1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:03,980 Commons license. 3 00:00:03,980 --> 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 00:00:22,320 --> 00:00:26,750 PROFESSOR: Welcome to Course Design today, how to plan a 9 00:00:26,750 --> 00:00:31,630 course and avoid the pitfalls that many courses fall into. 10 00:00:34,370 --> 00:00:38,230 In the past few sessions we've seen some of the results, for 11 00:00:38,230 --> 00:00:40,470 example the misconceptions, the rote 12 00:00:40,470 --> 00:00:42,410 learning, the lack of transfer. 13 00:00:42,410 --> 00:00:46,000 And how do you design a course so that your course doesn't 14 00:00:46,000 --> 00:00:48,190 commit more of that and contribute to that problem, 15 00:00:48,190 --> 00:00:49,980 but instead perhaps mitigates it? 16 00:00:49,980 --> 00:00:52,220 And it's a difficult problem. 17 00:00:52,220 --> 00:00:55,890 So related to that, sort of flowing almost directly from 18 00:00:55,890 --> 00:01:00,680 course design is that making large changes to courses is 19 00:01:00,680 --> 00:01:03,020 politically very difficult. 20 00:01:03,020 --> 00:01:06,330 And several people have asked me questions about that. 21 00:01:06,330 --> 00:01:10,160 So actually the penultimate session will be political 22 00:01:10,160 --> 00:01:12,730 barriers to educational change. 23 00:01:12,730 --> 00:01:16,420 So for example, the Benezet experiment, what happened to 24 00:01:16,420 --> 00:01:17,490 Benezet's experiment? 25 00:01:17,490 --> 00:01:18,890 Why isn't it done more? 26 00:01:18,890 --> 00:01:23,370 So actually, I went to the Manchester School Board, 27 00:01:23,370 --> 00:01:26,590 Manchester, New Hampshire, and looked at all the school board 28 00:01:26,590 --> 00:01:30,010 minutes from the 1930s to see what happened. 29 00:01:30,010 --> 00:01:33,110 So I'll talk a bit about that, talk about what are the 30 00:01:33,110 --> 00:01:36,790 structural obstacles to change so that you know what you're 31 00:01:36,790 --> 00:01:42,270 up against so that you can make strategic, sly choices 32 00:01:42,270 --> 00:01:45,710 and not get yourself shot at too much. 33 00:01:45,710 --> 00:01:47,270 But that's sort of a consequence 34 00:01:47,270 --> 00:01:48,600 of good course design. 35 00:01:48,600 --> 00:01:51,440 And that we'll do in the penultimate session. 36 00:01:51,440 --> 00:01:55,670 This time we'll talk about if you had your ideal world, what 37 00:01:55,670 --> 00:01:57,220 would you do? 38 00:01:57,220 --> 00:02:00,270 Sort of a process of successive approximation. 39 00:02:00,270 --> 00:02:02,000 In the ideal world what would you do? 40 00:02:02,000 --> 00:02:04,180 And then in the real world, how do you get as close to 41 00:02:04,180 --> 00:02:06,680 that as you can? 42 00:02:06,680 --> 00:02:14,220 So today, course design, which is how do you design a course 43 00:02:14,220 --> 00:02:17,360 so that you avoid the main problems with 44 00:02:17,360 --> 00:02:18,500 the traditional courses? 45 00:02:18,500 --> 00:02:22,270 So now before I say how do you design a course like that, let 46 00:02:22,270 --> 00:02:23,100 me review a bit. 47 00:02:23,100 --> 00:02:26,390 We've seen some of it in the previous sessions. 48 00:02:26,390 --> 00:02:28,705 But what are the problems with the traditional courses? 49 00:02:42,770 --> 00:02:46,990 So the problems in the traditional courses in broad 50 00:02:46,990 --> 00:02:55,490 outlines are, one, rote learning. 51 00:02:55,490 --> 00:02:57,390 I think that's the most fundamental problem. 52 00:03:06,090 --> 00:03:08,530 So we've seen many examples of that. 53 00:03:08,530 --> 00:03:09,790 And I'll just remind you of a few. 54 00:03:09,790 --> 00:03:12,080 And I'll show you a couple. 55 00:03:12,080 --> 00:03:13,820 So I'll remind you of a few just to 56 00:03:13,820 --> 00:03:16,140 summarize it in one second. 57 00:03:16,140 --> 00:03:18,535 And related to rote learning is that there's no transfer. 58 00:03:40,290 --> 00:03:44,740 So what are the causes? 59 00:03:44,740 --> 00:03:46,150 Well, we'll come to that in a second. 60 00:03:46,150 --> 00:03:48,200 But for example, what do I mean by rote learning? 61 00:03:48,200 --> 00:03:50,790 So rote learning is the fundamental problem. 62 00:03:50,790 --> 00:03:53,600 And it actually causes this one. 63 00:03:53,600 --> 00:03:56,830 If you learn by pattern matching, you're not going to 64 00:03:56,830 --> 00:03:59,770 be able to transfer to a new situation unless you happen to 65 00:03:59,770 --> 00:04:02,270 have by luck seen that pattern before. 66 00:04:02,270 --> 00:04:04,670 But any really new situation will be completely unfamiliar 67 00:04:04,670 --> 00:04:06,160 and you won't be able to do it. 68 00:04:06,160 --> 00:04:07,820 So the examples-- 69 00:04:20,649 --> 00:04:23,280 so the canonical example, because I find this actually 70 00:04:23,280 --> 00:04:26,360 very helpful to have a canonical example of what is 71 00:04:26,360 --> 00:04:30,600 rote learning, I think this is the canonical example. 72 00:04:34,990 --> 00:04:36,480 It's that. 73 00:04:36,480 --> 00:04:38,820 So I have that picture in my mind and the whole story 74 00:04:38,820 --> 00:04:40,700 behind that picture is this one. 75 00:04:45,510 --> 00:04:47,560 So this is from Wertheimer again. 76 00:04:47,560 --> 00:04:51,370 So students are learning to find the area of this 77 00:04:51,370 --> 00:04:53,130 parallelogram. 78 00:04:53,130 --> 00:05:02,420 And they move that triangle over there, make a rectangle. 79 00:05:02,420 --> 00:05:04,820 They know how to find the area of the rectangle. 80 00:05:04,820 --> 00:05:07,150 So rote learning, you can test for rote learning by giving 81 00:05:07,150 --> 00:05:09,560 them this picture. 82 00:05:09,560 --> 00:05:13,420 And the students who didn't understand but it only seemed 83 00:05:13,420 --> 00:05:18,486 like they understand, they take the triangle and they 84 00:05:18,486 --> 00:05:20,660 don't know what to do with it. 85 00:05:20,660 --> 00:05:24,840 So they can't find the area anymore, because what this 86 00:05:24,840 --> 00:05:27,350 reveals is that they didn't actually understand what they 87 00:05:27,350 --> 00:05:28,210 were doing. 88 00:05:28,210 --> 00:05:30,290 They didn't understand that the purpose of this procedure 89 00:05:30,290 --> 00:05:32,700 was to make a rectangle because you know how to find 90 00:05:32,700 --> 00:05:33,890 the area of a rectangle. 91 00:05:33,890 --> 00:05:36,210 They thought what you do is you chop off the left 92 00:05:36,210 --> 00:05:38,190 triangle, move it over there, and then you do 93 00:05:38,190 --> 00:05:40,240 some w times h. 94 00:05:40,240 --> 00:05:44,520 So operationally, it looks almost exactly the same. 95 00:05:44,520 --> 00:05:47,650 But cognitively, underneath, what's going on under the 96 00:05:47,650 --> 00:05:52,720 hood, is something completely different, you find out, when 97 00:05:52,720 --> 00:05:54,300 students have done rote learning, because they can't 98 00:05:54,300 --> 00:05:55,320 do this problem. 99 00:05:55,320 --> 00:06:05,400 So this one actually has all aspects of rote learning. 100 00:06:05,400 --> 00:06:07,610 So if they can't even do this problem, they haven't even 101 00:06:07,610 --> 00:06:08,730 done any learning. 102 00:06:08,730 --> 00:06:10,830 But if they can do this one but not this one, they've done 103 00:06:10,830 --> 00:06:12,300 rote learning. 104 00:06:12,300 --> 00:06:12,900 OK. 105 00:06:12,900 --> 00:06:14,990 So now if they haven't done any learning, that's a 106 00:06:14,990 --> 00:06:16,650 completely separate problem, generally not 107 00:06:16,650 --> 00:06:17,515 the problem we have. 108 00:06:17,515 --> 00:06:20,740 We have problems with students who have done way too much 109 00:06:20,740 --> 00:06:23,120 learning, but it's all in the wrong direction. 110 00:06:23,120 --> 00:06:26,280 So that's one example. 111 00:06:26,280 --> 00:06:27,800 Have I shown you folks-- 112 00:06:27,800 --> 00:06:31,880 probably some of you, the Army bus problem? 113 00:06:31,880 --> 00:06:34,340 The Army bus problem is very amusing. 114 00:06:34,340 --> 00:06:44,290 So there are 1,128 soldiers. 115 00:06:44,290 --> 00:06:49,150 And they have to be bused from one base to another. 116 00:06:49,150 --> 00:06:52,950 So this actually, again, was another National Assessment of 117 00:06:52,950 --> 00:06:55,180 Educational Progress problem. 118 00:06:55,180 --> 00:06:57,310 So it was given to a sample of about 119 00:06:57,310 --> 00:06:58,950 50,000 high school students. 120 00:06:58,950 --> 00:07:00,710 So it was a huge study. 121 00:07:00,710 --> 00:07:05,430 And there's 36 per bus that you can take. 122 00:07:05,430 --> 00:07:07,590 So the question is, how many buses? 123 00:07:13,790 --> 00:07:16,700 So it's not a rocket science question. 124 00:07:16,700 --> 00:07:20,000 They're just supposed to figure out how many buses to 125 00:07:20,000 --> 00:07:22,660 use and maybe one is the right answer, maybe. 126 00:07:22,660 --> 00:07:24,820 But you just keep shuttling back and forth. 127 00:07:24,820 --> 00:07:28,110 Let's assume that's not what was looked for. 128 00:07:28,110 --> 00:07:29,360 So I'll just give you this. 129 00:07:36,550 --> 00:07:39,560 So 1,128 over 36 is 31 and 1/3. 130 00:07:39,560 --> 00:07:42,350 So now I'm giving you that basically to simulate the 131 00:07:42,350 --> 00:07:45,250 state of mind of the students, because it turns out about 70% 132 00:07:45,250 --> 00:07:48,670 of the students did this division correctly. 133 00:07:48,670 --> 00:07:50,450 So now there's another 30% who didn't even 134 00:07:50,450 --> 00:07:51,820 learn division correctly. 135 00:07:51,820 --> 00:07:54,080 Let's leave those people aside. 136 00:07:54,080 --> 00:07:57,930 Of the 70%, in other words most of them, who could do the 137 00:07:57,930 --> 00:08:01,670 division correctly, what did they say? 138 00:08:01,670 --> 00:08:01,960 OK. 139 00:08:01,960 --> 00:08:04,720 So take a minute. 140 00:08:04,720 --> 00:08:07,270 Find a neighbor and see if you can predict what the students 141 00:08:07,270 --> 00:08:10,990 say and what the distribution of answers is. 142 00:08:10,990 --> 00:08:13,130 So this is practice understanding where students 143 00:08:13,130 --> 00:08:15,320 are coming from. 144 00:08:15,320 --> 00:08:17,020 This is American high school students. 145 00:08:19,800 --> 00:08:21,935 OK. 146 00:08:21,935 --> 00:08:25,350 So can someone suggest one answer that people gave? 147 00:08:28,700 --> 00:08:29,452 Yes. 148 00:08:29,452 --> 00:08:32,049 AUDIENCE: Actually 31 [INAUDIBLE] buses. 149 00:08:32,049 --> 00:08:32,490 PROFESSOR: Right. 150 00:08:32,490 --> 00:08:34,130 So that was one of the answers. 151 00:08:34,130 --> 00:08:37,950 So actually, the way that in America at least when I was in 152 00:08:37,950 --> 00:08:45,380 school you were taught to write it as 31 R 12. 153 00:08:45,380 --> 00:08:48,530 So that means 31 remainder 12, which I think is a completely 154 00:08:48,530 --> 00:08:49,760 broken way of doing things. 155 00:08:49,760 --> 00:08:51,230 But that's what we learned in school. 156 00:08:51,230 --> 00:08:54,140 And that's what some fraction of students wrote. 157 00:08:54,140 --> 00:08:54,630 OK. 158 00:08:54,630 --> 00:08:56,450 Another answer. 159 00:08:56,450 --> 00:08:57,380 AUDIENCE: 31. 160 00:08:57,380 --> 00:08:57,660 PROFESSOR: 31. 161 00:08:57,660 --> 00:08:59,130 AUDIENCE: 31 because they round off. 162 00:08:59,130 --> 00:09:01,440 PROFESSOR: 31 to round off. 163 00:09:01,440 --> 00:09:03,375 And another one? 164 00:09:03,375 --> 00:09:03,830 AUDIENCE: 32. 165 00:09:03,830 --> 00:09:07,450 PROFESSOR: 32 would be nice. 166 00:09:07,450 --> 00:09:07,810 Right. 167 00:09:07,810 --> 00:09:09,770 So these in fact were the three answers. 168 00:09:09,770 --> 00:09:13,340 And they were all equally chosen, except for this was 169 00:09:13,340 --> 00:09:16,050 sort of slightly preferred to the others. 170 00:09:16,050 --> 00:09:18,720 So they were all roughly 25% of-- 171 00:09:18,720 --> 00:09:20,260 this was, say, 75%. 172 00:09:20,260 --> 00:09:21,330 These were all about 25%. 173 00:09:21,330 --> 00:09:23,730 I think this was 28%. 174 00:09:23,730 --> 00:09:27,200 So this one was the winning one. 175 00:09:27,200 --> 00:09:30,520 Now just stare at that for a minute. 176 00:09:30,520 --> 00:09:31,960 What does that tell you? 177 00:09:31,960 --> 00:09:35,920 It tells you that-- what it tells me is that the problem 178 00:09:35,920 --> 00:09:39,490 had no meaning for the students. 179 00:09:39,490 --> 00:09:40,900 Again, they'd done learning. 180 00:09:40,900 --> 00:09:43,560 So of the rite learning, they'd done learning. 181 00:09:43,560 --> 00:09:45,290 There's no question about that. 182 00:09:45,290 --> 00:09:46,760 They'd learn how to divide. 183 00:09:46,760 --> 00:09:48,050 They all could divide. 