00:08:20,410 OK, let's just take a vote. 147 00:08:20,410 --> 00:08:24,790 So I recognize I haven't given you at all enough time to come 148 00:08:24,790 --> 00:08:27,120 up with an exact answer or calculate everything. 149 00:08:27,120 --> 00:08:28,980 And that's by design. 150 00:08:28,980 --> 00:08:31,400 So let's just get a straw poll. 151 00:08:31,400 --> 00:08:33,059 And then you'll have a chance to argue with your 152 00:08:33,059 --> 00:08:34,070 neighbor about it. 153 00:08:34,070 --> 00:08:37,900 So who votes for 1/4, which is that the-- 154 00:08:37,900 --> 00:08:38,320 so let's see-- 155 00:08:38,320 --> 00:08:42,090 1, 2, 3, 4, 5, 6. 156 00:08:42,090 --> 00:08:44,130 OK, 6. 157 00:08:44,130 --> 00:08:47,234 Who votes for 1/2? 158 00:08:47,234 --> 00:08:50,314 1, 2, 3, 4, 5, 6, 7-- 159 00:08:53,050 --> 00:08:53,950 12. 160 00:08:53,950 --> 00:08:55,200 Who votes for C? 161 00:08:58,800 --> 00:09:00,750 22. 162 00:09:00,750 --> 00:09:03,860 Who votes for D? 163 00:09:03,860 --> 00:09:04,930 No takers. 164 00:09:04,930 --> 00:09:07,660 No takers for D. OK, how about E? 165 00:09:11,060 --> 00:09:11,710 OK. 166 00:09:11,710 --> 00:09:16,830 So now find a neighbor or two, one or two neighbors. 167 00:09:16,830 --> 00:09:18,290 Introduce yourself to your neighbor. 168 00:09:18,290 --> 00:09:20,900 And also, by the way, unless you're taking notes on your 169 00:09:20,900 --> 00:09:22,980 laptop and really insist on doing that, if you could close 170 00:09:22,980 --> 00:09:25,840 your laptop, that would be very helpful for the purpose 171 00:09:25,840 --> 00:09:28,890 of discussion in this whole course. 172 00:09:28,890 --> 00:09:30,800 So find a neighbor or two. 173 00:09:30,800 --> 00:09:32,290 Introduce yourself. 174 00:09:32,290 --> 00:09:34,490 You'll be getting a chance to meet graduate students from 175 00:09:34,490 --> 00:09:35,520 across the institute. 176 00:09:35,520 --> 00:09:37,420 This is a great opportunity. 177 00:09:37,420 --> 00:09:39,790 And try to convince them of your answer, especially if you 178 00:09:39,790 --> 00:09:40,740 have a different answer. 179 00:09:40,740 --> 00:09:43,450 Or if you happen to share an answer, well, see if you can 180 00:09:43,450 --> 00:09:44,960 figure out why you're sure of it. 181 00:09:44,960 --> 00:09:47,770 Or if you're not sure of it, see if you can settle that. 182 00:09:47,770 --> 00:09:51,010 OK, so discussion time. 183 00:09:51,010 --> 00:09:53,630 And if you have any questions that come up as you're 184 00:09:53,630 --> 00:09:54,860 discussing, raise your hand. 185 00:09:54,860 --> 00:09:56,110 And I'll come and wander over. 186 00:09:59,250 --> 00:10:02,850 Meanwhile I also handed out feedback sheets for the end of 187 00:10:02,850 --> 00:10:05,920 the session, which I'll ask you to just spend a minute on 188 00:10:05,920 --> 00:10:06,380 at the end. 189 00:10:06,380 --> 00:10:10,020 But you'll notice one of the questions is, what's the most 190 00:10:10,020 --> 00:10:11,240 confusing thing? 191 00:10:11,240 --> 00:10:13,690 So if anything really confusing comes up during the 192 00:10:13,690 --> 00:10:15,480 whole session, you can just put it right then. 193 00:10:15,480 --> 00:10:16,860 You don't have to wait till the end. 194 00:10:16,860 --> 00:10:18,880 Or if there's something you really liked or hated-- 195 00:10:18,880 --> 00:10:21,680 that's question two-- you can put that whenever it happens 196 00:10:21,680 --> 00:10:23,170 to come up. 197 00:10:23,170 --> 00:10:26,700 But vote number two, and then we'll take some reasons. 198 00:10:26,700 --> 00:10:29,530 So 1/4? 199 00:10:32,160 --> 00:10:36,220 1, 2, 3. 200 00:10:36,220 --> 00:10:39,060 OK, 4. 201 00:10:39,060 --> 00:10:41,496 1/2-- 202 00:10:41,496 --> 00:10:43,020 the halves don't have it. 203 00:10:43,020 --> 00:10:44,140 Oh, no, there's 1. 204 00:10:44,140 --> 00:10:44,710 Oh, there's 2. 205 00:10:44,710 --> 00:10:45,360 OK great-- 206 00:10:45,360 --> 00:10:49,140 3, 4, 5, 6. 207 00:10:49,140 --> 00:10:50,880 Equal? 208 00:10:50,880 --> 00:10:54,250 OK, so that's about-- let's call it 30. 209 00:10:54,250 --> 00:10:55,500 2? 210 00:10:57,880 --> 00:11:00,670 And 4. 211 00:11:00,670 --> 00:11:04,280 OK so thanks for the votes. 212 00:11:04,280 --> 00:11:06,620 Let's take reasons for any of them. 213 00:11:06,620 --> 00:11:07,715 I'll take reasons for any of them, and 214 00:11:07,715 --> 00:11:09,690 I'll put them up here. 215 00:11:09,690 --> 00:11:11,090 You don't even have to agree with the reason. 216 00:11:11,090 --> 00:11:13,800 It's just something you guys discussed and thought maybe 217 00:11:13,800 --> 00:11:14,825 was plausible. 218 00:11:14,825 --> 00:11:16,220 AUDIENCE: C seems to have [INAUDIBLE]. 219 00:11:21,132 --> 00:11:23,430 When you do this kind of activities, there is always 220 00:11:23,430 --> 00:11:24,955 some guys who have seen it before. 221 00:11:24,955 --> 00:11:26,370 And he may choose to spoil it. 222 00:11:26,370 --> 00:11:28,803 So I may want to know what you would do in 223 00:11:28,803 --> 00:11:29,820 that kind of situation. 224 00:11:29,820 --> 00:11:30,965 PROFESSOR: So you're-- 225 00:11:30,965 --> 00:11:32,215 hm. 226 00:11:33,830 --> 00:11:35,080 I'm not sure how to phrase this. 227 00:11:38,130 --> 00:11:41,470 Let me just take other comments. 228 00:11:41,470 --> 00:11:43,560 I'll come to it afterwards. 229 00:11:43,560 --> 00:11:46,370 Other comments for any of the reasons? 230 00:11:46,370 --> 00:11:47,960 So again, it doesn't have to be things you necessarily 231 00:11:47,960 --> 00:11:50,310 believe, but things that are plausible. 232 00:11:50,310 --> 00:11:53,240 And that's actually more instructive than what you 233 00:11:53,240 --> 00:11:54,530 think is for sure right. 234 00:11:54,530 --> 00:11:57,060 Because now you're trying to figure out what might be true. 235 00:11:57,060 --> 00:11:58,830 And you're expanding the ways you're thinking. 236 00:11:58,830 --> 00:11:59,670 Yeah? 237 00:11:59,670 --> 00:12:02,900 AUDIENCE: C, because they have identical mass to 238 00:12:02,900 --> 00:12:04,830 surface area ratio. 239 00:12:04,830 --> 00:12:05,170 PROFESSOR: OK. 240 00:12:05,170 --> 00:12:09,490 C, so mass to area ratio is the same. 241 00:12:13,930 --> 00:12:16,160 OK, can people think of plausible reasons 242 00:12:16,160 --> 00:12:17,410 against that argument? 243 00:12:20,860 --> 00:12:21,260 Yes. 244 00:12:21,260 --> 00:12:23,602 AUDIENCE: So I have no idea what the actual formula is for 245 00:12:23,602 --> 00:12:24,416 calculating it. 246 00:12:24,416 --> 00:12:27,233 If there was a square in there, then that would 247 00:12:27,233 --> 00:12:29,540 [INAUDIBLE]. 248 00:12:29,540 --> 00:12:29,840 PROFESSOR: Right. 249 00:12:29,840 --> 00:12:34,420 So I'll call this Not C. So suppose the formula actually 250 00:12:34,420 --> 00:12:37,270 depended on the square root of A or square of A or 251 00:12:37,270 --> 00:12:39,740 something like that. 252 00:12:39,740 --> 00:12:42,600 It's, say, one chance out of three that it has A to the 253 00:12:42,600 --> 00:12:43,830 first power here. 254 00:12:43,830 --> 00:12:47,460 It could have A to the 1/2 or A to the 2. 255 00:12:47,460 --> 00:13:00,820 So could be m over A to the k for k not equal to 1. 256 00:13:03,580 --> 00:13:09,310 Others for or against C, intuitive reasons, or for any 257 00:13:09,310 --> 00:13:10,560 of the others? 258 00:13:18,070 --> 00:13:19,640 So hopefully that's-- 259 00:13:19,640 --> 00:13:20,360 oh, yes. 260 00:13:20,360 --> 00:13:20,580 Go ahead. 261 00:13:20,580 --> 00:13:21,830 AUDIENCE: [INAUDIBLE] 262 00:13:24,680 --> 00:13:26,998 The air resistance scales with the area. 263 00:13:26,998 --> 00:13:29,428 And the gravitational force would normally scale with the 264 00:13:29,428 --> 00:13:31,860 volume, [? except that it's ?] in the surface, [INAUDIBLE]. 265 00:13:31,860 --> 00:13:34,070 PROFESSOR: OK, so let's see. 266 00:13:34,070 --> 00:13:39,600 F drag proportional to area and weight 267 00:13:39,600 --> 00:13:40,890 proportional to area. 268 00:13:40,890 --> 00:13:43,155 So that's an argument for which choice? 269 00:13:43,155 --> 00:13:43,490 AUDIENCE: For C. 270 00:13:43,490 --> 00:13:44,740 PROFESSOR: For C, OK. 271 00:13:47,360 --> 00:13:50,490 How do you know that the drag scales with the area? 272 00:13:50,490 --> 00:13:54,270 Maybe it scales with square root of area. 273 00:13:58,350 --> 00:13:59,840 Any arguments pro or con? 274 00:14:05,220 --> 00:14:07,158 OK, yeah. 275 00:14:07,158 --> 00:14:09,553 AUDIENCE: You could argue that it scales with the area 276 00:14:09,553 --> 00:14:13,385 because then you just break it up into decimal pieces. 277 00:14:13,385 --> 00:14:15,780 Each one has the same force intensity. 278 00:14:15,780 --> 00:14:21,600 PROFESSOR: OK, so for this, let's say there's a thought 279 00:14:21,600 --> 00:14:22,830 experiment of subdividing. 280 00:14:22,830 --> 00:14:24,640 So I'll just note that as Subdividing Thought 281 00:14:24,640 --> 00:14:25,890 Experiment. 282 00:14:31,450 --> 00:14:32,360 OK, yeah. 283 00:14:32,360 --> 00:14:35,789 AUDIENCE: But then if you have some weird shape, the air has 284 00:14:35,789 --> 00:14:37,799 to flow through hitting some pieces and then flow through 285 00:14:37,799 --> 00:14:38,666 the rest of the pieces. 286 00:14:38,666 --> 00:14:40,290 So that [INAUDIBLE] 287 00:14:40,290 --> 00:14:41,000 may not work. 288 00:14:41,000 --> 00:14:42,330 [INAUDIBLE] 289 00:14:42,330 --> 00:14:46,510 PROFESSOR: So it may depend on the geometry. 290 00:14:46,510 --> 00:14:48,665 So I'll put that up here as Geometry. 291 00:14:51,700 --> 00:14:54,370 What else might depend on? 292 00:14:54,370 --> 00:14:58,090 For example, is air resistance, say, always 293 00:14:58,090 --> 00:14:59,340 proportional to area? 294 00:15:02,964 --> 00:15:04,443 Hm. 295 00:15:04,443 --> 00:15:05,429 Yep? 296 00:15:05,429 --> 00:15:07,894 AUDIENCE: It could depend on the material, surface 297 00:15:07,894 --> 00:15:08,890 roughness or something. 298 00:15:08,890 --> 00:15:12,030 PROFESSOR: OK, so it might depend on the material. 299 00:15:12,030 --> 00:15:15,900 And it certainly does, which is actually one reason I was 300 00:15:15,900 --> 00:15:17,350 very careful to construct them out of the 301 00:15:17,350 --> 00:15:18,850 same piece of paper. 302 00:15:18,850 --> 00:15:21,495 So let me put this is the material. 303 00:15:24,970 --> 00:15:26,900 So the surface roughness. 304 00:15:26,900 --> 00:15:27,363 Yeah? 305 00:15:27,363 --> 00:15:29,909 AUDIENCE: Well, this may not be relevant given how you said 306 00:15:29,909 --> 00:15:30,604 you dropped them. 307 00:15:30,604 --> 00:15:33,090 But it also might depend on [? exactly how they ?] fall. 308 00:15:33,090 --> 00:15:34,990 PROFESSOR: Right, OK, so whether they fall vertically 309 00:15:34,990 --> 00:15:35,670 or downward. 310 00:15:35,670 --> 00:15:36,610 Yeah, that's true. 311 00:15:36,610 --> 00:15:38,570 So it might depend on the way I drop them. 312 00:15:38,570 --> 00:15:42,170 So actually, yeah, to make us not have to worry about that, 313 00:15:42,170 --> 00:15:43,820 I'll just drop them 314 00:15:43,820 --> 00:15:46,750 simultaneously pointing downwards. 315 00:15:46,750 --> 00:15:52,550 Yeah, so the fall configuration. 316 00:15:52,550 --> 00:15:53,800 So there's all these other variables. 317 00:15:57,290 --> 00:15:59,595 So let's do the experiment. 318 00:15:59,595 --> 00:16:01,430 Then I'll come back to your question. 319 00:16:09,940 --> 00:16:13,110 So let's do the experiment this way, which is that I will 320 00:16:13,110 --> 00:16:19,380 stand on the table and pray that I have matching socks on, 321 00:16:19,380 --> 00:16:22,440 which is sort of 80% these days. 322 00:16:22,440 --> 00:16:24,200 It's increased. 323 00:16:24,200 --> 00:16:29,290 And I will drop them on the count of three. 324 00:16:29,290 --> 00:16:30,900 Are they both about-- 325 00:16:30,900 --> 00:16:33,450 the points about the same level? 326 00:16:33,450 --> 00:16:37,430 They look sort of to me, but my depth perception is 327 00:16:37,430 --> 00:16:40,180 actually quite bad. 328 00:16:40,180 --> 00:16:43,340 OK, so is that about equal? 329 00:16:43,340 --> 00:16:46,960 OK, one, two, three. 330 00:16:46,960 --> 00:16:48,340 Simultaneous. 331 00:16:48,340 --> 00:16:50,990 OK, so there you have choice C. 332 00:16:50,990 --> 00:16:54,810 So now the interesting consequence of that-- 333 00:16:54,810 --> 00:16:59,610 so what that shows is that drag, in this case, is 334 00:16:59,610 --> 00:17:01,730 proportional to area. 335 00:17:01,730 --> 00:17:05,130 Now, it turns out that that's not always the case. 336 00:17:05,130 --> 00:17:09,589 So drag very often-- well, not very often in everyday life. 337 00:17:09,589 --> 00:17:22,740 But very easily, drag can be proportional to size. 338 00:17:22,740 --> 00:17:24,900 And you don't know ahead of time which one 339 00:17:24,900 --> 00:17:26,430 it's going to be. 340 00:17:26,430 --> 00:17:31,120 So it turns out at slow speeds, low Reynolds number, 341 00:17:31,120 --> 00:17:32,200 this is true. 342 00:17:32,200 --> 00:17:34,480 Turns out at high Reynolds number, this is true. 343 00:17:34,480 --> 00:17:37,420 And this is the simplest experiment to show that. 344 00:17:37,420 --> 00:17:40,090 So what this shows is that drag is proportional to area. 345 00:17:40,090 --> 00:17:45,570 So that with the same velocity, the extra weight is 346 00:17:45,570 --> 00:17:51,020 balanced by the extra drag force by exactly 4 to 1. 347 00:17:51,020 --> 00:17:53,010 And what that shows, now-- 348 00:17:53,010 --> 00:17:54,850 the consequence-- 349 00:17:54,850 --> 00:17:56,100 is that-- 350 00:18:02,730 --> 00:18:07,530 I'm going to replace the proportional with a twiddle. 351 00:18:07,530 --> 00:18:08,990 So it has an area in it. 352 00:18:08,990 --> 00:18:10,010 So I'm just going to get something with the 353 00:18:10,010 --> 00:18:11,470 correct units now. 354 00:18:11,470 --> 00:18:13,140 So it has an area in it. 355 00:18:13,140 --> 00:18:15,570 And now you have left to play with 356 00:18:15,570 --> 00:18:20,130 density, speed, and viscosity. 