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 00:00:22,516 --> 00:00:25,840 PROFESSOR: OK, welcome everyone. 9 00:00:25,840 --> 00:00:28,870 It's 8:05, well, 9:05. 10 00:00:28,870 --> 00:00:31,680 So today's lecture and discussion is about how to 11 00:00:31,680 --> 00:00:35,800 make good problems, whether it's on homework problems, 12 00:00:35,800 --> 00:00:38,670 exams, even problems in class. 13 00:00:38,670 --> 00:00:41,530 Its general principles that you can use constructing 14 00:00:41,530 --> 00:00:45,710 questions that you ask, so problems broadly conceived. 15 00:00:45,710 --> 00:00:49,450 Now why problems? 16 00:00:49,450 --> 00:00:53,640 So problems are, I think, one of the central ways of 17 00:00:53,640 --> 00:00:56,010 thinking about teaching. 18 00:00:56,010 --> 00:01:02,940 And I'll show you how problems fit into the grand scheme of 19 00:01:02,940 --> 00:01:09,395 this course, of rethinking all the aspects of teaching. 20 00:01:14,580 --> 00:01:17,490 So one way that I like to think about teaching is called 21 00:01:17,490 --> 00:01:18,410 backward design. 22 00:01:18,410 --> 00:01:21,600 So this is a way of designing a whole course, could even be 23 00:01:21,600 --> 00:01:22,780 for a curriculum. 24 00:01:22,780 --> 00:01:25,840 And doing problems is one aspect of that. 25 00:01:35,810 --> 00:01:37,750 So why is it called backward design? 26 00:01:37,750 --> 00:01:39,530 Well, it's backward from the usual way. 27 00:01:39,530 --> 00:01:41,960 So I'll show you what backward is and then show you what the 28 00:01:41,960 --> 00:01:43,210 usual way is. 29 00:01:50,360 --> 00:01:53,950 So in backward design the highest-level thing you figure 30 00:01:53,950 --> 00:01:56,160 out-- not necessarily the first thing you figure out, 31 00:01:56,160 --> 00:01:58,380 but the highest level thing-- is your course goals. 32 00:02:01,070 --> 00:02:05,820 And that then feeds to OK, if those are your course goals 33 00:02:05,820 --> 00:02:09,509 how do you know whether students have reached them? 34 00:02:09,509 --> 00:02:10,759 And that's problems. 35 00:02:13,560 --> 00:02:18,010 Problems, tasks, projects, whatever it may be, things 36 00:02:18,010 --> 00:02:19,260 that students are going to do. 37 00:02:21,600 --> 00:02:24,630 And so generally speaking, things to do. 38 00:02:24,630 --> 00:02:31,850 And then given that you've operationalized the goals in 39 00:02:31,850 --> 00:02:35,910 these problems what are you going to do in class, so that 40 00:02:35,910 --> 00:02:38,500 students actually are able to do these kind of things? 41 00:02:44,760 --> 00:02:48,210 OK, so that is backward design because the 42 00:02:48,210 --> 00:02:50,030 usual way is the following. 43 00:02:50,030 --> 00:02:52,280 You say, OK, well, you have a bunch of lecture notes. 44 00:02:52,280 --> 00:02:53,030 Where do you have those? 45 00:02:53,030 --> 00:02:54,950 Well, either the last person who taught the course gives 46 00:02:54,950 --> 00:02:56,220 you their lecture notes. 47 00:02:56,220 --> 00:02:58,990 Or you just take the standard book in the subject and you 48 00:02:58,990 --> 00:03:03,070 just do the lectures one per chapter or one week per 49 00:03:03,070 --> 00:03:04,130 chapter, something like that. 50 00:03:04,130 --> 00:03:05,420 And you just go through in the order. 51 00:03:05,420 --> 00:03:08,180 So in the usual way you start with this. 52 00:03:08,180 --> 00:03:10,980 And then you think oh, whoops, oh yeah, I've got to make some 53 00:03:10,980 --> 00:03:12,930 problem sets. 54 00:03:12,930 --> 00:03:14,020 And oh, some exams. 55 00:03:14,020 --> 00:03:16,200 Well, what have we done this last couple weeks? 56 00:03:16,200 --> 00:03:18,060 OK, that's what we're going to do. 57 00:03:18,060 --> 00:03:20,100 So the usual way is you start with here. 58 00:03:20,100 --> 00:03:21,000 And then you get here. 59 00:03:21,000 --> 00:03:22,830 And you somehow never get here. 60 00:03:22,830 --> 00:03:24,570 The course goals are, basically, to 61 00:03:24,570 --> 00:03:26,670 get through the book. 62 00:03:26,670 --> 00:03:26,850 Right? 63 00:03:26,850 --> 00:03:28,070 That's the implicit course goal. 64 00:03:28,070 --> 00:03:29,820 But it's never explicitly planned. 65 00:03:29,820 --> 00:03:32,490 So that's a terrible way, but the normal way 66 00:03:32,490 --> 00:03:33,420 of designing a course. 67 00:03:33,420 --> 00:03:35,490 So this is backward design. 68 00:03:35,490 --> 00:03:41,880 So this is due to Wiggins and McTighe. 69 00:03:49,950 --> 00:03:53,530 OK, so here we're going to be discussing this today. 70 00:03:57,180 --> 00:03:58,910 So we're doing this first. 71 00:03:58,910 --> 00:04:01,030 And then the next session is this one. 72 00:04:01,030 --> 00:04:03,300 And I think the session after that is, what do you do in 73 00:04:03,300 --> 00:04:05,700 class, interactive teaching and things like that. 74 00:04:05,700 --> 00:04:07,860 So why am I doing it in this order? 75 00:04:07,860 --> 00:04:10,730 Well, in the levels of abstraction these 76 00:04:10,730 --> 00:04:12,550 are the most abstract. 77 00:04:12,550 --> 00:04:16,530 And this is the most concrete, OK, what question I'm going to 78 00:04:16,530 --> 00:04:18,600 ask students in class now. 79 00:04:18,600 --> 00:04:20,920 And this is things like goals. 80 00:04:20,920 --> 00:04:22,790 I want them to really understand conservation. 81 00:04:22,790 --> 00:04:23,980 They're really high level. 82 00:04:23,980 --> 00:04:28,600 So I think if you start here, by trying to figure out course 83 00:04:28,600 --> 00:04:31,780 goals, I haven't found that works very well for me because 84 00:04:31,780 --> 00:04:33,050 it's too high level. 85 00:04:33,050 --> 00:04:36,560 I can't think about course goals in absence of actual 86 00:04:36,560 --> 00:04:38,670 problems and things I want students to be able to do. 87 00:04:38,670 --> 00:04:43,830 So this has the right level between concrete and abstract. 88 00:04:43,830 --> 00:04:46,390 So it's actually where I start my thinking. 89 00:04:46,390 --> 00:04:49,370 Now, you may actually find you want to start somewhere else 90 00:04:49,370 --> 00:04:51,400 on the continuum. 91 00:04:51,400 --> 00:04:54,200 But this is what I found works quite well. 92 00:04:54,200 --> 00:04:58,260 You start here, you operationalize what your goals 93 00:04:58,260 --> 00:05:00,140 are in the problems that you think are interesting. 94 00:05:00,140 --> 00:05:01,580 And then you look at the problems. 95 00:05:01,580 --> 00:05:03,980 And that sort of gives you an idea of the course goals. 96 00:05:03,980 --> 00:05:05,740 And then you think about the course goals. 97 00:05:05,740 --> 00:05:07,090 And that helps you think of problems. 98 00:05:07,090 --> 00:05:08,580 But I start here. 99 00:05:08,580 --> 00:05:12,330 And then, once I have things like that, then class time is 100 00:05:12,330 --> 00:05:13,750 actually much easier to plan. 101 00:05:13,750 --> 00:05:17,030 Because class often is going to be problems like this, 102 00:05:17,030 --> 00:05:18,550 related to this, maybe shorter. 103 00:05:18,550 --> 00:05:22,120 But it's easier to plan here after that. 104 00:05:22,120 --> 00:05:24,400 Whereas we start here, you don't know, you're 105 00:05:24,400 --> 00:05:25,630 back in the old way. 106 00:05:25,630 --> 00:05:26,910 So I don't want to start here. 107 00:05:26,910 --> 00:05:28,430 This is too abstract, so I start here. 108 00:05:28,430 --> 00:05:30,160 So that's why we're doing this now. 109 00:05:30,160 --> 00:05:32,970 And then next week we're going to do this one. 110 00:05:39,444 --> 00:05:39,942 Question? 111 00:05:39,942 --> 00:05:41,796 AUDIENCE: So when you say that you're setting 112 00:05:41,796 --> 00:05:42,510 goals for your class-- 113 00:05:42,510 --> 00:05:43,470 PROFESSOR: Pardon? 114 00:05:43,470 --> 00:05:47,160 AUDIENCE: So if you say that, basically, setting the goals 115 00:05:47,160 --> 00:05:50,303 for your class, or for your own course. 116 00:05:50,303 --> 00:05:52,768 So when you design your course, basically you write 117 00:05:52,768 --> 00:05:56,219 out some kind of goals you want to reach? 118 00:05:56,219 --> 00:05:57,698 So how do you then do the problem? 119 00:05:57,698 --> 00:06:00,590 Do you go in detail before you've even 120 00:06:00,590 --> 00:06:01,960 started the whole class? 121 00:06:01,960 --> 00:06:04,185 Or do you do it that on a week-to-week basis? 122 00:06:04,185 --> 00:06:06,000 PROFESSOR: Oh, what do I tell the students 123 00:06:06,000 --> 00:06:06,980 about the course goals? 124 00:06:06,980 --> 00:06:09,932 AUDIENCE: Yeah, I mean, if you say, OK, basically, you have 125 00:06:09,932 --> 00:06:14,106 your goals and then you design problems so you 126 00:06:14,106 --> 00:06:14,941 can reach the goals? 127 00:06:14,941 --> 00:06:19,300 But then do you also design these problems before you even 128 00:06:19,300 --> 00:06:20,952 start the whole lecture? 129 00:06:20,952 --> 00:06:22,445 The whole semester? 130 00:06:22,445 --> 00:06:26,500 PROFESSOR: Oh, well, it's pretty rough. 131 00:06:26,500 --> 00:06:31,030 I mean, usually the first time you teach the thing it's too 132 00:06:31,030 --> 00:06:32,070 abstract to design-- 133 00:06:32,070 --> 00:06:32,870 I find-- 134 00:06:32,870 --> 00:06:35,110 everything in advance. 135 00:06:35,110 --> 00:06:39,400 Maybe that's my extrovert nature, which is that I find 136 00:06:39,400 --> 00:06:42,730 it hard to design things for people I don't know. 137 00:06:42,730 --> 00:06:47,190 If I don't know the audience I don't even know what to say. 138 00:06:47,190 --> 00:06:50,300 So I want to actually teach the course one time at least. 139 00:06:50,300 --> 00:06:53,440 So then the audience becomes concrete for me. 140 00:06:53,440 --> 00:06:56,260 So really, the first time through the course nothing is 141 00:06:56,260 --> 00:06:56,950 ever ideal. 142 00:06:56,950 --> 00:06:59,370 And you're doing everything on the fly. 143 00:06:59,370 --> 00:07:02,610 But the second time through the course, you can actually, 144 00:07:02,610 --> 00:07:04,650 basically, make all the problems ahead of time. 145 00:07:04,650 --> 00:07:06,930 So the second time through the course you actually refine 146 00:07:06,930 --> 00:07:09,165 your goals and your problems together. 147 00:07:13,310 --> 00:07:16,653 So that shows you the structure of where we are and 148 00:07:16,653 --> 00:07:17,930 where we're going to go and then later. 149 00:07:17,930 --> 00:07:20,040 So this is two weeks from now. 150 00:07:22,810 --> 00:07:24,060 Today, here. 151 00:07:26,530 --> 00:07:29,600 So how do you make problems? 152 00:07:29,600 --> 00:07:36,710 Well, the fundamental principle is, again, deduced 153 00:07:36,710 --> 00:07:41,140 by induction from what happens with regular problems. 154 00:07:41,140 --> 00:07:46,860 So if you remember, I gave you an example earlier of the 155 00:07:46,860 --> 00:07:49,470 results of standard problem solving. 156 00:07:49,470 --> 00:07:51,640 And I'll just remind you that we're putting up the 157 00:07:51,640 --> 00:07:52,890 percentages again. 158 00:08:06,550 --> 00:08:10,770 OK, so after doing lots and lots of standard 159 00:08:10,770 --> 00:08:13,880 multiplication problems, students were-- 160 00:08:13,880 --> 00:08:16,310 if you remember-- unable to do the following problem. 161 00:08:24,850 --> 00:08:28,360 So these 13-year-Olds and 17-year-Olds were asked to 162 00:08:28,360 --> 00:08:34,140 estimate 3.04 times 5.3. 163 00:08:34,140 --> 00:08:35,690 So here were the answers. 164 00:08:44,039 --> 00:08:47,410 So they were given four possible answers. 165 00:08:47,410 --> 00:08:50,670 And they could also not answer. 166 00:08:50,670 --> 00:08:51,920 So this is no answer. 167 00:09:08,540 --> 00:09:12,010 So that's the age 13. 168 00:09:12,010 --> 00:09:15,090 So of the four possible answers-- 169 00:09:15,090 --> 00:09:18,690 or let's say no answer is possible as well-- so five, 170 00:09:18,690 --> 00:09:24,580 they're 1% over 1/5 will get the correct answer. 171 00:09:24,580 --> 00:09:25,765 So that's a bit depressing. 172 00:09:25,765 --> 00:09:27,355 So you think, oh, OK, the 17-year-olds 173 00:09:27,355 --> 00:09:28,605 are going to be better. 174 00:09:31,350 --> 00:09:34,360 And they are, but they only have 37% correct. 175 00:09:38,320 --> 00:09:43,650 OK, so here is a serious problem, 176 00:09:43,650 --> 00:09:46,090 which is rote learning. 177 00:09:46,090 --> 00:09:48,090 And that's the fundamental thing to 178 00:09:48,090 --> 00:09:50,690 avoid when doing problems. 179 00:09:50,690 --> 00:09:54,020 So these students-- especially the 17-year-olds-- 180 00:09:54,020 --> 00:09:56,470 were actually perfectly capable of doing exactly 181 00:09:56,470 --> 00:09:56,805 multiplication. 182 00:09:56,805 --> 00:09:59,410 So on the same test they were asked questions like multiply 183 00:09:59,410 --> 00:10:04,420 2.7 by 8.32 and given just empty space on the page to 184 00:10:04,420 --> 00:10:05,700 multiply it out. 185 00:10:05,700 --> 00:10:07,380 About 80% did it right. 186 00:10:07,380 --> 00:10:10,160 So it's not that they don't know how to multiply. 187 00:10:10,160 --> 00:10:13,510 They just don't know what multiplication means, which is 188 00:10:13,510 --> 00:10:15,720 a far more serious problem. 189 00:10:15,720 --> 00:10:18,870 I'd rather they knew what multiplication meant and 190 00:10:18,870 --> 00:10:21,300 didn't really understand, didn't 191 00:10:21,300 --> 00:10:22,420 really know how to multiply. 192 00:10:22,420 --> 00:10:24,950 Because the algorithm you can teach them later if they 193 00:10:24,950 --> 00:10:26,280 understand what it means. 194 00:10:26,280 --> 00:10:28,990 But if they don't even understand what it means that 195 00:10:28,990 --> 00:10:31,270 basically it's 3 times 5, so it's got to be somewhere 196 00:10:31,270 --> 00:10:33,920 around 16, they don't understand what multiplication 197 00:10:33,920 --> 00:10:36,050 means or the number system means. 198 00:10:36,050 --> 00:10:37,880 That's a far more serious problem. 199 00:10:37,880 --> 00:10:41,830 And that's produced by the traditional kind of problems. 200 00:10:41,830 --> 00:10:44,730 The traditional kinds of problems are, generally 201 00:10:44,730 --> 00:10:48,140 speaking, too low level and can be solved, 202 00:10:48,140 --> 00:10:49,550 to easily, by rote. 203 00:10:49,550 --> 00:10:51,890 Even the complicated traditional problems can 204 00:10:51,890 --> 00:10:55,710 eventually be turned into rote learning, 205 00:10:55,710 --> 00:10:56,880 and that's the danger. 206 00:10:56,880 --> 00:11:01,490 So the main goal in making good problems is-- 207 00:11:01,490 --> 00:11:02,030 I would say-- 208 00:11:02,030 --> 00:11:06,190 how to make problems that fight rote learning. 209 00:11:06,190 --> 00:11:06,360 OK? 210 00:11:06,360 --> 00:11:09,560 That produce long-lasting actual conceptual 211 00:11:09,560 --> 00:11:12,090 understanding along with whatever else you're trying to 212 00:11:12,090 --> 00:11:13,500 produce and teach. 213 00:11:13,500 --> 00:11:16,030 But really, fight the rote learning because that is the 214 00:11:16,030 --> 00:11:18,730 fundamental problem. 215 00:11:18,730 --> 00:11:25,110 So a way of thinking about this is to categorize the 216 00:11:25,110 --> 00:11:28,260 levels of thinking that you're expecting of students when 217 00:11:28,260 --> 00:11:29,710 you're asking them to do a problem. 218 00:11:29,710 --> 00:11:37,060 And for that there is work from 50 years ago now-- 219 00:11:37,060 --> 00:11:38,440 which is still useful-- 220 00:11:49,530 --> 00:11:53,810 which is Bloom's Taxonomy. 221 00:11:53,810 --> 00:11:55,990 So Bloom's Taxonomy-- 222 00:11:55,990 --> 00:11:56,960 let's see, when was it? 223 00:11:56,960 --> 00:12:02,210 I think it was 1956. 224 00:12:02,210 --> 00:12:03,300 I think it was '56. 225 00:12:03,300 --> 00:12:07,420 I'll put a handout on the website for you which 226 00:12:07,420 --> 00:12:08,930 summarizes in one page. 227 00:12:08,930 --> 00:12:11,690 But I'll summarize it even shorter here. 228 00:12:14,700 --> 00:12:17,050 So what is it a taxonomy of? 229 00:12:17,050 --> 00:12:19,530 Well, when you read the title the book, it's Bloom's 230 00:12:19,530 --> 00:12:23,440 Taxonomy of Educational Objectives. 231 00:12:23,440 --> 00:12:25,430 And it's not really clear if that's going to be useful for 232 00:12:25,430 --> 00:12:26,040 anything at all. 233 00:12:26,040 --> 00:12:27,630 Because you think, what the hell is that? 234 00:12:27,630 --> 00:12:31,690 So the shortest way of understanding it is that it's 235 00:12:31,690 --> 00:12:33,290 six levels. 236 00:12:33,290 --> 00:12:39,980 And each level is higher than the one previous to it in 237 00:12:39,980 --> 00:12:44,590 terms of the level of thought required of a student. 238 00:12:44,590 --> 00:12:46,010 So it's not really a strict order. 239 00:12:46,010 --> 00:12:49,810 You can have really hard questions that seem to be low 240 00:12:49,810 --> 00:12:51,940 level just because they address misconceptions. 241 00:12:51,940 --> 00:12:54,190 But generally speaking, it's a rough order. 242 00:12:54,190 --> 00:13:02,950 So the order is knowledge questions. 243 00:13:02,950 --> 00:13:08,360 Those are things like define, name, state, list, You know, 244 00:13:08,360 --> 00:13:10,150 it's basically almost rote. 245 00:13:10,150 --> 00:13:13,340 I mean, these are the kind of problems that everyone would 246 00:13:13,340 --> 00:13:16,850 agree are rote, state the definition of 247 00:13:16,850 --> 00:13:18,100 Newton's Second Law. 248 00:13:28,880 --> 00:13:30,950 The second is comprehension. 249 00:13:30,950 --> 00:13:33,650 So that's sort of like knowledge but 250 00:13:33,650 --> 00:13:35,432 it's a higher level. 251 00:13:35,432 --> 00:13:39,110 So that's being able to grasp the meaning of the material, 252 00:13:39,110 --> 00:13:41,170 not just recite the facts. 253 00:13:43,750 --> 00:13:46,040 But generally, that doesn't include the idea of being able 254 00:13:46,040 --> 00:13:48,170 to transfer it to new situations. 255 00:13:48,170 --> 00:13:50,008 That's where application comes. 256 00:13:53,500 --> 00:13:57,410 So can you apply the material to something? 257 00:13:57,410 --> 00:14:04,660 For example, often compute, demonstrate, show that, those 258 00:14:04,660 --> 00:14:07,210 are typical verbs that are used when you 259 00:14:07,210 --> 00:14:08,460 have application questions. 260 00:14:13,620 --> 00:14:16,600 The next level is analysis. 261 00:14:16,600 --> 00:14:19,600 So that's really trying to understand the structure of 262 00:14:19,600 --> 00:14:21,080 the material. 