184 00:09:48,050 --> 00:09:50,540 But they didn't know what the hell they'd done. 185 00:09:50,540 --> 00:09:52,970 So if you wrote, oh, yeah, if you filled out on the 186 00:09:52,970 --> 00:09:57,250 requisition form for the Army I need 31 R 12 buses, where 187 00:09:57,250 --> 00:09:57,670 would you be? 188 00:09:57,670 --> 00:09:59,220 You'd probably be peeling potatoes for the 189 00:09:59,220 --> 00:10:01,720 next week, on KP duty. 190 00:10:01,720 --> 00:10:04,800 So this shows no meaning. 191 00:10:07,620 --> 00:10:10,950 And what it shows is that for most students, there was 192 00:10:10,950 --> 00:10:11,930 actually no meaning. 193 00:10:11,930 --> 00:10:19,310 Here, again this also shows no meaning, but in a more 194 00:10:19,310 --> 00:10:20,610 sophisticated way than this. 195 00:10:20,610 --> 00:10:23,390 At least they thought about what to do with the R 12. 196 00:10:23,390 --> 00:10:25,920 And they came up with the wrong answer, but they 197 00:10:25,920 --> 00:10:27,260 thought about it. 198 00:10:27,260 --> 00:10:29,415 And here, we'll hope they actually understood. 199 00:10:35,560 --> 00:10:40,050 So of the 100%, 30% couldn't do the division. 200 00:10:40,050 --> 00:10:43,990 Roughly another 20%, it had no meaning. 201 00:10:43,990 --> 00:10:45,230 Another 30%, no meaning. 202 00:10:45,230 --> 00:10:46,000 So now we're at 80%. 203 00:10:46,000 --> 00:10:49,040 And only about 20% really understood what was going on 204 00:10:49,040 --> 00:10:52,100 in a really fundamentally simple problem. 205 00:10:52,100 --> 00:10:57,970 So that is a striking example to me of how deep the rote 206 00:10:57,970 --> 00:10:59,340 learning is. 207 00:10:59,340 --> 00:11:02,020 It's the same as that problem I showed you last time, which 208 00:11:02,020 --> 00:11:06,040 was 3.04 times 5.3, I think it was. 209 00:11:06,040 --> 00:11:07,290 You had to multiply. 210 00:11:11,300 --> 00:11:12,770 And students had to choose-- 211 00:11:12,770 --> 00:11:14,030 they had to estimate it. 212 00:11:14,030 --> 00:11:16,080 They didn't actually have to do the calculation. 213 00:11:16,080 --> 00:11:21,100 They had to choose between 1.6, 16, 160, 214 00:11:21,100 --> 00:11:22,920 one of these four. 215 00:11:22,920 --> 00:11:25,960 And it was just chance, basically. 216 00:11:25,960 --> 00:11:27,230 So again, the number system didn't 217 00:11:27,230 --> 00:11:29,100 mean anything to people. 218 00:11:29,100 --> 00:11:32,090 So it's really fundamental. 219 00:11:32,090 --> 00:11:33,480 It's really terrible. 220 00:11:33,480 --> 00:11:37,780 And it's been studied a lot. 221 00:11:37,780 --> 00:11:40,430 So the problem is not just in American teaching. 222 00:11:40,430 --> 00:11:43,410 It's across the world. 223 00:11:43,410 --> 00:11:45,270 It shows up in physics. 224 00:11:45,270 --> 00:11:47,790 So the physics example I showed you was this. 225 00:11:55,730 --> 00:11:57,160 So this is the bouncing ball. 226 00:12:08,900 --> 00:12:11,550 So it's stationary just for an instant while it's bouncing. 227 00:12:17,840 --> 00:12:19,520 And what everyone drew was that there was-- 228 00:12:22,780 --> 00:12:26,380 normal force equals mg and there's mg. 229 00:12:26,380 --> 00:12:27,320 Why? 230 00:12:27,320 --> 00:12:29,680 Well, v equals zero. 231 00:12:35,520 --> 00:12:36,730 So there's several reasons. 232 00:12:36,730 --> 00:12:39,820 Here, partly there was rote learning involved, because n 233 00:12:39,820 --> 00:12:42,590 was always equal to mg in all these other problems. 234 00:12:42,590 --> 00:12:44,600 So they just triggered off of that. 235 00:12:44,600 --> 00:12:46,715 The other one is that there is indeed misconception. 236 00:12:52,750 --> 00:12:55,370 They actually think f equals mv. 237 00:12:55,370 --> 00:12:59,520 So that's the third. 238 00:12:59,520 --> 00:13:02,300 So here, there's deep rote learning. 239 00:13:02,300 --> 00:13:04,200 There's no transfer. 240 00:13:04,200 --> 00:13:05,340 What are the causes? 241 00:13:05,340 --> 00:13:07,417 So there you see one of the causes. 242 00:13:07,417 --> 00:13:08,391 AUDIENCE: Sorry. 243 00:13:08,391 --> 00:13:09,641 [INAUDIBLE]. 244 00:13:12,287 --> 00:13:15,696 Couldn't it also be a problem of multiple choice thing, 245 00:13:15,696 --> 00:13:17,160 because [INAUDIBLE]? 246 00:13:17,160 --> 00:13:20,320 PROFESSOR: It wasn't multiple choice. 247 00:13:20,320 --> 00:13:23,620 They were just given the problem just like this. 248 00:13:23,620 --> 00:13:24,080 No. 249 00:13:24,080 --> 00:13:26,040 I don't think anyone who made a multiple choice would ever 250 00:13:26,040 --> 00:13:28,752 have dreamt to put that one on there. 251 00:13:28,752 --> 00:13:30,360 AUDIENCE: Well, I mean this is [INAUDIBLE]. 252 00:13:38,260 --> 00:13:38,590 PROFESSOR: Yeah. 253 00:13:38,590 --> 00:13:40,910 But I think it was phrased like how many buses should you 254 00:13:40,910 --> 00:13:42,070 order, something like that. 255 00:13:42,070 --> 00:13:44,566 I mean, they should come up with some integer. 256 00:13:44,566 --> 00:13:45,900 AUDIENCE: They would write in an answer that they would get. 257 00:13:45,900 --> 00:13:46,390 PROFESSOR: Yeah. 258 00:13:46,390 --> 00:13:48,960 No, it was a blank, not a multiple choice. 259 00:13:48,960 --> 00:13:50,040 It was a short answer. 260 00:13:50,040 --> 00:13:52,600 So that's how they could see that they'd done the division 261 00:13:52,600 --> 00:13:54,390 correctly or not. 262 00:13:54,390 --> 00:13:57,140 And so all of the ones who had done the division correctly, 263 00:13:57,140 --> 00:13:59,700 this is what you got. 264 00:13:59,700 --> 00:14:00,455 Another question? 265 00:14:00,455 --> 00:14:00,750 No. 266 00:14:00,750 --> 00:14:02,078 OK. 267 00:14:02,078 --> 00:14:02,572 Question. 268 00:14:02,572 --> 00:14:03,560 AUDIENCE: So I have another question. 269 00:14:03,560 --> 00:14:07,512 You've shown us many studies that prove that there's more 270 00:14:07,512 --> 00:14:08,500 rote learning going on. 271 00:14:08,500 --> 00:14:12,280 And all those studies come from the '30s and the '60s. 272 00:14:12,280 --> 00:14:14,400 So why is it still a problem today? 273 00:14:14,400 --> 00:14:14,710 PROFESSOR: Oh. 274 00:14:14,710 --> 00:14:21,840 So this one was '84, I believe, '83 or '84. 275 00:14:21,840 --> 00:14:23,690 And let's see, when were some of the others? 276 00:14:23,690 --> 00:14:26,430 So Wertheimer was the '50s or the '40s. 277 00:14:26,430 --> 00:14:28,540 Those examples are the '40s, so yeah, you're right. 278 00:14:32,725 --> 00:14:34,590 AUDIENCE: Why is it still a problem? 279 00:14:34,590 --> 00:14:38,560 PROFESSOR: Well, every time I ask this one, I 280 00:14:38,560 --> 00:14:40,380 get the same results. 281 00:14:40,380 --> 00:14:46,320 So this I've asked between 1998 and 2009, and always got 282 00:14:46,320 --> 00:14:48,680 the same results. 283 00:14:48,680 --> 00:14:49,570 What are some of the others? 284 00:14:49,570 --> 00:14:52,960 So another one is quel age est le capitaine? 285 00:14:52,960 --> 00:14:54,680 So that's a French study. 286 00:14:54,680 --> 00:14:56,210 So they asked students-- 287 00:14:56,210 --> 00:14:57,360 the question was, how do we know it's 288 00:14:57,360 --> 00:15:00,210 still a problem today? 289 00:15:00,210 --> 00:15:04,460 So they've asked students, there are 26 sheep and 10 290 00:15:04,460 --> 00:15:05,580 goats on a ship. 291 00:15:05,580 --> 00:15:08,850 How old is the captain? 292 00:15:08,850 --> 00:15:11,160 It's a good question. 293 00:15:11,160 --> 00:15:12,630 The problem is the answer. 294 00:15:12,630 --> 00:15:15,940 The answer is that people answer 36, because they have 295 00:15:15,940 --> 00:15:18,860 to stir the numbers around somehow and get something. 296 00:15:18,860 --> 00:15:21,050 So that was done in the '80s, I believe. 297 00:15:21,050 --> 00:15:21,690 Yes? 298 00:15:21,690 --> 00:15:22,550 AUDIENCE: That's not quite what I'm asking. 299 00:15:22,550 --> 00:15:25,910 I'm asking, if there is so much evidence that supports 300 00:15:25,910 --> 00:15:28,390 the existence of the problem, why isn't it solved? 301 00:15:28,390 --> 00:15:29,270 PROFESSOR: Oh. 302 00:15:29,270 --> 00:15:29,540 OK. 303 00:15:29,540 --> 00:15:30,490 Good question. 304 00:15:30,490 --> 00:15:32,850 OK. 305 00:15:32,850 --> 00:15:33,000 Sorry. 306 00:15:33,000 --> 00:15:36,830 I thought your question was, wasn't it all done long ago so 307 00:15:36,830 --> 00:15:38,140 it's not a problem now. 308 00:15:38,140 --> 00:15:38,750 Oh, yeah. 309 00:15:38,750 --> 00:15:41,080 If there's so much evidence to support the existence of a 310 00:15:41,080 --> 00:15:43,980 problem, why isn't it solved? 311 00:15:43,980 --> 00:15:47,510 So I would say there's two parts to that answer. 312 00:15:47,510 --> 00:15:52,480 One part is that, a, lots of people don't know about this. 313 00:15:52,480 --> 00:15:54,150 So normally when you teach-- 314 00:15:54,150 --> 00:15:57,820 so there's sort of an implicit contract, which is that if I 315 00:15:57,820 --> 00:16:01,810 don't ask you questions like that, you won't reveal to me 316 00:16:01,810 --> 00:16:04,010 that I'm not teaching you any of these important things. 317 00:16:04,010 --> 00:16:09,770 So for example, if you just take a regular course, it's 318 00:16:09,770 --> 00:16:11,710 actually possible to do all the problems by 319 00:16:11,710 --> 00:16:14,450 pattern-matching, mostly. 320 00:16:14,450 --> 00:16:18,090 So as an example in physics, you'll have-- 321 00:16:18,090 --> 00:16:20,310 say you're doing circular motion. 322 00:16:20,310 --> 00:16:23,620 And someone will say, well, there's a car going around a 323 00:16:23,620 --> 00:16:26,740 turn and the radius of the turn is this. 324 00:16:26,740 --> 00:16:28,800 And it's going at 30 miles an hour. 325 00:16:28,800 --> 00:16:30,768 What's the force? 326 00:16:30,768 --> 00:16:34,432 Or the car has a mass, m, what's the force that the road 327 00:16:34,432 --> 00:16:36,410 has to exert to keep it in the turn? 328 00:16:36,410 --> 00:16:37,860 Well, you don't have to know anything 329 00:16:37,860 --> 00:16:39,260 about circular motion. 330 00:16:39,260 --> 00:16:42,800 All you have to know is that there must be some formula 331 00:16:42,800 --> 00:16:44,580 which has-- so let's look at the 332 00:16:44,580 --> 00:16:47,220 variables that I just said. 333 00:16:47,220 --> 00:16:51,070 There is F is the unknown. 334 00:16:51,070 --> 00:16:53,660 m is given. 335 00:16:53,660 --> 00:16:55,344 v is given. 336 00:16:55,344 --> 00:16:58,190 And r is given. 337 00:16:58,190 --> 00:17:00,860 So you just flip through the book until you find a formula 338 00:17:00,860 --> 00:17:04,550 with all of those guys, which happens to be F equals mv 339 00:17:04,550 --> 00:17:06,160 squared over r. 340 00:17:06,160 --> 00:17:07,859 And then you just plug everything in. 341 00:17:07,859 --> 00:17:09,869 So you can do all those problems without understanding 342 00:17:09,869 --> 00:17:12,780 anything about centrifugal and centripetal. 343 00:17:12,780 --> 00:17:16,760 For example, 95% of students who can find this formula with 344 00:17:16,760 --> 00:17:20,069 no problem, if you ask them, well, can you draw me a force 345 00:17:20,069 --> 00:17:25,510 diagram, 50/50 on whether the force is outwards or inwards. 346 00:17:25,510 --> 00:17:27,940 You can ask them things like, OK, a car is accelerating. 347 00:17:27,940 --> 00:17:29,190 Where does the force come from? 348 00:17:31,910 --> 00:17:33,150 Or a car is decelerating. 349 00:17:33,150 --> 00:17:35,120 Where does the force come from? 350 00:17:35,120 --> 00:17:36,450 Oh, you know, the road. 351 00:17:36,450 --> 00:17:37,410 That seems really strange. 352 00:17:37,410 --> 00:17:37,890 But it's true. 353 00:17:37,890 --> 00:17:38,830 It's in fact from the road. 354 00:17:38,830 --> 00:17:41,010 So they have huge misconceptions even about 355 00:17:41,010 --> 00:17:44,060 linear forces, let alone circular forces. 356 00:17:44,060 --> 00:17:49,300 So the regular way of teaching actually doesn't expose those. 357 00:17:49,300 --> 00:17:49,785 Yes? 358 00:17:49,785 --> 00:17:52,280 AUDIENCE: Do you think if the standardized exams had 359 00:17:52,280 --> 00:17:54,622 higher-level questions on them. 360 00:17:54,622 --> 00:17:57,782 like Bloom's Taxonomy, would that help [INAUDIBLE]? 361 00:18:00,940 --> 00:18:01,230 PROFESSOR: Yeah. 362 00:18:01,230 --> 00:18:02,310 That would help, actually. 363 00:18:02,310 --> 00:18:04,150 So I can say something about how-- 364 00:18:04,150 --> 00:18:05,710 maybe I should've said this last time, about how-- 365 00:18:05,710 --> 00:18:08,070 so the question was, if standardized exams were better 366 00:18:08,070 --> 00:18:10,220 and had higher-level questions, would that help? 367 00:18:10,220 --> 00:18:11,900 I think it would help. 368 00:18:11,900 --> 00:18:15,190 And you can still even do it multiple choice and still have 369 00:18:15,190 --> 00:18:16,080 higher-level questions. 370 00:18:16,080 --> 00:18:20,264 So here's actually a pretty striking example. 