357 00:18:20,130 --> 00:18:22,720 So now let's actually construct the drag force as a 358 00:18:22,720 --> 00:18:23,500 result of that. 359 00:18:23,500 --> 00:18:28,110 So we know by the experiment it's proportional to area. 360 00:18:28,110 --> 00:18:33,740 And now among these-- so this here is the kinematic 361 00:18:33,740 --> 00:18:37,110 viscosity, which is the one you may be more familiar with 362 00:18:37,110 --> 00:18:40,230 divided by rho, the density. 363 00:18:40,230 --> 00:18:43,590 So we have to put some of these guys in, some of these 364 00:18:43,590 --> 00:18:46,340 guys in, and some of these guys in, and make the units 365 00:18:46,340 --> 00:18:48,310 come out as a force. 366 00:18:48,310 --> 00:18:52,090 Well, one of them we can do right away. 367 00:18:52,090 --> 00:18:56,780 There's how many powers of mass over on this side? 368 00:18:56,780 --> 00:18:58,290 In a force-- just one. 369 00:18:58,290 --> 00:18:59,380 And there's none here, yet. 370 00:18:59,380 --> 00:19:02,650 So we need to get one power of mass on this side. 371 00:19:02,650 --> 00:19:04,350 Now, among all these guys, which of them 372 00:19:04,350 --> 00:19:05,560 have mass in them? 373 00:19:05,560 --> 00:19:07,390 Not this one, because you divided out. 374 00:19:07,390 --> 00:19:08,990 Not velocity. 375 00:19:08,990 --> 00:19:11,500 Only density, and density has one power of mass. 376 00:19:11,500 --> 00:19:12,760 So you have to put one density. 377 00:19:15,440 --> 00:19:16,330 Question. 378 00:19:16,330 --> 00:19:18,830 AUDIENCE: I don't know what the units of drag are. 379 00:19:18,830 --> 00:19:21,280 PROFESSOR: So this is a force. 380 00:19:21,280 --> 00:19:21,800 Good question. 381 00:19:21,800 --> 00:19:23,800 So drag as a force. 382 00:19:23,800 --> 00:19:32,990 So this is just newtons or mass, length per time squared. 383 00:19:32,990 --> 00:19:34,820 Does that help? 384 00:19:34,820 --> 00:19:39,250 So it's just newtons, in SI units. 385 00:19:39,250 --> 00:19:42,230 Or in general, mass length per time squared, so a mass times 386 00:19:42,230 --> 00:19:43,480 an acceleration. 387 00:19:46,980 --> 00:19:51,970 So now, we've matched the units of mass. 388 00:19:51,970 --> 00:19:54,170 But we haven't matched the units of time yet. 389 00:19:54,170 --> 00:19:55,420 So let's sort out the time. 390 00:19:55,420 --> 00:19:56,610 There's no time here. 391 00:19:56,610 --> 00:19:58,140 There's no time there. 392 00:19:58,140 --> 00:20:00,940 There's t to the minus 2 there. 393 00:20:00,940 --> 00:20:03,890 Well, what can we do about that? 394 00:20:06,950 --> 00:20:11,080 We have to throw in some v and some nu. 395 00:20:11,080 --> 00:20:12,960 And the problem is we don't know how much. 396 00:20:12,960 --> 00:20:16,640 So the time doesn't help us enough. 397 00:20:16,640 --> 00:20:20,900 Turns out to make the time and the length work, the 398 00:20:20,900 --> 00:20:27,020 simultaneous constraint, the only way to do it is that. 399 00:20:27,020 --> 00:20:30,580 You make the same argument to get the masses to match, the 400 00:20:30,580 --> 00:20:32,450 lengths to match, and the times to match. 401 00:20:32,450 --> 00:20:33,840 This is the only way to do it. 402 00:20:33,840 --> 00:20:35,790 So you don't have any viscosity. 403 00:20:35,790 --> 00:20:38,880 So actually, that's the simplest experiment I know to 404 00:20:38,880 --> 00:20:41,350 show that the drag at high speed-- 405 00:20:41,350 --> 00:20:43,390 in other words, most flows are actually high speed, high 406 00:20:43,390 --> 00:20:47,670 Reynolds number-- is independent of viscosity. 407 00:20:47,670 --> 00:20:51,510 So it's rho av squared. 408 00:20:51,510 --> 00:20:55,530 And that is a great result, because it tells you all kinds 409 00:20:55,530 --> 00:20:58,290 of stuff about everyday flows in everyday life. 410 00:20:58,290 --> 00:21:01,630 Like for example, why did people reduce the speed limit 411 00:21:01,630 --> 00:21:05,000 on the highway back in the '70s to preserve gas? 412 00:21:05,000 --> 00:21:08,450 Well, on the highway, you're burning 413 00:21:08,450 --> 00:21:11,140 gasoline to fight drag. 414 00:21:11,140 --> 00:21:13,740 So if you reduce the speed, you reduce the drag, you 415 00:21:13,740 --> 00:21:15,050 reduce the amount of gasoline. 416 00:21:15,050 --> 00:21:18,330 So in particular, if you reduce the speed by 20%, you 417 00:21:18,330 --> 00:21:22,385 reduce v squared by 40%, which reduces the drag by 40%. 418 00:21:22,385 --> 00:21:26,260 So you just decreased the gas consumption by about 40%. 419 00:21:26,260 --> 00:21:28,270 So you can see all these things right away just from 420 00:21:28,270 --> 00:21:31,280 this simple formula, which is a immediate consequence of 421 00:21:31,280 --> 00:21:34,430 this experiment. 422 00:21:34,430 --> 00:21:36,670 Now, it turns out this-- 423 00:21:36,670 --> 00:21:37,940 how do you get that to work? 424 00:21:37,940 --> 00:21:39,820 This is the low Reynolds number limit. 425 00:21:39,820 --> 00:21:41,600 You can't deduce it from this experiment. 426 00:21:41,600 --> 00:21:43,990 But if you know that this is true, you can make the same 427 00:21:43,990 --> 00:21:47,520 argument and figure out how the drag force varies for low 428 00:21:47,520 --> 00:21:49,930 Reynolds numbers. 429 00:21:49,930 --> 00:21:54,860 OK, so now let's just check whether this formula here that 430 00:21:54,860 --> 00:21:57,970 we've deduced works at all. 431 00:21:57,970 --> 00:21:59,930 So the follow-up question is the following, 432 00:21:59,930 --> 00:22:02,590 which is that I have-- 433 00:22:02,590 --> 00:22:04,430 one, two, three, four. 434 00:22:04,430 --> 00:22:09,240 Here on this side, I have four small cones. 435 00:22:09,240 --> 00:22:11,520 They're all identical to this small cone. 436 00:22:11,520 --> 00:22:17,040 So I have one small cone, two small cones, three small 437 00:22:17,040 --> 00:22:18,640 cones, four small cones. 438 00:22:18,640 --> 00:22:23,332 So I'm going to stack all four small cones into 439 00:22:23,332 --> 00:22:25,700 a thick small cone. 440 00:22:25,700 --> 00:22:29,680 I'm going to race it against one small cone. 441 00:22:29,680 --> 00:22:33,420 So the question is, what's the ratio of these 442 00:22:33,420 --> 00:22:35,310 guys' terminal speeds? 443 00:22:35,310 --> 00:22:37,100 So let's call it v4 and v1. 444 00:22:41,515 --> 00:22:44,390 So v4-- 445 00:23:10,280 --> 00:23:14,440 OK, so what is the ratio of their terminal speeds? 446 00:23:14,440 --> 00:23:18,020 1/4, 1/2, 1, 2, or 4. 447 00:23:18,020 --> 00:23:20,770 So talk to your neighbor for just a minute. 448 00:23:20,770 --> 00:23:22,040 I'll take a quick vote. 449 00:23:22,040 --> 00:23:24,810 We will do the experiment. 450 00:23:24,810 --> 00:23:27,750 OK, so let's take a vote. 451 00:23:27,750 --> 00:23:30,910 And then we'll do the experiment. 452 00:23:30,910 --> 00:23:32,085 1/4-- 453 00:23:32,085 --> 00:23:36,120 no votes for 1/4 ratio. 454 00:23:36,120 --> 00:23:37,490 Who votes for 1/2? 455 00:23:40,060 --> 00:23:42,810 1? 456 00:23:42,810 --> 00:23:44,560 2? 457 00:23:44,560 --> 00:23:46,300 That's about 35. 458 00:23:46,300 --> 00:23:48,740 4? 459 00:23:48,740 --> 00:23:51,920 About 10. 460 00:23:51,920 --> 00:23:53,670 So let's do the experiment. 461 00:23:58,160 --> 00:23:59,850 One, two, three, four of them. 462 00:24:04,110 --> 00:24:08,400 OK, so now let me drop them like that. 463 00:24:08,400 --> 00:24:10,760 Well, it's kind of hard to tell it, isn't it? 464 00:24:10,760 --> 00:24:13,870 So that was actually not a well-designed experiment, 465 00:24:13,870 --> 00:24:16,910 because you have to actually get out a timer and decide 466 00:24:16,910 --> 00:24:19,650 which one is going faster and measure how long they took. 467 00:24:19,650 --> 00:24:22,360 It would be nice if we had a way that was just like the 468 00:24:22,360 --> 00:24:23,380 other experiment. 469 00:24:23,380 --> 00:24:25,960 What was nice about the other experiment is when I dropped 470 00:24:25,960 --> 00:24:29,730 them, you got the answer by the fact that they hit 471 00:24:29,730 --> 00:24:31,610 simultaneously. 472 00:24:31,610 --> 00:24:34,890 So if we could make them hit simultaneously, then that 473 00:24:34,890 --> 00:24:35,460 would be nice. 474 00:24:35,460 --> 00:24:36,700 Now, what do I have to do to do that? 475 00:24:36,700 --> 00:24:42,270 Well, I have to switch their heights 4 to 1 or 2 to 1. 476 00:24:42,270 --> 00:24:44,105 So let's try 4 to 1. 477 00:24:44,105 --> 00:24:45,410 OK. 478 00:24:45,410 --> 00:24:46,636 Is that sort of 4 to 1? 479 00:24:46,636 --> 00:24:47,330 AUDIENCE: No. 480 00:24:47,330 --> 00:24:47,800 PROFESSOR: No? 481 00:24:47,800 --> 00:24:49,216 What do I have to do? 482 00:24:49,216 --> 00:24:50,090 AUDIENCE: That has to [? go-- ?] 483 00:24:50,090 --> 00:24:51,100 PROFESSOR: This guy's got to go down. 484 00:24:51,100 --> 00:24:52,700 Yeah, see, this is where my depth perception 485 00:24:52,700 --> 00:24:53,420 really fails me. 486 00:24:53,420 --> 00:24:56,710 So I only have monocular vision. 487 00:24:56,710 --> 00:24:59,110 I can see with both eyes, but I don't binocular fuse, so I 488 00:24:59,110 --> 00:25:00,235 can't tell depth. 489 00:25:00,235 --> 00:25:01,420 AUDIENCE: Lower them both. 490 00:25:01,420 --> 00:25:02,800 AUDIENCE: [INAUDIBLE] 491 00:25:02,800 --> 00:25:03,370 PROFESSOR: Oh, that's true. 492 00:25:03,370 --> 00:25:03,870 AUDIENCE: [INAUDIBLE] 493 00:25:03,870 --> 00:25:04,370 AUDIENCE: Lower them both. 494 00:25:04,370 --> 00:25:05,370 AUDIENCE: --corner of the desk. 495 00:25:05,370 --> 00:25:05,680 PROFESSOR: Pardon? 496 00:25:05,680 --> 00:25:07,682 AUDIENCE: If you go in the corner of the desk, then you 497 00:25:07,682 --> 00:25:10,480 drop one on the desk and the other one [INAUDIBLE]. 498 00:25:10,480 --> 00:25:11,960 PROFESSOR: Oh, but then you wouldn't be able 499 00:25:11,960 --> 00:25:13,890 to see it so well. 500 00:25:13,890 --> 00:25:16,580 So I want to do it on the desk just so everyone can see. 501 00:25:16,580 --> 00:25:18,200 OK, so if I lower them both like this, 502 00:25:18,200 --> 00:25:18,895 is that about right? 503 00:25:18,895 --> 00:25:19,785 AUDIENCE: Yeah. 504 00:25:19,785 --> 00:25:21,130 [INAUDIBLE] 505 00:25:21,130 --> 00:25:22,170 PROFESSOR: Lower? 506 00:25:22,170 --> 00:25:22,610 Wow. 507 00:25:22,610 --> 00:25:24,610 OK. 508 00:25:24,610 --> 00:25:25,850 OK. 509 00:25:25,850 --> 00:25:28,860 One, two, three, go. 510 00:25:28,860 --> 00:25:30,360 No, not very simultaneous. 511 00:25:30,360 --> 00:25:33,630 So let's try 2 to 1. 512 00:25:33,630 --> 00:25:37,240 OK, I'll overcompensate in my mind. 513 00:25:37,240 --> 00:25:37,460 [? And it's ?] 514 00:25:37,460 --> 00:25:38,850 probably about 2 to 1. 515 00:25:38,850 --> 00:25:40,210 Is that about 2 to 1? 516 00:25:40,210 --> 00:25:40,780 This one? 517 00:25:40,780 --> 00:25:41,480 AUDIENCE: [INAUDIBLE] 518 00:25:41,480 --> 00:25:42,450 PROFESSOR: [? Socks. ?] 519 00:25:42,450 --> 00:25:43,550 Every time. 520 00:25:43,550 --> 00:25:49,010 OK, 1, one thousand, 2, one thousand, 3, one thousand. 521 00:25:49,010 --> 00:25:50,120 Simultaneous. 522 00:25:50,120 --> 00:25:52,260 And what's always amazing to me is I always listen to the 523 00:25:52,260 --> 00:25:53,700 class every time I do this. 524 00:25:53,700 --> 00:25:56,570 And I never believe them when they say it's 525 00:25:56,570 --> 00:25:57,970 really 2 to 1 in height. 526 00:25:57,970 --> 00:25:59,770 And I was like, OK, I'll trust you guys. 527 00:25:59,770 --> 00:26:01,290 And it always comes out simultaneous. 528 00:26:01,290 --> 00:26:04,820 So people haven't lied to me yet. 529 00:26:04,820 --> 00:26:07,040 So 2 to 1-- why 2? 530 00:26:07,040 --> 00:26:09,630 Well, it had 4 times the weight. 531 00:26:09,630 --> 00:26:12,480 Same surface area, same density-- you 532 00:26:12,480 --> 00:26:14,180 couldn't change the air. 533 00:26:14,180 --> 00:26:15,395 So you have to change the v. 534 00:26:15,395 --> 00:26:16,870 How much do you change the v by? 535 00:26:16,870 --> 00:26:18,820 Factor of 2, because you square it. 536 00:26:18,820 --> 00:26:22,280 And you make up for the weight increase by factor of 4. 537 00:26:22,280 --> 00:26:24,440 So factor of 2. 538 00:26:24,440 --> 00:26:26,490 So there you have an application of it. 539 00:26:26,490 --> 00:26:30,430 So now, let me get to your question about what do you do 540 00:26:30,430 --> 00:26:33,260 if someone tries to spoil the experiment. 541 00:26:33,260 --> 00:26:37,030 So the first thing to do is-- 542 00:26:37,030 --> 00:26:39,370 well, let me say what were my reactions as 543 00:26:39,370 --> 00:26:40,810 soon as you did that. 544 00:26:40,810 --> 00:26:44,500 So my first reaction was, god damn, why did he do that? 545 00:26:44,500 --> 00:26:47,170 That was a really nasty thing to do. 546 00:26:47,170 --> 00:26:51,670 But then the second reaction is-- whoop. 547 00:26:51,670 --> 00:26:53,810 So now I've developed a habit, which is a good habit to 548 00:26:53,810 --> 00:26:57,650 learn, of just pausing before you react to things. 549 00:26:57,650 --> 00:27:01,450 Because you're much less likely to cause bad 550 00:27:01,450 --> 00:27:02,930 interactions if you pause. 551 00:27:02,930 --> 00:27:04,330 So I paused to myself. 552 00:27:04,330 --> 00:27:08,530 And I thought, there's actually no point in saying 553 00:27:08,530 --> 00:27:10,790 how annoyed I am right there. 554 00:27:10,790 --> 00:27:11,700 And this will happen. 555 00:27:11,700 --> 00:27:13,640 Suppose someone tries to wreck your experiment. 556 00:27:13,640 --> 00:27:15,320 You will be annoyed. 557 00:27:15,320 --> 00:27:19,020 So it doesn't help you to actually say how annoyed you 558 00:27:19,020 --> 00:27:21,280 are and really make that person feel terrible. 