263 00:14:21,080 --> 00:14:28,240 So things like diagram, differentiate, infer, outline, 264 00:14:28,240 --> 00:14:32,270 point out, identify, distinguish, discriminate, all 265 00:14:32,270 --> 00:14:35,365 those kinds of verbs com into analysis kinds of questions. 266 00:14:42,140 --> 00:14:44,400 Synthesis-- 267 00:14:44,400 --> 00:14:47,640 so this is breaking things apart. 268 00:14:47,640 --> 00:14:49,210 This is the ability to put things back 269 00:14:49,210 --> 00:14:51,600 together in new ways. 270 00:14:51,600 --> 00:14:51,840 OK? 271 00:14:51,840 --> 00:14:57,980 So design, explain, categorize, create, revise, 272 00:14:57,980 --> 00:15:00,915 rewrite, reorganize, devise. 273 00:15:10,090 --> 00:15:13,460 And the highest level is evaluation. 274 00:15:13,460 --> 00:15:19,950 So judging the value of material, for what purposes is 275 00:15:19,950 --> 00:15:23,450 this good versus that good? 276 00:15:23,450 --> 00:15:28,680 Explain, contrast, summarize, support, recommend, evaluate, 277 00:15:28,680 --> 00:15:31,040 criticize, appraise, so generally 278 00:15:31,040 --> 00:15:32,170 quite high-level skills. 279 00:15:32,170 --> 00:15:37,410 So this is the taxonomy and this is a higher level. 280 00:15:41,190 --> 00:15:42,780 OK, so a useful exercise-- 281 00:15:42,780 --> 00:15:45,330 whenever you're thinking of problems-- is to try to place 282 00:15:45,330 --> 00:15:46,630 them on this. 283 00:15:46,630 --> 00:15:51,550 Now it's not that you want no-knowledge kind of questions 284 00:15:51,550 --> 00:15:53,550 and you want only to ask these kind of questions. 285 00:15:53,550 --> 00:15:56,660 Because if you just ask these kind of questions people will 286 00:15:56,660 --> 00:15:57,730 not be ready for them. 287 00:15:57,730 --> 00:15:59,680 And they're not prepared. 288 00:15:59,680 --> 00:16:01,320 It doesn't actually teach anything. 289 00:16:01,320 --> 00:16:02,430 You want a mix of them. 290 00:16:02,430 --> 00:16:06,000 But generally speaking, what happens to often, is that most 291 00:16:06,000 --> 00:16:11,710 of the questions that happen are usually in this zone, 292 00:16:11,710 --> 00:16:13,540 maybe a few of those. 293 00:16:13,540 --> 00:16:15,850 And then only later in people's careers do 294 00:16:15,850 --> 00:16:17,080 they get over here. 295 00:16:17,080 --> 00:16:21,210 For example, in engineering curricula you learn a ton and 296 00:16:21,210 --> 00:16:26,390 ton of application, maybe comprehension, Maxwell's 297 00:16:26,390 --> 00:16:29,290 equations, differentiation, integration. 298 00:16:29,290 --> 00:16:30,940 Then we start to synthesize stuff. 299 00:16:30,940 --> 00:16:32,760 You know, in your senior year you do 300 00:16:32,760 --> 00:16:34,920 design and project classes. 301 00:16:34,920 --> 00:16:37,730 But you don't have to wait all the way until then. 302 00:16:37,730 --> 00:16:40,620 You can actually start putting stuff in much earlier. 303 00:16:40,620 --> 00:16:42,270 And it doesn't have to be an entire class. 304 00:16:42,270 --> 00:16:45,865 You can have tasks that are like that in a short time, on 305 00:16:45,865 --> 00:16:49,072 a problem set in the middle of lecture time. 306 00:16:49,072 --> 00:16:49,500 OK? 307 00:16:49,500 --> 00:16:51,655 So questions about Bloom's Taxonomy? 308 00:16:57,820 --> 00:17:03,400 OK, so what I'll do, is I'll give you an example of 309 00:17:03,400 --> 00:17:09,740 questions that in freshman physics mechanics-- 310 00:17:09,740 --> 00:17:11,800 on the topic of Newton's laws-- 311 00:17:11,800 --> 00:17:13,839 that fit into each of those levels. 312 00:17:16,920 --> 00:17:18,720 OK, so just to give you an example, to make it concrete, 313 00:17:18,720 --> 00:17:20,900 to see what those kinds of questions are. 314 00:17:20,900 --> 00:17:23,170 And some of the categorizations I'm going to 315 00:17:23,170 --> 00:17:24,839 give you are debatable. 316 00:17:24,839 --> 00:17:29,410 But the rough idea is that they go from high to low. 317 00:17:33,890 --> 00:17:39,760 So this is on the subject of Newton's second and third law. 318 00:17:39,760 --> 00:17:43,950 So a knowledge question, state Newton's second and third law. 319 00:17:48,570 --> 00:17:51,350 Newton's second law, state Newton's third law, so you can 320 00:17:51,350 --> 00:17:54,780 see, just because people can state it doesn't mean they can 321 00:17:54,780 --> 00:17:56,050 actually do anything with it. 322 00:17:56,050 --> 00:17:59,660 That's why this is way up just at the knowledge end. 323 00:17:59,660 --> 00:18:02,280 Computers are actually really good at this. 324 00:18:02,280 --> 00:18:02,510 Right? 325 00:18:02,510 --> 00:18:04,300 You can look it up on Google. 326 00:18:04,300 --> 00:18:06,950 But your computer can tell you what Newton's second and third 327 00:18:06,950 --> 00:18:09,480 law are but you can't actually do anything with them. 328 00:18:16,200 --> 00:18:17,450 So comprehension-- 329 00:18:27,390 --> 00:18:30,600 so give an example of Newton's Second Law, using Newton's 330 00:18:30,600 --> 00:18:31,850 Second Law. 331 00:18:38,820 --> 00:18:41,530 OK, this next one is an application. 332 00:18:41,530 --> 00:18:44,660 It turns out to be, actually, quite a hard application. 333 00:18:44,660 --> 00:18:45,910 But it's still an application. 334 00:18:54,660 --> 00:18:57,310 So it's to apply Newton's second and third law to show 335 00:18:57,310 --> 00:19:03,640 the following, which the following is suppose I have a 336 00:19:03,640 --> 00:19:07,080 piece of chalk in my hand and I stand on a weighing scale. 337 00:19:07,080 --> 00:19:09,600 I want the students to show that the weight that the scale 338 00:19:09,600 --> 00:19:12,560 reads is equal to the sum of the two individual weights. 339 00:19:12,560 --> 00:19:14,360 So I weigh myself. 340 00:19:14,360 --> 00:19:15,930 And then I put the chalk on the scale. 341 00:19:15,930 --> 00:19:17,150 And I add up those two weights. 342 00:19:17,150 --> 00:19:18,780 And that should be the same as when I hold 343 00:19:18,780 --> 00:19:20,290 the chalk in my hand. 344 00:19:20,290 --> 00:19:20,530 OK? 345 00:19:20,530 --> 00:19:23,035 So I'll diagram that as-- 346 00:19:35,430 --> 00:19:45,160 OK, so that's me plus chalk equals me plus chalk. 347 00:19:45,160 --> 00:19:46,410 So this is a scale. 348 00:19:48,860 --> 00:19:49,300 OK? 349 00:19:49,300 --> 00:19:50,970 So there is the piece of chalk. 350 00:19:50,970 --> 00:19:57,060 So now this is an example of where that's quite a hard 351 00:19:57,060 --> 00:20:00,100 application question, even though it's kind of high up on 352 00:20:00,100 --> 00:20:03,590 the Bloom's list, so towards the lower end. 353 00:20:03,590 --> 00:20:05,680 Because this is a serious misconception 354 00:20:05,680 --> 00:20:06,710 that students have. 355 00:20:06,710 --> 00:20:09,110 Newton's second and Newton's third law, people are 356 00:20:09,110 --> 00:20:11,390 completely confused about, you'll find. 357 00:20:11,390 --> 00:20:15,250 They don't know when to use which. 358 00:20:15,250 --> 00:20:18,890 And they think any time two forces are equal it's sort of 359 00:20:18,890 --> 00:20:21,150 50-50, whether it's because of Newton's third law or Newton's 360 00:20:21,150 --> 00:20:22,790 second law. 361 00:20:22,790 --> 00:20:25,210 So this-- if you're addressing misconceptions-- 362 00:20:25,210 --> 00:20:28,320 makes the problem, actually, all the much harder. 363 00:20:33,480 --> 00:20:35,060 So at analysis-- 364 00:20:35,060 --> 00:20:37,040 so the analysis comes out-- oh, question sorry. 365 00:20:37,040 --> 00:20:38,381 AUDIENCE: What are Newton's second and third laws? 366 00:20:38,381 --> 00:20:39,950 PROFESSOR: Ah, fair question. 367 00:20:39,950 --> 00:20:52,120 So Newton's Second Law says force equals mass times 368 00:20:52,120 --> 00:20:53,530 acceleration. 369 00:20:53,530 --> 00:20:57,140 Third law is-- 370 00:20:57,140 --> 00:21:00,010 the way it's usually stated, which it's terrible-- 371 00:21:05,470 --> 00:21:07,870 action equals reaction. 372 00:21:07,870 --> 00:21:11,840 Or for every action there's an equal and opposite reaction. 373 00:21:11,840 --> 00:21:13,690 Oh, which reminds me, one of the questions from before, 374 00:21:13,690 --> 00:21:15,660 which is what name would I give? 375 00:21:15,660 --> 00:21:18,560 Because I said I slagged off the reaction force as the name 376 00:21:18,560 --> 00:21:19,970 and the normal force as a name. 377 00:21:19,970 --> 00:21:21,800 People ask me, what should you call it? 378 00:21:21,800 --> 00:21:23,230 And I actually thought about that. 379 00:21:23,230 --> 00:21:25,970 And I think the answer is contact force. 380 00:21:25,970 --> 00:21:27,260 Because that tells you what the thing is. 381 00:21:27,260 --> 00:21:29,340 It's a force of contact. 382 00:21:29,340 --> 00:21:32,160 So Newton's third law says action equals reaction. 383 00:21:32,160 --> 00:21:36,510 So now, the problem is that students have, is that 384 00:21:36,510 --> 00:21:39,840 whenever they see two forces are equal they assume it's 385 00:21:39,840 --> 00:21:42,410 because the action equals reaction. 386 00:21:42,410 --> 00:21:47,730 Or they think Newton's third law is the reason for it. 387 00:21:47,730 --> 00:21:53,450 So for example, the bouncing-ball question that we 388 00:21:53,450 --> 00:21:55,100 talked about last time. 389 00:21:55,100 --> 00:21:57,320 So in the bouncing ball the question is, when it's 390 00:21:57,320 --> 00:21:59,480 stationary on the ground what are the forces on it? 391 00:21:59,480 --> 00:22:02,550 And they'll often say, well, there's a weight downwards. 392 00:22:02,550 --> 00:22:04,560 And there's the force upwards. 393 00:22:04,560 --> 00:22:07,640 And they'll often say, well, the force upwards equals the 394 00:22:07,640 --> 00:22:08,330 weight downwards. 395 00:22:08,330 --> 00:22:09,800 These are both forces on the ball because 396 00:22:09,800 --> 00:22:12,190 action equals reaction. 397 00:22:12,190 --> 00:22:15,310 And they won't realize that action and reaction have to be 398 00:22:15,310 --> 00:22:17,860 on different objects. 399 00:22:17,860 --> 00:22:18,130 OK? 400 00:22:18,130 --> 00:22:21,920 So they're fundamentally confused about the meaning of 401 00:22:21,920 --> 00:22:24,450 action and reaction, which you can bring out with the 402 00:22:24,450 --> 00:22:25,700 following analysis question-- 403 00:22:32,190 --> 00:22:36,740 When two forces are equal in magnitude how do you tell if 404 00:22:36,740 --> 00:22:38,440 it's Newton's two or Newton three? 405 00:22:41,570 --> 00:22:43,570 So how do you know if it's Newton two or Newton three? 406 00:22:43,570 --> 00:22:45,400 So just ask them that. 407 00:22:45,400 --> 00:22:47,172 Yes, question? 408 00:22:47,172 --> 00:22:50,148 AUDIENCE: This might be a little bit off subject, but 409 00:22:50,148 --> 00:22:54,612 should we use Newton's third law ever? 410 00:22:54,612 --> 00:22:57,588 It seems like it's a natural consequence from 411 00:22:57,588 --> 00:22:59,100 saying a equals 0. 412 00:22:59,100 --> 00:23:02,190 PROFESSOR: Ah, oh, OK, interesting. 413 00:23:02,190 --> 00:23:04,930 So OK, let me actually explain that one. 414 00:23:04,930 --> 00:23:07,020 I'll put it over there because I didn't do the 415 00:23:07,020 --> 00:23:09,460 boards right over here. 416 00:23:09,460 --> 00:23:13,580 So that is exactly the issue brought out by this question. 417 00:23:13,580 --> 00:23:14,925 And let me show you the difference. 418 00:23:19,150 --> 00:23:20,830 And then there was another question. 419 00:23:20,830 --> 00:23:22,780 That reminds me of another whole set of questions from 420 00:23:22,780 --> 00:23:26,540 the sheets, which was how do you develop 421 00:23:26,540 --> 00:23:29,440 your physics intuition? 422 00:23:29,440 --> 00:23:31,810 So let me answer that in a moment. 423 00:23:31,810 --> 00:23:33,820 After this and then we'll have a break. 424 00:23:33,820 --> 00:23:36,975 OK, so the bouncing-ball question-- 425 00:23:40,720 --> 00:23:41,990 actually let's not do the bouncing ball. 426 00:23:41,990 --> 00:23:48,630 Let's just do an object sitting on the ground. 427 00:23:52,446 --> 00:23:56,000 Oh, great, can you pass them around? 428 00:23:58,890 --> 00:24:04,060 Oh, Leeann's just coming around with a handout on 429 00:24:04,060 --> 00:24:05,413 Bloom's Taxonomy. 430 00:24:05,413 --> 00:24:08,900 And let's see, I'll do these after the break. 431 00:24:08,900 --> 00:24:11,140 OK, suppose you have this object sitting on the ground 432 00:24:11,140 --> 00:24:12,920 and it has Mass m. 433 00:24:12,920 --> 00:24:14,990 OK, let's look at what the forces on it are. 434 00:24:14,990 --> 00:24:18,580 Well, there's mg down-- 435 00:24:18,580 --> 00:24:25,370 and actually, in this case, the contact force, our normal 436 00:24:25,370 --> 00:24:28,830 force is equal to mg. 437 00:24:28,830 --> 00:24:32,690 OK, so now the question is, are these two equal because of 438 00:24:32,690 --> 00:24:34,490 Newton's Second Law or Newton's third law? 439 00:24:34,490 --> 00:24:36,430 That's what this question asks. 440 00:24:36,430 --> 00:24:37,760 So it's actually worth understanding 441 00:24:37,760 --> 00:24:40,420 the difference here. 442 00:24:40,420 --> 00:24:45,560 So these guys are equal because a equals 0. 443 00:24:45,560 --> 00:24:49,280 So this thing's just sitting on the ground, a equals 0. 444 00:24:49,280 --> 00:24:53,810 So the net force is 0, so these two 445 00:24:53,810 --> 00:24:55,780 forces have to cancel. 446 00:24:55,780 --> 00:24:59,230 OK, so that's Newton's Second Law. 447 00:25:08,100 --> 00:25:10,980 So then the question is, where does Newton's Third Law show 448 00:25:10,980 --> 00:25:11,990 up in this? 449 00:25:11,990 --> 00:25:14,970 Ah, Newton's Third Law shows up here. 450 00:25:18,600 --> 00:25:20,690 Here is the Earth. 451 00:25:20,690 --> 00:25:23,090 And here is your object. 452 00:25:23,090 --> 00:25:25,966 Let's just separate them just so you can see them separate, 453 00:25:25,966 --> 00:25:27,790 although this is sitting on there. 454 00:25:27,790 --> 00:25:30,380 So this is mg. 455 00:25:30,380 --> 00:25:34,140 Well, this is the mg because of gravity, right? 456 00:25:34,140 --> 00:25:37,260 The earth gravity is attracted to mass, m. 457 00:25:37,260 --> 00:25:40,500 Well, the mass is also attracted to the earth. 458 00:25:40,500 --> 00:25:44,585 So what's the force on the earth from the mass? 459 00:25:44,585 --> 00:25:45,507 AUDIENCE: mg. 460 00:25:45,507 --> 00:25:49,020 PROFESSOR: mg, it has to be. 461 00:25:49,020 --> 00:25:51,460 Now this mg equals that mg. 462 00:25:51,460 --> 00:25:56,500 Call this f2 and this is f1. 463 00:25:56,500 --> 00:26:02,970 So f1 equals f2 by Newton's third law. 464 00:26:02,970 --> 00:26:05,730 So that's a fundamentally different set of forces. 465 00:26:05,730 --> 00:26:08,480 So are equal and opposite. 466 00:26:08,480 --> 00:26:11,510 They're an action/reaction pair. 467 00:26:11,510 --> 00:26:13,650 So what Newton's third law really says-- 468 00:26:13,650 --> 00:26:16,070 when you understand it-- is that all forces in the world 469 00:26:16,070 --> 00:26:18,120 come in pairs. 470 00:26:18,120 --> 00:26:20,430 So if you ever see one force you have to hunt around for 471 00:26:20,430 --> 00:26:22,520 his other half. 472 00:26:22,520 --> 00:26:24,530 And the other half here is this. 473 00:26:24,530 --> 00:26:30,370 So actually, there's another question you could use for 474 00:26:30,370 --> 00:26:32,480 Newton's third law. 475 00:26:32,480 --> 00:26:34,550 So I don't have it on the list here. 476 00:26:34,550 --> 00:26:37,980 But I'll ask it right now, which is suppose someone comes 477 00:26:37,980 --> 00:26:41,730 to you and proposes the following gravitational law-- 478 00:26:41,730 --> 00:26:49,980 f gravity equals g m1 squared m2 over r squared when the g 479 00:26:49,980 --> 00:26:51,410 is the proper units. 480 00:26:51,410 --> 00:26:54,230 So m1 squared times m2, is that a legal 481 00:26:54,230 --> 00:26:57,220 force law for gravity? 482 00:26:57,220 --> 00:27:01,200 No, because when you switch m1 and m2 as you're doing here-- 483 00:27:01,200 --> 00:27:03,110 you're switching the mass and the earth-- 484 00:27:03,110 --> 00:27:05,100 you actually change the force. 485 00:27:05,100 --> 00:27:07,500 So then this would violate Newton's third law. 486 00:27:10,500 --> 00:27:11,000 OK? 487 00:27:11,000 --> 00:27:13,510 So Newton's third law, it actually is a constraint on 488 00:27:13,510 --> 00:27:14,440 the laws of physics. 489 00:27:14,440 --> 00:27:16,920 It's actually conservation of momentum. 490 00:27:16,920 --> 00:27:19,780 And for momentum to be conserved you can't have any 491 00:27:19,780 --> 00:27:22,100 arbitrary law of physics that you want. 492 00:27:22,100 --> 00:27:24,500 Does that help clarify that? 493 00:27:24,500 --> 00:27:27,470 AUDIENCE: Come up with a better set of taxonomy for 494 00:27:27,470 --> 00:27:30,597 describing it that doesn't lead people-- it leads people 495 00:27:30,597 --> 00:27:31,066 into thinking about that. 496 00:27:31,066 --> 00:27:32,500 PROFESSOR: I know. 497 00:27:32,500 --> 00:27:32,960 I agree. 498 00:27:32,960 --> 00:27:34,740 So I think the terms are very important. 499 00:27:34,740 --> 00:27:39,030 So that's why don't like this form, action equals reaction. 500 00:27:39,030 --> 00:27:43,940 I actually would prefer it were stated all forces come in 501 00:27:43,940 --> 00:27:45,860 pairs that are equal and opposite. 502 00:27:57,390 --> 00:28:00,580 Right, and language does have a powerful effect. 503 00:28:00,580 --> 00:28:00,935 Yes? 504 00:28:00,935 --> 00:28:03,820 AUDIENCE: The technical [? route's ?] obvious, just in 505 00:28:03,820 --> 00:28:06,399 calling the novel force the contact force, but that's not 506 00:28:06,399 --> 00:28:06,592 refined enough. 507 00:28:06,592 --> 00:28:09,327 Because both friction and novel are contact force? 508 00:28:09,327 --> 00:28:09,880 PROFESSOR: Yeah. 509 00:28:09,880 --> 00:28:12,850 AUDIENCE: [INAUDIBLE] constraint force because it 510 00:28:12,850 --> 00:28:14,295 could constrain into the [INAUDIBLE]. 511 00:28:14,295 --> 00:28:16,580 PROFESSOR: Yeah, that's probably a better name. 512 00:28:16,580 --> 00:28:17,490 Yeah, I agree with you. 513 00:28:17,490 --> 00:28:19,610 So the comment was that contact force isn't quite 514 00:28:19,610 --> 00:28:22,880 right because there's friction force as well. 515 00:28:22,880 --> 00:28:24,340 And that's also a contact force. 516 00:28:24,340 --> 00:28:26,170 And maybe a better name is constraint force. 