371 00:18:20,264 --> 00:18:21,990 Let's see if I can remember exactly. 372 00:18:21,990 --> 00:18:22,340 Oh, yeah. 373 00:18:22,340 --> 00:18:25,730 So you ask students-- 374 00:18:25,730 --> 00:18:29,000 these are young kids, but it applies generally. 375 00:18:29,000 --> 00:18:32,140 And it's a question about how to design tests. 376 00:18:32,140 --> 00:18:37,640 So you ask them, I have a piece of red cellophane and 377 00:18:37,640 --> 00:18:39,810 blue cellophane. 378 00:18:39,810 --> 00:18:41,450 And I put them together. 379 00:18:41,450 --> 00:18:43,760 What color do I get? 380 00:18:43,760 --> 00:18:44,110 OK. 381 00:18:44,110 --> 00:18:47,300 So now the question isn't so much what is the right answer? 382 00:18:47,300 --> 00:18:49,940 But what do you think students say when you ask them that? 383 00:18:49,940 --> 00:18:52,090 And these are young kids. 384 00:18:52,090 --> 00:18:56,525 So takes a minute and see if you come up with what they say 385 00:18:56,525 --> 00:18:59,310 as their answer, their most common answer. 386 00:18:59,310 --> 00:19:01,280 So you ask this as an open-ended question. 387 00:19:01,280 --> 00:19:04,740 You don't give them multiple choice. 388 00:19:04,740 --> 00:19:07,410 So talk to your neighbor about that. 389 00:19:10,010 --> 00:19:10,660 OK. 390 00:19:10,660 --> 00:19:17,200 So I think it's actually very difficult to predict what 391 00:19:17,200 --> 00:19:18,210 students actually say. 392 00:19:18,210 --> 00:19:21,120 And I'm willing to eat a chalk if anyone-- 393 00:19:21,120 --> 00:19:24,710 well, I don't know if I should say that. 394 00:19:24,710 --> 00:19:25,450 That's a bit risky. 395 00:19:25,450 --> 00:19:27,210 But let's just-- chalk is probably safe. 396 00:19:27,210 --> 00:19:29,540 But let's say I'm willing to eat a chalk, maybe with salt 397 00:19:29,540 --> 00:19:32,450 and pepper, if anyone can actually figure out what the 398 00:19:32,450 --> 00:19:35,590 students actually said, the main thing they say, because 399 00:19:35,590 --> 00:19:37,920 it's really, really counterintuitive. 400 00:19:37,920 --> 00:19:39,480 Yes? 401 00:19:39,480 --> 00:19:40,500 Oh, go ahead. 402 00:19:40,500 --> 00:19:40,810 AUDIENCE: Reddish-blue. 403 00:19:40,810 --> 00:19:41,110 PROFESSOR: OK. 404 00:19:41,110 --> 00:19:42,847 So reddish-blue is one thing. 405 00:19:42,847 --> 00:19:44,097 Yeah. 406 00:19:48,040 --> 00:19:49,420 So that's one answer they give. 407 00:19:49,420 --> 00:19:50,140 Yeah. 408 00:19:50,140 --> 00:19:50,986 Yes? 409 00:19:50,986 --> 00:19:51,680 AUDIENCE: Brown. 410 00:19:51,680 --> 00:19:52,420 PROFESSOR: Brown. 411 00:19:52,420 --> 00:19:55,910 Yes, they probably do say that. 412 00:19:55,910 --> 00:19:58,190 AUDIENCE: Reddish-blue is like violet? 413 00:19:58,190 --> 00:19:59,752 PROFESSOR: Reddish-blue is like violet. 414 00:19:59,752 --> 00:20:01,020 Yeah. 415 00:20:01,020 --> 00:20:03,260 But if they are young enough, they might not know of the 416 00:20:03,260 --> 00:20:05,210 color violet. 417 00:20:05,210 --> 00:20:06,610 They might, or purple. 418 00:20:06,610 --> 00:20:07,236 Yeah. 419 00:20:07,236 --> 00:20:09,560 AUDIENCE: I'll go with saying violet-purple. 420 00:20:09,560 --> 00:20:10,050 PROFESSOR: OK. 421 00:20:10,050 --> 00:20:11,300 So violet-purple. 422 00:20:15,440 --> 00:20:16,370 Yes? 423 00:20:16,370 --> 00:20:16,940 AUDIENCE: Yellow. 424 00:20:16,940 --> 00:20:17,420 PROFESSOR: Yellow. 425 00:20:17,420 --> 00:20:18,440 I'm still safe. 426 00:20:18,440 --> 00:20:19,610 So they do say all these. 427 00:20:19,610 --> 00:20:22,450 I don't know about all of them in particular, but they say 428 00:20:22,450 --> 00:20:23,290 most of these things. 429 00:20:23,290 --> 00:20:25,830 I'm so far safe from my chalk wager. 430 00:20:25,830 --> 00:20:26,110 Yes? 431 00:20:26,110 --> 00:20:26,890 AUDIENCE: Blue. 432 00:20:26,890 --> 00:20:27,340 PROFESSOR: Blue. 433 00:20:27,340 --> 00:20:28,590 OK. 434 00:20:33,730 --> 00:20:34,600 Yes? 435 00:20:34,600 --> 00:20:35,540 AUDIENCE: Black. 436 00:20:35,540 --> 00:20:36,480 PROFESSOR: Black. 437 00:20:36,480 --> 00:20:37,716 That would be nice. 438 00:20:37,716 --> 00:20:38,708 Yeah. 439 00:20:38,708 --> 00:20:39,700 Yes? 440 00:20:39,700 --> 00:20:42,180 AUDIENCE: Would they say it depends which one is on top? 441 00:20:42,180 --> 00:20:42,390 PROFESSOR: Uh-oh. 442 00:20:42,390 --> 00:20:43,640 I've got to eat my chalk. 443 00:20:46,400 --> 00:20:46,770 Yes. 444 00:20:46,770 --> 00:20:48,830 So does it matter which one's-- 445 00:20:48,830 --> 00:20:50,090 yeah. 446 00:20:50,090 --> 00:20:52,320 In particular, they say, which one's on top? 447 00:20:59,770 --> 00:21:01,020 Can I have salt with that? 448 00:21:04,430 --> 00:21:08,950 So that is in fact the main question. 449 00:21:08,950 --> 00:21:12,780 So now why do I bring this question up? 450 00:21:12,780 --> 00:21:15,320 Well, the normal way you'd make a multiple choice 451 00:21:15,320 --> 00:21:18,970 question is you'd ask the question yourself. 452 00:21:18,970 --> 00:21:20,510 You'd think, well, what are the plausible answers? 453 00:21:20,510 --> 00:21:24,230 You'd come up with many of the choices here. 454 00:21:24,230 --> 00:21:26,420 And you'd put them down in the multiple choice. 455 00:21:26,420 --> 00:21:29,970 And you'd never think of putting this one there. 456 00:21:29,970 --> 00:21:34,300 So one way to actually design the questions is that you 457 00:21:34,300 --> 00:21:37,950 first do it with a pilot group with a short answer. 458 00:21:37,950 --> 00:21:41,360 And then you make your multiple choices based on the 459 00:21:41,360 --> 00:21:44,270 main misconceptions that they have. 460 00:21:44,270 --> 00:21:44,550 OK. 461 00:21:44,550 --> 00:21:47,550 So now what's the obstacle when you do this? 462 00:21:47,550 --> 00:21:51,440 The obstacle when you do this is you get this very funny 463 00:21:51,440 --> 00:21:52,720 item response curve. 464 00:21:52,720 --> 00:21:54,420 So the item response curve is the following. 465 00:21:58,330 --> 00:22:00,519 So the idea response curve you get, so it-- 466 00:22:13,010 --> 00:22:13,230 OK. 467 00:22:13,230 --> 00:22:17,130 So on this axis is the student's overall grade. 468 00:22:17,130 --> 00:22:18,880 And this is the-- 469 00:22:27,020 --> 00:22:29,630 so you have a test say, of 50 questions or whatever. 470 00:22:29,630 --> 00:22:31,690 And this is their overall grade on this axis. 471 00:22:31,690 --> 00:22:34,990 On this axis is their probability of getting one 472 00:22:34,990 --> 00:22:36,590 particular question correct. 473 00:22:36,590 --> 00:22:39,910 So now, a usual, a normal question is 474 00:22:39,910 --> 00:22:43,760 something like that. 475 00:22:47,430 --> 00:22:49,660 If they don't know anything, they have no chance 476 00:22:49,660 --> 00:22:51,010 of getting it right. 477 00:22:51,010 --> 00:22:54,140 Maybe they have some monkey line level over here. 478 00:22:54,140 --> 00:22:57,020 So let's call it something like that. 479 00:22:57,020 --> 00:22:57,370 OK. 480 00:22:57,370 --> 00:22:59,460 But these kind of questions actually have a 481 00:22:59,460 --> 00:23:00,870 very different shape. 482 00:23:00,870 --> 00:23:15,260 Their shape is shaped like a J. So what happens is that-- 483 00:23:15,260 --> 00:23:19,700 so this is the good questions. 484 00:23:19,700 --> 00:23:21,430 I think they are much better questions. 485 00:23:21,430 --> 00:23:23,780 But they get this shape. 486 00:23:23,780 --> 00:23:27,320 So what happens is when the students are just guessing, 487 00:23:27,320 --> 00:23:28,850 they're somewhere down here. 488 00:23:28,850 --> 00:23:32,840 But as they start to think about it and learn more, then 489 00:23:32,840 --> 00:23:35,510 they fall into the misconceptions. 490 00:23:35,510 --> 00:23:37,800 So they actually go down. 491 00:23:37,800 --> 00:23:39,480 So they actually can even be below chance. 492 00:23:39,480 --> 00:23:41,380 And then only when they really understand things 493 00:23:41,380 --> 00:23:42,990 do they get up here. 494 00:23:42,990 --> 00:23:47,320 So now what happens, for example, if the SAT ever 495 00:23:47,320 --> 00:23:49,940 contains a question like this, they just throw it out. 496 00:23:49,940 --> 00:23:52,810 They say, oh, this question does not measure how good a 497 00:23:52,810 --> 00:23:53,850 student we have. 498 00:23:53,850 --> 00:23:55,260 It's actually skewed. 499 00:23:55,260 --> 00:23:55,940 It's all messed up. 500 00:23:55,940 --> 00:23:56,670 So you throw it out. 501 00:23:56,670 --> 00:24:00,240 So these normal, standard ways of making standardized tests 502 00:24:00,240 --> 00:24:02,310 actually throw out all the good questions. 503 00:24:02,310 --> 00:24:05,800 And all you're left with is these kind of questions. 504 00:24:05,800 --> 00:24:09,390 So I actually saw an example of this in 505 00:24:09,390 --> 00:24:10,850 Cambridge, which was-- 506 00:24:10,850 --> 00:24:14,950 so you remember the rolling down the plain question that I 507 00:24:14,950 --> 00:24:17,330 showed you last week or the week before? 508 00:24:17,330 --> 00:24:19,780 So the rolling down the plain question is 509 00:24:19,780 --> 00:24:20,530 an intuitive question. 510 00:24:20,530 --> 00:24:21,400 It's qualitative. 511 00:24:21,400 --> 00:24:23,990 It's hard. 512 00:24:23,990 --> 00:24:26,790 If you try to calculate it, you'll get yourself in a knot 513 00:24:26,790 --> 00:24:28,240 unless you know exactly what you're doing. 514 00:24:28,240 --> 00:24:30,150 But if you reason about it intuitively, you can do it 515 00:24:30,150 --> 00:24:31,200 quite well. 516 00:24:31,200 --> 00:24:31,480 OK. 517 00:24:31,480 --> 00:24:36,490 So that question was then put on the end-of-year exam for 518 00:24:36,490 --> 00:24:37,930 the sophomores. 519 00:24:37,930 --> 00:24:41,630 And the examiner said, well, actually this question was not 520 00:24:41,630 --> 00:24:44,260 a good question, because it didn't measure who the good 521 00:24:44,260 --> 00:24:45,880 students were. 522 00:24:45,880 --> 00:24:49,000 So what they meant was that the good students actually 523 00:24:49,000 --> 00:24:51,300 sometimes did worse on that question than 524 00:24:51,300 --> 00:24:53,020 the not-so-good students. 525 00:24:53,020 --> 00:24:53,640 So they said, OK. 526 00:24:53,640 --> 00:24:55,100 We're just going to throw that question out. 527 00:24:55,100 --> 00:24:56,410 I mean, they didn't throw it that time. 528 00:24:56,410 --> 00:24:58,660 But we're not going to use questions like that next time. 529 00:24:58,660 --> 00:25:01,550 So again, here you had a good qualitative question. 530 00:25:01,550 --> 00:25:03,460 And it didn't measure the quote, "good" students. 531 00:25:03,460 --> 00:25:04,970 So it didn't give them what they wanted. 532 00:25:04,970 --> 00:25:06,150 So they threw it out. 533 00:25:06,150 --> 00:25:09,320 So if you design a test like that, you're going to fill it 534 00:25:09,320 --> 00:25:11,730 with questions that are just sort of 535 00:25:11,730 --> 00:25:14,170 low on Bloom's Taxonomy. 536 00:25:14,170 --> 00:25:16,210 But it doesn't mean you have to do that it way. 537 00:25:16,210 --> 00:25:19,080 So if you want to make a test that is higher on Bloom's 538 00:25:19,080 --> 00:25:21,540 Taxonomy and tests misconception and qualitative 539 00:25:21,540 --> 00:25:23,440 reasoning and intuitive reasoning, the way you do it 540 00:25:23,440 --> 00:25:26,610 is you do a short answer first, put the main 541 00:25:26,610 --> 00:25:28,140 misconceptions down. 542 00:25:28,140 --> 00:25:30,160 And you just have to be willing to live with 543 00:25:30,160 --> 00:25:32,519 this kind of curve. 544 00:25:32,519 --> 00:25:36,125 AUDIENCE: But when you say you don't evaluate the good 545 00:25:36,125 --> 00:25:39,252 student, but the question is how do you in the first place 546 00:25:39,252 --> 00:25:41,750 evaluate the good students if you have a 547 00:25:41,750 --> 00:25:43,402 normal kind of system? 548 00:25:43,402 --> 00:25:46,230 How do you basically evaluate them? 549 00:25:46,230 --> 00:25:47,960 PROFESSOR: How do you tell who the good students are? 550 00:25:47,960 --> 00:25:48,360 AUDIENCE: Yeah. 551 00:25:48,360 --> 00:25:52,050 PROFESSOR: Well, it's a reification that's going on. 552 00:25:52,050 --> 00:25:53,500 I mean, there's this idea that there's such a 553 00:25:53,500 --> 00:25:54,800 thing as a good student. 554 00:25:54,800 --> 00:25:57,320 And just because you call it that doesn't mean there is 555 00:25:57,320 --> 00:25:58,470 such a thing. 556 00:25:58,470 --> 00:26:00,020 So you need some definitions. 557 00:26:00,020 --> 00:26:03,720 So like for example, what is IQ? 558 00:26:03,720 --> 00:26:06,630 The definition is it's what IQ tests measure. 559 00:26:06,630 --> 00:26:08,020 I mean, that's the only, I would say, valid 560 00:26:08,020 --> 00:26:09,100 definition of IQ tests. 561 00:26:09,100 --> 00:26:13,090 So here, good student meant doing well on 562 00:26:13,090 --> 00:26:14,980 the standard problems. 