559 00:27:21,280 --> 00:27:23,690 Because then what you've done is you've polarized the 560 00:27:23,690 --> 00:27:25,410 audience against yourself besides making 561 00:27:25,410 --> 00:27:27,440 that person feel bad. 562 00:27:27,440 --> 00:27:30,250 So it's much better to do what I did, which was say, 563 00:27:30,250 --> 00:27:30,960 OK, tell you what. 564 00:27:30,960 --> 00:27:34,560 I'll answer your question later. 565 00:27:34,560 --> 00:27:37,210 But also what I tried to do is answer it implicitly. 566 00:27:37,210 --> 00:27:40,140 I don't know if you noticed, but what I did was when I came 567 00:27:40,140 --> 00:27:43,010 to ask people, I figured, OK, so people sort of have an idea 568 00:27:43,010 --> 00:27:46,140 that it should be C just because of somebody said, 569 00:27:46,140 --> 00:27:48,860 well, I've seen the demonstration before. 570 00:27:48,860 --> 00:27:52,580 But what I wanted to know was not why you think C is right 571 00:27:52,580 --> 00:27:55,450 but why you think any of them could be plausible. 572 00:27:55,450 --> 00:27:58,860 So that was always part of the question, but I emphasized 573 00:27:58,860 --> 00:28:00,840 that part more. 574 00:28:00,840 --> 00:28:07,440 And it has a good educational purpose, which is that you're 575 00:28:07,440 --> 00:28:09,840 trying to predict not just what the quote "right answer" 576 00:28:09,840 --> 00:28:11,820 is, but you're trying to expand your 577 00:28:11,820 --> 00:28:12,960 repertoire of options. 578 00:28:12,960 --> 00:28:14,900 So you're actually making yourself more creative by 579 00:28:14,900 --> 00:28:16,950 thinking, what could be plausible? 580 00:28:16,950 --> 00:28:19,350 Because it's that way of thinking that you're able to 581 00:28:19,350 --> 00:28:20,400 use in other problems. 582 00:28:20,400 --> 00:28:24,460 So I tried to turn it around a bit and push it in a direction 583 00:28:24,460 --> 00:28:27,860 that it would still be a useful discussion for people. 584 00:28:27,860 --> 00:28:30,880 OK, maybe not as useful as if people didn't know ahead of 585 00:28:30,880 --> 00:28:34,850 time that the answer is C, but still a useful one. 586 00:28:34,850 --> 00:28:38,450 Does that help answer your question? 587 00:28:38,450 --> 00:28:42,360 OK, so now what we've done-- we've actually gone through a 588 00:28:42,360 --> 00:28:43,550 whole teaching example. 589 00:28:43,550 --> 00:28:45,094 Yes, question. 590 00:28:45,094 --> 00:28:47,529 AUDIENCE: So [INAUDIBLE] 591 00:28:47,529 --> 00:28:51,055 talk about when you're writing down the number of votes, if 592 00:28:51,055 --> 00:28:53,170 you should leave them actually like [INAUDIBLE]. 593 00:29:00,140 --> 00:29:01,050 PROFESSOR: I didn't see. 594 00:29:01,050 --> 00:29:01,850 That's a good point. 595 00:29:01,850 --> 00:29:03,582 AUDIENCE: And so that way, those people would be like, oh 596 00:29:03,582 --> 00:29:04,740 my God you didn't see me. 597 00:29:04,740 --> 00:29:06,600 PROFESSOR: This is a good point. 598 00:29:06,600 --> 00:29:07,230 And I didn't. 599 00:29:07,230 --> 00:29:09,540 And partly, it's because the lighting in 600 00:29:09,540 --> 00:29:10,960 this room is ghastly. 601 00:29:10,960 --> 00:29:12,720 Partly my eyes are not very good. 602 00:29:12,720 --> 00:29:15,370 But all of those reasons support exactly what you said, 603 00:29:15,370 --> 00:29:20,850 which is that, especially if you have a few people in the 604 00:29:20,850 --> 00:29:23,440 class, you can always get away with adding one. 605 00:29:23,440 --> 00:29:24,980 And another thing you can do is you can 606 00:29:24,980 --> 00:29:28,250 always add one for yourself. 607 00:29:28,250 --> 00:29:30,390 You think, well, I actually have a plausible reason for 608 00:29:30,390 --> 00:29:30,830 one of these. 609 00:29:30,830 --> 00:29:33,660 Well, I'm going to vote for one of them. 610 00:29:33,660 --> 00:29:36,290 And every once in a while, you vote for a correct answer-- 611 00:29:36,290 --> 00:29:38,280 you know, one out of five times. 612 00:29:38,280 --> 00:29:39,460 So the class learns. 613 00:29:39,460 --> 00:29:42,160 But generally, you vote sort of randomly just to give 614 00:29:42,160 --> 00:29:44,480 support to the various answers. 615 00:29:44,480 --> 00:29:45,770 So you're right. 616 00:29:45,770 --> 00:29:49,130 The question was, is it better to not use zip ever? 617 00:29:49,130 --> 00:29:50,160 And generally, it's true. 618 00:29:50,160 --> 00:29:52,690 Unless you're dead sure no one voted for anything. 619 00:29:52,690 --> 00:29:55,530 And it's hard to see in a large class. 620 00:29:55,530 --> 00:29:57,800 That's one of the advantages of the clickers. 621 00:29:57,800 --> 00:29:59,910 There's disadvantages and advantages of clickers. 622 00:29:59,910 --> 00:30:01,670 And we can talk about them. 623 00:30:01,670 --> 00:30:02,470 But you're right. 624 00:30:02,470 --> 00:30:04,220 One way to mitigate that-- 625 00:30:04,220 --> 00:30:07,120 just throw in an extra vote. 626 00:30:07,120 --> 00:30:08,370 Other questions? 627 00:30:10,820 --> 00:30:12,740 So as I promised, what we're going to do with 628 00:30:12,740 --> 00:30:14,150 this example is now-- 629 00:30:14,150 --> 00:30:18,110 because this is actually not an aerodynamics class. 630 00:30:18,110 --> 00:30:21,130 You may be surprised to find out now. 631 00:30:21,130 --> 00:30:23,350 So you may have thought the purpose was to actually learn 632 00:30:23,350 --> 00:30:24,830 the air resistance formula. 633 00:30:24,830 --> 00:30:26,540 If you do learn that, that's really useful. 634 00:30:26,540 --> 00:30:29,270 And I'd be really happy, because it's a great result 635 00:30:29,270 --> 00:30:32,260 which is very, very, very hard to derive in pretty 636 00:30:32,260 --> 00:30:34,042 much any other way. 637 00:30:34,042 --> 00:30:37,030 You certainly can't derive it from scratch from the 638 00:30:37,030 --> 00:30:38,080 Navier-Stokes equations. 639 00:30:38,080 --> 00:30:41,460 At least no one with current mathematical knowledge knows 640 00:30:41,460 --> 00:30:42,920 how to do that. 641 00:30:42,920 --> 00:30:47,480 So experiment really is one of the main ways of doing that. 642 00:30:47,480 --> 00:30:49,460 So it's a great result for that. 643 00:30:49,460 --> 00:30:53,420 But what I want to use it for is deconstructing it, looking 644 00:30:53,420 --> 00:30:57,810 at the way it was taught and why all the things 645 00:30:57,810 --> 00:30:59,700 were done that way. 646 00:30:59,700 --> 00:31:03,930 So in that discussion will come out general principles 647 00:31:03,930 --> 00:31:07,240 that we'll use throughout the semester in all of our 648 00:31:07,240 --> 00:31:09,680 examples of how to do teaching, like for example, 649 00:31:09,680 --> 00:31:12,320 how to make a lecture, how to design a course. 650 00:31:12,320 --> 00:31:17,270 So as always, those principles are not very effective if I 651 00:31:17,270 --> 00:31:18,640 just say, well, here are the principles, and we're 652 00:31:18,640 --> 00:31:19,040 going to use them. 653 00:31:19,040 --> 00:31:20,820 It's much better if we actually try them out in 654 00:31:20,820 --> 00:31:25,290 example and see where did they show up by constructing them. 655 00:31:25,290 --> 00:31:31,420 So the question for the next portion of this session is to 656 00:31:31,420 --> 00:31:35,980 identify all of the teaching elements in this. 657 00:31:35,980 --> 00:31:37,700 So for example, what's a teaching element? 658 00:31:37,700 --> 00:31:41,630 Well, for example, there was a vote or there 659 00:31:41,630 --> 00:31:43,660 was a second vote. 660 00:31:43,660 --> 00:31:47,260 So just deconstruct it to as fine a granularity as seems 661 00:31:47,260 --> 00:31:52,510 reasonable, and say, OK, this was done, or this happened. 662 00:31:52,510 --> 00:31:54,500 And then, why? 663 00:31:54,500 --> 00:31:55,750 So two questions-- 664 00:31:55,750 --> 00:31:57,130 do a two-column table. 665 00:32:02,500 --> 00:32:04,550 What and why? 666 00:32:04,550 --> 00:32:07,200 And there'll be a pretty long list because there was quite a 667 00:32:07,200 --> 00:32:09,740 lot of things done. 668 00:32:09,740 --> 00:32:12,030 So find a neighbor or two again. 669 00:32:12,030 --> 00:32:13,490 We'll discuss the what and why. 670 00:32:13,490 --> 00:32:18,602 And then I'll clump the whys into principles. 671 00:32:18,602 --> 00:32:22,680 So any questions about that question? 672 00:32:22,680 --> 00:32:25,660 ANNOUNCER: Due to technical difficulties, the rest of 673 00:32:25,660 --> 00:32:28,400 lecture one is unavailable. 674 00:32:28,400 --> 00:32:31,690 What follows is a summary of the material presented in the 675 00:32:31,690 --> 00:32:33,005 remaining part of the lecture. 676 00:32:35,970 --> 00:32:40,520 PROFESSOR: Think back to the question about the cones-- 677 00:32:40,520 --> 00:32:44,470 which fell faster, or were they the same speed, the big 678 00:32:44,470 --> 00:32:49,490 cone or the small cone, and how that question was asked. 679 00:32:49,490 --> 00:32:53,000 What were all the elements in the way the 680 00:32:53,000 --> 00:32:54,610 question was asked? 681 00:32:54,610 --> 00:32:55,680 What was discussed? 682 00:32:55,680 --> 00:32:58,800 What did you do? 683 00:32:58,800 --> 00:33:02,000 So it was scripted very carefully. 684 00:33:02,000 --> 00:33:06,670 And there were reasons for the elements of the script. 685 00:33:06,670 --> 00:33:09,600 So we've had a chance to think about that. 686 00:33:09,600 --> 00:33:13,890 And let me list many of these scripting elements and their 687 00:33:13,890 --> 00:33:15,140 reasons for them. 688 00:33:26,180 --> 00:33:29,710 So on the left side, I'll list the elements. 689 00:33:29,710 --> 00:33:33,530 For example, there was lots of interaction. 690 00:33:33,530 --> 00:33:35,600 You were talking to each other. 691 00:33:35,600 --> 00:33:36,850 You were asking questions. 692 00:33:46,370 --> 00:33:47,880 In fact, you weren't just asking questions. 693 00:33:47,880 --> 00:33:49,770 You were voting. 694 00:33:49,770 --> 00:33:51,870 So twice you voted. 695 00:33:57,730 --> 00:33:59,040 So voting twice, discussing. 696 00:34:06,770 --> 00:34:08,340 So what are the reasons for that? 697 00:34:08,340 --> 00:34:11,360 What are the educational principles behind designing a 698 00:34:11,360 --> 00:34:15,139 question that allows lots of interaction, voting, 699 00:34:15,139 --> 00:34:17,550 discussing? 700 00:34:17,550 --> 00:34:18,800 Well, first of all-- 701 00:34:22,389 --> 00:34:24,360 the why-- 702 00:34:24,360 --> 00:34:27,957 it gives the teacher, it gives me, an idea of how the class 703 00:34:27,957 --> 00:34:29,207 is thinking. 704 00:34:49,909 --> 00:34:53,880 If, for example, I ask a question, and in the first 705 00:34:53,880 --> 00:34:58,320 vote almost everyone gets it right, I know, OK, everyone 706 00:34:58,320 --> 00:35:02,620 pretty much understands this idea or this concept. 707 00:35:02,620 --> 00:35:05,520 I can spend very little extra time on it and move on to 708 00:35:05,520 --> 00:35:08,370 something that may be more confusing or more problematic. 709 00:35:08,370 --> 00:35:12,180 Whereas if most people get it wrong, I know, OK, either the 710 00:35:12,180 --> 00:35:13,470 book was confusing or what I 711 00:35:13,470 --> 00:35:15,440 explained already was confusing. 712 00:35:15,440 --> 00:35:19,160 And we need to spend more time discussing the core idea here. 713 00:35:19,160 --> 00:35:21,290 So it gives me instant feedback about 714 00:35:21,290 --> 00:35:22,140 where the class is. 715 00:35:22,140 --> 00:35:25,520 I don't have to wait till the end of the term to find out on 716 00:35:25,520 --> 00:35:27,330 the final exam, oh, no one understood that. 717 00:35:27,330 --> 00:35:29,230 I know right there when I have a chance to do 718 00:35:29,230 --> 00:35:30,480 something about it. 719 00:35:33,570 --> 00:35:37,390 The voting also has another benefit. 720 00:35:37,390 --> 00:35:39,700 So the first benefit is it tells me. 721 00:35:39,700 --> 00:35:44,060 Also, it makes this students form a public commitment. 722 00:35:56,870 --> 00:36:01,000 And that public commitment has a strong benefit, which is 723 00:36:01,000 --> 00:36:04,020 that the students become much more involved in learning what 724 00:36:04,020 --> 00:36:06,330 the outcome of the discussion is. 725 00:36:06,330 --> 00:36:08,470 Because they've actually made a public commitment to one 726 00:36:08,470 --> 00:36:10,465 choice or another choice. 727 00:36:10,465 --> 00:36:12,485 So it increases the level of engagement. 728 00:36:15,540 --> 00:36:17,250 Similarly, it creates tension. 729 00:36:17,250 --> 00:36:20,060 People want to know what's going to happen. 730 00:36:20,060 --> 00:36:23,190 So when the demonstration is actually done-- 731 00:36:23,190 --> 00:36:26,090 the final decider is the experiment-- 732 00:36:26,090 --> 00:36:27,990 everyone is paying very, very close attention. 733 00:36:31,800 --> 00:36:33,820 So I'll say not just tension, but I'll say it creates 734 00:36:33,820 --> 00:36:35,070 dramatic tension. 735 00:36:46,540 --> 00:36:51,160 Furthermore, the chance for lots of interaction increases 736 00:36:51,160 --> 00:36:55,460 the amount of interaction in the whole class. 737 00:36:55,460 --> 00:36:58,300 For example, students will ask questions much more easily if 738 00:36:58,300 --> 00:37:00,780 they've already had a chance to discuss their ideas in 739 00:37:00,780 --> 00:37:02,030 small groups. 740 00:37:13,500 --> 00:37:18,020 So that's one set of elements and the educational reasons 741 00:37:18,020 --> 00:37:21,550 for building those in to how one asks questions in class. 742 00:37:30,980 --> 00:37:36,460 Another one is that I used a physical object, in an actual 743 00:37:36,460 --> 00:37:39,510 demonstration, so these cones. 744 00:37:39,510 --> 00:37:43,740 And the physical object is also cheap. 745 00:37:43,740 --> 00:37:44,720 Anyone can make those. 746 00:37:44,720 --> 00:37:47,570 You just cut circles out of paper, cut a quarter away, and 747 00:37:47,570 --> 00:37:48,180 tape it together. 