517 00:28:26,170 --> 00:28:27,460 I think that is a better name. 518 00:28:31,660 --> 00:28:37,740 OK, so let me finish this list of two more examples of 519 00:28:37,740 --> 00:28:39,820 Newton's Second and third law. 520 00:28:39,820 --> 00:28:41,070 And then we'll have a break. 521 00:28:44,410 --> 00:28:45,660 OK, synthesis. 522 00:28:56,100 --> 00:28:58,700 So creating a problem using Newton's second and third law. 523 00:28:58,700 --> 00:29:00,700 So for example, this is a problem like that. 524 00:29:00,700 --> 00:29:02,520 But here I'm asking the students to make one up. 525 00:29:11,330 --> 00:29:15,970 And here is a very hard evaluate question, which is 526 00:29:15,970 --> 00:29:24,180 what, if any, are the limits of validity of Newton's Second 527 00:29:24,180 --> 00:29:25,430 and third law? 528 00:29:35,190 --> 00:29:36,450 So that's, actually, a very 529 00:29:36,450 --> 00:29:39,440 interesting historical question. 530 00:29:39,440 --> 00:29:41,710 Interesting historically because Einstein thought about 531 00:29:41,710 --> 00:29:43,150 that question. 532 00:29:43,150 --> 00:29:47,740 He wanted to know whether Newtonian gravitation and 533 00:29:47,740 --> 00:29:49,930 special relativity were compatible. 534 00:29:49,930 --> 00:29:55,030 And basically, they can't be because of Newton's third law. 535 00:29:55,030 --> 00:29:58,380 Because gravity should propagate with some speed, not 536 00:29:58,380 --> 00:30:00,230 the speed of light. 537 00:30:00,230 --> 00:30:02,970 So you can't actually conserve momentum right away. 538 00:30:02,970 --> 00:30:05,530 Suppose the sun does something strange. 539 00:30:05,530 --> 00:30:07,440 Well, it takes a while for the earth to 540 00:30:07,440 --> 00:30:08,900 actually respond to that. 541 00:30:08,900 --> 00:30:11,300 And it's in that intervening time Newton's third law seems 542 00:30:11,300 --> 00:30:12,310 to be violated. 543 00:30:12,310 --> 00:30:14,310 So Einstein thought very carefully about that question 544 00:30:14,310 --> 00:30:16,220 and came up with his theory of gravitation. 545 00:30:16,220 --> 00:30:18,160 So this is quite a high-level question. 546 00:30:18,160 --> 00:30:21,850 But it's to show the whole range of things you can ask 547 00:30:21,850 --> 00:30:24,270 about the second and Newton's third law as you 548 00:30:24,270 --> 00:30:25,760 climb Bloom's Taxonomy. 549 00:30:28,920 --> 00:30:32,150 OK, so what we're going to do in the second part is we're 550 00:30:32,150 --> 00:30:33,340 going to actually practice 551 00:30:33,340 --> 00:30:35,980 rewriting a couple of questions. 552 00:30:35,980 --> 00:30:38,820 And I'll show you a couple more examples. 553 00:30:38,820 --> 00:30:42,500 And seeing how we can make questions worse and better, 554 00:30:42,500 --> 00:30:44,750 because I find that's actually quite a good way to get 555 00:30:44,750 --> 00:30:47,870 practice with designing questions is taking good 556 00:30:47,870 --> 00:30:50,250 questions, making them bad, taking bad questions and 557 00:30:50,250 --> 00:30:51,340 making them good. 558 00:30:51,340 --> 00:30:53,810 Both ways are useful. 559 00:30:53,810 --> 00:30:56,620 OK, so we'll do that. 560 00:30:56,620 --> 00:31:04,110 Let's say it's 9:04, 9:10 let's say. 561 00:31:04,110 --> 00:31:05,670 So it's 904 on that clock. 562 00:31:05,670 --> 00:31:10,370 So see everyone, sorry it's 10:04 on that adjusted clock. 563 00:31:10,370 --> 00:31:14,840 So see everyone at 10:10 or 10:11. 564 00:31:14,840 --> 00:31:18,160 And meanwhile, here are the feedback sheets. 565 00:31:18,160 --> 00:31:21,430 So I'll just put a bunch in the two back things. 566 00:31:21,430 --> 00:31:24,510 So when you come back just grab those. 567 00:31:24,510 --> 00:31:31,990 OK, so I'll just answer a couple questions which I 568 00:31:31,990 --> 00:31:33,240 promised to answer. 569 00:31:36,070 --> 00:31:40,250 So the comment made by several people about last week's 570 00:31:40,250 --> 00:31:45,800 examples, say, of the rock and the rolling was that oh no, 571 00:31:45,800 --> 00:31:48,890 that showed me that my physics intuition is 572 00:31:48,890 --> 00:31:53,270 quite off, and bummer. 573 00:31:53,270 --> 00:31:55,130 And so then if you're going to teach it, how do you make 574 00:31:55,130 --> 00:31:58,650 sure, well, A, how do you learn to think intuitively 575 00:31:58,650 --> 00:31:59,660 about these things? 576 00:31:59,660 --> 00:32:02,290 And B, if you're going to teach it 577 00:32:02,290 --> 00:32:03,450 how do you make sure-- 578 00:32:03,450 --> 00:32:04,510 related to that-- 579 00:32:04,510 --> 00:32:08,750 you actually have the intuition before you teach it. 580 00:32:08,750 --> 00:32:09,750 There's two answers to that. 581 00:32:09,750 --> 00:32:13,440 One is that it's very rare that anyone ever achieved a 582 00:32:13,440 --> 00:32:17,120 goal that they didn't set out to do. 583 00:32:17,120 --> 00:32:18,470 And then just happened upon it. 584 00:32:18,470 --> 00:32:21,120 So I would say that's true, also, with developing 585 00:32:21,120 --> 00:32:22,720 intuition in these areas. 586 00:32:22,720 --> 00:32:25,120 You have to make it your goal. 587 00:32:25,120 --> 00:32:28,120 So it's not going to just happen by chance. 588 00:32:28,120 --> 00:32:30,490 So then questions, OK, if it is your goal how do 589 00:32:30,490 --> 00:32:32,610 you go about it? 590 00:32:32,610 --> 00:32:37,080 One way is anytime you do a calculation, at the end of the 591 00:32:37,080 --> 00:32:40,500 calculation ask yourself this question. 592 00:32:49,170 --> 00:32:52,360 So John Wheeler-- who was Feynman's adviser-- 593 00:32:52,360 --> 00:32:54,380 he recommended the following question, which I think is a 594 00:32:54,380 --> 00:32:55,300 fantastic question. 595 00:32:55,300 --> 00:33:00,540 So the question is if you could time travel back and 596 00:33:00,540 --> 00:33:04,120 talk to your earlier self what one or two sentences would you 597 00:33:04,120 --> 00:33:06,370 tell your earlier self before they started solving the 598 00:33:06,370 --> 00:33:08,930 problem that would make the problem just 599 00:33:08,930 --> 00:33:10,600 sort of flow smoothly? 600 00:33:10,600 --> 00:33:11,850 OK? 601 00:33:30,610 --> 00:33:33,180 So what sentence would you tell your earlier, pre-problem 602 00:33:33,180 --> 00:33:34,160 solved self? 603 00:33:34,160 --> 00:33:35,910 So this is after you solved the problem. 604 00:33:41,620 --> 00:33:47,340 So that forces you to give a insightful summary of what you 605 00:33:47,340 --> 00:33:48,720 learned from the problem. 606 00:33:48,720 --> 00:33:51,370 So it forces you towards the intuitive way of reasoning. 607 00:33:51,370 --> 00:33:52,880 And you'll find it's quite hard at first. 608 00:33:52,880 --> 00:33:54,550 Because you don't have the intuitive library. 609 00:33:54,550 --> 00:33:56,990 But at least it points you in the direction to be going. 610 00:33:56,990 --> 00:33:57,800 OK, now what else? 611 00:33:57,800 --> 00:34:04,870 Well, in chemistry there's various books that help 612 00:34:04,870 --> 00:34:05,830 develop intuition. 613 00:34:05,830 --> 00:34:07,450 They have all kinds of intuitive reasoning 614 00:34:07,450 --> 00:34:08,070 questions in them. 615 00:34:08,070 --> 00:34:09,870 And some are quite good. 616 00:34:09,870 --> 00:34:11,170 Some of the books are quite good. 617 00:34:11,170 --> 00:34:15,190 So the one in chemistry that I like is called Voyages in 618 00:34:15,190 --> 00:34:16,440 Conceptual Chemistry. 619 00:34:33,449 --> 00:34:37,420 And in physics one of the ones I like is called Thinking 620 00:34:37,420 --> 00:34:38,670 Physics by Epstein. 621 00:34:44,264 --> 00:34:45,820 I think Epstein's like that. 622 00:34:54,909 --> 00:34:59,810 So what that is, is that's basically, one 623 00:34:59,810 --> 00:35:00,800 question per page. 624 00:35:00,800 --> 00:35:03,210 And it's multiple-choice intuitive reasoning question. 625 00:35:03,210 --> 00:35:05,530 And they're about all kinds of interesting physics, like why 626 00:35:05,530 --> 00:35:07,900 do tea kettles whistle? 627 00:35:07,900 --> 00:35:12,420 If you shake bottle of soda up, why does it explode? 628 00:35:12,420 --> 00:35:15,900 And so it's filled with really, really fascinating 629 00:35:15,900 --> 00:35:17,660 puzzles and ways of thinking. 630 00:35:17,660 --> 00:35:18,950 And then with explanations. 631 00:35:18,950 --> 00:35:22,110 So just by thinking about them, reading the explanation, 632 00:35:22,110 --> 00:35:24,730 trying to understand, OK, then asking yourself Wheeler's 633 00:35:24,730 --> 00:35:27,650 question at the end of reading the explanation, even if you 634 00:35:27,650 --> 00:35:30,250 didn't solve it, you can develop a lot of intuition. 635 00:35:30,250 --> 00:35:34,820 I don't know a good one for math or biology. 636 00:35:34,820 --> 00:35:38,150 And if anyone does, I definitely appreciate any 637 00:35:38,150 --> 00:35:39,600 suggestions. 638 00:35:39,600 --> 00:35:39,990 OK? 639 00:35:39,990 --> 00:35:43,390 But there are resources in some fields. 640 00:35:43,390 --> 00:35:48,690 And the other is just whenever you find paradoxes go after 641 00:35:48,690 --> 00:35:49,920 them and share them with everyone. 642 00:35:49,920 --> 00:35:51,260 And ask everyone you know,do you know any 643 00:35:51,260 --> 00:35:52,680 paradoxes I can work on? 644 00:35:52,680 --> 00:35:54,910 That'll also developed intuition. 645 00:35:54,910 --> 00:35:58,800 OK, and then related to that, one comment was I've noticed 646 00:35:58,800 --> 00:36:00,380 that teaching is the best way of learning. 647 00:36:00,380 --> 00:36:03,400 How can you incorporate that into a course? 648 00:36:03,400 --> 00:36:04,420 So yeah, that's true. 649 00:36:04,420 --> 00:36:07,103 So sometimes you just have to accept that the first time you 650 00:36:07,103 --> 00:36:10,600 teach the thing you're going to be learning a lot. 651 00:36:10,600 --> 00:36:11,930 So that's fine. 652 00:36:11,930 --> 00:36:14,820 And the second time you teach it, it'll be much better. 653 00:36:14,820 --> 00:36:16,890 So you'll actually develop a lot of intuition the first 654 00:36:16,890 --> 00:36:18,290 time you teach a course. 655 00:36:18,290 --> 00:36:21,370 So for example, I found when I was a graduate student, I was 656 00:36:21,370 --> 00:36:25,270 a teaching assistant for Physics 1A at Caltech, which 657 00:36:25,270 --> 00:36:27,540 was like 801. 658 00:36:27,540 --> 00:36:29,300 And I found I had a huge number of 659 00:36:29,300 --> 00:36:31,130 misconceptions about tension. 660 00:36:31,130 --> 00:36:32,630 I just had no idea what tension was. 661 00:36:32,630 --> 00:36:34,640 For example, I thought tension was a force. 662 00:36:34,640 --> 00:36:37,520 And now that seems ridiculous to me. 663 00:36:37,520 --> 00:36:39,570 And it doesn't seem ridiculous to you that's because you're 664 00:36:39,570 --> 00:36:43,750 in exactly the same state I was in before I was taught 665 00:36:43,750 --> 00:36:44,260 physics 1A. 666 00:36:44,260 --> 00:36:47,840 And I've got myself all in a twist when I was trying to 667 00:36:47,840 --> 00:36:48,670 explain it. 668 00:36:48,670 --> 00:36:52,020 And I finally tracked it down to actually, that particular 669 00:36:52,020 --> 00:36:53,040 misconception. 670 00:36:53,040 --> 00:36:56,420 So then I developed a bunch of questions for myself, which I 671 00:36:56,420 --> 00:36:58,490 also asked students about tension. 672 00:36:58,490 --> 00:37:02,210 So teaching is learning. 673 00:37:02,210 --> 00:37:04,410 And then how do you incorporate that into a class 674 00:37:04,410 --> 00:37:05,300 for the students? 675 00:37:05,300 --> 00:37:07,890 Well, you can ask them to teach each other and argue 676 00:37:07,890 --> 00:37:08,780 with each other. 677 00:37:08,780 --> 00:37:10,390 So we'll talk about that in the session 678 00:37:10,390 --> 00:37:11,720 on interactive teaching. 679 00:37:11,720 --> 00:37:14,900 But yeah, it is the best way of learning. 680 00:37:14,900 --> 00:37:16,820 And so if you can get the students to do that as well 681 00:37:16,820 --> 00:37:18,770 you'll be increasing their learning. 682 00:37:18,770 --> 00:37:24,330 And then the last question for the moment was what's my 683 00:37:24,330 --> 00:37:26,530 response to the following article-- so it was in the 684 00:37:26,530 --> 00:37:29,910 globe on February 15, 2009. 685 00:37:29,910 --> 00:37:31,900 And it said, don't open with a joke. 686 00:37:31,900 --> 00:37:36,530 So it was summarizing a paper called "Increased 687 00:37:36,530 --> 00:37:39,450 Interestingness of Extraneous Details in a Multimedia 688 00:37:39,450 --> 00:37:43,220 Science Presentation Leads to Decreased Learning." Journal 689 00:37:43,220 --> 00:37:47,740 of Experimental Psychology, December, 2008. 690 00:37:47,740 --> 00:37:49,000 So they summarized that. 691 00:37:49,000 --> 00:37:51,980 So basically, what they found is that if you start with a 692 00:37:51,980 --> 00:37:55,210 joke that's extraneous to the material it actually decreases 693 00:37:55,210 --> 00:37:55,910 the learning. 694 00:37:55,910 --> 00:37:58,810 And that, I think, is quite plausible. 695 00:37:58,810 --> 00:38:02,030 So I recommend that you start with something interesting in 696 00:38:02,030 --> 00:38:03,400 the beginning. 697 00:38:03,400 --> 00:38:06,590 But it should be related to the material. 698 00:38:06,590 --> 00:38:08,040 So the problem wasn't the joke. 699 00:38:08,040 --> 00:38:09,430 The problem was that the joke wasn't 700 00:38:09,430 --> 00:38:12,280 related to the material. 701 00:38:12,280 --> 00:38:13,830 So the thing should be interesting. 702 00:38:13,830 --> 00:38:14,970 Because you want to draw people in. 703 00:38:14,970 --> 00:38:16,570 You don't want to conclude from that article that you 704 00:38:16,570 --> 00:38:18,200 shouldn't start with some interesting. 705 00:38:18,200 --> 00:38:19,570 But you should start with something interesting that's 706 00:38:19,570 --> 00:38:22,000 related to the material. 707 00:38:22,000 --> 00:38:26,750 OK, so redesigning questions. 708 00:38:26,750 --> 00:38:33,540 So here is an actual question that we will redesign. 709 00:38:33,540 --> 00:38:36,830 And I've left up the Bloom's Taxonomy there. 710 00:38:40,050 --> 00:38:42,410 So actually, I have a bunch of questions. 711 00:38:42,410 --> 00:38:44,090 We'll do a couple of them. 712 00:38:44,090 --> 00:38:46,480 And we'll review, probably, one of the questions we did 713 00:38:46,480 --> 00:38:48,440 earlier, which is about the cones. 714 00:39:06,350 --> 00:39:09,680 OK, so the question to start with-- and we're going to go 715 00:39:09,680 --> 00:39:11,170 that way and that way-- 716 00:39:11,170 --> 00:39:14,320 is find the eigenvalues of this matrix. 717 00:39:14,320 --> 00:39:18,630 So for those whose linear algebra is rusty, the 718 00:39:18,630 --> 00:39:30,720 eigenvalues of a matrix so a matrix, m, times some 719 00:39:30,720 --> 00:39:35,930 eigenvector e is equal to lambda times e. 720 00:39:35,930 --> 00:39:40,050 So if there's some vector that the matrix just brings back to 721 00:39:40,050 --> 00:39:42,885 itself with some constant, that's the eigenvalue. 722 00:39:47,920 --> 00:39:49,685 And this is the eigenvector. 723 00:39:53,540 --> 00:39:57,000 So eigen meaning own in German. 724 00:39:57,000 --> 00:40:02,790 So somehow this vector belongs to the matrix. 725 00:40:02,790 --> 00:40:04,450 It's said to be an eigenvector of the matrix. 726 00:40:04,450 --> 00:40:08,340 It's preserved when you hit it with the matrix. 727 00:40:08,340 --> 00:40:09,620 You get back the thing itself. 728 00:40:09,620 --> 00:40:11,975 And in that way it belongs to the matrix. 729 00:40:11,975 --> 00:40:16,150 OK, so there are recipes for computing it. 730 00:40:16,150 --> 00:40:18,940 And so here the question is, I'm asking students to use the 731 00:40:18,940 --> 00:40:22,050 recipe for computing the eigenvalue. 732 00:40:22,050 --> 00:40:26,940 OK, so now I'm going to ask you the following question, 733 00:40:26,940 --> 00:40:28,830 which is to design-- 734 00:40:28,830 --> 00:40:34,860 well, first of all, where would you say that guy goes? 735 00:40:34,860 --> 00:40:38,020 It's sort of comprehension. 736 00:40:38,020 --> 00:40:40,970 You know, it's basically computing. 737 00:40:40,970 --> 00:40:42,220 Maybe it's a bit of application. 738 00:40:42,220 --> 00:40:45,420 But it's basically comprehension. 739 00:40:45,420 --> 00:40:50,440 OK, so can we go lower on the taxonomy towards knowledge? 740 00:40:50,440 --> 00:40:56,610 Can we go higher towards the higher-level reasoning? 741 00:40:56,610 --> 00:40:58,775 Let's try to construct questions on this end. 742 00:41:09,090 --> 00:41:13,350 OK, so everyone understand the thing to work out? 743 00:41:13,350 --> 00:41:16,570 I'm going to ask you to try to think of stuff that could be 744 00:41:16,570 --> 00:41:17,590 put here and here. 745 00:41:17,590 --> 00:41:24,161 So this is lower level and this is higher. 746 00:41:31,010 --> 00:41:32,820 Does anyone need me to explain-- 747 00:41:32,820 --> 00:41:34,980 or want me to explain-- more about eigenvalues or 748 00:41:34,980 --> 00:41:36,230 eigenvectors? 749 00:41:39,550 --> 00:41:42,580 OK, so find a neighbor or two. 750 00:41:42,580 --> 00:41:44,330 And try to think of stuff that can go in 751 00:41:44,330 --> 00:41:48,840 this box or this box. 752 00:41:48,840 --> 00:41:52,020 And generally, the higher-level questions 753 00:41:52,020 --> 00:41:57,740 requires more knowledge about the material, which is one 754 00:41:57,740 --> 00:41:59,580 aspect of their being higher level. 755 00:41:59,580 --> 00:42:01,620 You need a bigger margin of safety when you're trying to 756 00:42:01,620 --> 00:42:02,560 design them. 757 00:42:02,560 --> 00:42:03,770 But don't let that bother you. 758 00:42:03,770 --> 00:42:05,040 See what you can construct. 759 00:42:05,040 --> 00:42:09,590 And you can use the levels on Bloom's Taxonomy to try to 760 00:42:09,590 --> 00:42:11,540 create some kind of questions around it. 761 00:42:16,810 --> 00:42:26,110 By the way, the answer to this question, by the way, is i and 762 00:42:26,110 --> 00:42:29,465 minus i, just in case you are curious. 763 00:42:33,930 --> 00:42:43,920 OK, so let's see what examples you've come up with, so 764 00:42:43,920 --> 00:42:45,280 related to this question. 765 00:42:45,280 --> 00:42:49,280 Obviously, you'll change it around some. 766 00:42:49,280 --> 00:42:52,840 Let's say either side, this side or this side. 767 00:42:52,840 --> 00:42:54,720 Someone I haven't heard from? 768 00:42:54,720 --> 00:42:55,950 Yes, can you tell me your name? 769 00:42:55,950 --> 00:42:56,880 AUDIENCE: Mike. 770 00:42:56,880 --> 00:42:57,470 PROFESSOR: Mike, yeah? 771 00:42:57,470 --> 00:42:58,655 AUDIENCE: What is an eigenvalue? 