563 00:26:14,980 --> 00:26:15,950 Now, I don't think that's a good 564 00:26:15,950 --> 00:26:17,450 definition of a good student. 565 00:26:17,450 --> 00:26:21,220 But that is the implicit definition in most courses. 566 00:26:21,220 --> 00:26:26,130 So to answer your question, it's the standard way things 567 00:26:26,130 --> 00:26:30,720 are done, the implicit definition that it makes it so 568 00:26:30,720 --> 00:26:33,320 hard to change the rote learning, but also so hard to 569 00:26:33,320 --> 00:26:34,940 even see that it's going on. 570 00:26:34,940 --> 00:26:38,990 And then the other half of the answer is that-- 571 00:26:38,990 --> 00:26:41,330 and when you try to change it, you find all 572 00:26:41,330 --> 00:26:43,040 these political obstacles. 573 00:26:43,040 --> 00:26:44,080 And that's what we're going to talk about in 574 00:26:44,080 --> 00:26:45,320 the penultimate session. 575 00:26:45,320 --> 00:26:47,590 But for example, people downstream. 576 00:26:47,590 --> 00:26:49,940 And one question was raised about this in the questions. 577 00:26:49,940 --> 00:26:53,080 The next courses will say, well, you didn't teach them X. 578 00:26:53,080 --> 00:26:54,760 Suppose you say, oh my god. 579 00:26:54,760 --> 00:26:57,590 I'm teaching them sophomore mechanics and they don't know 580 00:26:57,590 --> 00:26:58,950 Newton's three laws. 581 00:26:58,950 --> 00:27:02,580 Well, I could just do oiler's top and the herpolhodes and 582 00:27:02,580 --> 00:27:07,250 the polhodes, and all of that stuff and gyroscopes and all 583 00:27:07,250 --> 00:27:10,340 this complicated stuff, which is sort of a nonsense if they 584 00:27:10,340 --> 00:27:12,230 don't understand Newton's laws. 585 00:27:12,230 --> 00:27:14,520 Or I could actually sort out their misconceptions on 586 00:27:14,520 --> 00:27:14,820 Newton's laws. 587 00:27:14,820 --> 00:27:16,940 Well, suppose you take time to do that. 588 00:27:16,940 --> 00:27:17,750 Well, then they haven't learned what 589 00:27:17,750 --> 00:27:19,710 the herpolhode is. 590 00:27:19,710 --> 00:27:22,110 So who knows what the herpolhode is? 591 00:27:22,110 --> 00:27:23,620 So I sort of remember a while ago. 592 00:27:23,620 --> 00:27:26,800 But even I taught the course and I hardly remember it. 593 00:27:26,800 --> 00:27:29,320 But the next downstream course will say, they didn't know the 594 00:27:29,320 --> 00:27:33,230 herpolhode because you spent time on Newton's laws. 595 00:27:33,230 --> 00:27:35,350 So that's the political problem. 596 00:27:35,350 --> 00:27:38,270 So you have to then somehow get the people downstream to 597 00:27:38,270 --> 00:27:40,570 see that this is a serious problem, that we can only 598 00:27:40,570 --> 00:27:43,190 build sand castles in the air for so high before they 599 00:27:43,190 --> 00:27:46,050 collapse because the air can't support that much. 600 00:27:46,050 --> 00:27:47,260 And that's what I'm going to talk about in 601 00:27:47,260 --> 00:27:49,880 the penultimate session. 602 00:27:49,880 --> 00:27:50,652 Question? 603 00:27:50,652 --> 00:27:51,902 AUDIENCE: [INAUDIBLE] 604 00:27:55,032 --> 00:27:58,525 problem, was the purpose of the test, because if the 605 00:27:58,525 --> 00:28:02,267 purpose of the test is to evaluate the students, you 606 00:28:02,267 --> 00:28:06,030 don't want to throw in tricky questions. 607 00:28:06,030 --> 00:28:09,040 PROFESSOR: Well, so the question is which question you 608 00:28:09,040 --> 00:28:11,230 use, does it depend on the purpose of the test? 609 00:28:11,230 --> 00:28:11,970 It does. 610 00:28:11,970 --> 00:28:14,410 But I think you absolutely need these kind of questions, 611 00:28:14,410 --> 00:28:16,480 or you're not actually evaluating the right thing. 612 00:28:16,480 --> 00:28:19,240 So if you only put these kind of questions in, you're not 613 00:28:19,240 --> 00:28:21,360 exposing any misconceptions. 614 00:28:21,360 --> 00:28:23,190 So you're actually not evaluating some of the 615 00:28:23,190 --> 00:28:25,680 important questions about what the students understand. 616 00:28:25,680 --> 00:28:30,070 Because, for example, if you just give them colors on this 617 00:28:30,070 --> 00:28:32,250 question, you'll never realize that that's what they're 618 00:28:32,250 --> 00:28:33,300 thinking about. 619 00:28:33,300 --> 00:28:36,870 So actually you're just evaluating can they give you 620 00:28:36,870 --> 00:28:39,150 one of the pre-prescribed color answers. 621 00:28:39,150 --> 00:28:41,400 But that actually doesn't necessarily mean that they 622 00:28:41,400 --> 00:28:41,680 understand. 623 00:28:41,680 --> 00:28:43,320 So you're not actually evaluating their 624 00:28:43,320 --> 00:28:43,950 understanding. 625 00:28:43,950 --> 00:28:45,660 So to evaluate understanding you do need 626 00:28:45,660 --> 00:28:48,160 questions like this. 627 00:28:48,160 --> 00:28:50,750 And should you punish them for being down here? 628 00:28:50,750 --> 00:28:51,500 No. 629 00:28:51,500 --> 00:28:52,730 That's the other part of it. 630 00:28:52,730 --> 00:28:54,000 If they're down here, that means they're 631 00:28:54,000 --> 00:28:55,350 thinking about it. 632 00:28:55,350 --> 00:28:57,870 So if you then grade them and they came down here and you 633 00:28:57,870 --> 00:28:59,670 say, oh, you did really badly, no. 634 00:28:59,670 --> 00:29:02,400 Actually you're down here, that's because you're thinking 635 00:29:02,400 --> 00:29:04,430 about it and you got caught by the misconception. 636 00:29:04,430 --> 00:29:07,280 But that's the only way to sort out the misconception. 637 00:29:07,280 --> 00:29:10,950 You have to go beyond it. 638 00:29:10,950 --> 00:29:11,270 OK. 639 00:29:11,270 --> 00:29:12,080 Other questions? 640 00:29:12,080 --> 00:29:13,330 And then we'll take a break. 641 00:29:18,030 --> 00:29:18,450 OK. 642 00:29:18,450 --> 00:29:23,860 So it is 10:05, actually, according to that 643 00:29:23,860 --> 00:29:25,480 clock, plus an hour. 644 00:29:25,480 --> 00:29:28,690 So 9:15, according to that clock. 645 00:29:28,690 --> 00:29:32,010 So 10:15, see everyone back here. 646 00:29:32,010 --> 00:29:36,510 Take a short, 10-minute break, just as if it were two 1-hour 647 00:29:36,510 --> 00:29:38,480 classes with the 10 minute break. 648 00:29:38,480 --> 00:29:41,920 And then I'll put the feedback sheets in the corners. 649 00:29:41,920 --> 00:29:43,830 So when you come back, just make sure you 650 00:29:43,830 --> 00:29:46,460 grab a feedback sheet. 651 00:29:46,460 --> 00:29:47,610 OK. 652 00:29:47,610 --> 00:29:55,100 So before, we talked about the problems with what most 653 00:29:55,100 --> 00:30:00,230 courses do and how rote learning is a primary product. 654 00:30:00,230 --> 00:30:03,670 And as a consequence of that, there's no transfer to new 655 00:30:03,670 --> 00:30:04,065 situations. 656 00:30:04,065 --> 00:30:06,680 So the knowledge is very brittle. 657 00:30:06,680 --> 00:30:10,770 So what are the causes? 658 00:30:10,770 --> 00:30:12,650 And what can you do about it? 659 00:30:12,650 --> 00:30:17,540 So just briefly, the causes partly are no account is taken 660 00:30:17,540 --> 00:30:20,330 of the misconceptions students have. 661 00:30:20,330 --> 00:30:26,230 So new rote learning is piled on old misconceptions, because 662 00:30:26,230 --> 00:30:28,130 by definition learning is going to turn into rote 663 00:30:28,130 --> 00:30:31,700 learning if there's no understanding and meaning 664 00:30:31,700 --> 00:30:34,690 given to it, just like the 1,128 divided 665 00:30:34,690 --> 00:30:38,080 by 36 is 31 R 12. 666 00:30:38,080 --> 00:30:41,260 So no account is taken of what students have rote learned and 667 00:30:41,260 --> 00:30:43,620 what they've really understood, because the way 668 00:30:43,620 --> 00:30:47,660 the course is normally taught, those ideas, those common 669 00:30:47,660 --> 00:30:50,930 misconceptions aren't exposed in the normal run of the way 670 00:30:50,930 --> 00:30:52,730 the course happens. 671 00:30:52,730 --> 00:30:55,310 And another is-- so that's directly 672 00:30:55,310 --> 00:30:57,950 related to the problem. 673 00:30:57,950 --> 00:31:00,530 Another one is that the applications are very narrow. 674 00:31:10,980 --> 00:31:14,660 So because the applications in the class are so confined to 675 00:31:14,660 --> 00:31:18,180 the same area, it's very easy to produce rote learning. 676 00:31:18,180 --> 00:31:19,530 And so I have a-- 677 00:31:19,530 --> 00:31:22,370 I keep saying how pictures are the way to understand 678 00:31:22,370 --> 00:31:22,760 everything. 679 00:31:22,760 --> 00:31:24,630 So I have a picture for that. 680 00:31:24,630 --> 00:31:26,290 So I show everyone this picture. 681 00:31:26,290 --> 00:31:28,890 And if you keep this picture in your mind, it'll give you a 682 00:31:28,890 --> 00:31:31,200 guide for how you should make problems and 683 00:31:31,200 --> 00:31:32,890 what examples to choose. 684 00:31:32,890 --> 00:31:39,740 So suppose there is some idea you'd like to teach. 685 00:31:39,740 --> 00:31:42,130 We'll talk in a bit about why you'd like teach an idea at 686 00:31:42,130 --> 00:31:46,170 all, but some idea you want to teach. 687 00:31:46,170 --> 00:31:49,670 And you have a clear conception of this idea. 688 00:31:49,670 --> 00:31:55,500 For example, maybe the idea is something like DNA is the 689 00:31:55,500 --> 00:31:59,280 fundamental unit of information in living systems. 690 00:31:59,280 --> 00:32:01,490 OK, well that means something to you. 691 00:32:01,490 --> 00:32:02,360 But to the students, it doesn't 692 00:32:02,360 --> 00:32:03,110 actually mean anything. 693 00:32:03,110 --> 00:32:04,360 You need to give them examples. 694 00:32:09,600 --> 00:32:11,620 So you're giving them an example. 695 00:32:11,620 --> 00:32:14,120 A related one is you have some idea, which 696 00:32:14,120 --> 00:32:17,005 is dimensional analysis. 697 00:32:17,005 --> 00:32:19,300 And you want to give them an example of doing it, because 698 00:32:19,300 --> 00:32:21,760 just stating the Buckingham pi theorem for them doesn't 699 00:32:21,760 --> 00:32:22,550 really help them. 700 00:32:22,550 --> 00:32:24,070 So you do an example. 701 00:32:24,070 --> 00:32:26,940 But now picture yourself back in the student mind. 702 00:32:26,940 --> 00:32:28,200 What do the students see? 703 00:32:28,200 --> 00:32:31,890 Well, they don't have this idea as a separate unit yet, 704 00:32:31,890 --> 00:32:32,980 because they're still students. 705 00:32:32,980 --> 00:32:35,780 And the purpose of the course is to teach that. 706 00:32:35,780 --> 00:32:37,070 So they haven't got yet. 707 00:32:37,070 --> 00:32:41,130 So they have this merger of idea and example together. 708 00:32:41,130 --> 00:32:45,230 So they see this big package and have trouble making that 709 00:32:45,230 --> 00:32:47,850 division between idea and example, in other words, 710 00:32:47,850 --> 00:32:51,790 between transferable idea and thing that was particular to 711 00:32:51,790 --> 00:32:53,380 the situation. 712 00:32:53,380 --> 00:32:55,090 So of course what do you do? 713 00:32:55,090 --> 00:32:57,430 You give them another example. 714 00:32:57,430 --> 00:33:00,490 So the normal way it's done is here's your second example. 715 00:33:04,980 --> 00:33:06,260 So there's the second example. 716 00:33:06,260 --> 00:33:10,360 But now, again from the student's point of view, 717 00:33:10,360 --> 00:33:14,730 there's still quite a big overlap between idea plus 718 00:33:14,730 --> 00:33:17,015 example one and idea plus example two. 719 00:33:20,190 --> 00:33:22,940 So that overlap is-- 720 00:33:22,940 --> 00:33:25,540 if they intersect things mentally in their head and see 721 00:33:25,540 --> 00:33:29,430 what's common, they still get a lot of stuff that's beyond 722 00:33:29,430 --> 00:33:30,650 just the idea. 723 00:33:30,650 --> 00:33:33,410 For example, if you do a bunch of dimensional analysis 724 00:33:33,410 --> 00:33:37,700 examples related to entropy, then they'll think, oh, 725 00:33:37,700 --> 00:33:41,530 dimensional analysis is a way of solving entropy problems. 726 00:33:41,530 --> 00:33:46,370 So here, the overlap is too big. 727 00:33:46,370 --> 00:33:47,620 So what do you have to do? 728 00:33:50,801 --> 00:33:52,250 AUDIENCE: More examples. 729 00:33:52,250 --> 00:33:53,176 PROFESSOR: Pardon? 730 00:33:53,176 --> 00:33:53,640 AUDIENCE: More examples. 731 00:33:53,640 --> 00:33:54,350 PROFESSOR: More examples. 732 00:33:54,350 --> 00:33:57,840 And where should they be in this space? 733 00:33:57,840 --> 00:33:59,170 Yeah, way around, right? 734 00:33:59,170 --> 00:34:02,830 So you should make an example over here. 735 00:34:07,770 --> 00:34:10,170 So this example has very little intersection with the 736 00:34:10,170 --> 00:34:13,210 other example. 737 00:34:13,210 --> 00:34:17,120 So here, this one and this one and this one, they all have 738 00:34:17,120 --> 00:34:18,050 very little overlap. 