748 00:37:48,180 --> 00:37:49,430 You have a cone. 749 00:38:01,630 --> 00:38:03,140 What are the benefits of that? 750 00:38:03,140 --> 00:38:07,450 Well, first, it's much more convincing than if I just do a 751 00:38:07,450 --> 00:38:10,830 derivation from the Navier-Stokes equations or 752 00:38:10,830 --> 00:38:12,620 however one gets to the result. 753 00:38:12,620 --> 00:38:16,470 And say, OK, well, therefore the drag is proportional to 754 00:38:16,470 --> 00:38:17,830 the square of the speed. 755 00:38:17,830 --> 00:38:20,350 Or therefore, they all fall at the same speed 756 00:38:20,350 --> 00:38:21,770 whatever their size. 757 00:38:21,770 --> 00:38:24,410 If I just say that, or even if I prove it with equations, 758 00:38:24,410 --> 00:38:27,110 that's not nearly as convincing as seeing it 759 00:38:27,110 --> 00:38:28,360 actually happen. 760 00:38:38,480 --> 00:38:41,110 And that's where in terms of being convincing, it's also 761 00:38:41,110 --> 00:38:44,180 important that the demonstration be cheap. 762 00:38:44,180 --> 00:38:47,290 If, for example, to see it actually happen requires 763 00:38:47,290 --> 00:38:49,620 $100,000 of equipment-- 764 00:38:49,620 --> 00:38:53,050 well, who knows what happens in that $100,000 of equipment 765 00:38:53,050 --> 00:38:55,740 and sensors and test devices and whatnot. 766 00:38:55,740 --> 00:38:58,320 Whereas if it's a cheap piece of paper you can cut out for 767 00:38:58,320 --> 00:39:02,320 $0.02, well, then anyone can try it themself, too. 768 00:39:02,320 --> 00:39:06,410 And it's not so mediated by lots of sensory devices. 769 00:39:06,410 --> 00:39:08,590 It's much more immediate. 770 00:39:08,590 --> 00:39:09,640 It's much more convincing. 771 00:39:09,640 --> 00:39:11,370 So I'll say here in parentheses, a 772 00:39:11,370 --> 00:39:12,647 cheap physical object-- 773 00:39:15,990 --> 00:39:17,240 ideally, if possible. 774 00:39:20,070 --> 00:39:24,130 Furthermore, the physical object actually connects the 775 00:39:24,130 --> 00:39:26,920 mathematical and physical and engineering ideas to the 776 00:39:26,920 --> 00:39:28,170 physical world. 777 00:39:41,480 --> 00:39:44,220 In the end, we want to try to understand how the world 778 00:39:44,220 --> 00:39:45,880 works, maybe put it back together 779 00:39:45,880 --> 00:39:48,300 in ways of our choosing. 780 00:39:48,300 --> 00:39:52,910 So purely living in the formal world, we're 781 00:39:52,910 --> 00:39:54,160 living in the clouds. 782 00:39:54,160 --> 00:39:56,360 By bringing in a physical object, we actually put our 783 00:39:56,360 --> 00:39:57,750 feet on the ground as well. 784 00:40:05,320 --> 00:40:10,270 Another part of the demonstration of the script 785 00:40:10,270 --> 00:40:13,930 was various things that might have seemed extraneous. 786 00:40:13,930 --> 00:40:19,430 For example, I mentioned that I hope my socks were matched 787 00:40:19,430 --> 00:40:20,720 well when I stood on the table. 788 00:40:28,660 --> 00:40:30,120 I also discussed-- 789 00:40:30,120 --> 00:40:32,320 when I was standing on the table, I said, OK, I need the 790 00:40:32,320 --> 00:40:35,360 class's help here because I don't have depth perception. 791 00:40:35,360 --> 00:40:39,300 So I can't tell when I'm dropping them-- 792 00:40:39,300 --> 00:40:43,230 when I was dropping one cone versus four cones, I can't 793 00:40:43,230 --> 00:40:47,270 tell when I've got this one twice as high as this one. 794 00:40:47,270 --> 00:40:48,700 And so you need to tell me. 795 00:40:48,700 --> 00:40:51,920 So I talked about my failing in the depth perception 796 00:40:51,920 --> 00:40:53,170 department. 797 00:41:02,020 --> 00:41:04,200 So both of these might seem extraneous to 798 00:41:04,200 --> 00:41:05,320 engineering and science. 799 00:41:05,320 --> 00:41:08,620 But actually, they have a sound educational reason. 800 00:41:08,620 --> 00:41:13,600 So the socks joke-- well, that makes the teacher seem much 801 00:41:13,600 --> 00:41:14,850 more human. 802 00:41:28,190 --> 00:41:30,670 Similarly, for the lack of depth perception-- 803 00:41:30,670 --> 00:41:32,910 oh, well, the teacher has flaws, too. 804 00:41:32,910 --> 00:41:35,080 They're not this perfect person who seems to know 805 00:41:35,080 --> 00:41:35,960 everything. 806 00:41:35,960 --> 00:41:38,910 And in fact, that one, specifically because I didn't 807 00:41:38,910 --> 00:41:41,390 have depth perception, I needed the help of the class. 808 00:41:41,390 --> 00:41:44,760 So that, again, is an excuse to involve the whole class. 809 00:41:44,760 --> 00:41:48,625 So no depth perception makes a teacher human is also an 810 00:41:48,625 --> 00:41:49,970 excuse for more engagement. 811 00:42:06,880 --> 00:42:11,900 And related to discussing another element of the script, 812 00:42:11,900 --> 00:42:15,370 I want to amplify this one up there, the discussing. 813 00:42:15,370 --> 00:42:17,350 And I'll put it back down here. 814 00:42:17,350 --> 00:42:22,410 The discussion happened first by yourself, then in a small 815 00:42:22,410 --> 00:42:26,830 group, and then in the whole class together where people 816 00:42:26,830 --> 00:42:28,080 were suggesting reasons. 817 00:42:43,240 --> 00:42:45,620 So I'll say discussions at several scales-- 818 00:42:45,620 --> 00:42:50,445 self, group, and class. 819 00:42:57,880 --> 00:43:01,080 So what's the educational purpose of that? 820 00:43:01,080 --> 00:43:03,940 Well, I mentioned one purpose up there, which is it 821 00:43:03,940 --> 00:43:05,780 increases questions. 822 00:43:05,780 --> 00:43:07,920 And that's certainly true. 823 00:43:07,920 --> 00:43:11,830 Another one is by allowing people to think for themselves 824 00:43:11,830 --> 00:43:17,020 first, you're giving space for what's called the introverts. 825 00:43:17,020 --> 00:43:20,020 Some people like lots of time to think for themselves, and 826 00:43:20,020 --> 00:43:23,030 only then do they want to share with other people. 827 00:43:23,030 --> 00:43:25,330 Because otherwise, their thoughts get derailed by what 828 00:43:25,330 --> 00:43:26,440 everybody else is saying. 829 00:43:26,440 --> 00:43:28,750 Some people don't know what they're thinking till they 830 00:43:28,750 --> 00:43:29,910 talk to other people. 831 00:43:29,910 --> 00:43:31,290 Let's call them the extroverts. 832 00:43:31,290 --> 00:43:36,170 So by allowing space for self talk and group talk, you're 833 00:43:36,170 --> 00:43:37,845 teaching to the introverts and the extroverts. 834 00:43:37,845 --> 00:43:41,460 So you're matching to the learning styles of different 835 00:43:41,460 --> 00:43:42,710 students in the class. 836 00:44:01,570 --> 00:44:05,510 And then by scaling it up slowly from self to group to 837 00:44:05,510 --> 00:44:08,670 class, you make it safe. 838 00:44:08,670 --> 00:44:12,380 You make it not a huge transition to start to go to 839 00:44:12,380 --> 00:44:13,410 the next stage. 840 00:44:13,410 --> 00:44:15,980 Whereas if I just ask the question of the class, OK, 841 00:44:15,980 --> 00:44:17,880 whole class, now, you tell me what you think about this 842 00:44:17,880 --> 00:44:22,280 question and I skipped these parts, only the usual suspects 843 00:44:22,280 --> 00:44:25,410 would be offering me ideas here. 844 00:44:25,410 --> 00:44:27,340 The people who always raise their hand-- maybe they sit in 845 00:44:27,340 --> 00:44:28,170 the front row. 846 00:44:28,170 --> 00:44:32,160 Whereas by allowing people to think for themselves, then 847 00:44:32,160 --> 00:44:34,250 discuss in a group the ideas that they thought for 848 00:44:34,250 --> 00:44:36,890 themselves, check out what they've done there. 849 00:44:36,890 --> 00:44:39,040 If they still think they don't understand something and no 850 00:44:39,040 --> 00:44:41,260 one in the group understood it, then they feel safe asking 851 00:44:41,260 --> 00:44:42,220 the whole class. 852 00:44:42,220 --> 00:44:44,720 We're actually building a bridge for people to 853 00:44:44,720 --> 00:44:47,840 participate in the large group. 854 00:44:47,840 --> 00:44:50,120 So again, that point's up there. 855 00:44:50,120 --> 00:44:52,280 But it's so important I'm putting it down here, too. 856 00:44:56,930 --> 00:45:01,730 So I'll call it builds a bridge to collective 857 00:45:01,730 --> 00:45:02,980 participation. 858 00:45:11,320 --> 00:45:14,320 And that participation can be people contributing ideas or 859 00:45:14,320 --> 00:45:16,065 questions which are themselves ideas. 860 00:45:22,160 --> 00:45:28,490 Another feature of how the whole thing was done was that 861 00:45:28,490 --> 00:45:32,700 I walked around a fair amount. 862 00:45:32,700 --> 00:45:35,230 I used a lot of the space. 863 00:45:35,230 --> 00:45:37,270 For example, even some of the vertical space, 864 00:45:37,270 --> 00:45:38,840 standing on the table. 865 00:45:38,840 --> 00:45:43,080 Moving over here, moving over there to make sure I heard the 866 00:45:43,080 --> 00:45:44,565 question from that side of the class. 867 00:45:49,070 --> 00:45:51,975 So filling the lecture space. 868 00:46:00,380 --> 00:46:02,290 Well, what's the educational reason for that? 869 00:46:02,290 --> 00:46:07,030 Well, in a way it's the opposite of the socks joke. 870 00:46:09,840 --> 00:46:11,200 In one way, it's the opposite. 871 00:46:11,200 --> 00:46:12,170 In another way, it's the same. 872 00:46:12,170 --> 00:46:14,620 It's showing that the teacher is human and that teaching is 873 00:46:14,620 --> 00:46:16,390 a human activity. 874 00:46:16,390 --> 00:46:20,570 This is what actors do on stage. 875 00:46:20,570 --> 00:46:23,460 The stage, the whole stage is there for a reason. 876 00:46:23,460 --> 00:46:25,440 And the actors will use all of it. 877 00:46:25,440 --> 00:46:28,170 They won't just stand in the middle the whole time, except 878 00:46:28,170 --> 00:46:31,565 for rare comedy monologues or monologues. 879 00:46:31,565 --> 00:46:33,550 But otherwise, all the pieces of the stage 880 00:46:33,550 --> 00:46:34,410 are there for a reason. 881 00:46:34,410 --> 00:46:35,310 And the actors use it. 882 00:46:35,310 --> 00:46:37,560 They make that space their own space. 883 00:46:37,560 --> 00:46:39,550 They fill the lecture room space. 884 00:46:39,550 --> 00:46:42,870 So as a teacher, you want to do that because that shows 885 00:46:42,870 --> 00:46:44,310 that this is your space. 886 00:46:44,310 --> 00:46:45,660 You're comfortable there. 887 00:46:45,660 --> 00:46:47,725 And it increases your credibility with the students. 888 00:47:02,240 --> 00:47:06,530 And similar to this, it brings in students from all parts of 889 00:47:06,530 --> 00:47:08,880 the classroom, especially if it's a big classroom. 890 00:47:08,880 --> 00:47:11,830 They all feel somehow connected to what's going on. 891 00:47:11,830 --> 00:47:14,580 Because you haven't just stood in one corner of the room or 892 00:47:14,580 --> 00:47:18,820 just paid attention to one section of the class. 893 00:47:18,820 --> 00:47:22,720 So in one way, it's the opposite of the socks joke. 894 00:47:22,720 --> 00:47:25,890 Because in that way, the teacher is being a bit 895 00:47:25,890 --> 00:47:26,810 self-deprecating. 896 00:47:26,810 --> 00:47:29,510 Here, the lecturer is acting very confident 897 00:47:29,510 --> 00:47:30,790 by filling the space. 898 00:47:30,790 --> 00:47:32,370 But in another way, it's the same. 899 00:47:32,370 --> 00:47:37,590 They're both playing on the human part of teaching, which 900 00:47:37,590 --> 00:47:38,990 is inescapable. 901 00:47:38,990 --> 00:47:41,370 And if it's neglected, the teaching falls flat. 902 00:47:44,570 --> 00:47:48,510 And finally, there was one other point which may seem 903 00:47:48,510 --> 00:47:50,690 like a mechanical point. 904 00:47:50,690 --> 00:47:53,650 But it's so useful that I'll put it here, too. 905 00:47:53,650 --> 00:47:57,370 And I'll write it with big chalk. 906 00:47:57,370 --> 00:48:04,750 Point is, I wrote everything on the board using big chalk. 907 00:48:04,750 --> 00:48:06,920 And why is that important? 908 00:48:06,920 --> 00:48:10,210 Well, in a small classroom of maybe 10 or 15 people, it 909 00:48:10,210 --> 00:48:10,980 probably doesn't matter. 910 00:48:10,980 --> 00:48:12,310 Everyone can read everything. 911 00:48:12,310 --> 00:48:16,480 But if it's at all a large classroom, people can't read 912 00:48:16,480 --> 00:48:17,940 the writing way in the back. 913 00:48:17,940 --> 00:48:19,840 By using big chalk, you increase the 914 00:48:19,840 --> 00:48:21,090 signal to noise ratio. 915 00:48:31,380 --> 00:48:34,680 Now, that may not seem so important when 916 00:48:34,680 --> 00:48:35,750 you first think about. 917 00:48:35,750 --> 00:48:37,480 The reason being is that you already 918 00:48:37,480 --> 00:48:38,980 know what you're writing. 919 00:48:38,980 --> 00:48:45,720 So even if you see really thin lines, something that's not 920 00:48:45,720 --> 00:48:49,720 very clearly written, you still know what it should say. 921 00:48:49,720 --> 00:48:51,250 And you just read it correctly. 922 00:48:51,250 --> 00:48:53,350 But the students, on the other hand-- 923 00:48:53,350 --> 00:48:55,670 they don't have the knowledge that you have. 924 00:48:55,670 --> 00:48:59,890 So they can't error-correct any-- 925 00:48:59,890 --> 00:49:02,070 fill in the missing gaps in the lines. 926 00:49:02,070 --> 00:49:06,450 They need as much signal as possible to really copy down 927 00:49:06,450 --> 00:49:09,410 anything correctly, to make sure that they're not adding 928 00:49:09,410 --> 00:49:12,030 noise onto the signal that you're trying to get across. 929 00:49:12,030 --> 00:49:16,210 So in some ways, a small point, but in other ways, an 930 00:49:16,210 --> 00:49:16,860 important point. 931 00:49:16,860 --> 00:49:19,750 Because if you don't do it, you'll throw away most of your 932 00:49:19,750 --> 00:49:24,270 other benefits because the students will actually be 933 00:49:24,270 --> 00:49:27,320 incorporating wrong information, just errors, just 934 00:49:27,320 --> 00:49:29,180 by mistake without even realizing. 