772 00:42:58,655 --> 00:43:00,430 PROFESSOR: OK, so what is an eigenvalue? 773 00:43:00,430 --> 00:43:02,010 Where would you put that? 774 00:43:02,010 --> 00:43:04,460 AUDIENCE: Lower. 775 00:43:04,460 --> 00:43:05,710 [INAUDIBLE]? 776 00:43:07,800 --> 00:43:09,380 PROFESSOR: Oh, yeah, good question. 777 00:43:09,380 --> 00:43:11,590 It depends where you put this one. 778 00:43:11,590 --> 00:43:18,140 This one is computing, which I roughly put that somewhere 779 00:43:18,140 --> 00:43:21,870 between comprehension and application. 780 00:43:21,870 --> 00:43:29,790 So right now I would say, we're somewhere around there. 781 00:43:29,790 --> 00:43:33,270 So your question is to define eigenvalue? 782 00:43:33,270 --> 00:43:34,520 OK. 783 00:43:37,740 --> 00:43:40,810 I'm just short-handing it as defined lambda. 784 00:43:40,810 --> 00:43:43,430 OK, so that's one question. 785 00:43:43,430 --> 00:43:44,760 OK, another question. 786 00:43:44,760 --> 00:43:45,750 Can you tell me your name? 787 00:43:45,750 --> 00:43:46,040 AUDIENCE: Wendy. 788 00:43:46,040 --> 00:43:46,480 PROFESSOR: Wendy, yes? 789 00:43:46,480 --> 00:43:49,875 AUDIENCE: So related to that, is that you could put that 790 00:43:49,875 --> 00:43:51,339 question higher. 791 00:43:51,339 --> 00:43:54,884 If you asked them, what does an eigenvalue mean? 792 00:43:54,884 --> 00:43:59,163 If you word it differently instead of [INAUDIBLE]. 793 00:43:59,163 --> 00:44:03,030 PROFESSOR: OK, which may have been what you meant as well 794 00:44:03,030 --> 00:44:07,680 and I may have defined lambda. 795 00:44:07,680 --> 00:44:10,500 OK, so you're saying, well, you can actually ask them to 796 00:44:10,500 --> 00:44:14,120 say, what does eigenvalue mean? 797 00:44:14,120 --> 00:44:22,870 OK, so how would you if they know what it means? 798 00:44:22,870 --> 00:44:25,810 So what would you look for in something like that? 799 00:44:25,810 --> 00:44:30,013 AUDIENCE: If they could describe it to you, or maybe 800 00:44:30,013 --> 00:44:34,070 tell you a problem in which it'd be useful, in using it? 801 00:44:34,070 --> 00:44:36,650 PROFESSOR: OK, so yeah, let me write that too. 802 00:44:36,650 --> 00:44:51,700 Create a problem that would benefit from lambda, that 803 00:44:51,700 --> 00:44:52,950 would need lambda. 804 00:44:52,950 --> 00:44:58,010 OK, so for example here, create. 805 00:44:58,010 --> 00:45:01,430 That's gone pretty far down towards synthesis. 806 00:45:01,430 --> 00:45:04,970 I really should have flipped the list around. 807 00:45:04,970 --> 00:45:10,350 But synthesis is quite high on Bloom's taxonomy. 808 00:45:10,350 --> 00:45:12,020 So you're actually going to create a problem. 809 00:45:12,020 --> 00:45:16,060 It's like the Newton's law example. 810 00:45:16,060 --> 00:45:16,846 Yes? 811 00:45:16,846 --> 00:45:18,236 AUDIENCE: [INAUDIBLE] 812 00:45:18,236 --> 00:45:20,228 instead of saying, again, what does lambda mean? 813 00:45:20,228 --> 00:45:24,212 You could say what do the results from finding lambda? 814 00:45:24,212 --> 00:45:26,210 What are the results of that solution? 815 00:45:26,210 --> 00:45:29,370 PROFESSOR: OK, so how does it help you to know the 816 00:45:29,370 --> 00:45:30,010 eigenvalues? 817 00:45:30,010 --> 00:45:31,333 Is that the question? 818 00:45:31,333 --> 00:45:34,714 AUDIENCE: No, I'm just saying instead of the general asking 819 00:45:34,714 --> 00:45:37,129 for the definition, what does lambda mean? 820 00:45:37,129 --> 00:45:38,578 What is an eigenvalue? 821 00:45:38,578 --> 00:45:40,030 What does it mean? 822 00:45:40,030 --> 00:45:42,510 But after having solved the problem saying, what does your 823 00:45:42,510 --> 00:45:42,800 answer mean? 824 00:45:42,800 --> 00:45:46,260 PROFESSOR: Ah, OK, so even if you ask them this first you 825 00:45:46,260 --> 00:45:49,070 can say, OK, interpret your answer. 826 00:45:49,070 --> 00:45:50,650 Yeah, and that's a-- generally-- 827 00:45:50,650 --> 00:45:51,570 very good policy. 828 00:45:51,570 --> 00:45:52,820 So interpret. 829 00:45:58,540 --> 00:46:00,010 and where would I put that? 830 00:46:00,010 --> 00:46:02,400 Eh, interpret is somewhere like analysis, 831 00:46:02,400 --> 00:46:03,610 maybe a bit of synthesis. 832 00:46:03,610 --> 00:46:05,860 But yeah, it's quite high on the list. 833 00:46:05,860 --> 00:46:09,770 So interpret, that's another really key word. 834 00:46:09,770 --> 00:46:11,930 In fact, it's often neglected, right? 835 00:46:11,930 --> 00:46:14,450 We just ask students to solve the problem. 836 00:46:14,450 --> 00:46:15,940 And wander, wander, wander. 837 00:46:15,940 --> 00:46:18,260 They get the thing that looks like an answer. 838 00:46:18,260 --> 00:46:20,750 They put a box around it and they're done. 839 00:46:20,750 --> 00:46:24,150 But actually, you can massively increase the level 840 00:46:24,150 --> 00:46:26,420 of a problem just by adding to the problem, 841 00:46:26,420 --> 00:46:28,700 interpret your answer. 842 00:46:28,700 --> 00:46:31,520 What does it mean, that that's an eigenvalue? 843 00:46:31,520 --> 00:46:33,140 And maybe they would say something like this. 844 00:46:33,140 --> 00:46:37,690 But even that would be better than just having done the 845 00:46:37,690 --> 00:46:39,920 computational procedure and got an answer out of it. 846 00:46:42,800 --> 00:46:44,120 Yes, can you tell me your name? 847 00:46:44,120 --> 00:46:44,745 AUDIENCE: Ben. 848 00:46:44,745 --> 00:46:45,700 PROFESSOR: Ben, yes? 849 00:46:45,700 --> 00:46:49,095 AUDIENCE: I might ask, does that matrix have any 850 00:46:49,095 --> 00:46:49,580 eigenvalues? 851 00:46:49,580 --> 00:46:53,625 PROFESSOR: OK, so yeah, so let's put it over here. 852 00:47:02,510 --> 00:47:07,080 Right, so there what you're doing is you're not presuming. 853 00:47:07,080 --> 00:47:10,430 You're not key-wording what they should do. 854 00:47:10,430 --> 00:47:13,120 When you do this-- especially if it's a 855 00:47:13,120 --> 00:47:14,680 linear algebra course-- 856 00:47:14,680 --> 00:47:16,700 they've probably seen a bunch of things like this. 857 00:47:16,700 --> 00:47:18,280 Like in a calculus course, integrate 858 00:47:18,280 --> 00:47:19,600 these things by parts. 859 00:47:19,600 --> 00:47:23,040 They just know I have to integrate by parts, whereas 860 00:47:23,040 --> 00:47:25,590 here you're at least one step higher. 861 00:47:25,590 --> 00:47:27,260 Because they don't know whether there's an answer to 862 00:47:27,260 --> 00:47:28,110 the problem or not. 863 00:47:28,110 --> 00:47:29,990 And they have to think, well, how do I know if they're 864 00:47:29,990 --> 00:47:30,550 eigenvalues? 865 00:47:30,550 --> 00:47:33,800 So there's actually one intervening level of 866 00:47:33,800 --> 00:47:36,420 sophistication. 867 00:47:36,420 --> 00:47:37,470 Other suggestions? 868 00:47:37,470 --> 00:47:38,763 Yes, Adrian? 869 00:47:38,763 --> 00:47:43,615 AUDIENCE: Just give them two numbers and say write a matrix 870 00:47:43,615 --> 00:47:45,465 that has these as the eigenvalues? 871 00:47:45,465 --> 00:47:49,855 PROFESSOR: OK, so let me continue the list over here. 872 00:48:00,890 --> 00:48:06,800 OK, so create a matrix which has the following eigenvalues. 873 00:48:17,860 --> 00:48:21,410 So say lambda equals 2 comma 3. 874 00:48:21,410 --> 00:48:27,390 So create a matrix, create a meaning. 875 00:48:27,390 --> 00:48:31,200 We're already high up in the taxonomy toward synthesis. 876 00:48:31,200 --> 00:48:34,640 And actually, I would even use a related one, which is-- 877 00:48:48,260 --> 00:48:52,990 so create a real matrix with eigenvalues i comma minus i. 878 00:48:52,990 --> 00:48:55,170 So that one, is quite related to this. 879 00:48:55,170 --> 00:48:59,190 And this is the answer. 880 00:48:59,190 --> 00:49:02,910 So it's quite a hard question. 881 00:49:02,910 --> 00:49:08,240 Even if people can do this and find i comma minus i, this one 882 00:49:08,240 --> 00:49:12,190 is very hard because you're asking to apply a constraint 883 00:49:12,190 --> 00:49:14,170 that the thing be real. 884 00:49:14,170 --> 00:49:15,630 So it's not just any matrix. 885 00:49:15,630 --> 00:49:16,830 But it's that the thing be real. 886 00:49:16,830 --> 00:49:18,580 And then you have to really understand quite a lot about 887 00:49:18,580 --> 00:49:21,180 matrices to do that. 888 00:49:21,180 --> 00:49:22,110 Yes, can you tell me your name? 889 00:49:22,110 --> 00:49:22,830 AUDIENCE: Scott. 890 00:49:22,830 --> 00:49:23,230 PROFESSOR: Scott. 891 00:49:23,230 --> 00:49:26,436 AUDIENCE: So, I was thinking of a synthesis question which 892 00:49:26,436 --> 00:49:31,380 would be is after multiplying the item the eigenvector by 893 00:49:31,380 --> 00:49:34,352 the matrix how is it rotated? 894 00:49:34,352 --> 00:49:39,460 PROFESSOR: OK, so what is the geometric effect on the 895 00:49:39,460 --> 00:49:42,892 eigenvector of the matrix on the eigenvector? 896 00:49:42,892 --> 00:49:45,181 AUDIENCE: Right, but the question is if they understand 897 00:49:45,181 --> 00:49:46,635 what an eigenvalue is. 898 00:49:46,635 --> 00:49:51,090 PROFESSOR: They should be able to answer that right away. 899 00:49:51,090 --> 00:49:53,370 Right, but it really tests for understanding of what the 900 00:49:53,370 --> 00:49:53,800 meaning is. 901 00:49:53,800 --> 00:49:57,720 So it's another way of approaching the question of do 902 00:49:57,720 --> 00:49:59,185 they understand eigenvalue means? 903 00:50:13,880 --> 00:50:16,040 What is the geometric effect of the matrix on the 904 00:50:16,040 --> 00:50:18,860 eigenvector? 905 00:50:18,860 --> 00:50:21,960 And then hopefully, they'll be able to say well, actually, it 906 00:50:21,960 --> 00:50:22,740 doesn't rotate it. 907 00:50:22,740 --> 00:50:23,690 It just scales it. 908 00:50:23,690 --> 00:50:27,740 And the eigenvalue is the amount of scaling. 909 00:50:27,740 --> 00:50:30,640 OK, and that demonstrates quite a high level of 910 00:50:30,640 --> 00:50:31,850 understanding too. 911 00:50:31,850 --> 00:50:35,200 And This is one reason that oral exams, generally, are 912 00:50:35,200 --> 00:50:36,830 quite good ways of evaluating. 913 00:50:36,830 --> 00:50:38,380 Because you can ask these kind of questions. 914 00:50:38,380 --> 00:50:41,430 And as soon as you see that they understand you move on to 915 00:50:41,430 --> 00:50:42,610 something else. 916 00:50:42,610 --> 00:50:45,330 Which of the flip side is that's why oral exams are very 917 00:50:45,330 --> 00:50:46,990 disconcerting for the students. 918 00:50:46,990 --> 00:50:50,100 Because you spend no time on the things they understand. 919 00:50:50,100 --> 00:50:50,600 Right? 920 00:50:50,600 --> 00:50:52,510 So as soon as you know they understand it, you move on to 921 00:50:52,510 --> 00:50:53,210 something else. 922 00:50:53,210 --> 00:50:54,500 So the student just feels like, what the 923 00:50:54,500 --> 00:50:55,930 hell happened to me? 924 00:50:55,930 --> 00:50:56,820 I was doing fine. 925 00:50:56,820 --> 00:50:58,230 And they asked me about something else. 926 00:50:58,230 --> 00:50:59,090 Yeah, that's exactly right. 927 00:50:59,090 --> 00:51:01,000 That's why they asked you about something else. 928 00:51:01,000 --> 00:51:02,920 They knew there was nothing more here to find out. 929 00:51:02,920 --> 00:51:05,040 You understood it. 930 00:51:05,040 --> 00:51:07,720 But that's why oral exams are such a good way-- so 931 00:51:07,720 --> 00:51:08,480 efficient-- 932 00:51:08,480 --> 00:51:09,730 for evaluating. 933 00:51:12,370 --> 00:51:17,810 So in Cambridge we used to do oral exam interviews for 934 00:51:17,810 --> 00:51:19,730 admission for undergraduate. 935 00:51:19,730 --> 00:51:22,280 So people would be admitted to the major right away. 936 00:51:22,280 --> 00:51:25,720 So we had two 20-minute interviews. 937 00:51:25,720 --> 00:51:27,780 And we found those were much more reliable than all the 938 00:51:27,780 --> 00:51:30,440 exams that they did in high school, the 939 00:51:30,440 --> 00:51:32,010 equivalent of AP exams. 940 00:51:32,010 --> 00:51:34,200 Because you could really ask questions that really probed 941 00:51:34,200 --> 00:51:37,330 understanding and right away see what people could do and 942 00:51:37,330 --> 00:51:39,760 couldn't do. 943 00:51:39,760 --> 00:51:43,750 So geometric effective of m on e creating a matrix, so you're 944 00:51:43,750 --> 00:51:46,650 asking, so what's the geometric effect? 945 00:51:46,650 --> 00:51:48,000 It's not just comprehension. 946 00:51:48,000 --> 00:51:51,507 You're asking them to apply it and maybe, in a 947 00:51:51,507 --> 00:51:53,170 bit in a new area. 948 00:51:53,170 --> 00:51:55,690 They hadn't really thought of eigenvalues and eigenvectors 949 00:51:55,690 --> 00:51:56,675 as geometric at all. 950 00:51:56,675 --> 00:51:58,320 And now, all of sudden, you're asking them that. 951 00:51:58,320 --> 00:52:00,700 You're asking them to transfer their knowledge, which is one 952 00:52:00,700 --> 00:52:04,230 of the fundamental goals. 953 00:52:04,230 --> 00:52:04,615 Yes? 954 00:52:04,615 --> 00:52:06,157 AUDIENCE: Once you give them two matrices that has the same 955 00:52:06,157 --> 00:52:09,660 eigenvalues you can ask them to see if they are 956 00:52:09,660 --> 00:52:11,560 related in some ways. 957 00:52:20,648 --> 00:52:23,630 PROFESSOR: Right, so for example, let's do this one. 958 00:52:23,630 --> 00:52:39,870 So how are those two matrices related? 959 00:52:39,870 --> 00:52:42,700 So they both have eigenvalues i and minus i. 960 00:52:42,700 --> 00:52:46,190 This one obviously does because those are the diagonal 961 00:52:46,190 --> 00:52:47,720 values and there's nothing else. 962 00:52:47,720 --> 00:52:51,290 And this one, you have to do it by the magic procedure. 963 00:52:51,290 --> 00:52:52,190 You don't have to. 964 00:52:52,190 --> 00:52:55,160 And so how are they related? 965 00:52:55,160 --> 00:53:01,820 So that is some kind of analysis question. 966 00:53:01,820 --> 00:53:03,860 And it's quite a difficult analysis question. 967 00:53:03,860 --> 00:53:06,560 It tests for really, do they understand what matrices mean? 968 00:53:06,560 --> 00:53:09,290 So that's why I've underlined this word. 969 00:53:09,290 --> 00:53:14,220 The questions all in this column are all somehow testing 970 00:53:14,220 --> 00:53:16,570 that they understand what things mean. 971 00:53:16,570 --> 00:53:20,250 So that ties back to the point I made earlier, which is that 972 00:53:20,250 --> 00:53:23,780 the whole fundamental point of asking good questions is to 973 00:53:23,780 --> 00:53:25,830 avoid rote learning. 974 00:53:25,830 --> 00:53:27,950 Is that by asking good questions you're 975 00:53:27,950 --> 00:53:29,000 fighting rote learning. 976 00:53:29,000 --> 00:53:32,970 And rote learning is the bane of most education. 977 00:53:32,970 --> 00:53:33,210 Right? 978 00:53:33,210 --> 00:53:38,970 Rote learning is too often the result of education. 979 00:53:38,970 --> 00:53:40,570 And it's the-- in my view-- 980 00:53:40,570 --> 00:53:42,500 fundamental problem with education. 981 00:53:42,500 --> 00:53:45,190 So by asking questions that are different you're actually 982 00:53:45,190 --> 00:53:47,180 starting to fight that and break the habit. 983 00:53:47,180 --> 00:53:49,380 So for example, how does rote learning show up? 984 00:53:49,380 --> 00:53:56,800 Well, in the bouncing-ball question, so the force is-- in 985 00:53:56,800 --> 00:53:57,510 the instant that it's 986 00:53:57,510 --> 00:53:59,390 stationary, while it's bouncing-- 987 00:53:59,390 --> 00:54:00,640 people say mg. 988 00:54:05,337 --> 00:54:06,810 While this mg is right. 989 00:54:06,810 --> 00:54:09,830 The gravity, but the contact-- 990 00:54:09,830 --> 00:54:11,830 let's say the constraint force-- 991 00:54:11,830 --> 00:54:15,030 in this case it is a very full-contact force is mg. 992 00:54:15,030 --> 00:54:19,940 One of the reasons they say that is the misconception that 993 00:54:19,940 --> 00:54:23,220 they think a equals 0 because v equals 0. 994 00:54:23,220 --> 00:54:25,620 So that's one reason. 995 00:54:25,620 --> 00:54:28,010 But the other reason is that they've done so many problems 996 00:54:28,010 --> 00:54:33,020 with books resting on tables, balls resting on tables, where 997 00:54:33,020 --> 00:54:34,810 the force is mg. 998 00:54:34,810 --> 00:54:35,010 Right? 999 00:54:35,010 --> 00:54:38,090 So they've now induced a new rule of physics, let's call it 1000 00:54:38,090 --> 00:54:40,390 Newton's fourth law. 1001 00:54:40,390 --> 00:54:46,020 That anytime you see a contact force it is mg. 1002 00:54:46,020 --> 00:54:51,690 So contact force equals mg maybe times cosine of theta. 1003 00:54:51,690 --> 00:54:52,610 [LAUGHTER] 1004 00:54:52,610 --> 00:54:53,340 PROFESSOR: Right? 1005 00:54:53,340 --> 00:54:54,080 or sine theta. 1006 00:54:54,080 --> 00:54:57,480 I guess it's mg-- 1007 00:54:57,480 --> 00:54:58,820 well, it depends how you measure theta. 1008 00:54:58,820 --> 00:55:00,500 But theta is the tilt of the plane. 1009 00:55:00,500 --> 00:55:03,440 So if the plane is tilted 0 degrees just to ground, well 1010 00:55:03,440 --> 00:55:06,050 it's then mg. 1011 00:55:06,050 --> 00:55:10,140 So that kind of learning is the result of rote learning 1012 00:55:10,140 --> 00:55:12,660 because they've solved problems without understanding 1013 00:55:12,660 --> 00:55:13,650 what they mean. 1014 00:55:13,650 --> 00:55:16,520 So instead of figuring out that oh, actually, you could 1015 00:55:16,520 --> 00:55:18,990 understand it from Newton's Second Law and understanding 1016 00:55:18,990 --> 00:55:22,400 acceleration, they think oh, there's a new pattern here. 1017 00:55:22,400 --> 00:55:22,700 Right? 1018 00:55:22,700 --> 00:55:25,630 Oh, a new pattern is whenever I see contact forces it's mg 1019 00:55:25,630 --> 00:55:27,520 times maybe cos theta or sine theta. 1020 00:55:27,520 --> 00:55:27,850 Yes? 1021 00:55:27,850 --> 00:55:29,760 AUDIENCE: What's the exact question with that system and 1022 00:55:29,760 --> 00:55:31,850 what's the normal [INAUDIBLE]? 1023 00:55:31,850 --> 00:55:35,490 PROFESSOR: Yeah, so the question was so you drop the 1024 00:55:35,490 --> 00:55:36,730 ball, say from here. 1025 00:55:36,730 --> 00:55:38,870 And when it bounces off the steel table there's one 1026 00:55:38,870 --> 00:55:41,480 instant when it's stationary on steel table. 1027 00:55:41,480 --> 00:55:45,276 And what are the forces on it at that instant? 