739 00:34:18,050 --> 00:34:20,400 So now the overlap among all three is pretty 740 00:34:20,400 --> 00:34:25,310 much just the idea. 741 00:34:25,310 --> 00:34:27,790 But think how different that is from the way most courses 742 00:34:27,790 --> 00:34:29,020 are designed. 743 00:34:29,020 --> 00:34:32,290 Most courses, the examples, you'll do 18 problems with the 744 00:34:32,290 --> 00:34:33,150 ideal gas law. 745 00:34:33,150 --> 00:34:36,469 You'll do 18 integration by parts. 746 00:34:36,469 --> 00:34:38,750 You'll do 18 solutions of first order 747 00:34:38,750 --> 00:34:41,520 differential equations. 748 00:34:41,520 --> 00:34:45,360 You'll solve 18 ion channel problems 749 00:34:45,360 --> 00:34:47,830 with a Nernst equation. 750 00:34:47,830 --> 00:34:50,909 All of those actually don't teach you the fundamental idea 751 00:34:50,909 --> 00:34:52,199 to be able to transfer it. 752 00:34:52,199 --> 00:34:54,630 So that's another cause, see, that the 753 00:34:54,630 --> 00:34:56,570 applications are too narrow. 754 00:34:56,570 --> 00:34:57,960 So you have to choose your applications 755 00:34:57,960 --> 00:34:59,750 as widely as possible. 756 00:34:59,750 --> 00:35:02,550 And this makes teaching very hard, because it means you 757 00:35:02,550 --> 00:35:05,416 can't really-- yes, question? 758 00:35:05,416 --> 00:35:08,797 AUDIENCE: So it can't just be like also the structure 759 00:35:08,797 --> 00:35:12,015 involved with it. it's defined as having a 760 00:35:12,015 --> 00:35:14,000 class and having problems. 761 00:35:14,000 --> 00:35:15,606 So obviously, do something in written. 762 00:35:15,606 --> 00:35:17,410 But you never really communicate that. 763 00:35:17,410 --> 00:35:20,608 And if you would have like let's say in physics, you 764 00:35:20,608 --> 00:35:22,330 would have [INAUDIBLE]. 765 00:35:22,330 --> 00:35:24,298 And maybe you have an exam, an oral exam where you basically 766 00:35:24,298 --> 00:35:28,234 can evaluate the students and really can find out if the 767 00:35:28,234 --> 00:35:31,186 students understood the main idea. 768 00:35:31,186 --> 00:35:34,630 And then he has to be transferred, 769 00:35:34,630 --> 00:35:36,106 transfer the skills. 770 00:35:36,106 --> 00:35:41,300 So I mean in terms of like broadening the way of how you 771 00:35:41,300 --> 00:35:44,380 question the students will help basically 772 00:35:44,380 --> 00:35:45,840 get the idea across. 773 00:35:45,840 --> 00:35:46,970 PROFESSOR: I think that's right. 774 00:35:46,970 --> 00:35:50,100 So the suggestion was that oral exams are actually-- 775 00:35:50,100 --> 00:35:52,530 in general, it's true, are a much better way of evaluating 776 00:35:52,530 --> 00:35:54,840 whether the student understands or not. 777 00:35:54,840 --> 00:35:57,600 It's very disconcerting for the students, because, I think 778 00:35:57,600 --> 00:35:59,890 I said this last time, basically in an oral exam, as 779 00:35:59,890 --> 00:36:02,050 soon as the student understands something, you ask 780 00:36:02,050 --> 00:36:03,230 something else. 781 00:36:03,230 --> 00:36:04,090 So you're like, OK. 782 00:36:04,090 --> 00:36:04,560 They know that. 783 00:36:04,560 --> 00:36:05,550 Let me ask them about something else. 784 00:36:05,550 --> 00:36:07,110 So the student feels like they're never talk about 785 00:36:07,110 --> 00:36:07,940 something they know. 786 00:36:07,940 --> 00:36:10,100 But that's the purpose of it. 787 00:36:10,100 --> 00:36:12,710 So yeah, an oral exam, like a PhD qualifying 788 00:36:12,710 --> 00:36:14,460 exam, forces transfer. 789 00:36:14,460 --> 00:36:15,550 That's what you're checking for in the 790 00:36:15,550 --> 00:36:16,980 PhD qualifying exam. 791 00:36:16,980 --> 00:36:19,360 So if you do things like that in the undergraduate course, 792 00:36:19,360 --> 00:36:24,280 that's setting a goal of transfer, that this is one of 793 00:36:24,280 --> 00:36:25,930 the goals of the course, that you be able to use these 794 00:36:25,930 --> 00:36:28,180 skills in new situations I'm going to ask about. 795 00:36:28,180 --> 00:36:30,610 But of course, to be fair, you have to give them practice in 796 00:36:30,610 --> 00:36:31,580 doing that. 797 00:36:31,580 --> 00:36:33,596 You can't just give them regular problems and all of a 798 00:36:33,596 --> 00:36:35,560 sudden give them an oral exam where you say now transfer it 799 00:36:35,560 --> 00:36:36,120 to a new thing. 800 00:36:36,120 --> 00:36:37,490 They'll just hit a brick wall. 801 00:36:37,490 --> 00:36:39,930 But it helps you in designing the course. 802 00:36:39,930 --> 00:36:44,600 So I'll put the backward design diagram up again, to 803 00:36:44,600 --> 00:36:47,010 show that process. 804 00:36:47,010 --> 00:36:49,000 So here, you want to choose from as 805 00:36:49,000 --> 00:36:51,300 wide a set as possible. 806 00:36:51,300 --> 00:36:52,750 And generally, that's not done. 807 00:36:52,750 --> 00:36:56,050 So I wanted to read a couple of selections from the Eric 808 00:36:56,050 --> 00:37:00,390 experiment about what happens in class. 809 00:37:00,390 --> 00:37:02,550 So I know you had a choice of reading. 810 00:37:02,550 --> 00:37:06,780 So who chose the Eric experiment? 811 00:37:06,780 --> 00:37:08,020 I thought they were all fascinating. 812 00:37:08,020 --> 00:37:10,790 So if you remember, there was a couple 813 00:37:10,790 --> 00:37:12,290 quotes from Eric himself. 814 00:37:12,290 --> 00:37:16,480 So for those who didn't read it, Eric was a non-physics 815 00:37:16,480 --> 00:37:19,020 student who took a summer session physics course 816 00:37:19,020 --> 00:37:20,940 freshman, physics course, and recorded-- 817 00:37:20,940 --> 00:37:23,180 I think he was a philosophy major. 818 00:37:23,180 --> 00:37:24,910 And he recorded his impressions of what it was 819 00:37:24,910 --> 00:37:26,760 like to be in a physics class. 820 00:37:26,760 --> 00:37:27,975 So that's actually-- 821 00:37:27,975 --> 00:37:30,370 you get quite a different view of what a physics class should 822 00:37:30,370 --> 00:37:32,890 be when someone from outside comes, sort of like this 823 00:37:32,890 --> 00:37:35,570 diagram all over again. 824 00:37:35,570 --> 00:37:38,880 He said the class consisted basically of problem solving 825 00:37:38,880 --> 00:37:41,950 and not of any interesting or inspiring exchange of ideas. 826 00:37:41,950 --> 00:37:44,810 The professor spent the first 15 minutes defining terms. 827 00:37:44,810 --> 00:37:46,800 And apparently that was all the new information we were 828 00:37:46,800 --> 00:37:48,570 going to get on kinematics. 829 00:37:48,570 --> 00:37:51,710 Then he spent 50 minutes doing problems from Chapter 1. 830 00:37:51,710 --> 00:37:53,890 He was not particularly good at explaining why he did what 831 00:37:53,890 --> 00:37:56,590 he did to solve the problems, nor did he have any real 832 00:37:56,590 --> 00:37:58,905 patience for people who wanted explanations. 833 00:37:58,905 --> 00:38:02,130 You know, the why, the what were the ideas, why would you 834 00:38:02,130 --> 00:38:04,440 do it this way rather than that way, those weren't 835 00:38:04,440 --> 00:38:05,730 generally part of the course. 836 00:38:05,730 --> 00:38:08,050 So by not making them part of the course, you're actually 837 00:38:08,050 --> 00:38:11,270 pushing towards their rote learning. 838 00:38:11,270 --> 00:38:15,480 And that doesn't mean that there are not all these 839 00:38:15,480 --> 00:38:16,260 interesting questions. 840 00:38:16,260 --> 00:38:18,445 So later on in this selection, he says, well, actually, you 841 00:38:18,445 --> 00:38:20,500 know, I wonder about all the names that physicists give. 842 00:38:20,500 --> 00:38:22,530 But there was no space to ask those questions in class. 843 00:38:22,530 --> 00:38:26,580 He says action/reaction, that's Newton's third law, 844 00:38:26,580 --> 00:38:29,000 that presupposes a cause and effect relationship, which 845 00:38:29,000 --> 00:38:30,250 implies duration. 846 00:38:30,250 --> 00:38:33,710 But in physics, actually action-reaction happen 847 00:38:33,710 --> 00:38:34,940 simultaneously. 848 00:38:34,940 --> 00:38:37,400 So those are the kind of the questions that he's asking 849 00:38:37,400 --> 00:38:38,990 himself, Eric, the student, that get 850 00:38:38,990 --> 00:38:40,180 away from rote learning. 851 00:38:40,180 --> 00:38:42,320 But the structure of the class doesn't encourage 852 00:38:42,320 --> 00:38:44,460 anything like that. 853 00:38:44,460 --> 00:38:47,050 And the only reason he has time to think about that is 854 00:38:47,050 --> 00:38:49,060 he's not actually trying to just survive the class. 855 00:38:49,060 --> 00:38:51,930 He's sort of going in as an experimental student, whereas 856 00:38:51,930 --> 00:38:53,670 the students who are just trying to survive the class, 857 00:38:53,670 --> 00:38:56,120 if any thoughts like that occur to them, they 858 00:38:56,120 --> 00:38:57,150 just say, forget it. 859 00:38:57,150 --> 00:38:59,850 No time to think about that. i have to solve the 10 problems 860 00:38:59,850 --> 00:39:02,710 on the end of Chapter 3 right now. 861 00:39:02,710 --> 00:39:06,480 So those are the causes. 862 00:39:06,480 --> 00:39:08,100 What do you do about it? 863 00:39:08,100 --> 00:39:10,780 Well, there are several principles of design. 864 00:39:14,440 --> 00:39:18,610 So last time I talked about two organizational principles, 865 00:39:18,610 --> 00:39:22,615 the signals and systems model of how to teach a course. 866 00:39:39,670 --> 00:39:41,640 So this was the teaching equation. 867 00:39:41,640 --> 00:39:44,555 So this is the output, what students can do. 868 00:39:44,555 --> 00:39:46,240 So you choose that. 869 00:39:46,240 --> 00:39:55,680 You also have to understand students', students' thinking. 870 00:39:55,680 --> 00:40:03,210 And then you figure out your teaching given what Given you 871 00:40:03,210 --> 00:40:06,380 want them to be able to do and how students think, the 872 00:40:06,380 --> 00:40:11,410 misconceptions, how people learn, visual, by examples, 873 00:40:11,410 --> 00:40:13,960 diagrams like that, how should I teach? 874 00:40:13,960 --> 00:40:17,360 So that gives you an overall structure for course design. 875 00:40:17,360 --> 00:40:19,320 The other structure, which is quite 876 00:40:19,320 --> 00:40:20,930 similar, is backward design. 877 00:40:35,710 --> 00:40:40,470 So backward design, you invert the normal order. 878 00:40:40,470 --> 00:40:43,910 So the highest level in backward design is-- 879 00:40:46,780 --> 00:40:48,070 that's the and over there. 880 00:41:13,620 --> 00:41:17,750 So this is a hierarchical structure. 881 00:41:17,750 --> 00:41:20,870 Basically, you choose your course goals. 882 00:41:20,870 --> 00:41:23,990 You find ways to make them operational. 883 00:41:23,990 --> 00:41:27,110 So in other words, how would you measure, for example, 884 00:41:27,110 --> 00:41:32,770 being able to solve Newton's laws problems in designed 885 00:41:32,770 --> 00:41:35,220 bridges, for example, might be one of your goals. 886 00:41:35,220 --> 00:41:37,260 Well, you would actually give them some bridges to design, 887 00:41:37,260 --> 00:41:38,530 things like that. 888 00:41:38,530 --> 00:41:40,380 And then given that you want them to be able to do that, 889 00:41:40,380 --> 00:41:41,810 what do you do in class? 890 00:41:41,810 --> 00:41:44,290 So this was last time. 891 00:41:51,960 --> 00:41:53,220 That's this time. 892 00:41:53,220 --> 00:41:55,360 And this is next time. 893 00:41:58,680 --> 00:42:01,470 And as I said before, I start here, just because I find this 894 00:42:01,470 --> 00:42:03,830 is at the right level, balanced between 895 00:42:03,830 --> 00:42:05,990 concrete and abstract. 896 00:42:05,990 --> 00:42:07,290 So we did that last time. 897 00:42:07,290 --> 00:42:09,050 But now we're here. 898 00:42:09,050 --> 00:42:11,170 How do you choose course goals? 899 00:42:11,170 --> 00:42:14,390 And that, the paper by Middlebrook-- 900 00:42:14,390 --> 00:42:17,210 so who read Middlebrook's paper? 901 00:42:17,210 --> 00:42:17,900 A few people. 902 00:42:17,900 --> 00:42:18,130 OK. 903 00:42:18,130 --> 00:42:20,965 So if you haven't read it, I didn't want to overload you 904 00:42:20,965 --> 00:42:23,360 with reading, but I think it's also a brilliant paper. 905 00:42:23,360 --> 00:42:27,140 And I know Middlebrook because he was my teacher at Caltech. 906 00:42:27,140 --> 00:42:30,080 And I took the course that he describes in the paper. 907 00:42:30,080 --> 00:42:33,360 And he identified a fundamental problem and a 908 00:42:33,360 --> 00:42:34,840 fundamental solution to it. 909 00:42:34,840 --> 00:42:37,380 In other words, how do you choose the goals? 910 00:42:37,380 --> 00:42:40,840 And I myself have actually come to pretty much the same 911 00:42:40,840 --> 00:42:43,570 conclusion through years of hard experience. 