935 00:49:29,180 --> 00:49:30,970 And the big chalk can actually minimize that. 936 00:49:30,970 --> 00:49:33,410 So just a mechanical point. 937 00:49:33,410 --> 00:49:37,615 I always keep pieces of big chalk in my backpack. 938 00:49:37,615 --> 00:49:40,700 And wherever I happen to be teaching, I can always pull 939 00:49:40,700 --> 00:49:42,320 them out and use them. 940 00:49:42,320 --> 00:49:45,010 Because you will find many classrooms only have standard 941 00:49:45,010 --> 00:49:46,420 chalk provided. 942 00:49:46,420 --> 00:49:48,940 And the big chalk is something you have to do yourself. 943 00:49:48,940 --> 00:49:53,270 So just carry a few pieces with you as you need. 944 00:49:53,270 --> 00:49:57,410 So those are some of the many scripting 945 00:49:57,410 --> 00:50:01,610 elements in this example. 946 00:50:01,610 --> 00:50:05,320 And you'll see a similar example in a subsequent 947 00:50:05,320 --> 00:50:08,040 lecture, in the lecture on teaching interactively, which 948 00:50:08,040 --> 00:50:09,280 is lecture six. 949 00:50:09,280 --> 00:50:12,830 And you'll see some of these points come up again and some 950 00:50:12,830 --> 00:50:15,710 of these reasons discussed again in a different example. 951 00:50:15,710 --> 00:50:20,000 So you'll have two different engineering examples, but done 952 00:50:20,000 --> 00:50:20,890 in a similar way. 953 00:50:20,890 --> 00:50:24,910 And you can see the scripting elements and how they're 954 00:50:24,910 --> 00:50:26,790 different and how they're the same in both examples. 955 00:50:26,790 --> 00:50:30,330 And see which ones you can use in your own teaching. 956 00:50:30,330 --> 00:50:35,910 So now, from these scripting elements, we've extracted 957 00:50:35,910 --> 00:50:37,910 teaching principles. 958 00:50:37,910 --> 00:50:40,490 So credibility, signal to noise ratio-- 959 00:50:40,490 --> 00:50:42,360 just remember those. 960 00:50:42,360 --> 00:50:46,320 And then here's a bunch more. 961 00:50:46,320 --> 00:50:50,310 I want to summarize them, extract the main highlights 962 00:50:50,310 --> 00:50:54,800 from that so that you can come away with a clean picture of 963 00:50:54,800 --> 00:50:59,770 what to watch for throughout this semester. 964 00:50:59,770 --> 00:51:03,270 So the main themes of all of these are-- 965 00:51:13,650 --> 00:51:15,880 I would say they fall into three categories. 966 00:51:15,880 --> 00:51:16,820 Let me list them. 967 00:51:16,820 --> 00:51:19,100 And then I'll break them into three categories. 968 00:51:19,100 --> 00:51:27,855 There's ways to promote questions and discussion. 969 00:51:33,660 --> 00:51:36,230 There's using stories and humor. 970 00:51:43,560 --> 00:51:48,260 And demos and, related to that, things you can see-- 971 00:51:48,260 --> 00:51:49,630 visual examples. 972 00:51:57,260 --> 00:52:02,040 And another pair of environments-- 973 00:52:02,040 --> 00:52:03,290 credibility-- 974 00:52:07,480 --> 00:52:09,310 filling the lecture space-- 975 00:52:09,310 --> 00:52:15,650 and what I haven't directly said yet as such, but we'll 976 00:52:15,650 --> 00:52:22,150 call it a safe environment for learning. 977 00:52:22,150 --> 00:52:24,160 Creating a safe environment for learning. 978 00:52:24,160 --> 00:52:28,490 That's what discussion at several scales enables. 979 00:52:28,490 --> 00:52:30,710 You create a safe environment for people to think for 980 00:52:30,710 --> 00:52:33,960 themselves, which then makes it safe for them to think in a 981 00:52:33,960 --> 00:52:36,490 group and discuss in group, which then makes it safe for 982 00:52:36,490 --> 00:52:40,050 them to think in a whole class. 983 00:52:40,050 --> 00:52:44,420 And so that makes safe bridge, or two bridges, towards 984 00:52:44,420 --> 00:52:46,260 collective participation. 985 00:52:46,260 --> 00:52:50,540 So you've made a safe learning and questioning environment. 986 00:52:50,540 --> 00:52:53,750 Without this environment, that won't happen. 987 00:52:53,750 --> 00:52:56,740 So I put these in three columns because I think they 988 00:52:56,740 --> 00:53:01,630 fall into sort of three pieces of the brain. 989 00:53:01,630 --> 00:53:02,880 Questions and discussion-- 990 00:53:05,510 --> 00:53:06,760 sort of left brain. 991 00:53:09,470 --> 00:53:19,990 Stories, humor, demos, and visual-- that's right brain. 992 00:53:19,990 --> 00:53:22,360 And credibility and a safe environment-- 993 00:53:22,360 --> 00:53:31,240 I'll call that the emotional brain, the amygdala. 994 00:53:31,240 --> 00:53:34,910 Maybe you could put humor over there, as well. 995 00:53:34,910 --> 00:53:37,800 But the reason I put preamble stories with the right brain 996 00:53:37,800 --> 00:53:41,770 is it's a different kind of learning than we think of when 997 00:53:41,770 --> 00:53:43,560 we think of left-brain learning, for example, 998 00:53:43,560 --> 00:53:47,990 learning an analytical method or the sequence 999 00:53:47,990 --> 00:53:49,740 of steps or a recipe. 1000 00:53:49,740 --> 00:53:52,140 The learning that happens from stories-- 1001 00:53:52,140 --> 00:53:55,260 for example, about the depth perception-- 1002 00:53:55,260 --> 00:53:56,110 is a different kind. 1003 00:53:56,110 --> 00:53:57,930 It's kind of implicit in a way, more 1004 00:53:57,930 --> 00:53:59,810 perceptive and the holistic. 1005 00:53:59,810 --> 00:54:01,810 So I put it in the right-brain category. 1006 00:54:01,810 --> 00:54:06,610 So these are main themes in creating your own classroom 1007 00:54:06,610 --> 00:54:09,370 teaching environment and structuring how 1008 00:54:09,370 --> 00:54:10,520 you're going to teach. 1009 00:54:10,520 --> 00:54:15,140 And sure, there's also all the questions of content. 1010 00:54:15,140 --> 00:54:18,060 But the reason I'm focusing on all of these is that the 1011 00:54:18,060 --> 00:54:19,990 questions of content-- 1012 00:54:19,990 --> 00:54:22,220 those have been done so many, so many times. 1013 00:54:22,220 --> 00:54:23,890 You can find all the content in a 1014 00:54:23,890 --> 00:54:25,630 gazillion different textbooks. 1015 00:54:25,630 --> 00:54:27,320 But the question is, how do you integrate all of that 1016 00:54:27,320 --> 00:54:30,990 content into something that makes for 1017 00:54:30,990 --> 00:54:32,390 good student learning? 1018 00:54:32,390 --> 00:54:35,990 And to do that, you need to take account of all this, all 1019 00:54:35,990 --> 00:54:39,030 of these features, all these aspects of the brain. 1020 00:54:39,030 --> 00:54:42,540 Because humans are not computers. 1021 00:54:42,540 --> 00:54:45,490 And they can't just learn by being programmed. 1022 00:54:45,490 --> 00:54:54,740 So from all these themes, extract one giant theme, which 1023 00:54:54,740 --> 00:55:03,527 is that teaching is not necessarily equal to learning. 1024 00:55:06,390 --> 00:55:10,820 Just standing up there and teaching stuff is no guarantee 1025 00:55:10,820 --> 00:55:11,917 that students will learn it. 1026 00:55:11,917 --> 00:55:15,270 You need to pay attention to all these features, all of the 1027 00:55:15,270 --> 00:55:17,430 human interaction to make sure that 1028 00:55:17,430 --> 00:55:20,160 learning actually happens. 1029 00:55:20,160 --> 00:55:24,900 So that's, if anything, the main theme. 1030 00:55:24,900 --> 00:55:33,270 Or phrased another way is that meaning and knowledge must be 1031 00:55:33,270 --> 00:55:34,730 constructed by the learner. 1032 00:55:50,020 --> 00:55:54,700 And all these ideas up here, these scripting elements, 1033 00:55:54,700 --> 00:55:58,270 these principles here are ways to help that 1034 00:55:58,270 --> 00:55:59,690 construction happen. 1035 00:55:59,690 --> 00:56:01,680 Just telling them doesn't do it. 1036 00:56:01,680 --> 00:56:06,250 You have to enable, facilitate, that construction. 1037 00:56:06,250 --> 00:56:09,440 So what we're going to do for the rest of the semester is 1038 00:56:09,440 --> 00:56:12,720 we're going to see these principles, these principles, 1039 00:56:12,720 --> 00:56:17,705 these boiled-down themes, this idea, this large idea-- 1040 00:56:23,550 --> 00:56:27,370 the big idea of the entire course exemplified in several 1041 00:56:27,370 --> 00:56:31,230 topics and areas that are central to teaching science 1042 00:56:31,230 --> 00:56:32,870 and engineering and mathematics 1043 00:56:32,870 --> 00:56:35,490 at the college level. 1044 00:56:35,490 --> 00:56:38,460 And so the outline for the rest of the 1045 00:56:38,460 --> 00:56:39,750 semester is as follows. 1046 00:56:43,180 --> 00:56:44,330 Today was lecture one. 1047 00:56:44,330 --> 00:56:46,270 And that was general principles of teaching. 1048 00:56:55,800 --> 00:56:58,115 The next one will be on how to teach equations. 1049 00:57:04,640 --> 00:57:07,600 Equations are central in all science and mathematics and 1050 00:57:07,600 --> 00:57:08,300 engineering teaching. 1051 00:57:08,300 --> 00:57:09,900 So how do you teach equations-- 1052 00:57:09,900 --> 00:57:12,150 in other words, some of the central content-- 1053 00:57:12,150 --> 00:57:14,400 taking account of all of these ideas? 1054 00:57:18,440 --> 00:57:20,240 Can you tell stories when you teach equations? 1055 00:57:20,240 --> 00:57:21,430 How can you do that? 1056 00:57:21,430 --> 00:57:23,940 Well, we'll see. 1057 00:57:23,940 --> 00:57:27,030 The third lecture, the third topic, is taking account of 1058 00:57:27,030 --> 00:57:44,270 students' misconceptions and thereby 1059 00:57:44,270 --> 00:57:47,390 avoiding rote learning. 1060 00:57:47,390 --> 00:57:50,720 So you can see already where some of the ideas that we've 1061 00:57:50,720 --> 00:57:52,510 been talking about here are going to help here. 1062 00:57:52,510 --> 00:57:56,450 For example, having lots of interaction and voting-- 1063 00:57:56,450 --> 00:57:58,050 you find out where the students are. 1064 00:57:58,050 --> 00:58:00,630 You'll find out if they have funny ways of thinking about 1065 00:58:00,630 --> 00:58:04,390 stuff, maybe even predictable ways, but ways that don't help 1066 00:58:04,390 --> 00:58:06,250 them actually solve problems in the real world. 1067 00:58:06,250 --> 00:58:08,590 Well, how do you take account of that? 1068 00:58:08,590 --> 00:58:11,070 There's one way right there already. 1069 00:58:11,070 --> 00:58:17,685 Then designing homework and exam problems. 1070 00:58:27,220 --> 00:58:29,140 And the fifth one is course design. 1071 00:58:38,370 --> 00:58:40,310 How do you structure a whole course? 1072 00:58:48,390 --> 00:58:49,920 Sixth one is teaching interactively. 1073 00:59:00,180 --> 00:59:03,200 As an example, you've already seen one example, which is 1074 00:59:03,200 --> 00:59:04,510 this kind of question. 1075 00:59:04,510 --> 00:59:05,340 Well, what are the general 1076 00:59:05,340 --> 00:59:07,350 principles behind such questions? 1077 00:59:07,350 --> 00:59:09,760 Can you make longer versions, shorter ones? 1078 00:59:09,760 --> 00:59:12,380 Are there short ways of building in interaction and 1079 00:59:12,380 --> 00:59:13,640 questions into learning? 1080 00:59:17,940 --> 00:59:19,900 Then what do you actually do when you 1081 00:59:19,900 --> 00:59:20,960 come into the classroom? 1082 00:59:20,960 --> 00:59:22,500 Lecture planning and performing-- 1083 00:59:22,500 --> 00:59:24,080 how do you plan one lecture? 1084 00:59:24,080 --> 00:59:27,630 So this is the overall structure of the whole course. 1085 00:59:27,630 --> 00:59:29,510 How do you plan and perform one lecture? 1086 00:59:43,650 --> 00:59:49,080 Topic eight is teaching with blackboards and slides. 1087 00:59:49,080 --> 00:59:52,130 So what are the advantages, generally speaking, of 1088 00:59:52,130 --> 00:59:52,880 blackboards? 1089 00:59:52,880 --> 00:59:56,650 But what are situations where slides are actually a really 1090 00:59:56,650 --> 00:59:59,840 helpful way to teach? 1091 00:59:59,840 --> 01:00:02,330 Slides meaning-- well, it could be old-style 1092 01:00:02,330 --> 01:00:07,170 photographic slides, but pre-prepared PDF files that 1093 01:00:07,170 --> 01:00:09,700 projected on the screen with an LCD projector is generally 1094 01:00:09,700 --> 01:00:10,950 how it's done now. 1095 01:00:16,340 --> 01:00:18,450 And then how do you plan blackboard work? 1096 01:00:18,450 --> 01:00:21,610 How do you construct slides so that they're effective in 1097 01:00:21,610 --> 01:00:22,860 creating learning? 1098 01:00:25,290 --> 01:00:27,650 Ninth is sort of a result of all these. 1099 01:00:27,650 --> 01:00:29,860 Well, if you're going to apply all these principles, you'll 1100 01:00:29,860 --> 01:00:32,660 find yourself wanting to change a lot about how the 1101 01:00:32,660 --> 01:00:35,230 course is done or how it was done previously. 1102 01:00:35,230 --> 01:00:36,820 Well, what are the barriers to that? 1103 01:00:36,820 --> 01:00:39,280 In particular, what are the political barriers to 1104 01:00:39,280 --> 01:00:40,530 educational change? 1105 01:00:54,720 --> 01:00:58,810 So that by being aware of the barriers, you're more able to 1106 01:00:58,810 --> 01:01:03,770 go around them, surmount them, take account of them, plan for 1107 01:01:03,770 --> 01:01:05,380 doing it bit by bit by bit. 1108 01:01:05,380 --> 01:01:07,960 But eventually, hopefully designing courses in ways that 1109 01:01:07,960 --> 01:01:10,080 you think are good for promoting learning. 1110 01:01:10,080 --> 01:01:13,540 And then the 10th topic will be a summary of everything, 1111 01:01:13,540 --> 01:01:15,730 using the examples we've done the whole semester and a 1112 01:01:15,730 --> 01:01:16,580 chance for-- 1113 01:01:16,580 --> 01:01:20,600 well, you'd ask questions about the whole course. 