1028 00:55:45,276 --> 00:55:47,530 AUDIENCE: I remember from last week. 1029 00:55:47,530 --> 00:55:48,780 PROFESSOR: Yeah, no, fair enough. 1030 00:55:48,780 --> 00:55:50,590 I should have stated the question out again. 1031 00:55:50,590 --> 00:55:54,569 So this is stationary for an instant. 1032 00:56:03,670 --> 00:56:08,650 All right, so actually the ball is quite compressed here. 1033 00:56:08,650 --> 00:56:09,138 Yes? 1034 00:56:09,138 --> 00:56:12,879 AUDIENCE: Isn't it impossible to give an exact answer for 1035 00:56:12,879 --> 00:56:16,458 the force with the [INAUDIBLE] 1036 00:56:16,458 --> 00:56:19,890 if you don't have the duration? 1037 00:56:19,890 --> 00:56:21,990 PROFESSOR: It is, right. 1038 00:56:21,990 --> 00:56:24,900 So it is impossible to give the exact answer. 1039 00:56:24,900 --> 00:56:28,340 But what you ask them is, well, how big is it roughly? 1040 00:56:28,340 --> 00:56:30,750 So I always protect myself by saying roughly. 1041 00:56:30,750 --> 00:56:33,220 And then you can ask anything you want. 1042 00:56:33,220 --> 00:56:38,020 And because, really, all I'm interested in is do they think 1043 00:56:38,020 --> 00:56:40,590 it's 1 times mg or do they realize it's 10 1044 00:56:40,590 --> 00:56:42,020 to the 4 times mg? 1045 00:56:42,020 --> 00:56:45,410 And those are so far apart that I don't care about 1046 00:56:45,410 --> 00:56:48,230 factors of two or three or even 10. 1047 00:56:48,230 --> 00:56:51,140 Now, how can you know that it's 10 to the 4 times mg? 1048 00:56:51,140 --> 00:56:54,070 Well, that is quite a hard question. 1049 00:56:54,070 --> 00:56:55,790 That's way down there. 1050 00:56:55,790 --> 00:56:59,880 Even though you'll see some lists of Bloom's Taxonomy say 1051 00:56:59,880 --> 00:57:04,120 estimate is a low-level skill, not that 1052 00:57:04,120 --> 00:57:05,190 high in Bloom's Taxonomy. 1053 00:57:05,190 --> 00:57:07,570 It's almost like computing somewhere in comprehension. 1054 00:57:07,570 --> 00:57:08,830 I don't agree with that. 1055 00:57:08,830 --> 00:57:12,430 Because as you saw from the example where students 1056 00:57:12,430 --> 00:57:16,240 couldn't estimate 3.04 times 5.3, they're terrible at 1057 00:57:16,240 --> 00:57:17,680 estimation. 1058 00:57:17,680 --> 00:57:21,660 So estimation actually hits one of the big misconceptions 1059 00:57:21,660 --> 00:57:24,240 and reveals a lot of the misconceptions. 1060 00:57:24,240 --> 00:57:28,190 So I put estimation almost at the level of synthesis because 1061 00:57:28,190 --> 00:57:30,740 it forces you to really synthesize your understanding. 1062 00:57:30,740 --> 00:57:32,070 You can't hide behind formulas. 1063 00:57:32,070 --> 00:57:35,860 So the next thing I'll do is say, OK, let's estimate this 1064 00:57:35,860 --> 00:57:36,990 and see if you can do that. 1065 00:57:36,990 --> 00:57:38,670 And if they really understand the system they 1066 00:57:38,670 --> 00:57:39,390 can estimate it. 1067 00:57:39,390 --> 00:57:40,280 But it's quite hard. 1068 00:57:40,280 --> 00:57:42,710 And I find almost no students can do it on their own. 1069 00:57:42,710 --> 00:57:46,060 But the method of estimation is, as you say, you do need to 1070 00:57:46,060 --> 00:57:49,490 know the contact time. 1071 00:57:49,490 --> 00:57:55,930 So the acceleration is not 0 as you say. 1072 00:57:55,930 --> 00:58:00,340 But it's delta v over delta t, where delta t 1073 00:58:00,340 --> 00:58:03,050 is the contact time. 1074 00:58:03,050 --> 00:58:05,475 Well, it's going v and then it's pretty much going v up, 1075 00:58:05,475 --> 00:58:07,340 so that's about 2v. 1076 00:58:07,340 --> 00:58:09,080 But I don't care about factors of 2. 1077 00:58:11,680 --> 00:58:13,150 And then, what's the contact time? 1078 00:58:13,150 --> 00:58:16,860 Well, there's a couple methods for doing the contact time. 1079 00:58:16,860 --> 00:58:20,030 One is you listen for the pitch. 1080 00:58:20,030 --> 00:58:23,480 And whatever the highest frequency in the pitch is-- 1081 00:58:23,480 --> 00:58:26,540 suppose it's 10 to the 4 hertz-- 1082 00:58:26,540 --> 00:58:29,420 well, then 1 over that time, 1 over the frequency 1083 00:58:29,420 --> 00:58:30,730 is roughly a time. 1084 00:58:30,730 --> 00:58:33,170 So it's probably the contact time. 1085 00:58:33,170 --> 00:58:34,520 So that's one approach. 1086 00:58:34,520 --> 00:58:36,860 The other approach is to say well, actually, physically 1087 00:58:36,860 --> 00:58:39,170 what's happening? 1088 00:58:39,170 --> 00:58:42,260 The ball is hitting the bottom. 1089 00:58:42,260 --> 00:58:45,260 And this end compressing. 1090 00:58:45,260 --> 00:58:46,310 But this end keeps going. 1091 00:58:46,310 --> 00:58:49,690 Because it has no knowledge that the bottom of the ball 1092 00:58:49,690 --> 00:58:50,740 hit the ground. 1093 00:58:50,740 --> 00:58:52,290 How's it going to know about that? 1094 00:58:52,290 --> 00:58:54,110 Well, the bottom of the ball has to tell it. 1095 00:58:54,110 --> 00:58:55,130 How's it going to tell it? 1096 00:58:55,130 --> 00:58:56,210 Well, it has to send some kind of signal. 1097 00:58:56,210 --> 00:58:57,270 How does it send signal? 1098 00:58:57,270 --> 00:58:58,130 Sound. 1099 00:58:58,130 --> 00:59:06,170 So it sends a sound wave upward. 1100 00:59:06,170 --> 00:59:09,980 And the sound wave travels in steel about 5 or 10 kilometers 1101 00:59:09,980 --> 00:59:11,070 per second. 1102 00:59:11,070 --> 00:59:14,270 So you suppose it's a 5-centimeter ball, then it's 1103 00:59:14,270 --> 00:59:17,260 about 10 to the minus 5 seconds is your contact time. 1104 00:59:17,260 --> 00:59:18,510 So this is really short. 1105 00:59:23,930 --> 00:59:28,640 So suppose v is something like a meter per second, and divide 1106 00:59:28,640 --> 00:59:30,440 it by 10 to the 5 seconds. 1107 00:59:30,440 --> 00:59:32,700 You're talking about something like 10 to the 5 meters per 1108 00:59:32,700 --> 00:59:37,915 second squared, which is 10 to the 4 times the acceleration 1109 00:59:37,915 --> 00:59:40,040 due to gravity. 1110 00:59:40,040 --> 00:59:40,430 OK? 1111 00:59:40,430 --> 00:59:45,960 So I went through because I think it's interesting but 1112 00:59:45,960 --> 00:59:49,160 also to show that estimating actually requires generally, 1113 00:59:49,160 --> 00:59:50,180 very high-level skills. 1114 00:59:50,180 --> 00:59:52,090 And it's quite hard for the students. 1115 00:59:52,090 --> 00:59:53,540 Therefore you should do it. 1116 00:59:53,540 --> 00:59:55,530 So there are some people who say, well, it's very hard for 1117 00:59:55,530 --> 00:59:56,000 the students. 1118 00:59:56,000 --> 00:59:57,420 Don't do it. 1119 00:59:57,420 --> 00:59:59,690 But again, there's another rule of thumb in teaching, 1120 00:59:59,690 --> 01:00:02,330 which is nobody ever learned anything that you didn't 1121 01:00:02,330 --> 01:00:03,465 actually try to help them with. 1122 01:00:03,465 --> 01:00:04,440 Well, that's not quite true. 1123 01:00:04,440 --> 01:00:06,490 But if you never teach something they're not very 1124 01:00:06,490 --> 01:00:07,400 likely to learn it. 1125 01:00:07,400 --> 01:00:09,900 So if it's something hard but valuable you have to start 1126 01:00:09,900 --> 01:00:14,520 teaching at some point, which is why I put 1127 01:00:14,520 --> 01:00:15,585 up that graph earlier. 1128 01:00:15,585 --> 01:00:16,790 Oh, it's gone now. 1129 01:00:16,790 --> 01:00:20,120 Where in the earlier stages of teaching you do things more 1130 01:00:20,120 --> 01:00:21,050 approximately. 1131 01:00:21,050 --> 01:00:25,340 And then in the later stages you do it more exactly. 1132 01:00:25,340 --> 01:00:28,380 So what I've told you now is a slight lie. 1133 01:00:28,380 --> 01:00:29,960 So this brings up the question from last 1134 01:00:29,960 --> 01:00:31,960 time, what about lying? 1135 01:00:31,960 --> 01:00:32,530 Is it useful? 1136 01:00:32,530 --> 01:00:36,210 Yes, it's essential because this argument is simple enough 1137 01:00:36,210 --> 01:00:37,430 that once you understand it you can just 1138 01:00:37,430 --> 01:00:38,870 keep it in your head. 1139 01:00:38,870 --> 01:00:43,150 And it's a bit of a lie, the reason being that the ball 1140 01:00:43,150 --> 01:00:45,360 doesn't have a uniform cross section. 1141 01:00:45,360 --> 01:00:49,130 So as the ball compresses the contact area changes, whereas 1142 01:00:49,130 --> 01:00:52,900 if the ball were cube or a rod the contact area would stay 1143 01:00:52,900 --> 01:00:54,140 the same as it compressed. 1144 01:00:54,140 --> 01:00:57,210 So there's a correction factor because the 1145 01:00:57,210 --> 01:00:58,840 contact area changes. 1146 01:00:58,840 --> 01:01:01,700 Now, that correction factor is not very big. 1147 01:01:01,700 --> 01:01:03,920 It turns out to be the fifth root of some 1148 01:01:03,920 --> 01:01:05,420 dimensionless thing. 1149 01:01:05,420 --> 01:01:09,640 And so this sound-wave argument you put in to the 4/5 1150 01:01:09,640 --> 01:01:12,070 power and then you put in the other thing to the 1/5 power. 1151 01:01:12,070 --> 01:01:14,970 So it's almost correct for this spherical ball. 1152 01:01:14,970 --> 01:01:17,560 So in a later of course it actually 1153 01:01:17,560 --> 01:01:19,360 adjusts for that factor. 1154 01:01:19,360 --> 01:01:21,370 And then in a much later course, probably, what I would 1155 01:01:21,370 --> 01:01:26,040 do is calculate the exact 2 pi over whatever factor that 1156 01:01:26,040 --> 01:01:31,600 shows up as well, by way of increasing the symbolic 1157 01:01:31,600 --> 01:01:32,730 complexity. 1158 01:01:32,730 --> 01:01:37,760 But even this estimate, doing that is conceptually hard. 1159 01:01:37,760 --> 01:01:41,040 So I would say start that early. 1160 01:01:41,040 --> 01:01:42,520 AUDIENCE: I think the point I was trying to 1161 01:01:42,520 --> 01:01:45,260 make was that this-- 1162 01:01:45,260 --> 01:01:49,350 I suspect that the students answered that wrong because of 1163 01:01:49,350 --> 01:01:52,682 real problem solving, and that they expect there to be a 1164 01:01:52,682 --> 01:01:57,080 solution given the data that you [INAUDIBLE]. 1165 01:01:57,080 --> 01:02:00,160 PROFESSOR: Well, if you've worked with them a bit on 1166 01:02:00,160 --> 01:02:02,280 estimating they know that they're going to have to do 1167 01:02:02,280 --> 01:02:02,970 some thinking. 1168 01:02:02,970 --> 01:02:07,530 If you say compute the force I agree with you for sure. 1169 01:02:07,530 --> 01:02:09,760 They're going to think they have to be able to do it from 1170 01:02:09,760 --> 01:02:10,410 the data there. 1171 01:02:10,410 --> 01:02:12,555 And they'll just say it's got to be mg because that's the 1172 01:02:12,555 --> 01:02:13,420 only other force I know. 1173 01:02:13,420 --> 01:02:17,550 But if you say estimate then there is a bit of a queue that 1174 01:02:17,550 --> 01:02:20,080 they have to include some other information which might 1175 01:02:20,080 --> 01:02:21,350 not put in the problem. 1176 01:02:21,350 --> 01:02:22,820 And so that mitigates the rote learning. 1177 01:02:22,820 --> 01:02:25,670 But what I find, even then, is they usually still can't do it 1178 01:02:25,670 --> 01:02:29,270 because their misconceptions about acceleration are so deep 1179 01:02:29,270 --> 01:02:30,750 and about equilibrium and force. 1180 01:02:30,750 --> 01:02:32,255 They think f equals mv, basically. 1181 01:02:36,980 --> 01:02:43,630 OK, so let's just look at what we've done here. 1182 01:02:43,630 --> 01:02:46,970 So I would say you can define lambda. 1183 01:02:46,970 --> 01:02:49,260 You can define eigenvector. 1184 01:02:49,260 --> 01:02:52,970 You can even say state the computational procedure. 1185 01:02:52,970 --> 01:02:56,640 I'm not sure where I would put that. 1186 01:02:56,640 --> 01:03:00,360 Depending on how people learn it, this could be purely a 1187 01:03:00,360 --> 01:03:01,610 knowledge question. 1188 01:03:09,120 --> 01:03:10,960 Because people could state the procedure but not really 1189 01:03:10,960 --> 01:03:12,930 understand it, not be able to do anything. 1190 01:03:12,930 --> 01:03:16,410 Or actually, you could say program the procedure. 1191 01:03:16,410 --> 01:03:18,530 Well, that would be something over here probably. 1192 01:03:18,530 --> 01:03:20,400 Because to program it you probably have to understand 1193 01:03:20,400 --> 01:03:22,130 what you're doing pretty well. 1194 01:03:22,130 --> 01:03:25,480 So stating the procedure, it depends how you ask them to 1195 01:03:25,480 --> 01:03:27,250 state it, whether it's a low-level or 1196 01:03:27,250 --> 01:03:28,140 a high-level question. 1197 01:03:28,140 --> 01:03:30,806 So I'll put program over here. 1198 01:03:47,570 --> 01:03:51,120 OK, so we've gone down and up. 1199 01:03:51,120 --> 01:03:54,340 And again, I want to remind you, I'm not saying all your 1200 01:03:54,340 --> 01:03:55,940 questions need to be here. 1201 01:03:55,940 --> 01:04:01,380 But generally, the questions are too much over here and not 1202 01:04:01,380 --> 01:04:02,470 enough over here. 1203 01:04:02,470 --> 01:04:05,530 So this gives you a recipe for thinking of new questions. 1204 01:04:05,530 --> 01:04:05,820 Yes? 1205 01:04:05,820 --> 01:04:08,774 AUDIENCE: So throughout the course do you basically, maybe 1206 01:04:08,774 --> 01:04:12,260 start on the first three in the beginning and then you 1207 01:04:12,260 --> 01:04:15,248 move it more through until you reach the end of the course? 1208 01:04:15,248 --> 01:04:17,670 PROFESSOR: More fractal. 1209 01:04:17,670 --> 01:04:21,030 The question was as the course moves on do you move more 1210 01:04:21,030 --> 01:04:22,340 towards synthesis? 1211 01:04:22,340 --> 01:04:24,230 I actually try to make it fractal. 1212 01:04:24,230 --> 01:04:29,330 So within each unit and each day even, I try to maybe have 1213 01:04:29,330 --> 01:04:31,850 something, knowledge or comprehension just to make 1214 01:04:31,850 --> 01:04:33,270 sure everyone's tracking. 1215 01:04:33,270 --> 01:04:36,910 But try to have something interesting as 1216 01:04:36,910 --> 01:04:37,860 well, all the time. 1217 01:04:37,860 --> 01:04:41,690 So something synthesis, analysis, maybe some evaluate. 1218 01:04:41,690 --> 01:04:43,920 And so each problem set-- for example-- 1219 01:04:43,920 --> 01:04:46,530 I'll put, generally, warm-up questions. 1220 01:04:46,530 --> 01:04:50,460 So basically they're marked warm up so that people know 1221 01:04:50,460 --> 01:04:53,000 OK, those are going to be knowledge and comprehension. 1222 01:04:53,000 --> 01:04:53,940 And you need that. 1223 01:04:53,940 --> 01:04:56,290 Because otherwise there's no point trying to do synthesis 1224 01:04:56,290 --> 01:04:58,060 if you don't have the base knowledge. 1225 01:04:58,060 --> 01:04:59,930 But just make sure you understand those, 1226 01:04:59,930 --> 01:05:01,310 just in your sleep. 1227 01:05:01,310 --> 01:05:04,210 And then regular problems, which tend to be somewhere in 1228 01:05:04,210 --> 01:05:07,750 the middle, say application or analysis. 1229 01:05:07,750 --> 01:05:09,890 And then bonus problems which are just optional. 1230 01:05:09,890 --> 01:05:12,210 But they're for people who either find all the other 1231 01:05:12,210 --> 01:05:14,750 problems easy or are really curious. 1232 01:05:14,750 --> 01:05:17,970 For them I put either synthesis or evaluation. 1233 01:05:17,970 --> 01:05:25,200 For example, in the approximation class the last 1234 01:05:25,200 --> 01:05:29,320 problem set had design an email indexing system. 1235 01:05:29,320 --> 01:05:31,420 So that was the bonus problem. 1236 01:05:31,420 --> 01:05:34,630 And there was a bunch of warm-up and regular problems 1237 01:05:34,630 --> 01:05:37,240 which were involving Unix text processing. 1238 01:05:37,240 --> 01:05:39,170 And then for the people who are really curious actually, 1239 01:05:39,170 --> 01:05:42,780 put it all together and make a really fast email-indexing 1240 01:05:42,780 --> 01:05:45,020 system so you can just find any email that you want just 1241 01:05:45,020 --> 01:05:46,350 by doing keyword search. 1242 01:05:46,350 --> 01:05:51,180 Sort of like a web search but just on your email inbox. 1243 01:05:51,180 --> 01:05:53,210 Because I actually use that myself. 1244 01:05:53,210 --> 01:05:55,980 Because I find folders are just hopeless. 1245 01:05:55,980 --> 01:05:57,150 It just takes all my time. 1246 01:05:57,150 --> 01:05:58,910 I have to figure out what folder things are in. 1247 01:05:58,910 --> 01:06:00,210 And that could be many. 1248 01:06:00,210 --> 01:06:03,060 So I just keep it all in one giant inbox with, I think, 1249 01:06:03,060 --> 01:06:05,570 150,000 messages in it. 1250 01:06:05,570 --> 01:06:06,880 And I just search through that. 1251 01:06:06,880 --> 01:06:09,680 And I have an index that's rebuilt every week or so. 1252 01:06:09,680 --> 01:06:11,870 And so I can search through it really fast. 1253 01:06:11,870 --> 01:06:15,360 So it's actually very practical problem and it gives 1254 01:06:15,360 --> 01:06:17,290 you an example of the levels of things you can ask. 1255 01:06:17,290 --> 01:06:19,520 So try to do it on a fractal scale. 1256 01:06:19,520 --> 01:06:23,490 Each class should have something, mix the levels each 1257 01:06:23,490 --> 01:06:26,090 homework, the exam. 1258 01:06:26,090 --> 01:06:29,886 So the general rule is to mix them up all the way. 1259 01:06:29,886 --> 01:06:30,820 OK? 1260 01:06:30,820 --> 01:06:37,200 So hopefully, from that, you feel confident that you have 1261 01:06:37,200 --> 01:06:41,250 tools that you can make interesting questions. 1262 01:06:41,250 --> 01:06:44,830 And this does have lots of payoffs, which one of them is 1263 01:06:44,830 --> 01:06:48,520 that questions that are enjoyable and educational, 1264 01:06:48,520 --> 01:06:49,940 students love them. 1265 01:06:49,940 --> 01:06:54,870 So when I practiced what I preached and made these kind 1266 01:06:54,870 --> 01:06:59,320 of problems, mix of problems for my classes, often students 1267 01:06:59,320 --> 01:07:04,450 have said, oh, can you please have more problems? 1268 01:07:04,450 --> 01:07:06,710 Which is very rare. 1269 01:07:06,710 --> 01:07:08,450 They said, oh, these are some of the most interesting 1270 01:07:08,450 --> 01:07:10,140 problems I'm likely to get at MIT. 1271 01:07:10,140 --> 01:07:13,570 And I used to read them out in my living of my 1272 01:07:13,570 --> 01:07:15,820 independent-living group just so that other people could 1273 01:07:15,820 --> 01:07:17,170 hear the interesting problems and we'd try 1274 01:07:17,170 --> 01:07:18,680 to solve them together. 