912 00:42:47,270 --> 00:42:49,960 So this is all to answer, what do you do about it? 913 00:42:49,960 --> 00:42:54,960 Which is, you choose course goals such that the course 914 00:42:54,960 --> 00:42:56,330 itself will produce transfer. 915 00:43:01,800 --> 00:43:05,020 So let me explain the problem that Middlebrook identified 916 00:43:05,020 --> 00:43:06,220 and what his solution is. 917 00:43:06,220 --> 00:43:12,300 So his particular class is an analog circuit design class. 918 00:43:12,300 --> 00:43:15,760 And generally, the way analog circuit design is taught is 919 00:43:15,760 --> 00:43:20,250 you have a circuit. 920 00:43:20,250 --> 00:43:22,260 And you ask the students to analyze it. 921 00:43:30,480 --> 00:43:34,320 For example, you give them a circuit that filters out high 922 00:43:34,320 --> 00:43:40,110 frequency noise, for example, in an audio recorder in a CD 923 00:43:40,110 --> 00:43:42,010 recording studio. 924 00:43:42,010 --> 00:43:43,360 And you analyze it. 925 00:43:43,360 --> 00:43:46,990 And you see that its behavior does do-- 926 00:43:46,990 --> 00:43:47,990 what is its behavior? 927 00:43:47,990 --> 00:43:48,330 OK. 928 00:43:48,330 --> 00:43:50,190 It throws away high frequencies. 929 00:43:50,190 --> 00:43:50,480 OK. 930 00:43:50,480 --> 00:43:53,150 So now that's the general run of the mill. 931 00:43:53,150 --> 00:43:54,650 You'll just get tons and tons and tons of 932 00:43:54,650 --> 00:43:55,830 problems like that. 933 00:43:55,830 --> 00:43:57,970 And you learn a wave of analysis that allows you to go 934 00:43:57,970 --> 00:43:59,910 from here to there. 935 00:43:59,910 --> 00:44:03,840 But then what happens when the student graduates? 936 00:44:03,840 --> 00:44:05,180 What happens is what Middlebrook calls 937 00:44:05,180 --> 00:44:06,820 a fall off a cliff. 938 00:44:06,820 --> 00:44:08,890 So either they go into graduate 939 00:44:08,890 --> 00:44:10,670 school or into a company. 940 00:44:10,670 --> 00:44:13,740 But either way, what happens is they're 941 00:44:13,740 --> 00:44:16,060 actually given that. 942 00:44:16,060 --> 00:44:19,770 Somebody says, well, actually, I need a circuit that doesn't 943 00:44:19,770 --> 00:44:26,150 cost too much but is quite exact and cuts off all 944 00:44:26,150 --> 00:44:28,760 frequencies beyond 22 kilohertz and doesn't mess up 945 00:44:28,760 --> 00:44:30,810 the frequencies below 20 kilohertz. 946 00:44:30,810 --> 00:44:31,810 This is actually a real problem. 947 00:44:31,810 --> 00:44:34,700 That's how you need to do that to record. 948 00:44:34,700 --> 00:44:36,680 The people who developed the CD standard had to make 949 00:44:36,680 --> 00:44:38,150 something like this. 950 00:44:38,150 --> 00:44:40,360 So basically you're making a, quote, "antialias" filter. 951 00:44:40,360 --> 00:44:41,550 So I want that. 952 00:44:41,550 --> 00:44:45,550 Now here, the problem is that the student has learned 953 00:44:45,550 --> 00:44:48,430 methods of analysis that cannot be inverted. 954 00:44:48,430 --> 00:44:51,050 For example, one method of analysis is you have a circuit 955 00:44:51,050 --> 00:44:53,060 and you just simulate the thing. 956 00:44:53,060 --> 00:44:55,320 You just feed it to your computer, which does all the 957 00:44:55,320 --> 00:44:56,830 analysis for you. 958 00:44:56,830 --> 00:45:01,790 An analogy for that is if someone gives you a function 959 00:45:01,790 --> 00:45:05,030 to graph, you can use your graphing calculator to see 960 00:45:05,030 --> 00:45:06,760 what the graph looks like. 961 00:45:06,760 --> 00:45:09,190 But suppose someone says, well, I want a graph that 962 00:45:09,190 --> 00:45:10,790 looks like this. 963 00:45:10,790 --> 00:45:13,480 The graphing calculator can't answer that question. 964 00:45:13,480 --> 00:45:16,400 So they've learned methods of analysis that are not 965 00:45:16,400 --> 00:45:17,650 invertible. 966 00:45:22,940 --> 00:45:27,650 So they're actually useless, because the real world problem 967 00:45:27,650 --> 00:45:29,840 is exactly opposite of the school problem. 968 00:45:29,840 --> 00:45:32,250 The school problem, the circuit is the start. 969 00:45:32,250 --> 00:45:35,305 In the real world, the specification is the start. 970 00:45:40,850 --> 00:45:43,850 So to have any hope of going from there to there-- 971 00:45:43,850 --> 00:45:46,300 this is a one-way arrow, it's like a diet-- you need a 972 00:45:46,300 --> 00:45:47,550 different method. 973 00:45:49,680 --> 00:45:51,760 You need to learn invertible methods of analysis. 974 00:46:03,390 --> 00:46:05,760 So if you have invertible methods of analysis, you can 975 00:46:05,760 --> 00:46:07,265 go both ways. 976 00:46:10,300 --> 00:46:14,020 And this problem I think is central to many, many, many, 977 00:46:14,020 --> 00:46:16,480 many courses, not just to this particular analog circuit 978 00:46:16,480 --> 00:46:17,620 design course. 979 00:46:17,620 --> 00:46:22,850 So then, what Middlebrook slowly evolved to was not just 980 00:46:22,850 --> 00:46:25,460 teaching invertible methods of analysis, but he made those 981 00:46:25,460 --> 00:46:27,710 the foreground of the course. 982 00:46:27,710 --> 00:46:33,060 As he described, "I found in teaching this stuff for a long 983 00:46:33,060 --> 00:46:36,460 time, I've actually had to put names and words to ideas for 984 00:46:36,460 --> 00:46:39,030 the students to get hold of them. 985 00:46:39,030 --> 00:46:42,340 This came about because for a long time I taught by example. 986 00:46:42,340 --> 00:46:44,450 I used a lot of methods, saying we're going to look 987 00:46:44,450 --> 00:46:46,070 into the properties of a certain circuit. 988 00:46:46,070 --> 00:46:48,500 And I would use some shortcut method or trick that I thought 989 00:46:48,500 --> 00:46:50,140 was a neater way to do it. 990 00:46:50,140 --> 00:46:52,170 And I just showed them this without actually emphasizing 991 00:46:52,170 --> 00:46:53,240 the method. 992 00:46:53,240 --> 00:46:54,190 That was fine. 993 00:46:54,190 --> 00:46:56,020 But when they did the homework problems and exams, their 994 00:46:56,020 --> 00:46:59,420 minds just automatically reset to the old way of doing it. 995 00:46:59,420 --> 00:47:00,610 So that didn't work very well. 996 00:47:00,610 --> 00:47:02,640 And I finally realized I had to give names to these 997 00:47:02,640 --> 00:47:03,290 things." 998 00:47:03,290 --> 00:47:05,750 And those are the names that he introduces in the paper. 999 00:47:05,750 --> 00:47:08,950 So those names, some of those are 1000 00:47:08,950 --> 00:47:10,340 specific to analog circuits. 1001 00:47:10,340 --> 00:47:11,990 Some are general. 1002 00:47:11,990 --> 00:47:16,030 But it's the giving of names that is the central 1003 00:47:16,030 --> 00:47:17,260 [INAUDIBLE]. 1004 00:47:17,260 --> 00:47:20,820 So you give names to the big ideas in the course. 1005 00:47:20,820 --> 00:47:24,370 And you don't just use them in passing, but you make them the 1006 00:47:24,370 --> 00:47:27,700 focus of the course. 1007 00:47:27,700 --> 00:47:28,950 So let's see. 1008 00:47:40,850 --> 00:47:43,130 So in answer to what should the course 1009 00:47:43,130 --> 00:47:44,860 goals be, roughly speaking-- 1010 00:48:12,020 --> 00:48:12,290 OK. 1011 00:48:12,290 --> 00:48:16,490 Questions about that, because it's very different from how 1012 00:48:16,490 --> 00:48:17,740 it's normally done? 1013 00:48:20,890 --> 00:48:25,410 So if you look, for example, at a biology course, it might 1014 00:48:25,410 --> 00:48:29,660 be organized by, say in cell biology, organized by the 1015 00:48:29,660 --> 00:48:35,250 organ to organelle, the little system inside the cell. 1016 00:48:35,250 --> 00:48:38,130 But those aren't necessarily transferable to anything 1017 00:48:38,130 --> 00:48:40,720 except that particular subject. 1018 00:48:40,720 --> 00:48:44,050 A physics class might be organized by a whole bunch of 1019 00:48:44,050 --> 00:48:46,320 kinematics problems and dynamics problems. 1020 00:48:46,320 --> 00:48:50,210 But a big organizational principle that is implicit 1021 00:48:50,210 --> 00:48:52,500 there but isn't said is that, well, actually what we're 1022 00:48:52,500 --> 00:48:55,560 doing is we're approximating down to something simple 1023 00:48:55,560 --> 00:48:57,100 enough that we can do. 1024 00:48:57,100 --> 00:48:58,550 That's an organizational principle 1025 00:48:58,550 --> 00:49:00,470 that you can transfer. 1026 00:49:00,470 --> 00:49:01,380 But that's never said. 1027 00:49:01,380 --> 00:49:02,150 It's just implicit. 1028 00:49:02,150 --> 00:49:04,990 If you look at Chapter 1, the systems are simpler. 1029 00:49:04,990 --> 00:49:06,520 And then Chapter 2, they get harder. 1030 00:49:06,520 --> 00:49:07,982 Maybe they have two dimensions in them. 1031 00:49:07,982 --> 00:49:10,210 In Chapter 5, they have two particles in them. 1032 00:49:10,210 --> 00:49:13,110 In Chapter 7, they have n particles in them. 1033 00:49:13,110 --> 00:49:16,330 So it's this process of successive complication. 1034 00:49:16,330 --> 00:49:19,110 And the beginning part of it, where we simplified real-world 1035 00:49:19,110 --> 00:49:22,110 things into just one particle moving in one dimension at 1036 00:49:22,110 --> 00:49:25,150 constant acceleration, that was 1037 00:49:25,150 --> 00:49:26,480 never told to the students. 1038 00:49:26,480 --> 00:49:29,730 So the transferable principle just went straight by them, 1039 00:49:29,730 --> 00:49:31,850 because we never made it explicit. 1040 00:49:31,850 --> 00:49:35,140 So you have to, if you ever want to have any hope of 1041 00:49:35,140 --> 00:49:37,520 teaching these ideas, you have to make them explicit and give 1042 00:49:37,520 --> 00:49:39,770 them names. 1043 00:49:39,770 --> 00:49:42,460 Giving things names is absolutely essential to have 1044 00:49:42,460 --> 00:49:43,820 any chance of learning them. 1045 00:49:43,820 --> 00:49:48,180 And this was known in all the old legends. 1046 00:49:48,180 --> 00:49:50,500 The gods did not want the mortals to have names for the 1047 00:49:50,500 --> 00:49:54,730 gods, because it would give the mortals too much power 1048 00:49:54,730 --> 00:49:56,340 over the gods. 1049 00:49:56,340 --> 00:50:00,550 So some gods were He-who-has-no-name. 1050 00:50:00,550 --> 00:50:03,780 And maybe only the high priest knew the name. 1051 00:50:03,780 --> 00:50:06,400 Well, you don't want to be the high priest. 1052 00:50:06,400 --> 00:50:09,200 You want to share the names with the students. 1053 00:50:09,200 --> 00:50:12,260 And that involves a lot and a lot and a lot of thinking. 1054 00:50:12,260 --> 00:50:15,440 That's where most of the work in course design goes, is 1055 00:50:15,440 --> 00:50:20,960 figuring out those main ideas, those transferable goals and 1056 00:50:20,960 --> 00:50:23,180 ways of reasoning that students can use no matter 1057 00:50:23,180 --> 00:50:24,870 what they do. 1058 00:50:24,870 --> 00:50:29,660 And then to teach them, you need to have it from as wide a 1059 00:50:29,660 --> 00:50:31,370 set of examples as possible. 1060 00:50:31,370 --> 00:50:33,850 So for example, to give you an illustration, when I teach 1061 00:50:33,850 --> 00:50:38,505 dimensional analysis, which is the idea, and I want them to 1062 00:50:38,505 --> 00:50:41,130 be able to use it wherever, the first example-- 1063 00:50:41,130 --> 00:50:42,700 I forget whether it's the first or second. i sort of 1064 00:50:42,700 --> 00:50:43,840 flip it around. 1065 00:50:43,840 --> 00:50:50,740 The first example is in economics, because you can 1066 00:50:50,740 --> 00:50:53,540 identify a lot of bogus stuff in economics, because it has 1067 00:50:53,540 --> 00:50:54,740 the wrong dimensions. 1068 00:50:54,740 --> 00:50:55,965 So I want them to see it there. 1069 00:50:55,965 --> 00:50:59,300 The second example is solid geometry, volumes of 1070 00:50:59,300 --> 00:51:02,390 tetrahedrons and cones and things. 1071 00:51:02,390 --> 00:51:05,520 And then we do sort of a more standard physics one. 1072 00:51:05,520 --> 00:51:08,730 So I want them to see the broad sweep of this idea so 1073 00:51:08,730 --> 00:51:10,430 that the idea comes clear. 1074 00:51:10,430 --> 00:51:16,510 So the thing to do is to identify large ideas. 1075 00:51:16,510 --> 00:51:19,150 So these are the-- 1076 00:51:22,630 --> 00:51:23,000 OK. 1077 00:51:23,000 --> 00:51:29,040 So to practice, choose right now a course in your own mind 1078 00:51:29,040 --> 00:51:33,020 that either you are interested in teaching or teaching now or 1079 00:51:33,020 --> 00:51:34,570 would like to teach. 