1114 01:01:31,760 --> 01:01:37,400 OK, so that's the themes of this entire semester of 1115 01:01:37,400 --> 01:01:40,110 teaching college-level science and engineering 1116 01:01:40,110 --> 01:01:42,110 one topic at a time. 1117 01:01:42,110 --> 01:01:43,820 See everyone next week. 1118 01:01:46,682 --> 01:01:48,900 ANNOUNCER: Answers from lecture two to questions 1119 01:01:48,900 --> 01:01:51,800 generated in lecture one. 1120 01:01:51,800 --> 01:01:53,720 PROFESSOR: What I'm going to do is answer your questions 1121 01:01:53,720 --> 01:02:00,230 from last time on the feedback sheets. 1122 01:02:00,230 --> 01:02:03,000 And I'll pass out a new set of feedback sheets in a moment. 1123 01:02:03,000 --> 01:02:05,340 So I should say that the questions 1124 01:02:05,340 --> 01:02:07,280 were, as always, excellent. 1125 01:02:07,280 --> 01:02:10,290 And I learned a lot by thinking about them. 1126 01:02:10,290 --> 01:02:15,140 And I hope that you'll learn a lot as you hear the results of 1127 01:02:15,140 --> 01:02:18,810 everyone else's questions together, and that they 1128 01:02:18,810 --> 01:02:21,480 reflect concerns that maybe all of you had at different 1129 01:02:21,480 --> 01:02:24,640 levels and the question that you may have put down may not 1130 01:02:24,640 --> 01:02:26,370 have been all of your concerns. 1131 01:02:26,370 --> 01:02:29,930 But collectively, hopefully it captures most of them. 1132 01:02:29,930 --> 01:02:33,180 So I'll categorize the first section of 1133 01:02:33,180 --> 01:02:34,995 questions as in reality. 1134 01:02:39,260 --> 01:02:40,430 I've typed in all the questions. 1135 01:02:40,430 --> 01:02:42,200 I'm going to put them all on the course website. 1136 01:02:42,200 --> 01:02:43,410 So you can see the questions. 1137 01:02:43,410 --> 01:02:46,260 And the answers will be here, but you'll see the questions. 1138 01:02:46,260 --> 01:02:48,380 So in reality-- 1139 01:02:48,380 --> 01:02:52,550 one question along that line is, what about grading? 1140 01:02:52,550 --> 01:02:56,060 How do you actually implement your grading policy as an 1141 01:02:56,060 --> 01:02:59,150 assistant professor in a traditional department? 1142 01:02:59,150 --> 01:03:02,810 So my grading policy is generally that, especially in 1143 01:03:02,810 --> 01:03:07,930 a pass/fail course, that the grading be very minimal. 1144 01:03:07,930 --> 01:03:09,380 And in general, I think that's a good 1145 01:03:09,380 --> 01:03:12,650 policy for grading overall. 1146 01:03:12,650 --> 01:03:15,300 And we can talk throughout the semester about why and the 1147 01:03:15,300 --> 01:03:17,160 research behind that. 1148 01:03:17,160 --> 01:03:21,580 But how would you do that if you're starting out new? 1149 01:03:21,580 --> 01:03:25,650 And the general rule is there's no right answer. 1150 01:03:25,650 --> 01:03:28,060 For example, one solution-- 1151 01:03:28,060 --> 01:03:29,980 it's not quite the answer to the question-- 1152 01:03:29,980 --> 01:03:33,950 is to take a position at a place where you're the 1153 01:03:33,950 --> 01:03:35,750 department head. 1154 01:03:35,750 --> 01:03:40,510 So actually, I was offered a teaching position like that 1155 01:03:40,510 --> 01:03:41,650 after I finished graduate school. 1156 01:03:41,650 --> 01:03:43,300 And I thought long and hard about it. 1157 01:03:43,300 --> 01:03:45,970 So I would have been the head of the physics and math 1158 01:03:45,970 --> 01:03:47,700 department. 1159 01:03:47,700 --> 01:03:49,570 Now, that was the good side. 1160 01:03:49,570 --> 01:03:53,260 The bad side was that I was the only member of both 1161 01:03:53,260 --> 01:03:54,670 departments. 1162 01:03:54,670 --> 01:03:56,400 And so on the one hand, I was a department head. 1163 01:03:56,400 --> 01:03:59,080 But also, I was the only one doing all the teaching. 1164 01:03:59,080 --> 01:04:01,870 And I would have only me to boss around. 1165 01:04:01,870 --> 01:04:05,220 But in that situation, you do have a huge amount of freedom. 1166 01:04:05,220 --> 01:04:08,670 And I could have done pretty much whatever I wanted. 1167 01:04:08,670 --> 01:04:12,130 Now, I decided not to take that position because I really 1168 01:04:12,130 --> 01:04:15,920 wasn't sure exactly what I wanted to do in terms of 1169 01:04:15,920 --> 01:04:16,740 improving teaching. 1170 01:04:16,740 --> 01:04:18,770 And I thought, well, I really need some more experience. 1171 01:04:18,770 --> 01:04:22,080 And I decided to do a post-doc. 1172 01:04:22,080 --> 01:04:25,150 But that is one solution to that problem. 1173 01:04:25,150 --> 01:04:28,100 It's not a very generalizable solution. 1174 01:04:28,100 --> 01:04:30,220 There are not many positions like that. 1175 01:04:30,220 --> 01:04:37,560 Another solution is to what I call the Clark Kent solution. 1176 01:04:37,560 --> 01:04:42,290 So you go around as a traditional faculty member, in 1177 01:04:42,290 --> 01:04:44,130 the Clark Kent outfit. 1178 01:04:44,130 --> 01:04:46,780 And then as soon as you get tenure, foom, 1179 01:04:46,780 --> 01:04:48,270 off comes the suit. 1180 01:04:48,270 --> 01:04:50,430 And everyone realizes that oh, actually, we hired someone 1181 01:04:50,430 --> 01:04:52,830 else completely, who actually has all these interesting 1182 01:04:52,830 --> 01:04:54,820 ideas about teaching. 1183 01:04:54,820 --> 01:05:01,210 So that is generally legally protected to some extent. 1184 01:05:01,210 --> 01:05:07,370 And you won't easily be fired, although a colleague of mine 1185 01:05:07,370 --> 01:05:09,150 in Canada-- 1186 01:05:09,150 --> 01:05:12,740 the university is trying to fire him for 1187 01:05:12,740 --> 01:05:16,440 giving all As in a course. 1188 01:05:16,440 --> 01:05:19,350 So this does speak to this question. 1189 01:05:19,350 --> 01:05:20,620 And it shows it is a tricky issue. 1190 01:05:20,620 --> 01:05:23,450 So he believes-- and I agree with him-- 1191 01:05:23,450 --> 01:05:27,450 that grades generally just produce obedient people. 1192 01:05:27,450 --> 01:05:29,850 One of their main functions is to produce obedient people and 1193 01:05:29,850 --> 01:05:32,620 obedient students, rather than students who love learning and 1194 01:05:32,620 --> 01:05:34,290 want to question. 1195 01:05:34,290 --> 01:05:37,410 So he wanted to teach one of his courses-- he's a tenured 1196 01:05:37,410 --> 01:05:38,230 professor of physics. 1197 01:05:38,230 --> 01:05:40,570 He wanted to teach one of his courses pass/fail. 1198 01:05:40,570 --> 01:05:42,300 And the university said, no. 1199 01:05:42,300 --> 01:05:45,250 By university regulations, that course is graded only. 1200 01:05:45,250 --> 01:05:47,120 It has to be taught with grades. 1201 01:05:47,120 --> 01:05:48,700 So he said, OK, fine. 1202 01:05:48,700 --> 01:05:50,660 On the first day of class, he just told everyone they were 1203 01:05:50,660 --> 01:05:53,390 going to get an A+. 1204 01:05:53,390 --> 01:05:55,590 And according to the TA-- 1205 01:05:55,590 --> 01:06:00,050 at least, this was then reported in Canada's Globe and 1206 01:06:00,050 --> 01:06:02,760 Mail, their sort of New York Times-- 1207 01:06:02,760 --> 01:06:04,490 one of the teaching assistants for the course said, yeah, 1208 01:06:04,490 --> 01:06:07,010 there were a few students who took advantage of that fact. 1209 01:06:07,010 --> 01:06:12,240 But most actually did more work and were very interested 1210 01:06:12,240 --> 01:06:13,800 in the material because of it. 1211 01:06:13,800 --> 01:06:16,540 So I would say, basically, the thing was a success. 1212 01:06:16,540 --> 01:06:19,610 And that's generally what I find, that the less emphasis 1213 01:06:19,610 --> 01:06:21,120 you put on grades-- 1214 01:06:21,120 --> 01:06:22,810 especially at a place like MIT-- 1215 01:06:22,810 --> 01:06:26,620 the students' natural interest in the material comes out. 1216 01:06:26,620 --> 01:06:29,050 And they're more and more willing to work and learn. 1217 01:06:29,050 --> 01:06:30,600 And that produces long-lasting learning. 1218 01:06:30,600 --> 01:06:32,510 Because they're doing it for their own reasons, not because 1219 01:06:32,510 --> 01:06:34,450 you stood over them with a grade and beat 1220 01:06:34,450 --> 01:06:35,640 them over the head. 1221 01:06:35,640 --> 01:06:38,020 So that was good. 1222 01:06:38,020 --> 01:06:41,190 The bad part is the university basically said, well, you're 1223 01:06:41,190 --> 01:06:44,290 defying us, and you're going against the purpose of the 1224 01:06:44,290 --> 01:06:44,665 university. 1225 01:06:44,665 --> 01:06:46,820 It's not really clear what the purpose of the university is, 1226 01:06:46,820 --> 01:06:49,190 except maybe to produce obedient people. 1227 01:06:49,190 --> 01:06:52,550 So they said, we're going to institute proceedings for your 1228 01:06:52,550 --> 01:06:56,850 dismissal, to strip you of your tenure and fire you, 1229 01:06:56,850 --> 01:06:59,550 which is a big step for a tenured professor. 1230 01:06:59,550 --> 01:07:02,130 And meanwhile, they banned him from campus. 1231 01:07:02,130 --> 01:07:05,310 So he's now not allowed on his own university campus. 1232 01:07:05,310 --> 01:07:08,010 So then he came to campus for a film screening, because he 1233 01:07:08,010 --> 01:07:10,460 runs a film series on the campus. 1234 01:07:10,460 --> 01:07:13,020 So he came for that, and the university 1235 01:07:13,020 --> 01:07:14,560 police arrested him. 1236 01:07:14,560 --> 01:07:16,830 So he was arrested for going to his own university. 1237 01:07:16,830 --> 01:07:19,320 So then it got into the national press in Canada, 1238 01:07:19,320 --> 01:07:21,450 which doesn't make the university look so good. 1239 01:07:21,450 --> 01:07:24,520 But that's all by way of saying that grading is a very 1240 01:07:24,520 --> 01:07:27,210 touchy issue with universities. 1241 01:07:27,210 --> 01:07:29,690 And it's really not clear what to do about it, because it's 1242 01:07:29,690 --> 01:07:31,510 so embedded in the system. 1243 01:07:31,510 --> 01:07:35,690 So I can't really offer you any solutions to that question 1244 01:07:35,690 --> 01:07:39,070 except to say that it's a very tricky negotiation and you 1245 01:07:39,070 --> 01:07:42,700 want to plan your activities carefully. 1246 01:07:42,700 --> 01:07:46,610 If you're going to use a lighter grading system, don't 1247 01:07:46,610 --> 01:07:47,760 do it all at once. 1248 01:07:47,760 --> 01:07:52,140 Get people around you to accept it slowly, slowly. 1249 01:07:52,140 --> 01:07:53,860 Get students on your side slowly. 1250 01:07:53,860 --> 01:07:55,190 Do things slowly. 1251 01:07:55,190 --> 01:07:59,240 Don't make any sudden moves that get yourself fired. 1252 01:07:59,240 --> 01:08:02,040 Work with other people of like minds. 1253 01:08:02,040 --> 01:08:03,960 Work together collectively. 1254 01:08:03,960 --> 01:08:07,330 So it's not a long-term instant solution. 1255 01:08:07,330 --> 01:08:10,220 But any kind of social problem-- and I think grading 1256 01:08:10,220 --> 01:08:11,330 is a social problem-- 1257 01:08:11,330 --> 01:08:14,210 doesn't have any instant solutions. 1258 01:08:14,210 --> 01:08:17,069 So I wanted to answer that one first, to basically tell you 1259 01:08:17,069 --> 01:08:19,020 that I don't have all the answers to all the questions. 1260 01:08:19,020 --> 01:08:23,020 And I want to give you honest answers as far as I know them. 1261 01:08:23,020 --> 01:08:25,170 OK, next question about reality. 1262 01:08:25,170 --> 01:08:27,340 You've obviously done this many times before. 1263 01:08:27,340 --> 01:08:29,979 As someone who needs to figure out a logical order for the 1264 01:08:29,979 --> 01:08:32,600 material in addition to balancing preparation time and 1265 01:08:32,600 --> 01:08:35,470 research, how do we juggle all this in addition to simply 1266 01:08:35,470 --> 01:08:37,149 focusing on style? 1267 01:08:37,149 --> 01:08:40,270 So I want to dispel one misconception was that last 1268 01:08:40,270 --> 01:08:44,500 time, I wasn't saying that you can substitute style for 1269 01:08:44,500 --> 01:08:46,859 preparation and really knowing the material. 1270 01:08:46,859 --> 01:08:50,640 It's really that I wanted to up the importance that people 1271 01:08:50,640 --> 01:08:55,490 give to what people would call style by saying that the way 1272 01:08:55,490 --> 01:08:57,950 you present, how you present, is as 1273 01:08:57,950 --> 01:08:59,380 important as what you present. 1274 01:08:59,380 --> 01:09:02,359 In fact, it is, to some extent, what you present. 1275 01:09:02,359 --> 01:09:04,870 If, for example, you're very interested in the material, 1276 01:09:04,870 --> 01:09:08,810 and you present it in that way, well, the students are 1277 01:09:08,810 --> 01:09:12,630 very naturally going to become interested in the material. 1278 01:09:12,630 --> 01:09:14,609 As a test of this, you can actually do little home 1279 01:09:14,609 --> 01:09:16,870 experiments on this principle. 1280 01:09:16,870 --> 01:09:18,014 So just go around to somebody. 1281 01:09:18,014 --> 01:09:20,630 You can do these little like Candid Camera experiments. 1282 01:09:20,630 --> 01:09:24,899 Just go up to them and smile, just like this, and then watch 1283 01:09:24,899 --> 01:09:25,930 what they do. 1284 01:09:25,930 --> 01:09:27,830 And a whole bunch of people actually just smiled back at 1285 01:09:27,830 --> 01:09:30,560 me for no reason at all, just because I smiled. 1286 01:09:30,560 --> 01:09:31,939 Now, not no reason at all. 1287 01:09:31,939 --> 01:09:33,750 It's because we're social creatures. 1288 01:09:33,750 --> 01:09:37,399 We're programmed from millions of years of evolution to pick 1289 01:09:37,399 --> 01:09:40,689 up other people's emotions and ways of being. 1290 01:09:40,689 --> 01:09:43,229 So if you're enthusiastic about the material, if you're 1291 01:09:43,229 --> 01:09:44,840 interested in it, and you present it like it's 1292 01:09:44,840 --> 01:09:47,910 important, well, that actually gets transmitted very 1293 01:09:47,910 --> 01:09:51,010 effectively and picked up at the other end very 1294 01:09:51,010 --> 01:09:51,720 effectively. 1295 01:09:51,720 --> 01:09:53,720 So actually, that is part of the content. 1296 01:09:53,720 --> 01:09:56,910 So I wouldn't say style is separate from the content. 