1275 01:07:18,680 --> 01:07:21,860 And then I've had several emails after class finished, 1276 01:07:21,860 --> 01:07:24,270 saying, oh, you promised to post the optional problem set. 1277 01:07:24,270 --> 01:07:26,080 Where is it? 1278 01:07:26,080 --> 01:07:29,840 So it's because the problems, actually, somehow connect to 1279 01:07:29,840 --> 01:07:32,710 things that people find real and interesting. 1280 01:07:32,710 --> 01:07:35,870 So that's a mix of the perceptual. 1281 01:07:35,870 --> 01:07:38,180 Don't make it just purely symbol manipulation. 1282 01:07:38,180 --> 01:07:40,540 Try to connect to ways people look at the world. 1283 01:07:40,540 --> 01:07:44,994 But also, try to connect to higher-level reasoning skills. 1284 01:07:44,994 --> 01:07:45,466 Question? 1285 01:07:45,466 --> 01:07:47,354 AUDIENCE: Do you always use bonus problems? 1286 01:07:47,354 --> 01:07:48,330 PROFESSOR: I do. 1287 01:07:48,330 --> 01:07:49,570 I find that works really well. 1288 01:07:49,570 --> 01:07:52,955 Because it's like a pressure-escape valve. 1289 01:07:55,950 --> 01:07:59,740 It caters for the diversity of backgrounds in the class. 1290 01:07:59,740 --> 01:08:03,980 The people who are feeling very worried by the material, 1291 01:08:03,980 --> 01:08:06,680 they can just skip them, no problem. 1292 01:08:06,680 --> 01:08:08,480 And they don't feel like they have to do them. 1293 01:08:08,480 --> 01:08:10,600 And they don't feel like, oh my god, I can't do them. 1294 01:08:10,600 --> 01:08:12,640 I'm going to get points off. 1295 01:08:12,640 --> 01:08:15,030 And the people who find the other stuff easy, they find 1296 01:08:15,030 --> 01:08:16,080 something for them too. 1297 01:08:16,080 --> 01:08:20,450 So yeah, I try to always use bonus problems. 1298 01:08:20,450 --> 01:08:26,330 And I learned that from Knuth's book, called Concrete 1299 01:08:26,330 --> 01:08:27,800 Mathematics. 1300 01:08:27,800 --> 01:08:30,279 So actually, I think they have five levels of problems at the 1301 01:08:30,279 --> 01:08:31,050 end of every chapter. 1302 01:08:31,050 --> 01:08:32,460 There's warm ups. 1303 01:08:32,460 --> 01:08:34,850 There's homework problems. 1304 01:08:34,850 --> 01:08:38,590 There's exam problems, bonus problems, 1305 01:08:38,590 --> 01:08:39,630 and research problems. 1306 01:08:39,630 --> 01:08:41,029 So the research problems were the ones 1307 01:08:41,029 --> 01:08:43,370 that are not yet solved. 1308 01:08:43,370 --> 01:08:44,680 So at least you know they're not yet solved. 1309 01:08:44,680 --> 01:08:47,910 So you're going to be spending a while on them. 1310 01:08:47,910 --> 01:08:49,850 And then in the second edition I think some of them were 1311 01:08:49,850 --> 01:08:52,500 actually solved. 1312 01:08:52,500 --> 01:08:58,290 OK, so if everyone could just take a one minute and fill out 1313 01:08:58,290 --> 01:08:59,970 the feedback sheet? 1314 01:08:59,970 --> 01:09:04,410 Oh yeah, and let me just say, why I'm doing this now at 1315 01:09:04,410 --> 01:09:09,180 10:50, of the questions on the sheets before was the feedback 1316 01:09:09,180 --> 01:09:11,700 sheet, the person said, I've been using them in my class 1317 01:09:11,700 --> 01:09:12,560 and they've been really useful. 1318 01:09:12,560 --> 01:09:15,340 But I find that the response rate has been dropping. 1319 01:09:15,340 --> 01:09:16,819 What do you do about that? 1320 01:09:16,819 --> 01:09:19,840 And I have to say, that I found the same thing. 1321 01:09:19,840 --> 01:09:21,550 This year I found the same thing. 1322 01:09:21,550 --> 01:09:24,779 Not in this class but in my other class, whereas I didn't 1323 01:09:24,779 --> 01:09:25,630 find that last year. 1324 01:09:25,630 --> 01:09:26,850 And I was trying to figure out why. 1325 01:09:26,850 --> 01:09:29,410 And theory I have is that I was trying to put in too much 1326 01:09:29,410 --> 01:09:32,470 material in the class and not leaving the students time 1327 01:09:32,470 --> 01:09:36,020 before the five-minute mark to fill out the sheet. 1328 01:09:36,020 --> 01:09:39,790 So one thing, I've been trying to mend my ways and make sure 1329 01:09:39,790 --> 01:09:43,979 I end class at 9:50 or 10 minutes to the hour so the 1330 01:09:43,979 --> 01:09:46,160 students have at least one or two minutes to fill out the 1331 01:09:46,160 --> 01:09:47,910 sheet without feeling pressured to get 1332 01:09:47,910 --> 01:09:49,370 to their new class. 1333 01:09:49,370 --> 01:09:52,420 So I'll let you know how that goes over the next week. 1334 01:09:52,420 --> 01:09:56,250 So take a minute now and then that'll maybe make you think 1335 01:09:56,250 --> 01:09:57,760 of some questions which we can answer in 1336 01:09:57,760 --> 01:09:59,510 the next two minutes. 1337 01:09:59,510 --> 01:10:01,140 And then while you're doing that, just a couple 1338 01:10:01,140 --> 01:10:02,010 announcements. 1339 01:10:02,010 --> 01:10:05,890 So sorry I didn't say anything before about what to do with 1340 01:10:05,890 --> 01:10:08,160 the equation treatments that you shared with each other. 1341 01:10:08,160 --> 01:10:11,540 So just discuss them with each other. 1342 01:10:11,540 --> 01:10:12,750 You have a collaborator. 1343 01:10:12,750 --> 01:10:16,250 And then revise your treatment based on what 1344 01:10:16,250 --> 01:10:17,240 that person told you. 1345 01:10:17,240 --> 01:10:18,790 You don't have to turn in your revised treatment. 1346 01:10:18,790 --> 01:10:20,310 You guys are all graduate students, or 1347 01:10:20,310 --> 01:10:21,290 almost all of you. 1348 01:10:21,290 --> 01:10:23,600 You're all taking the class because you're interested. 1349 01:10:23,600 --> 01:10:24,900 I'm not trying to police everyone. 1350 01:10:24,900 --> 01:10:26,990 But the goal here, and what you should do, is take the 1351 01:10:26,990 --> 01:10:29,070 benefit of the collaboration, revise your equation 1352 01:10:29,070 --> 01:10:31,080 treatment, and share it with each other. 1353 01:10:31,080 --> 01:10:36,180 And then just bring in your original one next week. 1354 01:10:36,180 --> 01:10:40,290 And then I'll also have a couple of readings for you to 1355 01:10:40,290 --> 01:10:41,690 do for next week. 1356 01:10:41,690 --> 01:10:47,010 And also a short problem to work on, things to think about 1357 01:10:47,010 --> 01:10:49,710 to bring in next week as well. 1358 01:10:49,710 --> 01:10:53,674 OK, so sheets and then questions. 1359 01:10:53,674 --> 01:10:54,924 Question? 1360 01:10:57,578 --> 01:11:00,366 AUDIENCE: So I tried doing these sheets for a class that 1361 01:11:00,366 --> 01:11:01,970 I was teaching yesterday. 1362 01:11:01,970 --> 01:11:05,386 In fact, I found that I got a response rate of 15%. 1363 01:11:08,802 --> 01:11:12,605 If your response rate from the beginning's very low and 1364 01:11:12,605 --> 01:11:16,090 [INAUDIBLE] to increase that rate? 1365 01:11:16,090 --> 01:11:18,660 PROFESSOR: Right, so 15%, yeah, I find I'm getting that 1366 01:11:18,660 --> 01:11:19,530 around now too. 1367 01:11:19,530 --> 01:11:21,600 And I think what's happened is that I've got people in the 1368 01:11:21,600 --> 01:11:24,010 habit of not filling them out because I wasn't giving them 1369 01:11:24,010 --> 01:11:25,420 enough time. 1370 01:11:25,420 --> 01:11:28,830 So I may be hosed because now they're in the habit. 1371 01:11:28,830 --> 01:11:30,015 So I'm trying to mend it. 1372 01:11:30,015 --> 01:11:32,340 And I'll let you know if that fixes it by giving people 1373 01:11:32,340 --> 01:11:34,880 actual time before they feel rushed. 1374 01:11:34,880 --> 01:11:36,360 But it may be too late. 1375 01:11:36,360 --> 01:11:37,630 And I worry that it is too late. 1376 01:11:37,630 --> 01:11:39,870 Because last year I was actually more diligent about 1377 01:11:39,870 --> 01:11:41,250 making sure they had time. 1378 01:11:41,250 --> 01:11:44,420 And I found the response rate stayed about 60%, 70%. 1379 01:11:44,420 --> 01:11:47,710 But even I find the 15% very useful. 1380 01:11:47,710 --> 01:11:50,080 And I found that-- 1381 01:11:50,080 --> 01:11:52,970 people even in the past, when the response rate was 30% in 1382 01:11:52,970 --> 01:11:54,960 another class people said, I didn't have a 1383 01:11:54,960 --> 01:11:56,050 question all the time. 1384 01:11:56,050 --> 01:11:58,450 But I knew when I did I could ask it. 1385 01:11:58,450 --> 01:12:00,420 So even the 15% isn't bad. 1386 01:12:00,420 --> 01:12:01,670 It's still useful. 1387 01:12:01,670 --> 01:12:03,090 But yeah, I would like it to be higher. 1388 01:12:03,090 --> 01:12:06,108 And I'll tell you how that goes. 1389 01:12:06,108 --> 01:12:06,570 Question? 1390 01:12:06,570 --> 01:12:08,880 AUDIENCE: [INAUDIBLE]? 1391 01:12:08,880 --> 01:12:09,804 Wiggins and-- 1392 01:12:09,804 --> 01:12:10,900 PROFESSOR: McTighe, yeah. 1393 01:12:10,900 --> 01:12:13,640 AUDIENCE: Oh, McTighe. 1394 01:12:13,640 --> 01:12:14,960 Where are they based? 1395 01:12:14,960 --> 01:12:17,010 PROFESSOR: So where are they? 1396 01:12:17,010 --> 01:12:18,730 They're in New Jersey, and they actually consult on 1397 01:12:18,730 --> 01:12:23,230 educational course design and run workshops and courses. 1398 01:12:23,230 --> 01:12:24,770 And we actually invited Wiggins last 1399 01:12:24,770 --> 01:12:25,770 year to come and speak. 1400 01:12:25,770 --> 01:12:29,000 So I'll put a short reading selection from their book 1401 01:12:29,000 --> 01:12:33,870 called Understanding By Design for optional reading for 1402 01:12:33,870 --> 01:12:37,060 people so then you can learn more about that. 1403 01:12:37,060 --> 01:12:40,600 I find the basic form that they say very useful. 1404 01:12:40,600 --> 01:12:44,300 I find applying it the way they describe, sometimes I 1405 01:12:44,300 --> 01:12:45,750 just can't square it. 1406 01:12:45,750 --> 01:12:48,990 But it may resonate with you quite well. 1407 01:12:48,990 --> 01:12:50,820 And the overall approach resonates very 1408 01:12:50,820 --> 01:12:51,570 strongly with me. 1409 01:12:51,570 --> 01:12:53,410 So hopefully you will like it too. 1410 01:12:53,410 --> 01:12:56,820 So I'll put that on the website and some readings for 1411 01:12:56,820 --> 01:13:00,284 next time about course design. 1412 01:13:00,284 --> 01:13:00,780 Yes? 1413 01:13:00,780 --> 01:13:02,880 AUDIENCE: Just a comment, actually on your web page, 1414 01:13:02,880 --> 01:13:05,620 where the response sheet [INAUDIBLE] 1415 01:13:05,620 --> 01:13:09,644 and situation where only a few people were very dislike the 1416 01:13:09,644 --> 01:13:10,894 current [INAUDIBLE]. 1417 01:13:13,198 --> 01:13:16,010 They don't like it this way and so they want to change it. 1418 01:13:16,010 --> 01:13:18,714 But the 80% who don't feel [INAUDIBLE] is 1419 01:13:18,714 --> 01:13:20,090 actually OK with it. 1420 01:13:20,090 --> 01:13:20,640 [INAUDIBLE] the change. 1421 01:13:20,640 --> 01:13:22,730 It makes most people unhappy. 1422 01:13:22,730 --> 01:13:25,180 PROFESSOR: Unhappy, right, so that can happen. 1423 01:13:25,180 --> 01:13:28,480 And so that's the silent majority problem. 1424 01:13:28,480 --> 01:13:30,540 So what I do when I get comments like people saying, 1425 01:13:30,540 --> 01:13:32,500 well, I wasn't happy about this. 1426 01:13:32,500 --> 01:13:34,220 Sometimes what I do is-- 1427 01:13:34,220 --> 01:13:35,780 especially if it doesn't resonate with my intuition 1428 01:13:35,780 --> 01:13:37,470 about how things were going, and I thought 1429 01:13:37,470 --> 01:13:38,400 they were going well-- 1430 01:13:38,400 --> 01:13:41,950 I'll say, well, there were a few comments about this issue. 1431 01:13:41,950 --> 01:13:43,700 What do people think? 1432 01:13:43,700 --> 01:13:46,040 And just take an informal straw pole 1433 01:13:46,040 --> 01:13:47,636 before I make big changes. 1434 01:13:47,636 --> 01:13:49,872 AUDIENCE: I think it helps to have a positive question on 1435 01:13:49,872 --> 01:13:52,348 [INAUDIBLE], like, what did you take 1436 01:13:52,348 --> 01:13:53,324 away from this lecture? 1437 01:13:53,324 --> 01:13:54,300 Or what did you really understand? 1438 01:13:54,300 --> 01:13:55,630 PROFESSOR: Right, I think that's right. 1439 01:13:55,630 --> 01:13:57,050 It helps to have a positive question. 1440 01:13:57,050 --> 01:14:01,110 So that's why I say, either what you take away, or what 1441 01:14:01,110 --> 01:14:01,980 helped or hurt? 1442 01:14:01,980 --> 01:14:05,830 So there's an opportunity to say something helpful. 1443 01:14:05,830 --> 01:14:10,390 And any other comments is also interpreted in a positive way. 1444 01:14:10,390 --> 01:14:12,780 Answers from Lecture 5 to questions 1445 01:14:12,780 --> 01:14:14,340 generated in Lecture 4. 1446 01:14:16,944 --> 01:14:19,760 PROFESSOR: OK, and questions from last time. 1447 01:14:19,760 --> 01:14:23,340 So they grouped into several ones. 1448 01:14:23,340 --> 01:14:29,300 One is how should you choose your levels of your problems-- 1449 01:14:29,300 --> 01:14:31,200 say, in class or in homeworks-- among the 1450 01:14:31,200 --> 01:14:34,470 different levels of Bloom's Taxonomy? 1451 01:14:34,470 --> 01:14:38,620 Should it be, for example all towards the evaluation? 1452 01:14:38,620 --> 01:14:41,340 So your side would be here, sort of the high level. 1453 01:14:41,340 --> 01:14:42,370 A Mix? 1454 01:14:42,370 --> 01:14:43,090 A flat mix? 1455 01:14:43,090 --> 01:14:45,770 Should it be peaked towards the middle with some tails? 1456 01:14:45,770 --> 01:14:49,700 So that depends, partly, on your course design. 1457 01:14:49,700 --> 01:14:52,110 So to answer that question, you can't really answer that 1458 01:14:52,110 --> 01:14:55,360 question until you figure out what your course goals are. 1459 01:14:55,360 --> 01:14:58,800 So in some ways there's an argument for doing course 1460 01:14:58,800 --> 01:15:03,320 design first and then working on what problems to do and how 1461 01:15:03,320 --> 01:15:04,470 to design problems. 1462 01:15:04,470 --> 01:15:06,410 But actually, I like the other way around. 1463 01:15:06,410 --> 01:15:08,400 I like doing course design second. 1464 01:15:08,400 --> 01:15:11,020 Because actually, doing problems is concrete enough to 1465 01:15:11,020 --> 01:15:11,800 do something. 1466 01:15:11,800 --> 01:15:16,130 And then it leads to questions about course design, which 1467 01:15:16,130 --> 01:15:19,650 we'll answer how to mix the levels. 1468 01:15:19,650 --> 01:15:25,380 OK, another one was several people wanted to know, why is 1469 01:15:25,380 --> 01:15:27,640 tension not a force? 1470 01:15:27,640 --> 01:15:29,130 Or in fact, maybe is a force. 1471 01:15:29,130 --> 01:15:30,390 So let me explain that. 1472 01:15:30,390 --> 01:15:33,680 Because that actually gives you another example of sorting 1473 01:15:33,680 --> 01:15:34,700 out misconceptions. 1474 01:15:34,700 --> 01:15:35,690 So it's always useful. 1475 01:15:35,690 --> 01:15:38,820 So I'll show you the sequence of questions I used with 1476 01:15:38,820 --> 01:15:41,910 myself when I finally convinced that 1477 01:15:41,910 --> 01:15:43,360 tension wasn't a force. 1478 01:15:43,360 --> 01:15:46,230 And here's how I did it. 1479 01:15:46,230 --> 01:15:49,230 And then I used the same sequence of questions with 1480 01:15:49,230 --> 01:15:51,550 students to fight the misconception that's been 1481 01:15:51,550 --> 01:15:54,260 induced by many pictures of-- 1482 01:15:54,260 --> 01:15:55,920 for example-- a pulley. 1483 01:15:55,920 --> 01:16:00,170 And here's a rope and there's tension. 1484 01:16:00,170 --> 01:16:01,440 Sorry, this is actually done the other way. 1485 01:16:01,440 --> 01:16:02,690 So here's the rope. 1486 01:16:05,140 --> 01:16:07,010 And there's a t labeled there. 1487 01:16:07,010 --> 01:16:11,430 And then on the mass there's a force labeled as t upward. 1488 01:16:11,430 --> 01:16:13,565 So when you see that you think, oh, tension's a force. 1489 01:16:13,565 --> 01:16:15,250 So you see that a whole bunch of times and you're pretty 1490 01:16:15,250 --> 01:16:16,460 sure of it. 1491 01:16:16,460 --> 01:16:21,060 So the sequence of questions is as follows-- 1492 01:16:21,060 --> 01:16:27,210 say OK, here's a tree. 1493 01:16:31,800 --> 01:16:37,840 And I'm going to tie a rope to the tree, rope or a string, 1494 01:16:37,840 --> 01:16:39,590 it's a mass-less thing. 1495 01:16:39,590 --> 01:16:40,900 And I put a force on it. 1496 01:16:45,880 --> 01:16:48,130 OK, so I'm going to pull that tree. 1497 01:16:48,130 --> 01:16:49,250 The tree's not going to go anywhere. 1498 01:16:49,250 --> 01:16:50,500 We're going to pull on the rope with 1499 01:16:50,500 --> 01:16:52,240 100 newtons of force. 1500 01:16:52,240 --> 01:16:55,910 OK, so you can try this yourself too. 1501 01:16:55,910 --> 01:16:57,350 What's the tension in the string? 1502 01:17:01,660 --> 01:17:05,880 OK, so take 30 seconds and I'll take a tension. 1503 01:17:11,220 --> 01:17:12,470 OK, a tension, anyone? 1504 01:17:21,204 --> 01:17:22,945 AUDIENCE: 100 newtons. 1505 01:17:22,945 --> 01:17:27,570 PROFESSOR: OK, so in fact that is 100 newtons. 1506 01:17:27,570 --> 01:17:29,140 And most people will say 100 newtons. 1507 01:17:29,140 --> 01:17:32,770 OK, so now the next question is this-- 1508 01:17:32,770 --> 01:17:43,010 here is a river and here's a rope. 1509 01:17:43,010 --> 01:17:52,660 And me and a friend each pull on the rope with 100 newtons. 1510 01:17:52,660 --> 01:17:53,910 OK? 1511 01:18:03,800 --> 01:18:07,350 OK, so discuss with your neighbor-- 1512 01:18:07,350 --> 01:18:10,800 a, b, or c, what's the tension in the rope? 1513 01:18:10,800 --> 01:18:12,050 And we'll take a vote. 1514 01:18:14,770 --> 01:18:19,200 OK, so take 10 seconds, get your vote ready. 1515 01:18:19,200 --> 01:18:23,440 We'll take a quick straw pole. 1516 01:18:23,440 --> 01:18:24,980 Who votes for 0 newtons? 1517 01:18:30,040 --> 01:18:31,345 Who votes for 100 newtons? 1518 01:18:36,420 --> 01:18:38,210 Who votes for 200 newtons? 1519 01:18:42,190 --> 01:18:48,820 OK, so now here, how do you know what it's going to be? 1520 01:18:48,820 --> 01:18:50,320 Well, you make a force diagram. 1521 01:18:50,320 --> 01:18:53,090 And there's a way to convince yourself that there's no doubt 1522 01:18:53,090 --> 01:18:54,560 about what it should be. 1523 01:18:54,560 --> 01:18:56,630 And we just draw the forces on the rope here. 1524 01:18:56,630 --> 01:18:58,140 Oh, we've already done that. 1525 01:18:58,140 --> 01:18:59,730 Let's draw the forces on the rope up there. 1526 01:19:07,640 --> 01:19:09,230 Well, what are the forces on the rope here? 1527 01:19:09,230 --> 01:19:11,520 Well, it's 100 newtons from you. 1528 01:19:11,520 --> 01:19:13,620 But there must also be 100 newtons from the tree. 1529 01:19:16,290 --> 01:19:16,740 All right? 