1080 00:51:34,570 --> 00:51:37,830 And see if you can come up with some big ideas for that 1081 00:51:37,830 --> 00:51:42,400 course, just to practice what some big ideas are. 1082 00:51:42,400 --> 00:51:46,430 And I will show you as an example the large ideas for 1083 00:51:46,430 --> 00:51:48,350 my-- just to give you an idea of what they are. 1084 00:51:50,960 --> 00:51:55,180 I'll show you the tree for my approximation course just so 1085 00:51:55,180 --> 00:51:58,070 you can see what level these ideas kind of live at. 1086 00:52:04,280 --> 00:52:07,100 So the whole course is designed around how do you 1087 00:52:07,100 --> 00:52:10,230 deal with complex problems and how do you handle the fact 1088 00:52:10,230 --> 00:52:11,900 that the world is really messy? 1089 00:52:11,900 --> 00:52:19,240 And I broke that down into either you manage it or you 1090 00:52:19,240 --> 00:52:20,490 throw it away. 1091 00:52:23,770 --> 00:52:26,350 Those are still too high-level to actually do anything with. 1092 00:52:26,350 --> 00:52:28,860 But I wanted to organize the big ideas as well. 1093 00:52:28,860 --> 00:52:34,290 So you can manage it by divide and conquer reasoning, so 1094 00:52:34,290 --> 00:52:36,210 subdividing into smaller problems. 1095 00:52:36,210 --> 00:52:37,460 Or you can make abstractions. 1096 00:52:40,290 --> 00:52:42,870 Abstractions is basically the process of giving names to 1097 00:52:42,870 --> 00:52:46,190 things, which is what we're talking about now. 1098 00:52:46,190 --> 00:52:49,580 To throw away complexity, you can either do it losslessly-- 1099 00:52:53,780 --> 00:52:57,420 so this is methods of reasoning that find complexity 1100 00:52:57,420 --> 00:53:00,910 that isn't there but look like it is there and get rid of it. 1101 00:53:00,910 --> 00:53:04,740 So symmetry is number one. 1102 00:53:04,740 --> 00:53:06,950 And examples of symmetry reasoning are proportional 1103 00:53:06,950 --> 00:53:10,010 reasoning and dimensional analysis. 1104 00:53:10,010 --> 00:53:12,010 So those are all lossless ways. 1105 00:53:12,010 --> 00:53:13,490 They don't actually cost you anything. 1106 00:53:13,490 --> 00:53:15,730 If they work, they make your life so much easier. 1107 00:53:15,730 --> 00:53:17,740 And you haven't thrown any information away. 1108 00:53:17,740 --> 00:53:21,090 Or you can make lossy compression. 1109 00:53:21,090 --> 00:53:26,190 So you can do extreme cases, look at only the simple cases 1110 00:53:26,190 --> 00:53:28,940 of things so you're throwing out information. 1111 00:53:28,940 --> 00:53:33,810 Or you can make spring models. 1112 00:53:33,810 --> 00:53:36,152 So even though things aren't-- like chemical bonds, you can 1113 00:53:36,152 --> 00:53:37,400 just say, well, they're just like springs. 1114 00:53:37,400 --> 00:53:40,070 So that's a very useful but lossy way. 1115 00:53:40,070 --> 00:53:44,590 Or the final one is you can lump. 1116 00:53:44,590 --> 00:53:47,640 So you can lump changing processes into one. 1117 00:53:47,640 --> 00:53:51,520 For example, a curve, you want to find the area under the 1118 00:53:51,520 --> 00:53:53,870 curve, well, replace it by one rectangle. 1119 00:53:53,870 --> 00:53:56,920 So that general pattern-- 1120 00:53:56,920 --> 00:54:00,110 those are what I've found are the most useful ways of 1121 00:54:00,110 --> 00:54:01,340 dealing with complex problems. 1122 00:54:01,340 --> 00:54:08,430 So these are the big ideas in that course. 1123 00:54:08,430 --> 00:54:10,420 And the whole course is organized that way. 1124 00:54:10,420 --> 00:54:14,460 And I show this tree once a week usually, just so people 1125 00:54:14,460 --> 00:54:15,710 know where they are. 1126 00:54:17,780 --> 00:54:21,530 So now, depending on the course, what stuff you have in 1127 00:54:21,530 --> 00:54:22,820 your big ideas will be different. 1128 00:54:22,820 --> 00:54:25,940 But I just want to give you an idea of what some large ideas, 1129 00:54:25,940 --> 00:54:27,740 some structuring principles are. 1130 00:54:27,740 --> 00:54:30,420 And then the course itself is actually organized Unit 1, 1131 00:54:30,420 --> 00:54:33,010 Unit 2, 3, 4, 5, 6, 7, 8. 1132 00:54:33,010 --> 00:54:35,680 So what I've found is, just like Middlebrook found, that 1133 00:54:35,680 --> 00:54:38,330 not only do you have to give names to the things, but I 1134 00:54:38,330 --> 00:54:40,530 found that I had to actually organize the course around 1135 00:54:40,530 --> 00:54:43,370 them, rather than organizing them around the topics that 1136 00:54:43,370 --> 00:54:46,530 they apply to, if I really wanted the techniques, the 1137 00:54:46,530 --> 00:54:48,960 ways of reasoning, to transfer. 1138 00:54:48,960 --> 00:54:49,270 OK. 1139 00:54:49,270 --> 00:54:52,780 So questions about what these large ideas, these reasoning 1140 00:54:52,780 --> 00:54:53,820 principles, are? 1141 00:54:53,820 --> 00:54:55,400 What kind of things to look for? 1142 00:54:55,400 --> 00:54:56,400 Yes. 1143 00:54:56,400 --> 00:54:58,900 AUDIENCE: What's the topic of the course? 1144 00:54:58,900 --> 00:55:00,560 PROFESSOR: The course is called The Art of 1145 00:55:00,560 --> 00:55:03,350 Approximation in Science and Engineering. 1146 00:55:03,350 --> 00:55:04,700 So actually, it's carte blanche 1147 00:55:04,700 --> 00:55:06,970 to talk about anything. 1148 00:55:06,970 --> 00:55:11,000 So that's why these are probably higher-level objects 1149 00:55:11,000 --> 00:55:13,210 than in most courses which will be narrower. 1150 00:55:13,210 --> 00:55:16,420 But even there, like for example in physics, in the 1151 00:55:16,420 --> 00:55:19,120 Intro Physics, one of the core ideas is successive 1152 00:55:19,120 --> 00:55:20,830 approximation. 1153 00:55:20,830 --> 00:55:22,420 And that's not brought out normally. 1154 00:55:22,420 --> 00:55:23,780 But you could bring it out. 1155 00:55:23,780 --> 00:55:25,290 You could say, look, we're using successive 1156 00:55:25,290 --> 00:55:26,370 approximation again. 1157 00:55:26,370 --> 00:55:29,090 Or here's the structure of the course, so that it's plain for 1158 00:55:29,090 --> 00:55:29,665 the student. 1159 00:55:29,665 --> 00:55:31,830 Does that help? 1160 00:55:31,830 --> 00:55:32,230 OK. 1161 00:55:32,230 --> 00:55:34,990 So pick that course in your mind. 1162 00:55:34,990 --> 00:55:36,510 And talk to your neighbor. 1163 00:55:36,510 --> 00:55:40,090 And see if you come up with, say, two or three large ideas. 1164 00:55:40,090 --> 00:55:41,760 And now what we're going to do is we're going to put them on 1165 00:55:41,760 --> 00:55:45,630 the board, the reason being that you'll find that people's 1166 00:55:45,630 --> 00:55:48,520 big ideas and large ideas from other courses you'll be able 1167 00:55:48,520 --> 00:55:50,880 to use in your course, not every single 1168 00:55:50,880 --> 00:55:51,750 one, but many of them. 1169 00:55:51,750 --> 00:55:54,440 That's almost by definition what makes something a large 1170 00:55:54,440 --> 00:55:56,370 idea, that it's not just limited to that course. 1171 00:55:56,370 --> 00:55:59,880 So it helps to see what other people's are. 1172 00:55:59,880 --> 00:56:05,230 So I'll make some space on the board to draw those up. 1173 00:56:05,230 --> 00:56:11,260 So I'll give you a chance to develop your list farther in 1174 00:56:11,260 --> 00:56:12,790 the homework. 1175 00:56:12,790 --> 00:56:15,250 Oh, I should say something about the homework, which is 1176 00:56:15,250 --> 00:56:18,000 that you guys are all grad students, or 1177 00:56:18,000 --> 00:56:19,250 almost all of you. 1178 00:56:19,250 --> 00:56:21,160 You're all taking the course for fun. 1179 00:56:21,160 --> 00:56:23,880 It's kind of pointless of me to police whether you're doing 1180 00:56:23,880 --> 00:56:25,150 stuff or not. 1181 00:56:25,150 --> 00:56:29,310 But all the same, I will give you an assignment to do-- 1182 00:56:29,310 --> 00:56:30,900 and I'll just trust that you'll do it-- 1183 00:56:30,900 --> 00:56:34,980 which is to work with each other on making large ideas 1184 00:56:34,980 --> 00:56:38,220 for a course and then figuring out examples for those large 1185 00:56:38,220 --> 00:56:41,780 ideas, so basically a sketch of a course design And the 1186 00:56:41,780 --> 00:56:45,250 reason to do this, starting now and also later, is that 1187 00:56:45,250 --> 00:56:48,180 basically that is the hardest work of course design. 1188 00:56:48,180 --> 00:56:51,340 Once you've done that, everything else sort of flows. 1189 00:56:51,340 --> 00:56:54,280 The syllabus writing, all that stuff, just flows. 1190 00:56:54,280 --> 00:56:56,420 But if you haven't done this, you're just 1191 00:56:56,420 --> 00:56:57,080 kind of spinning around. 1192 00:56:57,080 --> 00:56:58,590 And you don't actually know what you're doing. 1193 00:56:58,590 --> 00:57:01,240 It's really hard to actually figure out how you should 1194 00:57:01,240 --> 00:57:02,590 start and what you should do. 1195 00:57:02,590 --> 00:57:04,740 So, big ideas. 1196 00:57:04,740 --> 00:57:06,045 Any big idea in any course? 1197 00:57:09,540 --> 00:57:11,180 AUDIENCE: Separation of scale. 1198 00:57:11,180 --> 00:57:11,490 PROFESSOR: OK. 1199 00:57:11,490 --> 00:57:14,930 Separation of scale, so that behavior at one scale and 1200 00:57:14,930 --> 00:57:18,020 another scale, you can often separate them and analyze them 1201 00:57:18,020 --> 00:57:20,826 differently and without interfering with each other. 1202 00:57:20,826 --> 00:57:23,730 AUDIENCE: [INAUDIBLE] 1203 00:57:23,730 --> 00:57:27,920 past problems and then [INAUDIBLE]. 1204 00:57:27,920 --> 00:57:28,350 PROFESSOR: OK. 1205 00:57:28,350 --> 00:57:29,570 Separation of scale. 1206 00:57:29,570 --> 00:57:34,640 So for example, I've seen that done in neurobiology. 1207 00:57:34,640 --> 00:57:36,630 It's done in physics all the time. 1208 00:57:36,630 --> 00:57:42,840 So in neurobiology, the calcium flux, the calcium 1209 00:57:42,840 --> 00:57:47,390 concentration changes slowly, so you do the calcium 1210 00:57:47,390 --> 00:57:49,590 concentration separate from, say, the sodium and the 1211 00:57:49,590 --> 00:57:53,360 potassium, which is done with the action potential spikes. 1212 00:57:53,360 --> 00:57:56,690 So separation scales, very important principle across 1213 00:57:56,690 --> 00:57:57,280 many fields. 1214 00:57:57,280 --> 00:57:58,200 Yes? 1215 00:57:58,200 --> 00:57:58,880 AUDIENCE: Equilibrium. 1216 00:57:58,880 --> 00:58:00,130 PROFESSOR: Equilibrium. 1217 00:58:05,180 --> 00:58:05,660 Is that right? 1218 00:58:05,660 --> 00:58:07,950 So equilibrium, right away you can see if you really want 1219 00:58:07,950 --> 00:58:11,440 students to understand the value of equilibrium, you have 1220 00:58:11,440 --> 00:58:14,940 a whole set of examples to use, to steal from. 1221 00:58:14,940 --> 00:58:17,250 You can use chemistry, physics, mechanical 1222 00:58:17,250 --> 00:58:19,680 engineering. 1223 00:58:19,680 --> 00:58:22,350 And they all have slightly different senses to 1224 00:58:22,350 --> 00:58:23,880 equilibrium, statistical mechanics. 1225 00:58:23,880 --> 00:58:26,580 But there's some core idea that's the same. 1226 00:58:26,580 --> 00:58:29,910 And so it also is an argument for team teaching, or actually 1227 00:58:29,910 --> 00:58:31,870 talking to colleagues from different fields to steal 1228 00:58:31,870 --> 00:58:34,540 examples from them. 1229 00:58:34,540 --> 00:58:35,550 Yes? 1230 00:58:35,550 --> 00:58:38,005 AUDIENCE: I don't know how to describe this, but it 1231 00:58:38,005 --> 00:58:41,933 describes a process which we all do research, and that is 1232 00:58:41,933 --> 00:58:43,897 how to deal with scientific problems. 1233 00:58:43,897 --> 00:58:45,147 [INAUDIBLE]. 1234 00:58:49,320 --> 00:58:49,790 PROFESSOR: OK. 1235 00:58:49,790 --> 00:58:56,450 So identifying a scientific question and how to start 1236 00:58:56,450 --> 00:58:57,185 studying it. 1237 00:58:57,185 --> 00:58:57,490 AUDIENCE: [INAUDIBLE]. 1238 00:58:57,490 --> 00:58:58,740 PROFESSOR: Yeah. 1239 00:59:09,580 --> 00:59:12,035 Identifying and studying. 1240 00:59:15,080 --> 00:59:15,205 Right. 1241 00:59:15,205 --> 00:59:18,180 And there's many things that are common across many fields. 1242 00:59:18,180 --> 00:59:20,990 And there's many things that are different in each field. 1243 00:59:20,990 --> 00:59:22,920 And you can actually have a very fruitful-- 1244 00:59:22,920 --> 00:59:25,230 I could imagine a really fruitful interesting-- 1245 00:59:25,230 --> 00:59:26,760 you could almost teach a whole class on this. 1246 00:59:26,760 --> 00:59:29,630 Actually, that sounds kind of fun. 1247 00:59:29,630 --> 00:59:31,830 You could teach a history of science class on scientific 1248 00:59:31,830 --> 00:59:33,980 questions that were identified, how they were 1249 00:59:33,980 --> 00:59:36,130 studied, what principles still are done today. 1250 00:59:36,130 --> 00:59:39,470 You could have people read papers from across many fields 1251 00:59:39,470 --> 00:59:42,400 and read the intro and see how they would study that 1252 00:59:42,400 --> 00:59:45,200 question, see what questions there are. 1253 00:59:45,200 --> 00:59:45,770 Yes. 1254 00:59:45,770 --> 00:59:46,450 Sharon. 1255 00:59:46,450 --> 00:59:46,840 AUDIENCE: Resonance. 