1297 01:09:56,910 --> 01:10:00,060 How you present, how you think about the material is a 1298 01:10:00,060 --> 01:10:02,350 crucially important part of the material. 1299 01:10:02,350 --> 01:10:04,650 Because that's when students are going to be taking away. 1300 01:10:04,650 --> 01:10:06,700 And that's going to be affecting how they think about 1301 01:10:06,700 --> 01:10:07,650 the material. 1302 01:10:07,650 --> 01:10:12,190 So it's not just focusing on style-- 1303 01:10:12,190 --> 01:10:14,250 that sort of gives it too little importance. 1304 01:10:14,250 --> 01:10:16,430 Instead, yeah, how do you think about all those issues 1305 01:10:16,430 --> 01:10:19,010 as well as surviving your research grant? 1306 01:10:19,010 --> 01:10:22,450 And again, there I would say the way to do 1307 01:10:22,450 --> 01:10:24,710 it is to start slow. 1308 01:10:24,710 --> 01:10:27,970 When you're an assistant professor, you need to focus 1309 01:10:27,970 --> 01:10:29,430 on your research to get tenure. 1310 01:10:29,430 --> 01:10:32,250 So focus on your research and just try small teaching 1311 01:10:32,250 --> 01:10:34,480 experiments bit by bit. 1312 01:10:34,480 --> 01:10:38,170 Maybe in your first year, just try putting in one small 1313 01:10:38,170 --> 01:10:42,170 conceptual question per lecture or per week. 1314 01:10:42,170 --> 01:10:44,400 And if that goes OK, maybe try longer ones. 1315 01:10:44,400 --> 01:10:47,340 Try more the next semester or the next year. 1316 01:10:47,340 --> 01:10:49,070 So just try small things. 1317 01:10:49,070 --> 01:10:51,620 And as they work, grow them. 1318 01:10:51,620 --> 01:10:54,510 So that's one way, so you don't have to sacrifice your 1319 01:10:54,510 --> 01:10:57,570 research and hose yourself. 1320 01:10:57,570 --> 01:11:01,600 So preparation time, as well-- so try to borrow notes from 1321 01:11:01,600 --> 01:11:02,460 colleagues. 1322 01:11:02,460 --> 01:11:06,640 Try to get as much from other people as you can share. 1323 01:11:06,640 --> 01:11:08,295 Talent invents, genius steals. 1324 01:11:08,295 --> 01:11:11,570 So steal all the good stuff around you. 1325 01:11:11,570 --> 01:11:14,380 So another one is how does this work in the real world, 1326 01:11:14,380 --> 01:11:15,910 which is basically the same thing. 1327 01:11:15,910 --> 01:11:17,800 So what I'm trying to do in this class is show you general 1328 01:11:17,800 --> 01:11:22,640 principles that you can use always to guide yourself in as 1329 01:11:22,640 --> 01:11:25,340 far as you want to go in your teaching. 1330 01:11:25,340 --> 01:11:28,400 So now how far you go in your particular situation depends 1331 01:11:28,400 --> 01:11:32,700 on your situation and how much importance you put on doing 1332 01:11:32,700 --> 01:11:36,570 new teaching methods, new experiments right then. 1333 01:11:36,570 --> 01:11:39,490 But I'm not saying you have to start everything tomorrow, 1334 01:11:39,490 --> 01:11:42,090 like the first day you're a TA, all of sudden throw out 1335 01:11:42,090 --> 01:11:45,000 all the regular stuff and do everything like I'm 1336 01:11:45,000 --> 01:11:45,770 demonstrating now. 1337 01:11:45,770 --> 01:11:48,840 I'm showing you this as examples to illustrate 1338 01:11:48,840 --> 01:11:52,130 principles for directions you could go and for threads you 1339 01:11:52,130 --> 01:11:55,670 can pick up as you see best. 1340 01:11:55,670 --> 01:11:58,080 Syllabus and logistics for this class-- 1341 01:11:58,080 --> 01:11:59,550 any exams or problem sets? 1342 01:11:59,550 --> 01:12:02,810 Yeah, there's problem sets, which you've seen one already. 1343 01:12:02,810 --> 01:12:05,520 No exams. 1344 01:12:05,520 --> 01:12:07,610 And so how are you being evaluated? 1345 01:12:07,610 --> 01:12:10,060 Basically again, very light touch. 1346 01:12:10,060 --> 01:12:11,510 Basically, just make a reasonable effort on the 1347 01:12:11,510 --> 01:12:14,050 problem sets, and you'll be fine. 1348 01:12:14,050 --> 01:12:17,150 I'm hoping basically that the material's interesting enough 1349 01:12:17,150 --> 01:12:21,010 that you don't need a stick beating you, saying, oh, you 1350 01:12:21,010 --> 01:12:23,310 must do this, you must do that, you must do this. 1351 01:12:23,310 --> 01:12:24,630 It's not a required course. 1352 01:12:24,630 --> 01:12:26,710 People are taking it really because they're interested. 1353 01:12:26,710 --> 01:12:29,700 So I'm not going to try to ruin that with a whole bunch 1354 01:12:29,700 --> 01:12:33,410 of grading sticks. 1355 01:12:33,410 --> 01:12:36,150 Does it matter which subject number we're assigned for? 1356 01:12:36,150 --> 01:12:38,610 No, and I don't even remember what the subject numbers are. 1357 01:12:38,610 --> 01:12:40,600 I know 595, and there's a whole bunch of them. 1358 01:12:40,600 --> 01:12:41,620 So I just write et cetera. 1359 01:12:41,620 --> 01:12:44,740 No, it doesn't matter, as far as I know. 1360 01:12:44,740 --> 01:12:46,270 Could we have a break after one hour? 1361 01:12:46,270 --> 01:12:47,330 Yeah, I think that's a good idea. 1362 01:12:47,330 --> 01:12:50,230 So I'll give everyone like a two- or three-minute break at 1363 01:12:50,230 --> 01:12:52,300 the hour just so you can stand and get your 1364 01:12:52,300 --> 01:12:54,100 blood flowing again. 1365 01:12:54,100 --> 01:12:56,370 Biology examples-- can we have biology examples? 1366 01:12:56,370 --> 01:12:57,290 A fair point-- 1367 01:12:57,290 --> 01:13:00,550 so actually, today our first example of equations is a 1368 01:13:00,550 --> 01:13:02,630 biology example, amazingly. 1369 01:13:06,060 --> 01:13:08,430 OK, so now, interactive teaching-- how do you teach a 1370 01:13:08,430 --> 01:13:10,450 class interactively if you have a lot of 1371 01:13:10,450 --> 01:13:12,020 material to get through? 1372 01:13:12,020 --> 01:13:13,200 This is a very interesting question. 1373 01:13:13,200 --> 01:13:14,850 It comes up quite often. 1374 01:13:14,850 --> 01:13:17,850 And the answer is that you don't get 1375 01:13:17,850 --> 01:13:20,280 through it in the lecture. 1376 01:13:20,280 --> 01:13:23,010 So the lecture is a terrible place to get 1377 01:13:23,010 --> 01:13:25,090 through lots of material. 1378 01:13:25,090 --> 01:13:28,050 In fact, even the word "get through," "cover"-- 1379 01:13:28,050 --> 01:13:30,860 those all have the wrong sense to them. 1380 01:13:30,860 --> 01:13:34,660 And so Victor Weisskopf, MIT physics professor for many 1381 01:13:34,660 --> 01:13:38,750 years, he said-- and I think it's a great saying-- 1382 01:13:38,750 --> 01:13:42,140 instead of covering a lot of material, I prefer to uncover 1383 01:13:42,140 --> 01:13:44,630 a few key ideas. 1384 01:13:44,630 --> 01:13:48,350 So uncover is the right verb. 1385 01:13:48,350 --> 01:13:51,830 Cover has the sense of smother. 1386 01:13:51,830 --> 01:13:53,220 You can't see it anymore. 1387 01:13:53,220 --> 01:13:56,260 And that is what happens when you cover too much material. 1388 01:13:56,260 --> 01:14:00,385 You want to uncover a few ideas and let them bloom. 1389 01:14:00,385 --> 01:14:03,720 So a lecture is something that's paced at human scale. 1390 01:14:03,720 --> 01:14:07,180 You talk at maybe 150 words a minute. 1391 01:14:07,180 --> 01:14:09,040 People can't write that fast. 1392 01:14:09,040 --> 01:14:11,930 They can write maybe 15 words a minute. 1393 01:14:11,930 --> 01:14:14,300 Reading is much faster. 1394 01:14:14,300 --> 01:14:18,220 Reading-- people can read 300, maybe 400 words a minute. 1395 01:14:18,220 --> 01:14:21,070 So if you have lots of material to get through, don't 1396 01:14:21,070 --> 01:14:24,410 fall into the trap of putting it all on the blackboard or on 1397 01:14:24,410 --> 01:14:25,840 the overhead slides. 1398 01:14:25,840 --> 01:14:29,110 And we'll talk about that in the session on making good 1399 01:14:29,110 --> 01:14:31,020 slides and using the blackboard. 1400 01:14:31,020 --> 01:14:33,800 You want key ideas to be there. 1401 01:14:33,800 --> 01:14:38,030 And you can leave lots of the details for reading. 1402 01:14:38,030 --> 01:14:40,310 So that's one answer. 1403 01:14:40,310 --> 01:14:42,510 The other answer is that sometimes, actually, I think 1404 01:14:42,510 --> 01:14:44,500 one of the fundamental problems with so much teaching 1405 01:14:44,500 --> 01:14:46,600 is that we try to cover too much material. 1406 01:14:46,600 --> 01:14:50,140 And one of the goals should be for good teaching is to reduce 1407 01:14:50,140 --> 01:14:51,950 how much material one covers. 1408 01:14:51,950 --> 01:14:56,520 And there's a simple estimation argument to show 1409 01:14:56,520 --> 01:14:57,775 why that's important. 1410 01:14:57,775 --> 01:15:01,470 The estimation argument is that basically, suppose you 1411 01:15:01,470 --> 01:15:03,660 cover 100% of the material. 1412 01:15:03,660 --> 01:15:06,180 But because it's so much material, students remember 1413 01:15:06,180 --> 01:15:09,130 only 10%, and really learn only 10%, which I think is 1414 01:15:09,130 --> 01:15:11,280 actually a reasonable estimate. 1415 01:15:11,280 --> 01:15:12,700 Because they're just so overloaded. 1416 01:15:12,700 --> 01:15:14,930 They have no time to make connections, and it just 1417 01:15:14,930 --> 01:15:15,670 flitters away. 1418 01:15:15,670 --> 01:15:17,850 So 10% is all they retain. 1419 01:15:17,850 --> 01:15:21,310 Well, you could cover, say, half the material. 1420 01:15:21,310 --> 01:15:24,060 And let's say that they still don't remember everything, 1421 01:15:24,060 --> 01:15:24,860 even though you've done half. 1422 01:15:24,860 --> 01:15:27,140 Maybe they remember half of that, because they have time 1423 01:15:27,140 --> 01:15:29,490 to struggle with it, make connections. 1424 01:15:29,490 --> 01:15:32,850 So now, they're at half of half, which is 25% retention 1425 01:15:32,850 --> 01:15:34,130 instead of 10%. 1426 01:15:34,130 --> 01:15:36,390 So that's a plausible model. 1427 01:15:36,390 --> 01:15:38,830 I'm not claiming those figures are actually based on exact 1428 01:15:38,830 --> 01:15:39,710 research or anything. 1429 01:15:39,710 --> 01:15:42,380 But just a plausible model for how reducing the amount of 1430 01:15:42,380 --> 01:15:45,310 stuff you cover can actually increase learning. 1431 01:15:45,310 --> 01:15:48,380 So try to reduce material when possible. 1432 01:15:48,380 --> 01:15:50,210 Almost always, there's too much material. 1433 01:15:53,270 --> 01:15:55,470 OK, so again, how do you pace lectures? 1434 01:15:55,470 --> 01:15:57,820 If you do too many demos and you have less material, 1435 01:15:57,820 --> 01:15:59,820 advanced students might get bored. 1436 01:15:59,820 --> 01:16:02,750 Actually, I find advanced students are actually quite 1437 01:16:02,750 --> 01:16:05,680 interested in demos and questions like this that we 1438 01:16:05,680 --> 01:16:06,770 used last time. 1439 01:16:06,770 --> 01:16:09,220 They want to really understand what's going on. 1440 01:16:09,220 --> 01:16:11,790 And it's those kind of questions that help them. 1441 01:16:11,790 --> 01:16:13,220 Covering lots of material-- 1442 01:16:13,220 --> 01:16:15,700 again, they can read it in a book much faster than you can 1443 01:16:15,700 --> 01:16:16,690 write it on the board. 1444 01:16:16,690 --> 01:16:19,240 So put it there. 1445 01:16:19,240 --> 01:16:21,000 Can these principles be applied to upper-level 1446 01:16:21,000 --> 01:16:22,130 graduate classes? 1447 01:16:22,130 --> 01:16:23,460 For sure. 1448 01:16:23,460 --> 01:16:25,520 You can apply them all the way from kindergarten through 1449 01:16:25,520 --> 01:16:27,280 graduate school because they're really based on how 1450 01:16:27,280 --> 01:16:28,540 people think. 1451 01:16:28,540 --> 01:16:32,100 And they're based on common ways that people perceive the 1452 01:16:32,100 --> 01:16:32,980 world and reason. 1453 01:16:32,980 --> 01:16:34,380 And that doesn't change-- 1454 01:16:34,380 --> 01:16:36,840 I mean, life does change when you become a graduate student. 1455 01:16:36,840 --> 01:16:38,650 But your whole way of looking at the world 1456 01:16:38,650 --> 01:16:39,900 doesn't change that much. 1457 01:16:43,170 --> 01:16:45,170 So how do you deal with classes where someone 1458 01:16:45,170 --> 01:16:47,440 dominates a discussion or the class does not like to 1459 01:16:47,440 --> 01:16:47,820 participate? 1460 01:16:47,820 --> 01:16:50,270 Sort of two ends of the same coin. 1461 01:16:50,270 --> 01:16:53,080 So what I like to do is if someone keeps trying to say 1462 01:16:53,080 --> 01:16:56,320 stuff, I just say, oh, well, actually I want everybody to 1463 01:16:56,320 --> 01:16:58,040 participate. 1464 01:16:58,040 --> 01:16:59,690 Could I hear from someone I haven't heard from? 1465 01:16:59,690 --> 01:17:00,680 Just with a light touch. 1466 01:17:00,680 --> 01:17:03,070 You don't have to make a big confrontation 1467 01:17:03,070 --> 01:17:04,325 in class about it. 1468 01:17:04,325 --> 01:17:06,570 If people don't like to participate-- 1469 01:17:06,570 --> 01:17:08,850 for example, suppose you ask them to discuss with each 1470 01:17:08,850 --> 01:17:09,990 other and they don't. 1471 01:17:09,990 --> 01:17:12,430 So here's a trick I learned actually from one of the 1472 01:17:12,430 --> 01:17:16,080 teaching seminars when I was in England, which is that you 1473 01:17:16,080 --> 01:17:19,600 just turn your back. 1474 01:17:19,600 --> 01:17:20,990 And why do you do that? 1475 01:17:20,990 --> 01:17:25,450 Well, your back is not as interesting as your front. 1476 01:17:25,450 --> 01:17:28,830 So students are actually taught with, say, 12 years of 1477 01:17:28,830 --> 01:17:31,440 teaching to watch the teacher, watch the teacher. 1478 01:17:31,440 --> 01:17:33,420 So one of the reluctances to talk to each other is they're 1479 01:17:33,420 --> 01:17:34,750 watching the teacher, figuring out what the 1480 01:17:34,750 --> 01:17:36,680 teacher's saying and doing. 