1530 01:19:16,740 --> 01:19:20,350 So in fact, these two situations are identical. 1531 01:19:20,350 --> 01:19:22,415 So yeah, 100 newtons seems pretty clear here. 1532 01:19:22,415 --> 01:19:24,670 So it has to be 100 newtons up there too. 1533 01:19:28,590 --> 01:19:30,930 OK, now that-- 1534 01:19:30,930 --> 01:19:32,410 so far-- isn't the hard part. 1535 01:19:32,410 --> 01:19:36,320 But now is when you actually create the contradiction with 1536 01:19:36,320 --> 01:19:37,540 the idea of it being a force. 1537 01:19:37,540 --> 01:19:42,480 It can't be a force because if it were a force you would just 1538 01:19:42,480 --> 01:19:44,700 add up vectors. 1539 01:19:44,700 --> 01:19:44,940 Right? 1540 01:19:44,940 --> 01:19:47,570 So there's a couple answers you get if it was a force. 1541 01:19:47,570 --> 01:19:49,960 If you're a bit sloppy you'd just add up the magnitudes and 1542 01:19:49,960 --> 01:19:51,870 get 200 newtons. 1543 01:19:51,870 --> 01:19:53,460 If it's really a vector-- 1544 01:19:53,460 --> 01:19:55,260 you're putting two vectors on it, two forces-- 1545 01:19:55,260 --> 01:19:57,440 you should get 0 because they're two opposite forces. 1546 01:19:57,440 --> 01:19:59,460 But actually you get 100. 1547 01:19:59,460 --> 01:20:01,630 The only way to get 100 is that the tension has to be 1548 01:20:01,630 --> 01:20:03,810 something completely different from a force. 1549 01:20:03,810 --> 01:20:05,610 So that's how you know it's not a force. 1550 01:20:05,610 --> 01:20:06,880 But how do what it is? 1551 01:20:06,880 --> 01:20:12,170 Well, it turns out to be a tensor. 1552 01:20:12,170 --> 01:20:13,310 So it's not a vector. 1553 01:20:13,310 --> 01:20:14,320 Forces are vectors. 1554 01:20:14,320 --> 01:20:17,960 It adds differently than vectors do. 1555 01:20:17,960 --> 01:20:19,730 It adds like a tensor. 1556 01:20:19,730 --> 01:20:23,130 So tension is more like a pressure. 1557 01:20:23,130 --> 01:20:25,190 It doesn't have a particular direction. 1558 01:20:25,190 --> 01:20:26,560 Pressure is in all directions. 1559 01:20:26,560 --> 01:20:29,590 So things like that, they can't be described by vectors. 1560 01:20:29,590 --> 01:20:30,610 So you need something else. 1561 01:20:30,610 --> 01:20:32,520 And that's why we introduced tensors. 1562 01:20:32,520 --> 01:20:35,010 So now, in freshman physics I wouldn't give them a whole 1563 01:20:35,010 --> 01:20:36,360 story about tensors. 1564 01:20:36,360 --> 01:20:40,650 But I do actually teach this much of it so that they know 1565 01:20:40,650 --> 01:20:42,230 that is a different object. 1566 01:20:42,230 --> 01:20:44,880 And then what do I do about this? 1567 01:20:44,880 --> 01:20:50,840 Well, I won't write t unless it's for myself. 1568 01:20:50,840 --> 01:20:53,180 But for the students I think it's sloppy and it increases 1569 01:20:53,180 --> 01:20:54,300 misconception. 1570 01:20:54,300 --> 01:20:58,020 It's much better to write the force sub t, which is the 1571 01:20:58,020 --> 01:20:59,630 force due to tension. 1572 01:20:59,630 --> 01:21:00,030 OK? 1573 01:21:00,030 --> 01:21:03,170 So even a slight change like that can mitigate the rote 1574 01:21:03,170 --> 01:21:05,930 learning, where people think oh, tension's a force. 1575 01:21:05,930 --> 01:21:08,100 Because you always see it drawn like every other force. 1576 01:21:08,100 --> 01:21:14,077 There's mg down, There's t up, must be a force too. 1577 01:21:14,077 --> 01:21:15,327 AUDIENCE: [INAUDIBLE]? 1578 01:21:22,170 --> 01:21:25,120 PROFESSOR: What are the two objects you hit it with to 1579 01:21:25,120 --> 01:21:26,370 make a scalar? 1580 01:21:29,890 --> 01:21:31,920 It's the two directions that you're 1581 01:21:31,920 --> 01:21:33,600 interested in, basically. 1582 01:21:33,600 --> 01:21:39,210 So it would be the x direction or the direction along the 1583 01:21:39,210 --> 01:21:42,854 string and the direction along the string. 1584 01:21:42,854 --> 01:21:45,546 AUDIENCE: So it's the two direction then? 1585 01:21:45,546 --> 01:21:48,700 PROFESSOR: You can use the same direction twice. 1586 01:21:48,700 --> 01:21:49,840 So it's the direction along the string 1587 01:21:49,840 --> 01:21:50,560 and along the string. 1588 01:21:50,560 --> 01:21:53,620 There's no cross direction. 1589 01:21:53,620 --> 01:21:54,580 So it has no shear. 1590 01:21:54,580 --> 01:21:56,700 So there's no cross direction. 1591 01:21:56,700 --> 01:21:59,880 So it's some component, tension is one component of 1592 01:21:59,880 --> 01:22:02,530 the stress tensor. 1593 01:22:02,530 --> 01:22:04,895 So now, again, freshman don't need to know all the details. 1594 01:22:08,030 --> 01:22:13,980 This is back to the subject of lying they do need to not be 1595 01:22:13,980 --> 01:22:15,310 told fundamental lies. 1596 01:22:15,310 --> 01:22:20,080 Like for example, tension is a force. 1597 01:22:20,080 --> 01:22:24,520 OK, so now, how do you deal with misconceptions that show 1598 01:22:24,520 --> 01:22:25,880 up on problem sets? 1599 01:22:25,880 --> 01:22:26,690 This is a good question. 1600 01:22:26,690 --> 01:22:29,150 So the point was made well, in class you can sort it out 1601 01:22:29,150 --> 01:22:29,630 right then. 1602 01:22:29,630 --> 01:22:32,030 Suppose you ask a question, say, about the Ideal Gas Law. 1603 01:22:32,030 --> 01:22:34,760 And you find that people have confused the Ideal Gas Law and 1604 01:22:34,760 --> 01:22:35,910 the Adiabatic Gas Law. 1605 01:22:35,910 --> 01:22:38,050 Well, you can talk about it right then, which is a good 1606 01:22:38,050 --> 01:22:39,740 reason to do those things in class. 1607 01:22:39,740 --> 01:22:41,900 What happens on the problem set if you find there's a 1608 01:22:41,900 --> 01:22:43,120 bunch of misconceptions? 1609 01:22:43,120 --> 01:22:45,860 Well, one thing is, the first time you do the problem set, 1610 01:22:45,860 --> 01:22:46,830 yeah it's a bit of a problem. 1611 01:22:46,830 --> 01:22:49,180 Because you don't know what the misconceptions are unless 1612 01:22:49,180 --> 01:22:51,260 you've researched ahead of time. 1613 01:22:51,260 --> 01:22:54,660 But the second time you do the class you know what they are. 1614 01:22:54,660 --> 01:22:56,700 So you can address the misconceptions in 1615 01:22:56,700 --> 01:22:58,040 the solution set. 1616 01:22:58,040 --> 01:23:01,870 So when I'm not totally sleep deprived I always try to get 1617 01:23:01,870 --> 01:23:05,110 the solution set out the exact same day that the problem set 1618 01:23:05,110 --> 01:23:05,880 is turned in. 1619 01:23:05,880 --> 01:23:07,840 So the students can right away see. 1620 01:23:07,840 --> 01:23:09,920 They can turn in their problem set, pick up a solution set or 1621 01:23:09,920 --> 01:23:11,330 look at it online. 1622 01:23:11,330 --> 01:23:13,390 So they can right away get quick feedback. 1623 01:23:13,390 --> 01:23:17,710 And they can sort out the misconceptions that way. 1624 01:23:17,710 --> 01:23:20,050 So that's a good question. 1625 01:23:20,050 --> 01:23:20,860 So it is harder. 1626 01:23:20,860 --> 01:23:21,480 Yes, question? 1627 01:23:21,480 --> 01:23:25,316 AUDIENCE: What do you do about the fact that a lot of people 1628 01:23:25,316 --> 01:23:27,842 will just ignore the solution sets? 1629 01:23:27,842 --> 01:23:31,050 Or do you just consider that their problem? 1630 01:23:31,050 --> 01:23:33,300 PROFESSOR: So the question is, what do I do about people who 1631 01:23:33,300 --> 01:23:34,540 just ignore the solution sets? 1632 01:23:34,540 --> 01:23:35,930 Because a lot of students do that. 1633 01:23:35,930 --> 01:23:40,200 Yeah, partly I consider it their problem. 1634 01:23:40,200 --> 01:23:43,420 Because look, that's there for them to learn. 1635 01:23:43,420 --> 01:23:46,640 But partly, to the extent that they're ignoring the solution 1636 01:23:46,640 --> 01:23:49,140 set because they only cared about the grade. 1637 01:23:49,140 --> 01:23:50,970 So one cause of that is they really only 1638 01:23:50,970 --> 01:23:51,760 care about the grade. 1639 01:23:51,760 --> 01:23:54,050 So they just want to wait for the grader to give them back 1640 01:23:54,050 --> 01:23:57,440 their solutions, their problem set with a mark on it. 1641 01:23:57,440 --> 01:23:59,060 And they don't care what's right and wrong. 1642 01:23:59,060 --> 01:24:01,390 That, I think, partly, is our responsibility that we've 1643 01:24:01,390 --> 01:24:04,620 chosen boring problems. 1644 01:24:04,620 --> 01:24:08,300 So to fix that, I think, one of the key areas is to use 1645 01:24:08,300 --> 01:24:10,650 more of the Bloom's Taxonomy and make interesting problems. 1646 01:24:10,650 --> 01:24:14,420 And the flip side is to deemphasize the grading. 1647 01:24:14,420 --> 01:24:17,770 So actually, I like the PDF scale on homework. 1648 01:24:17,770 --> 01:24:20,180 I think we are too micromanaging, generally, 1649 01:24:20,180 --> 01:24:22,150 about homework, you know, grading it on a percentage 1650 01:24:22,150 --> 01:24:26,070 scale, on A, B, C, D. P, you did a reasonable. 1651 01:24:26,070 --> 01:24:29,290 And D, you blew it off. 1652 01:24:29,290 --> 01:24:30,810 You did something but it was a joke. 1653 01:24:30,810 --> 01:24:32,660 And F, you didn't turn it in. 1654 01:24:32,660 --> 01:24:35,910 I think that scale puts the right emphasis on the grading. 1655 01:24:35,910 --> 01:24:38,590 Look, we just want you to do the thing and try it. 1656 01:24:38,590 --> 01:24:42,160 And if the problems are interesting that allows people 1657 01:24:42,160 --> 01:24:43,840 to actually get involved in it. 1658 01:24:43,840 --> 01:24:47,010 So there's lots of studies that show that if you reward 1659 01:24:47,010 --> 01:24:49,570 people for things they already enjoy-- 1660 01:24:49,570 --> 01:24:51,580 so you start paying them more for doing things they really 1661 01:24:51,580 --> 01:24:54,551 like-- they actually start liking them less. 1662 01:24:54,551 --> 01:24:57,250 So I'll talk about that as one of the political barriers to 1663 01:24:57,250 --> 01:24:58,080 educational change. 1664 01:24:58,080 --> 01:25:01,550 Because that's completely against the conventional 1665 01:25:01,550 --> 01:25:04,210 psychology of this society, where everything has to be 1666 01:25:04,210 --> 01:25:06,280 rewarded, merit-based pay and this and that. 1667 01:25:06,280 --> 01:25:07,560 So how do you go against that? 1668 01:25:07,560 --> 01:25:08,770 It's quite difficult. 1669 01:25:08,770 --> 01:25:11,550 But one way, in general, in those problem sets is to 1670 01:25:11,550 --> 01:25:13,030 deemphasize the grading. 1671 01:25:13,030 --> 01:25:14,140 Related method-- 1672 01:25:14,140 --> 01:25:16,730 which I haven't tried yet but I'm planning to-- 1673 01:25:16,730 --> 01:25:19,540 is reading memos on the solution set. 1674 01:25:19,540 --> 01:25:21,720 So I talked about reading memos before. 1675 01:25:21,720 --> 01:25:24,250 And maybe one of you will try it before me and can tell me 1676 01:25:24,250 --> 01:25:24,970 how it works. 1677 01:25:24,970 --> 01:25:25,710 A reading memo is-- 1678 01:25:25,710 --> 01:25:28,710 I talked about-- where you have the students take a 1679 01:25:28,710 --> 01:25:31,690 reading and mark-- either online or 1680 01:25:31,690 --> 01:25:32,980 on a piece of paper-- 1681 01:25:32,980 --> 01:25:35,360 things that were confusing or things that were interesting 1682 01:25:35,360 --> 01:25:37,610 and things they noticed. 1683 01:25:37,610 --> 01:25:39,980 Well, you can do that with the solution set too. 1684 01:25:39,980 --> 01:25:44,870 You say, OK, your assignment, homework 3A is to look at the 1685 01:25:44,870 --> 01:25:47,230 solution set for homework two and mark 1686 01:25:47,230 --> 01:25:48,890 anything that's confusing. 1687 01:25:48,890 --> 01:25:51,200 So that forces people to read the solution set. 1688 01:25:51,200 --> 01:25:53,615 And often what you'll find is that they'll find mistakes in 1689 01:25:53,615 --> 01:25:56,210 the solution set, which is good to know because you can 1690 01:25:56,210 --> 01:25:57,120 correct them right away. 1691 01:25:57,120 --> 01:26:01,028 But you'll see what parts are confusing to students or not. 1692 01:26:01,028 --> 01:26:02,880 Did that help answer your question? 1693 01:26:02,880 --> 01:26:05,290 Great. 1694 01:26:05,290 --> 01:26:07,480 Do I ever asked Wheeler's question explicitly? 1695 01:26:07,480 --> 01:26:09,140 Yes, sometimes. 1696 01:26:09,140 --> 01:26:11,610 I should do it more in class in lecture. 1697 01:26:11,610 --> 01:26:13,380 But I do it a lot to myself. 1698 01:26:13,380 --> 01:26:15,090 Whenever I solve a problem I think oh, 1699 01:26:15,090 --> 01:26:16,590 what was the key idea? 1700 01:26:16,590 --> 01:26:20,440 And then once I see the key idea happen many times I think 1701 01:26:20,440 --> 01:26:21,830 oh, that's a very key idea. 1702 01:26:21,830 --> 01:26:24,190 That should be taught explicitly in class. 1703 01:26:24,190 --> 01:26:25,190 So I do that. 1704 01:26:25,190 --> 01:26:27,100 And I'm going to talk about that principle of course 1705 01:26:27,100 --> 01:26:29,990 design today, basically organizing courses around 1706 01:26:29,990 --> 01:26:32,980 large themes and principles, which is one of the main 1707 01:26:32,980 --> 01:26:35,850 [? cures. ?] 1708 01:26:35,850 --> 01:26:39,730 OK, so what's wrong with tension as a force? 1709 01:26:39,730 --> 01:26:43,380 How far should I go down the taxonomy? 1710 01:26:43,380 --> 01:26:46,290 Basically, where in the course should I be? 1711 01:26:46,290 --> 01:26:49,150 Really low in the taxonomy early and higher later? 1712 01:26:49,150 --> 01:26:50,650 Well, I talked about that a bit last time. 1713 01:26:50,650 --> 01:26:52,560 The fractal picture is not bad. 1714 01:26:52,560 --> 01:26:56,600 So yeah, you have a few low-level examples and 1715 01:26:56,600 --> 01:26:57,530 higher-level examples. 1716 01:26:57,530 --> 01:26:59,560 But you do that throughout the course. 1717 01:26:59,560 --> 01:27:01,200 So you don't wait until the end of the course to get the 1718 01:27:01,200 --> 01:27:05,120 reward of the really interesting problems. 1719 01:27:05,120 --> 01:27:08,350 And then related to that, what about exams and homework? 1720 01:27:08,350 --> 01:27:10,500 Should they be the same or different? 1721 01:27:10,500 --> 01:27:14,380 My view is they should be the same given the constraint that 1722 01:27:14,380 --> 01:27:16,200 maybe the exam is done in a shorter time. 1723 01:27:16,200 --> 01:27:17,460 So if anything, the exam should be 1724 01:27:17,460 --> 01:27:19,190 easier than the homework. 1725 01:27:19,190 --> 01:27:21,010 Generally, homework people will spend six 1726 01:27:21,010 --> 01:27:23,070 or seven hours on. 1727 01:27:23,070 --> 01:27:25,160 When I was an undergraduate we had take-home exams. 1728 01:27:25,160 --> 01:27:26,680 And we would spend 24 hours on them. 1729 01:27:26,680 --> 01:27:27,900 You pick them up, you signed it out. 1730 01:27:27,900 --> 01:27:29,070 You'd turned it in in 24 hours. 1731 01:27:29,070 --> 01:27:30,200 So that was misery. 1732 01:27:30,200 --> 01:27:31,680 And it was interesting. 1733 01:27:31,680 --> 01:27:32,430 You learnt a lot. 1734 01:27:32,430 --> 01:27:34,670 But it was kind of miserable because it just wiped out a 1735 01:27:34,670 --> 01:27:36,960 whole day from your quarter. 1736 01:27:36,960 --> 01:27:38,285 And you had that for four classes. 1737 01:27:38,285 --> 01:27:40,950 So four days from your quarter were just gone. 1738 01:27:40,950 --> 01:27:44,220 So generally, exams are three hours, maybe two hours. 1739 01:27:44,220 --> 01:27:46,430 And so that's much less time than a homework set. 1740 01:27:46,430 --> 01:27:48,600 So if anything, exams should be easier, 1741 01:27:48,600 --> 01:27:49,860 definitely not harder. 1742 01:27:49,860 --> 01:27:53,210 Student loath when the exam does different things than the 1743 01:27:53,210 --> 01:27:54,700 problem sets. 1744 01:27:54,700 --> 01:27:56,850 And that is a general principle of course design, 1745 01:27:56,850 --> 01:27:58,720 that if you want to prepare them for being able to do 1746 01:27:58,720 --> 01:28:00,580 stuff-- for example on the exam-- 1747 01:28:00,580 --> 01:28:02,110 you have to prepare them with things. 1748 01:28:02,110 --> 01:28:04,560 You have to "teach to the test." That's actually good. 1749 01:28:04,560 --> 01:28:06,940 You want your homeworks to be like the exam. 1750 01:28:06,940 --> 01:28:09,580 And that's fine if the test is good. 1751 01:28:09,580 --> 01:28:12,770 If the test tests real-world, interesting skills sure, then 1752 01:28:12,770 --> 01:28:14,610 it's fine to teach the test because they'll come out being 1753 01:28:14,610 --> 01:28:16,290 able to do that, no problem. 1754 01:28:16,290 --> 01:28:18,580 So the exam and homework-- as a rough rule of function-- 1755 01:28:18,580 --> 01:28:19,770 will be pretty much the same. 1756 01:28:19,770 --> 01:28:21,790 Or if anything, the exam should be easier. 1757 01:28:32,880 --> 01:28:35,150 Oh yeah, the first time you teach a class. 1758 01:28:35,150 --> 01:28:38,000 So all this Bloom's Taxonomy and designing questions, it 1759 01:28:38,000 --> 01:28:38,860 takes a long time. 1760 01:28:38,860 --> 01:28:40,580 And it's really hard to make good questions. 1761 01:28:40,580 --> 01:28:43,040 It's easy to make define XYZ questions. 1762 01:28:43,040 --> 01:28:44,710 But what about the higher-level questions? 1763 01:28:44,710 --> 01:28:47,620 What do you do to mitigate that problem of a 1764 01:28:47,620 --> 01:28:49,550 huge amount of time? 1765 01:28:49,550 --> 01:28:53,850 Well, one of the cures is to cooperate with other teachers. 1766 01:28:53,850 --> 01:28:55,870 So you steal their good problems. 1767 01:28:55,870 --> 01:28:58,830 So I gave you the T.S. Eliot saying before, that talent 1768 01:28:58,830 --> 01:29:00,850 invents and genius steals. 1769 01:29:00,850 --> 01:29:03,070 So be a genius. 1770 01:29:03,070 --> 01:29:05,010 Whenever you see a good problem just use it. 1771 01:29:05,010 --> 01:29:07,590 And whenever someone wants a good problem, if you 1772 01:29:07,590 --> 01:29:09,050 have one, share it. 1773 01:29:09,050 --> 01:29:11,830 And now, should you guard your problems? 1774 01:29:11,830 --> 01:29:17,030 I think those days of guarding problems are gone. 1775 01:29:17,030 --> 01:29:20,840 They've gone by because of things like OpenCourseWare, 1776 01:29:20,840 --> 01:29:22,610 putting problem sets online. 1777 01:29:22,610 --> 01:29:24,980 It's just not possible anymore to guard problems. 