1256 00:59:46,840 --> 00:59:47,190 PROFESSOR: Pardon? 1257 00:59:47,190 --> 00:59:48,430 AUDIENCE: Resonance. 1258 00:59:48,430 --> 00:59:49,680 PROFESSOR: Resonance. 1259 00:59:58,300 --> 00:59:58,560 Right. 1260 00:59:58,560 --> 01:00:00,520 Resonance you can have a field day with. 1261 01:00:00,520 --> 01:00:01,720 It's in electric circuits. 1262 01:00:01,720 --> 01:00:04,710 It's in mechanical systems, the earth-moon system, the 1263 01:00:04,710 --> 01:00:07,940 tides are driven almost on resonance by the 1264 01:00:07,940 --> 01:00:10,350 moon and the sun. 1265 01:00:10,350 --> 01:00:11,440 Resonance is everywhere. 1266 01:00:11,440 --> 01:00:12,590 It's in mechanical systems. 1267 01:00:12,590 --> 01:00:15,090 There's beautiful films you can show of the 1268 01:00:15,090 --> 01:00:17,710 Tacoma Narrows Bridge. 1269 01:00:17,710 --> 01:00:19,830 I think the London Millennium Footbridge as 1270 01:00:19,830 --> 01:00:22,740 well got hit by resonance. 1271 01:00:22,740 --> 01:00:25,340 So resonance, another very transferable idea. 1272 01:00:25,340 --> 01:00:25,940 Yes? 1273 01:00:25,940 --> 01:00:29,230 AUDIENCE: How to develop 3D models. 1274 01:00:29,230 --> 01:00:29,750 PROFESSOR: OK. 1275 01:00:29,750 --> 01:00:32,025 So how to build models. 1276 01:00:37,500 --> 01:00:37,760 Right. 1277 01:00:37,760 --> 01:00:40,630 And that's something that there are 1278 01:00:40,630 --> 01:00:41,660 general patterns to it. 1279 01:00:41,660 --> 01:00:43,470 And some of it's specific to a particular course. 1280 01:00:43,470 --> 01:00:44,450 But there are general patterns. 1281 01:00:44,450 --> 01:00:46,080 And that's something the students can use no matter 1282 01:00:46,080 --> 01:00:47,930 what they do later. 1283 01:00:47,930 --> 01:00:49,610 Whenever you go to a new field-- 1284 01:00:49,610 --> 01:00:51,490 so there's a Nobel Prize winner at 1285 01:00:51,490 --> 01:00:53,390 Harvard, Walter Gilbert. 1286 01:00:53,390 --> 01:00:55,700 So he's worked in I think chemistry, physics, and 1287 01:00:55,700 --> 01:00:57,410 biology, many different fields. 1288 01:00:57,410 --> 01:00:59,080 And he said, oh, yeah. 1289 01:00:59,080 --> 01:01:01,980 Whenever you go to a new field, there's only a few key 1290 01:01:01,980 --> 01:01:03,210 ideas in that new field. 1291 01:01:03,210 --> 01:01:05,350 And the hard work is figuring out what those are. 1292 01:01:05,350 --> 01:01:06,800 But that's what you have to do. 1293 01:01:06,800 --> 01:01:10,430 So that is one of the transferable skills as well. 1294 01:01:10,430 --> 01:01:10,940 Others? 1295 01:01:10,940 --> 01:01:11,840 Yes. 1296 01:01:11,840 --> 01:01:14,720 AUDIENCE: Problem solving requires communication. 1297 01:01:14,720 --> 01:01:15,100 PROFESSOR: OK. 1298 01:01:15,100 --> 01:01:16,350 So communication. 1299 01:01:21,920 --> 01:01:22,160 Right. 1300 01:01:22,160 --> 01:01:25,420 If you can't communicate, you haven't solved the problem, 1301 01:01:25,420 --> 01:01:28,480 which reminds me of my Caltech students, when I 1302 01:01:28,480 --> 01:01:30,430 had them keep a journal. 1303 01:01:30,430 --> 01:01:32,990 And then I told them I wanted them to explain-- 1304 01:01:32,990 --> 01:01:33,850 the journal they liked. 1305 01:01:33,850 --> 01:01:35,150 But then I said, on the homeworks, I want you to 1306 01:01:35,150 --> 01:01:37,590 explain your reasoning so that it reads. 1307 01:01:37,590 --> 01:01:40,460 It's not just hence and thus and therefore. 1308 01:01:40,460 --> 01:01:42,250 And they said, well, why we have to do that? 1309 01:01:42,250 --> 01:01:43,080 We're physics students. 1310 01:01:43,080 --> 01:01:45,280 I said, well, later on, you're going to have to communicate 1311 01:01:45,280 --> 01:01:46,640 your answers to someone. 1312 01:01:46,640 --> 01:01:49,810 They said, oh, we'll just hire someone who does that. 1313 01:01:49,810 --> 01:01:52,550 So then I said to them, "well, how are you going to explain 1314 01:01:52,550 --> 01:01:54,470 it to that person? 1315 01:01:54,470 --> 01:01:59,487 How will they know?" I said, "oh you're going--" "oh, I'll 1316 01:01:59,487 --> 01:02:01,470 explain it to them." I said, "oh, so you are explaining 1317 01:02:01,470 --> 01:02:01,740 something?" 1318 01:02:01,740 --> 01:02:04,050 They said "oh, no." Somebody said, "oh, well, actually that 1319 01:02:04,050 --> 01:02:06,510 person will understand it already." So then I said to 1320 01:02:06,510 --> 01:02:10,550 them, "well, so that person understands it already and can 1321 01:02:10,550 --> 01:02:11,480 communicate it. 1322 01:02:11,480 --> 01:02:13,135 And you just understand it. 1323 01:02:13,135 --> 01:02:15,740 Who are people going to turn? " 1324 01:02:15,740 --> 01:02:17,840 So only then did they agree that it was a good thing to 1325 01:02:17,840 --> 01:02:20,480 actually write problem sets so they could communicate. 1326 01:02:20,480 --> 01:02:22,360 So that's something you can teach in any 1327 01:02:22,360 --> 01:02:23,780 field and across fields. 1328 01:02:23,780 --> 01:02:25,150 You could look at scientific writing. 1329 01:02:25,150 --> 01:02:27,090 You could look at writing scientific papers. 1330 01:02:27,090 --> 01:02:29,780 You can look at giving presentations. 1331 01:02:29,780 --> 01:02:32,200 Doing it on problem sets so they communicate, you can have 1332 01:02:32,200 --> 01:02:34,330 students exchange problem sets with each other. 1333 01:02:34,330 --> 01:02:36,430 If they can't understand the other problem set, clearly it 1334 01:02:36,430 --> 01:02:38,960 wasn't communicated. 1335 01:02:38,960 --> 01:02:40,100 Other transferable ideas? 1336 01:02:40,100 --> 01:02:40,530 Yes. 1337 01:02:40,530 --> 01:02:40,920 AUDIENCE: Coordinates. 1338 01:02:40,920 --> 01:02:42,120 PROFESSOR: Coordinates. 1339 01:02:42,120 --> 01:02:42,550 Yes. 1340 01:02:42,550 --> 01:02:49,650 So coordinates and-- 1341 01:02:49,650 --> 01:02:52,250 it's also fun to make this kind of list, because you 1342 01:02:52,250 --> 01:02:54,540 start to see commonalities and they start to 1343 01:02:54,540 --> 01:02:55,400 suggest other ones. 1344 01:02:55,400 --> 01:02:57,630 So when you say coordinates, I also think, oh, yeah. 1345 01:02:57,630 --> 01:03:01,080 That's a general example of representations. 1346 01:03:01,080 --> 01:03:02,720 So there's different-- 1347 01:03:02,720 --> 01:03:04,050 this is probably what you meant is coordinate 1348 01:03:04,050 --> 01:03:06,150 representations, what you were thinking of. 1349 01:03:06,150 --> 01:03:08,800 But you can also think of the general idea of choosing good 1350 01:03:08,800 --> 01:03:11,140 representations for solving particular problems. 1351 01:03:11,140 --> 01:03:12,530 Like for some problems, a symbolic 1352 01:03:12,530 --> 01:03:13,880 representation may be right. 1353 01:03:13,880 --> 01:03:17,020 And some, there's a pictorial representation. 1354 01:03:17,020 --> 01:03:19,610 You want to use in circuits, the time domain 1355 01:03:19,610 --> 01:03:21,550 representation, or the frequency domain 1356 01:03:21,550 --> 01:03:22,370 representation. 1357 01:03:22,370 --> 01:03:25,160 So coordinates, I'll put dot, dot, dot, to say that almost 1358 01:03:25,160 --> 01:03:35,090 leads to the next one, which is representation in general. 1359 01:03:35,090 --> 01:03:35,480 Others? 1360 01:03:35,480 --> 01:03:35,910 Yes. 1361 01:03:35,910 --> 01:03:36,770 AUDIENCE: Symmetry. 1362 01:03:36,770 --> 01:03:37,340 PROFESSOR: Symmetry. 1363 01:03:37,340 --> 01:03:37,780 Yes. 1364 01:03:37,780 --> 01:03:39,250 Symmetry, incredibly powerful. 1365 01:03:47,461 --> 01:03:47,960 Yes. 1366 01:03:47,960 --> 01:03:48,520 Adrian, and then you're next. 1367 01:03:48,520 --> 01:03:49,465 Yeah? 1368 01:03:49,465 --> 01:03:53,350 AUDIENCE: Then you have approximation [INAUDIBLE]. 1369 01:03:53,350 --> 01:03:53,750 PROFESSOR: OK. 1370 01:03:53,750 --> 01:03:57,200 So linearization. 1371 01:03:57,200 --> 01:03:59,920 And that is of course also huge. 1372 01:03:59,920 --> 01:04:01,870 I mean, symmetry is used in almost every field. 1373 01:04:01,870 --> 01:04:03,630 Linearization, basically you can't do 1374 01:04:03,630 --> 01:04:04,770 anything that's nonlinear. 1375 01:04:04,770 --> 01:04:06,540 So every field does linearization. 1376 01:04:06,540 --> 01:04:10,280 So that core idea would be beautiful to convey that. 1377 01:04:10,280 --> 01:04:11,026 Yes? 1378 01:04:11,026 --> 01:04:13,310 AUDIENCE: Error. 1379 01:04:13,310 --> 01:04:15,440 PROFESSOR: OK. 1380 01:04:15,440 --> 01:04:15,950 Errors . 1381 01:04:15,950 --> 01:04:17,060 How do you deal with errors? 1382 01:04:17,060 --> 01:04:19,170 There are common principles, probability theory, 1383 01:04:19,170 --> 01:04:21,870 statistics, that deal with errors in any field. 1384 01:04:21,870 --> 01:04:22,530 What are those? 1385 01:04:22,530 --> 01:04:24,680 Well, that's what you want to understand so you can move to 1386 01:04:24,680 --> 01:04:26,050 any other field. 1387 01:04:26,050 --> 01:04:28,700 I'll put a dot, dot here, so symmetry, another one that's 1388 01:04:28,700 --> 01:04:30,590 related to symmetry is conservation. 1389 01:04:33,580 --> 01:04:37,000 Noether's theorem is that every conservation law 1390 01:04:37,000 --> 01:04:39,590 corresponds to a symmetry and vice versa. 1391 01:04:39,590 --> 01:04:41,310 I think I've stated that correctly. 1392 01:04:41,310 --> 01:04:43,490 But they flow from each other. 1393 01:04:43,490 --> 01:04:47,830 So actually I do conservation here as part of symmetry. 1394 01:04:47,830 --> 01:04:51,100 So let me stop the list right there, just to 1395 01:04:51,100 --> 01:04:53,590 say that right away-- 1396 01:04:53,590 --> 01:04:55,645 so let me put the other one which I talked about before, 1397 01:04:55,645 --> 01:05:01,570 which is successive approximation, that you don't 1398 01:05:01,570 --> 01:05:03,750 want to solve a hard problem all at once. 1399 01:05:03,750 --> 01:05:05,240 It's sort of like divide and conquer. 1400 01:05:05,240 --> 01:05:07,700 But you want to try to solve it approximately and then less 1401 01:05:07,700 --> 01:05:10,630 approximately, then less less approximately, so you get 1402 01:05:10,630 --> 01:05:13,010 closer and closer, as close as you need. 1403 01:05:13,010 --> 01:05:16,470 That's a general principle of engineering design as well. 1404 01:05:16,470 --> 01:05:19,940 So these, just to show you that all of a sudden you 1405 01:05:19,940 --> 01:05:21,980 thought of a whole bunch of examples. 1406 01:05:21,980 --> 01:05:24,160 And probably you can use that in any course you take. 1407 01:05:24,160 --> 01:05:26,160 So now you all have like 11. 1408 01:05:26,160 --> 01:05:27,230 Right now I'm not saying you have to use 1409 01:05:27,230 --> 01:05:28,320 all 11 in your course. 1410 01:05:28,320 --> 01:05:30,800 But you can start to restructure courses around 1411 01:05:30,800 --> 01:05:33,860 those ideas and make them explicit and choose which you 1412 01:05:33,860 --> 01:05:36,630 think are the most important in your field in the ways of 1413 01:05:36,630 --> 01:05:39,350 thinking and illustrate them with things from your field 1414 01:05:39,350 --> 01:05:41,330 but nearby as well. 1415 01:05:41,330 --> 01:05:45,260 So this evening I'll post a reading for next week. 1416 01:05:45,260 --> 01:05:48,040 And I'll post a short assignment basically to 1417 01:05:48,040 --> 01:05:50,790 continue this line of thinking, just to give you 1418 01:05:50,790 --> 01:05:53,140 some more practice in course design, 1419 01:05:53,140 --> 01:05:54,290 fleshing it out farther. 1420 01:05:54,290 --> 01:05:58,840 But what you've done is the key step, the hardest step to 1421 01:05:58,840 --> 01:05:59,710 course design. 1422 01:05:59,710 --> 01:06:03,420 So if you could fill out the question sheet, 1423 01:06:03,420 --> 01:06:05,250 as always very helpful. 1424 01:06:05,250 --> 01:06:07,840 And also there was a question before. 1425 01:06:07,840 --> 01:06:10,770 Could I make sure to list on the website things I 1426 01:06:10,770 --> 01:06:12,720 mentioned in class? 1427 01:06:12,720 --> 01:06:13,040 Yes. 1428 01:06:13,040 --> 01:06:13,790 I should do that. 1429 01:06:13,790 --> 01:06:17,710 So if I could request people to, if you have in your notes 1430 01:06:17,710 --> 01:06:19,300 any of the books that I mentioned in class but didn't 1431 01:06:19,300 --> 01:06:22,050 put on the website, if you could email me those, I will 1432 01:06:22,050 --> 01:06:24,070 put them on the website. 1433 01:06:24,070 --> 01:06:26,800 So as a sort of divide and conquer approach, I'm sure 1434 01:06:26,800 --> 01:06:30,630 actually collectively you have all of them. 1435 01:06:30,630 --> 01:06:30,980 OK. 1436 01:06:30,980 --> 01:06:35,440 So just when you're done, you can put the sheets up here. 1437 01:06:35,440 --> 01:06:38,510 And then outside of that door, we'll have office hours as 1438 01:06:38,510 --> 01:06:42,810 usual so that the next class doesn't get delayed by us 1439 01:06:42,810 --> 01:06:44,060 being in here.