1481 01:17:36,680 --> 01:17:41,210 Kind of like Clever Hans was watching his trainer-- 1482 01:17:41,210 --> 01:17:43,502 do I do more clips on my foot? 1483 01:17:43,502 --> 01:17:44,490 Is that 42? 1484 01:17:44,490 --> 01:17:46,230 6 times 7-- 1485 01:17:46,230 --> 01:17:47,020 OK. 1486 01:17:47,020 --> 01:17:49,930 So students are actually taught, basically, after 12 1487 01:17:49,930 --> 01:17:53,180 years of conditioning, do that very automatically. 1488 01:17:53,180 --> 01:17:54,850 So you just have to break that conditioning a bit. 1489 01:17:54,850 --> 01:17:57,150 If you just turn around, there's nothing really that 1490 01:17:57,150 --> 01:17:58,800 interesting to look at, unless you're maybe-- 1491 01:17:58,800 --> 01:18:03,040 I don't know, some fashion model or a GQ model, which I'm 1492 01:18:03,040 --> 01:18:04,720 not claiming to be. 1493 01:18:04,720 --> 01:18:07,680 So then the students will just naturally be more likely to 1494 01:18:07,680 --> 01:18:08,340 talk to each other. 1495 01:18:08,340 --> 01:18:09,950 So you create the conditions for that. 1496 01:18:09,950 --> 01:18:10,820 Another one-- 1497 01:18:10,820 --> 01:18:12,270 and I often use this trick, because it's 1498 01:18:12,270 --> 01:18:13,340 actually not a trick-- 1499 01:18:13,340 --> 01:18:14,530 is sometimes I'm thirsty. 1500 01:18:14,530 --> 01:18:17,420 I just walk out of the room and go get a drink of water. 1501 01:18:17,420 --> 01:18:19,440 So if it's an interesting enough question, the students 1502 01:18:19,440 --> 01:18:20,870 will be talking to each other about it. 1503 01:18:20,870 --> 01:18:24,240 And there's definitely not you around there, watching them or 1504 01:18:24,240 --> 01:18:25,990 worrying them, for them to focus on. 1505 01:18:25,990 --> 01:18:28,270 So that's one very useful trick. 1506 01:18:28,270 --> 01:18:31,810 Generally, though, the overall point is if the class doesn't 1507 01:18:31,810 --> 01:18:35,080 want to participate, you just make it more and more safe to 1508 01:18:35,080 --> 01:18:35,455 participate. 1509 01:18:35,455 --> 01:18:37,820 You make sure you never criticize people if they say 1510 01:18:37,820 --> 01:18:39,340 something that wasn't right. 1511 01:18:39,340 --> 01:18:42,030 You make sure you value the wrong answers 1512 01:18:42,030 --> 01:18:43,060 and you explain why. 1513 01:18:43,060 --> 01:18:46,450 So all of the things I talked about last time about safety 1514 01:18:46,450 --> 01:18:48,630 means you just have to do them double if people aren't 1515 01:18:48,630 --> 01:18:49,880 participating. 1516 01:18:56,370 --> 01:18:58,320 How do you cope with a variety of confidence 1517 01:18:58,320 --> 01:19:00,740 levels among students? 1518 01:19:00,740 --> 01:19:01,570 Also interesting. 1519 01:19:01,570 --> 01:19:05,210 So there, I find actually that most 1520 01:19:05,210 --> 01:19:07,770 students aren't very confident. 1521 01:19:07,770 --> 01:19:09,020 They have different levels-- 1522 01:19:11,450 --> 01:19:14,060 they're all generally much lower than you think. 1523 01:19:14,060 --> 01:19:16,960 So they do have some different levels, but it's generally 1524 01:19:16,960 --> 01:19:18,520 overall lower than you think. 1525 01:19:18,520 --> 01:19:20,680 So I spend more of my effort making sure everyone feels 1526 01:19:20,680 --> 01:19:22,000 comfortable. 1527 01:19:22,000 --> 01:19:25,750 But again, if some students are much more confident than 1528 01:19:25,750 --> 01:19:29,360 others, I try to mix up the level of questions that I ask. 1529 01:19:29,360 --> 01:19:31,530 I ask some questions that I know most people are not going 1530 01:19:31,530 --> 01:19:33,690 to be able to answer and some questions that I know most 1531 01:19:33,690 --> 01:19:37,290 people will answer, just so everyone has something. 1532 01:19:37,290 --> 01:19:39,910 And then on the problem sets as well-- 1533 01:19:39,910 --> 01:19:41,080 warm-up problems, regular 1534 01:19:41,080 --> 01:19:43,720 problems, really hard problems. 1535 01:19:43,720 --> 01:19:47,700 Like in Donald Knuth's textbooks, the fifth set of, 1536 01:19:47,700 --> 01:19:50,130 kind of, problem at the end of the chapters is unsolved 1537 01:19:50,130 --> 01:19:51,520 research problems. 1538 01:19:51,520 --> 01:19:52,250 And you never know. 1539 01:19:52,250 --> 01:19:54,210 Someone might actually solve one of them. 1540 01:19:54,210 --> 01:19:56,680 So you can put something for everyone in there. 1541 01:19:59,690 --> 01:20:00,820 What about the left brain? 1542 01:20:00,820 --> 01:20:04,076 Surely humor and demos can't take you all the way. 1543 01:20:04,076 --> 01:20:05,770 Yeah, and that's true. 1544 01:20:05,770 --> 01:20:09,200 And so my answer to what about the left brain is that the 1545 01:20:09,200 --> 01:20:13,460 left brain is what basically most teaching has focused on 1546 01:20:13,460 --> 01:20:16,370 for most people's experience over the last 15 or 16 years. 1547 01:20:16,370 --> 01:20:19,020 So I'm not saying, forget about the left brain. 1548 01:20:19,020 --> 01:20:21,430 I'm saying that you basically already know how to do the 1549 01:20:21,430 --> 01:20:23,480 left-brain side of teaching. 1550 01:20:23,480 --> 01:20:25,520 You have so many models of that. 1551 01:20:25,520 --> 01:20:27,670 It is pretty much what we think of as teaching. 1552 01:20:27,670 --> 01:20:30,030 You go up to the blackboard, and you write down a series of 1553 01:20:30,030 --> 01:20:31,720 symbols one after another, write 1554 01:20:31,720 --> 01:20:32,940 down a series of equations. 1555 01:20:32,940 --> 01:20:35,990 So you already have models for that. 1556 01:20:35,990 --> 01:20:37,910 And we'll talk about how to improve those. 1557 01:20:37,910 --> 01:20:39,800 But I'm not so worried about that part. 1558 01:20:39,800 --> 01:20:41,970 What I'm worried about is the neglected part. 1559 01:20:41,970 --> 01:20:44,500 So this you could think of as the balance. 1560 01:20:44,500 --> 01:20:46,840 And then you'll be able to find ways of integrating the 1561 01:20:46,840 --> 01:20:47,370 left brain. 1562 01:20:47,370 --> 01:20:50,300 And we'll do left-brain things, equations. 1563 01:20:50,300 --> 01:20:52,870 But how do you integrate that with all the quote "right 1564 01:20:52,870 --> 01:20:54,300 brain," the humor and the demos? 1565 01:20:58,690 --> 01:21:00,450 How do you project confidence? 1566 01:21:00,450 --> 01:21:02,710 Fake it till you make it? 1567 01:21:02,710 --> 01:21:06,130 Yeah, that's basically right. 1568 01:21:06,130 --> 01:21:10,500 So one way is to actually make sure your voice is clear. 1569 01:21:10,500 --> 01:21:15,950 So to do that, my piano teacher in graduate school-- 1570 01:21:15,950 --> 01:21:18,080 actually, she was a voice teacher, as well. 1571 01:21:18,080 --> 01:21:22,456 She gave me a really useful exercise, which is-- 1572 01:21:22,456 --> 01:21:25,320 I do this for like 30 seconds before I come to lecture. 1573 01:21:25,320 --> 01:21:29,510 So the exercise is you first just close your lips. 1574 01:21:29,510 --> 01:21:32,780 And you mmm, you hum. 1575 01:21:32,780 --> 01:21:34,150 So we'll all do this together. 1576 01:21:34,150 --> 01:21:37,210 So you hum until you can feel it vibrating in your nose. 1577 01:21:37,210 --> 01:21:37,800 That's step one. 1578 01:21:37,800 --> 01:21:38,740 So let's all do that together. 1579 01:21:38,740 --> 01:21:43,670 [HUMMING] 1580 01:21:43,670 --> 01:21:46,000 And if you have hay fever, you can tell if you're doing it 1581 01:21:46,000 --> 01:21:47,300 right in the spring. 1582 01:21:47,300 --> 01:21:49,290 Because you'll dislodge pollen grains and 1583 01:21:49,290 --> 01:21:50,260 you'll probably sneeze. 1584 01:21:50,260 --> 01:21:51,840 That's what I find in the spring. 1585 01:21:51,840 --> 01:21:54,010 When I do that, I actually start sneezing. 1586 01:21:54,010 --> 01:21:56,800 My theory is that I'm dislodging pollen grains and 1587 01:21:56,800 --> 01:21:59,110 then I'm sneezing as a result of them. 1588 01:21:59,110 --> 01:22:00,170 So mmm-- 1589 01:22:00,170 --> 01:22:02,610 so now you've got a resonance up here. 1590 01:22:02,610 --> 01:22:07,610 And now what you want to do is with the same mmm sound, now 1591 01:22:07,610 --> 01:22:10,350 do it in the back of your teeth with your mouth closed. 1592 01:22:10,350 --> 01:22:11,890 So you feel behind your teeth. 1593 01:22:11,890 --> 01:22:14,600 So we'll do step one and then step two. 1594 01:22:14,600 --> 01:22:16,280 Mmm and then the teeth. 1595 01:22:16,280 --> 01:22:18,010 Mmm, teeth. 1596 01:22:18,010 --> 01:22:20,250 [HUMMING] 1597 01:22:20,250 --> 01:22:22,580 And you should feel in your lips 1598 01:22:22,580 --> 01:22:24,090 vibrating, kind of tickling. 1599 01:22:24,090 --> 01:22:26,520 OK, so that's step two. 1600 01:22:26,520 --> 01:22:31,100 Step three is to then make the vowel sound that is most 1601 01:22:31,100 --> 01:22:33,140 likely to make your mouth resonate and be 1602 01:22:33,140 --> 01:22:34,020 really wide and open. 1603 01:22:34,020 --> 01:22:41,280 That's E. So we'll go hmm and them mmm and eee. 1604 01:22:41,280 --> 01:22:42,940 OK, so nose-- 1605 01:22:42,940 --> 01:22:44,950 [HUMMING] 1606 01:22:44,950 --> 01:22:45,320 lips-- 1607 01:22:45,320 --> 01:22:46,790 [HUMMING] 1608 01:22:46,790 --> 01:22:48,040 eeeeeee. 1609 01:22:50,550 --> 01:22:51,330 OK, that's step three. 1610 01:22:51,330 --> 01:22:53,580 And then the final step is you just add some words. 1611 01:22:53,580 --> 01:22:55,050 You modulate it with words. 1612 01:22:55,050 --> 01:22:57,640 All right, so I'll give you a demonstration. 1613 01:22:57,640 --> 01:22:59,252 Then we'll do all of it together. 1614 01:22:59,252 --> 01:23:00,520 [HUMMING] 1615 01:23:00,520 --> 01:23:04,280 Eeeee-- (SPEAKING ON SAME NOTE) how are youuuuuu. 1616 01:23:04,280 --> 01:23:06,300 OK, so now, that sounds a bit strange. 1617 01:23:06,300 --> 01:23:09,230 But you find after you do that, your voice 1618 01:23:09,230 --> 01:23:10,330 is much more resonant. 1619 01:23:10,330 --> 01:23:12,420 Actually, I can hear it right now. 1620 01:23:12,420 --> 01:23:14,270 To my own ears, my voice sounds much more 1621 01:23:14,270 --> 01:23:16,200 resonant and clear. 1622 01:23:16,200 --> 01:23:17,606 So let's do that. 1623 01:23:17,606 --> 01:23:21,890 [HUMMING] 1624 01:23:21,890 --> 01:23:24,170 Eeeee-- 1625 01:23:24,170 --> 01:23:28,030 (SPEAKING ON SAME NOTE) how are youuuuuu. 1626 01:23:28,030 --> 01:23:30,510 So you'll find, actually, what you've done is you've shifted 1627 01:23:30,510 --> 01:23:34,800 your voice from here, where it just makes your throat tight, 1628 01:23:34,800 --> 01:23:36,070 to the front. 1629 01:23:36,070 --> 01:23:39,140 And just by doing that, you will project. 1630 01:23:39,140 --> 01:23:42,210 And by projecting, you actually sound more confident. 1631 01:23:42,210 --> 01:23:43,460 And you'll feel more confident. 1632 01:23:45,860 --> 01:23:47,590 So that's one way. 1633 01:23:47,590 --> 01:23:50,460 But another way is to be confident of your material. 1634 01:23:50,460 --> 01:23:53,190 And another way is, as you said in the question, just 1635 01:23:53,190 --> 01:23:54,516 fake it till you make it. 1636 01:23:58,070 --> 01:23:59,660 Now, there's a few more questions. 1637 01:23:59,660 --> 01:24:02,820 I'll answer some of them on the website. 1638 01:24:02,820 --> 01:24:05,410 But I wanted to answer one more. 1639 01:24:05,410 --> 01:24:08,640 How long did it take you to become such a good teacher? 1640 01:24:08,640 --> 01:24:11,650 So I'm glad people think I'm a good teacher, or at least one 1641 01:24:11,650 --> 01:24:14,250 person thinks so. 1642 01:24:14,250 --> 01:24:16,340 But there's a general answer to that question, which is 1643 01:24:16,340 --> 01:24:18,360 actually going to be one of the topics today, which is, 1644 01:24:18,360 --> 01:24:21,660 how do you become an expert in anything? 1645 01:24:21,660 --> 01:24:26,370 And the first example I'm going to show you-- it's 1646 01:24:26,370 --> 01:24:27,740 biology equations. 1647 01:24:27,740 --> 01:24:28,740 I'm going to use that. 1648 01:24:28,740 --> 01:24:32,340 And then after that, when I talk about expertise in 1649 01:24:32,340 --> 01:24:36,850 general, not just in teaching, and where that comes from. 1650 01:24:36,850 --> 01:24:40,530 And I'll show you the results of some studies. 1651 01:24:40,530 --> 01:24:42,440 And then I'll come back to that question. 1652 01:24:42,440 --> 01:24:45,980 And I'll hopefully answer it then. 1653 01:24:45,980 --> 01:24:48,930 So those are I would say 2/3 of the questions. 1654 01:24:48,930 --> 01:24:52,770 The ones I haven't answered I'll try to answer online. 1655 01:24:52,770 --> 01:24:55,730 And I'll pass out these in just a moment. 1656 01:24:55,730 --> 01:24:58,550 But right now, what we're going to do is we're going to 1657 01:24:58,550 --> 01:25:01,000 do the first example of equations, 1658 01:25:01,000 --> 01:25:02,360 which is from biology. 1659 01:25:02,360 --> 01:25:04,400 Now, before I do that, any questions that have occurred 1660 01:25:04,400 --> 01:25:07,585 to you meanwhile? 1661 01:25:07,585 --> 01:25:11,160 Did I create any new questions? 1662 01:25:11,160 --> 01:25:11,770 Yes. 1663 01:25:11,770 --> 01:25:14,476 AUDIENCE: Very germane, but if this is P/D/F, are we supposed 1664 01:25:14,476 --> 01:25:16,280 to be registered as P/D/F? 1665 01:25:16,280 --> 01:25:17,570 PROFESSOR: I think it's automatic. 1666 01:25:17,570 --> 01:25:20,075 I don't think there's any way not to register as P/D/F. 1667 01:25:20,075 --> 01:25:21,620 AUDIENCE: OK, thank you. 1668 01:25:21,620 --> 01:25:23,880 PROFESSOR: So the question was, if this is pass/fail, do 1669 01:25:23,880 --> 01:25:25,110 you have to specifically register as that? 1670 01:25:25,110 --> 01:25:25,690 I don't think so. 1671 01:25:25,690 --> 01:25:26,940 I think it's automatic. 1672 01:25:29,190 --> 01:25:31,140 So yeah, basically, don't worry about your grades. 1673 01:25:31,140 --> 01:25:32,920 Everyone's going to P.