1778 01:29:24,980 --> 01:29:26,500 I'm not sure it was ever a good idea. 1779 01:29:26,500 --> 01:29:28,290 But now it's not even practical. 1780 01:29:28,290 --> 01:29:32,940 So everything is online, all from the previous year. 1781 01:29:32,940 --> 01:29:34,760 So the problems can't be guarded. 1782 01:29:34,760 --> 01:29:37,480 And it's not practical to make up a whole set of new good 1783 01:29:37,480 --> 01:29:38,830 problems for the next year. 1784 01:29:38,830 --> 01:29:40,730 You'll never sleep. 1785 01:29:40,730 --> 01:29:45,050 So I just trust the students not to cheat by looking at the 1786 01:29:45,050 --> 01:29:46,280 old solution sets. 1787 01:29:46,280 --> 01:29:51,550 And if you're grading, that's yet another reason to minimize 1788 01:29:51,550 --> 01:29:53,350 how strict the grading is. 1789 01:29:53,350 --> 01:29:55,740 So if the grading is really, just that they make an effort 1790 01:29:55,740 --> 01:29:58,410 and try to learn something, then there's no benefit to 1791 01:29:58,410 --> 01:30:01,080 cheating and looking at the old solution sets. 1792 01:30:01,080 --> 01:30:05,220 So you actually make the incentive structure so that 1793 01:30:05,220 --> 01:30:06,280 they don't need to do all that. 1794 01:30:06,280 --> 01:30:06,700 Question? 1795 01:30:06,700 --> 01:30:08,197 AUDIENCE: Do you have to change your problem to a 1796 01:30:08,197 --> 01:30:11,357 certain extent in terms of plagiarism? 1797 01:30:14,145 --> 01:30:16,000 PROFESSOR: So the question is, do I have to change the 1798 01:30:16,000 --> 01:30:18,560 problems to a certain extent to avoid plagiarism? 1799 01:30:18,560 --> 01:30:19,770 I don't even care. 1800 01:30:19,770 --> 01:30:20,980 I don't even change them. 1801 01:30:20,980 --> 01:30:24,060 I think, again, it's sort of what Adrian has said, is it 1802 01:30:24,060 --> 01:30:25,330 their problem if they do it? 1803 01:30:25,330 --> 01:30:27,240 And to some extent it is their problem. 1804 01:30:27,240 --> 01:30:30,390 If they're going to cheat and look at the old solution set 1805 01:30:30,390 --> 01:30:33,020 and not acknowledge it. 1806 01:30:33,020 --> 01:30:34,970 There's only so much you can do. 1807 01:30:34,970 --> 01:30:38,550 And you then get in an arms race with them. 1808 01:30:38,550 --> 01:30:40,870 You change the problem to some extent. 1809 01:30:40,870 --> 01:30:43,370 But then someone else makes it. 1810 01:30:43,370 --> 01:30:44,670 So they can always subvert that. 1811 01:30:44,670 --> 01:30:46,700 One person can solve the new problem and give it to 1812 01:30:46,700 --> 01:30:47,800 everybody else. 1813 01:30:47,800 --> 01:30:52,030 So you have no hope of actually winning that war, 1814 01:30:52,030 --> 01:30:54,470 even if it were a moral war to try to win. 1815 01:30:54,470 --> 01:30:55,610 So I don't even change them. 1816 01:30:55,610 --> 01:30:57,500 And I say look, just acknowledge, just like you 1817 01:30:57,500 --> 01:30:59,620 would in science. 1818 01:30:59,620 --> 01:31:03,230 I think it's Larry Lessig, the copyright scholar, 1819 01:31:03,230 --> 01:31:04,210 professor of law. 1820 01:31:04,210 --> 01:31:04,980 He used to be at Harvard. 1821 01:31:04,980 --> 01:31:06,170 Now it's Stanford. 1822 01:31:06,170 --> 01:31:10,640 He founded Creative Commons and various fantastic 1823 01:31:10,640 --> 01:31:11,410 copyright projects. 1824 01:31:11,410 --> 01:31:15,650 So he said, well, there's a couple ways to get-- not 1825 01:31:15,650 --> 01:31:16,560 compliance-- 1826 01:31:16,560 --> 01:31:17,460 people to do things. 1827 01:31:17,460 --> 01:31:20,360 One is you can do it through rules. 1828 01:31:20,360 --> 01:31:21,580 For example, this is illegal. 1829 01:31:21,580 --> 01:31:23,390 You just can't do this. 1830 01:31:23,390 --> 01:31:24,657 We'll punish you if you do this. 1831 01:31:24,657 --> 01:31:26,360 The other one is through norm. 1832 01:31:26,360 --> 01:31:28,120 So this is just not done. 1833 01:31:28,120 --> 01:31:30,690 In our community we just don't do things like that. 1834 01:31:30,690 --> 01:31:33,560 And generally, this kind of-- not exhortation-- 1835 01:31:33,560 --> 01:31:38,940 but push works much better than the punishment kind. 1836 01:31:38,940 --> 01:31:44,260 So I just tell them, look, in science when you grow up and 1837 01:31:44,260 --> 01:31:48,300 become a scientist of course you acknowledge your peers and 1838 01:31:48,300 --> 01:31:49,140 people you learn from. 1839 01:31:49,140 --> 01:31:50,640 Because that's just polite. 1840 01:31:50,640 --> 01:31:51,910 It's just how we are. 1841 01:31:51,910 --> 01:31:52,830 We say, please. 1842 01:31:52,830 --> 01:31:55,090 We don't say gimme, gimme, gimme. 1843 01:31:55,090 --> 01:31:56,860 I'm working on teaching my daughter that right now. 1844 01:31:56,860 --> 01:31:59,490 She says, daddy read. 1845 01:31:59,490 --> 01:32:00,020 Daddy read. 1846 01:32:00,020 --> 01:32:00,780 Mommy read. 1847 01:32:00,780 --> 01:32:01,600 Elsa read. 1848 01:32:01,600 --> 01:32:02,990 I'm like OK, I'm fine with the Elsa read. 1849 01:32:02,990 --> 01:32:04,530 But daddy read, mommy read, that's nice. 1850 01:32:04,530 --> 01:32:05,320 And we love reading. 1851 01:32:05,320 --> 01:32:07,660 But how do you ask? 1852 01:32:07,660 --> 01:32:10,410 And now she says mommy read please, daddy read please. 1853 01:32:10,410 --> 01:32:13,380 And so it's the start. 1854 01:32:13,380 --> 01:32:15,170 So people already learnt that from young. 1855 01:32:15,170 --> 01:32:16,380 So you can tap into that. 1856 01:32:16,380 --> 01:32:19,370 Look, how do you act as a member of the community? 1857 01:32:19,370 --> 01:32:20,320 We're social animals. 1858 01:32:20,320 --> 01:32:21,320 So you don't have to put too much 1859 01:32:21,320 --> 01:32:22,660 pressure in that direction. 1860 01:32:22,660 --> 01:32:24,490 Whereas if you try to do it through a punishment you have 1861 01:32:24,490 --> 01:32:26,760 to work much harder. 1862 01:32:26,760 --> 01:32:29,030 The punishment one-- 1863 01:32:29,030 --> 01:32:29,650 underneath-- 1864 01:32:29,650 --> 01:32:32,670 has the idea that we don't trust the students. 1865 01:32:32,670 --> 01:32:32,870 Right? 1866 01:32:32,870 --> 01:32:36,250 And in that way it's common with changing the numbers on 1867 01:32:36,250 --> 01:32:38,420 the problems set. 1868 01:32:38,420 --> 01:32:41,130 It's that we don't trust you so we're changing the numbers. 1869 01:32:41,130 --> 01:32:45,550 So I try to avoid those things as much as possible and try to 1870 01:32:45,550 --> 01:32:47,170 go more towards this. 1871 01:32:47,170 --> 01:32:47,620 Yes? 1872 01:32:47,620 --> 01:32:50,987 AUDIENCE: Has anyone tried to have problem 1873 01:32:50,987 --> 01:32:52,430 sets without solutions? 1874 01:32:52,430 --> 01:32:56,278 So then there's no grading. 1875 01:32:56,278 --> 01:32:59,660 And then the problem sets are just for practicing. 1876 01:32:59,660 --> 01:33:03,090 PROFESSOR: Yeah, have problem sets for practice with no 1877 01:33:03,090 --> 01:33:05,600 solutions or no grading on the problem sets? 1878 01:33:05,600 --> 01:33:06,410 Have people tried that? 1879 01:33:06,410 --> 01:33:08,020 So there's actually whole educational 1880 01:33:08,020 --> 01:33:09,540 systems based on that. 1881 01:33:09,540 --> 01:33:12,580 Not so much in America, but in England, the Oxford and 1882 01:33:12,580 --> 01:33:14,520 Cambridge tutorial system. 1883 01:33:14,520 --> 01:33:16,030 You're given problems to work on. 1884 01:33:16,030 --> 01:33:19,100 So I was on both sides of that system. 1885 01:33:19,100 --> 01:33:21,790 You're given problems to work with your tutor. 1886 01:33:21,790 --> 01:33:23,650 And they're not graded. 1887 01:33:23,650 --> 01:33:25,370 I mean, your tutor helps you make sure that 1888 01:33:25,370 --> 01:33:26,640 you can do the problems. 1889 01:33:26,640 --> 01:33:29,380 But everything that's graded happens at the end. 1890 01:33:29,380 --> 01:33:31,240 Well, when I was an undergraduate it happened at 1891 01:33:31,240 --> 01:33:32,640 the end of your entire degree. 1892 01:33:32,640 --> 01:33:36,050 There was eight three-hour exams that counted for 1893 01:33:36,050 --> 01:33:36,460 everything. 1894 01:33:36,460 --> 01:33:37,920 And nothing else counted. 1895 01:33:37,920 --> 01:33:40,550 So it had some craziness. 1896 01:33:40,550 --> 01:33:42,960 That time at the end was pretty stressful. 1897 01:33:42,960 --> 01:33:46,610 But before that your tutor was actually your friend. 1898 01:33:46,610 --> 01:33:48,570 And your tutor wasn't the person doing the exams. 1899 01:33:48,570 --> 01:33:51,190 So you would do problems because you wanted to learn 1900 01:33:51,190 --> 01:33:53,070 and your tutor would help you so that you would do well on 1901 01:33:53,070 --> 01:33:54,900 the exam that other people were setting. 1902 01:33:54,900 --> 01:33:58,476 So you had a nice alliance with your tutor. 1903 01:33:58,476 --> 01:34:00,284 AUDIENCE: Does that work well? 1904 01:34:03,105 --> 01:34:04,750 PROFESSOR: I would say it works well. 1905 01:34:04,750 --> 01:34:07,190 At MIT it would work great. 1906 01:34:07,190 --> 01:34:08,220 Given [INAUDIBLE] 1907 01:34:08,220 --> 01:34:10,880 that people are too overloaded. 1908 01:34:10,880 --> 01:34:13,430 And they would say, oh well, if there's not going to be any 1909 01:34:13,430 --> 01:34:15,700 grading at all, I don't have to do anything, while I'd 1910 01:34:15,700 --> 01:34:17,230 really like to do this problem set. 1911 01:34:17,230 --> 01:34:19,590 But I have four other classes that are making me work 20 1912 01:34:19,590 --> 01:34:20,180 hours a week. 1913 01:34:20,180 --> 01:34:21,630 And I don't have any time. 1914 01:34:21,630 --> 01:34:23,580 So then because of the other pressures 1915 01:34:23,580 --> 01:34:24,290 they might fall away. 1916 01:34:24,290 --> 01:34:25,300 But they would like to do it. 1917 01:34:25,300 --> 01:34:28,510 So that's why I compromise by just saying, you have to do 1918 01:34:28,510 --> 01:34:29,940 the thing and make an effort. 1919 01:34:29,940 --> 01:34:32,500 And then I trust that once they start trying it they'll 1920 01:34:32,500 --> 01:34:35,700 enjoy doing it. 1921 01:34:35,700 --> 01:34:38,490 So I tried to make it as light as I think you can get away 1922 01:34:38,490 --> 01:34:40,020 with at MIT, given the pressures from 1923 01:34:40,020 --> 01:34:41,410 all the other teachers. 1924 01:34:41,410 --> 01:34:44,230 But in the ideal world I think that's what we would do here. 1925 01:34:44,230 --> 01:34:45,195 There wouldn't be that pressure. 1926 01:34:45,195 --> 01:34:47,760 AUDIENCE: [INAUDIBLE]? 1927 01:34:47,760 --> 01:34:51,880 PROFESSOR: Yeah, in Oxford and Cambridge it works very well, 1928 01:34:51,880 --> 01:34:53,440 provided you have a good tutor. 1929 01:34:53,440 --> 01:34:57,790 And there's many students who are there just because it's a 1930 01:34:57,790 --> 01:35:00,200 thing to do, to go to Oxford and Cambridge. 1931 01:35:00,200 --> 01:35:02,780 But if you factor out those students who are just there 1932 01:35:02,780 --> 01:35:06,040 for the stamp of the place, for the other students it 1933 01:35:06,040 --> 01:35:07,305 works fantastically well. 1934 01:35:07,305 --> 01:35:11,210 I mean, the tutorials are a great discussion time. 1935 01:35:11,210 --> 01:35:14,460 You can really kindle people's curiosity because it's really 1936 01:35:14,460 --> 01:35:16,130 not based on grading, it's based on helping. 1937 01:35:16,130 --> 01:35:17,380 AUDIENCE: [INAUDIBLE]? 1938 01:35:20,189 --> 01:35:22,210 PROFESSOR: It's so hard to do. 1939 01:35:22,210 --> 01:35:23,360 I mean, I don't know of any comparative 1940 01:35:23,360 --> 01:35:25,360 studies within one culture. 1941 01:35:25,360 --> 01:35:27,380 And I don't think you could really do them well between, 1942 01:35:27,380 --> 01:35:30,290 say, the English universities and the American just because 1943 01:35:30,290 --> 01:35:32,220 there's so many other social variables that are so 1944 01:35:32,220 --> 01:35:36,760 different like the population that goes to university, which 1945 01:35:36,760 --> 01:35:40,200 universities are talking about the exam system itself, so I 1946 01:35:40,200 --> 01:35:43,440 don't know of any studies that have been done across cultures 1947 01:35:43,440 --> 01:35:44,900 and that I would trust. 1948 01:35:44,900 --> 01:35:47,310 And within I don't know of any. 1949 01:35:47,310 --> 01:35:49,570 But it's a good question. 1950 01:35:49,570 --> 01:35:53,490 I know studies in general about rewards, which is that 1951 01:35:53,490 --> 01:35:58,480 the more you reward people for things that they like the less 1952 01:35:58,480 --> 01:36:00,570 they like doing them. 1953 01:36:00,570 --> 01:36:03,510 So I might give you some readings for that for very 1954 01:36:03,510 --> 01:36:05,860 last penultimate session. 1955 01:36:05,860 --> 01:36:09,170 And for the reading that I'm going to give you for the next 1956 01:36:09,170 --> 01:36:11,365 session is going to be about tutoring, actually. 1957 01:36:11,365 --> 01:36:15,040 So I'll put that on the website today. 1958 01:36:15,040 --> 01:36:16,110 OK, questions? 1959 01:36:16,110 --> 01:36:16,608 Yes? 1960 01:36:16,608 --> 01:36:19,098 AUDIENCE: [INAUDIBLE] of a question. 1961 01:36:19,098 --> 01:36:23,331 So I was wondering, if you do exams or homework problems 1962 01:36:23,331 --> 01:36:25,904 throughout the semester, you can, maybe, also better 1963 01:36:25,904 --> 01:36:30,350 monitor how the students develop compared to having one 1964 01:36:30,350 --> 01:36:32,326 big exam on the end. 1965 01:36:32,326 --> 01:36:34,796 And then maybe using [INAUDIBLE] lectures. 1966 01:36:34,796 --> 01:36:38,860 PROFESSOR: Right, so having continuous assessment is one 1967 01:36:38,860 --> 01:36:39,500 phrase for it. 1968 01:36:39,500 --> 01:36:42,170 It allows you to monitor, make sure things are going OK. 1969 01:36:42,170 --> 01:36:44,640 So all of a sudden you don't find, oh my god, the person 1970 01:36:44,640 --> 01:36:45,100 didn't know anything. 1971 01:36:45,100 --> 01:36:47,220 They got a third, which is like straight D's in your 1972 01:36:47,220 --> 01:36:48,770 whole undergraduate. 1973 01:36:48,770 --> 01:36:51,140 So in Oxford and Cambridge things are graded on first, 1974 01:36:51,140 --> 01:36:52,000 second, third. 1975 01:36:52,000 --> 01:36:54,980 And all of a sudden you had had no idea the student was 1976 01:36:54,980 --> 01:36:56,600 going to get a third, or they were sick or 1977 01:36:56,600 --> 01:36:57,660 something like that. 1978 01:36:57,660 --> 01:36:59,340 So I think, yeah. 1979 01:36:59,340 --> 01:37:04,100 So homework problems and exams have a really good purpose in 1980 01:37:04,100 --> 01:37:06,890 assessment and helping students get feedback on how 1981 01:37:06,890 --> 01:37:09,620 they're doing as well. 1982 01:37:09,620 --> 01:37:12,140 So for that purpose, grading is useful. 1983 01:37:12,140 --> 01:37:16,300 And one solution to that dilemma-- because I don't like 1984 01:37:16,300 --> 01:37:18,940 to grade exactly because it stresses them 1985 01:37:18,940 --> 01:37:19,790 out with the grade-- 1986 01:37:19,790 --> 01:37:22,030 is to give them the solution set right away. 1987 01:37:22,030 --> 01:37:24,580 So they can get feedback from the solution set whether they 1988 01:37:24,580 --> 01:37:28,103 understood things, not whether they had a 90 or and 80, but 1989 01:37:28,103 --> 01:37:29,620 whether it made sense to them. 1990 01:37:29,620 --> 01:37:31,980 And that's, I think, a much more important thing. 1991 01:37:31,980 --> 01:37:34,160 But then the other part of grading, which is that it's 1992 01:37:34,160 --> 01:37:35,310 used publicly-- 1993 01:37:35,310 --> 01:37:37,630 as part of your record and written to other people-- 1994 01:37:37,630 --> 01:37:40,420 that part of grading I think is not right. 1995 01:37:40,420 --> 01:37:43,440 I don't think it's morally right to, basically, reveal 1996 01:37:43,440 --> 01:37:45,860 information about students to other people without their 1997 01:37:45,860 --> 01:37:46,300 permission. 1998 01:37:46,300 --> 01:37:48,530 I don't think that should be the purpose of the university. 1999 01:37:48,530 --> 01:37:51,600 But the other purpose of grading, helping students know 2000 01:37:51,600 --> 01:37:52,550 where they are. 2001 01:37:52,550 --> 01:37:54,980 And helping us know where they are so we can help them more, 2002 01:37:54,980 --> 01:37:56,550 I think, is a completely valid purpose. 2003 01:37:59,710 --> 01:38:06,280 OK, so there was another suggestion which was to use as 2004 01:38:06,280 --> 01:38:09,180 many non-physics and math examples as possible. 2005 01:38:09,180 --> 01:38:12,710 So I'll try to reform my ways for the non physicists and 2006 01:38:12,710 --> 01:38:13,100 mathematicians. 2007 01:38:13,100 --> 01:38:16,530 It's just those come most naturally for me. 2008 01:38:16,530 --> 01:38:18,950 OK, so I think that was the main-- 2009 01:38:18,950 --> 01:38:19,750 yes, question? 2010 01:38:19,750 --> 01:38:22,630 AUDIENCE: [INAUDIBLE] 2011 01:38:22,630 --> 01:38:25,990 for evaluating the students or for teaching the students. 2012 01:38:25,990 --> 01:38:26,970 PROFESSOR: Pardon? 2013 01:38:26,970 --> 01:38:27,890 AUDIENCE: Homeworks? 2014 01:38:27,890 --> 01:38:30,230 PROFESSOR: Yes, for evaluating versus for teaching? 2015 01:38:30,230 --> 01:38:35,367 AUDIENCE: Yes, because that's one thing to evaluate, right? 2016 01:38:35,367 --> 01:38:36,768 [INAUDIBLE]? 2017 01:38:36,768 --> 01:38:38,360 PROFESSOR: It's both. 2018 01:38:38,360 --> 01:38:39,900 So there's two, yeah. 2019 01:38:39,900 --> 01:38:42,870 So the other purpose is that they learn and they do things. 2020 01:38:42,870 --> 01:38:43,780 That's for sure. 2021 01:38:43,780 --> 01:38:45,210 So you want them to do that. 2022 01:38:45,210 --> 01:38:46,930 And you can do that in class and homework. 2023 01:38:46,930 --> 01:38:49,900 And the take-home exams that we had when I was an 2024 01:38:49,900 --> 01:38:51,405 undergraduate had that purpose too. 2025 01:38:51,405 --> 01:38:54,510 You spent 24 hours really learning stuff. 2026 01:38:54,510 --> 01:38:57,170 So that purpose is very valid too. 2027 01:38:57,170 --> 01:38:59,740 But it's also very valid to know where the students are. 2028 01:38:59,740 --> 01:39:03,230 So for example, that basically closes the feedback loop. 2029 01:39:03,230 --> 01:39:05,090 You're doing all this stuff. 2030 01:39:05,090 --> 01:39:07,000 And now you're seeing the result of it. 2031 01:39:07,000 --> 01:39:08,990 And you want to know, well, did any of it take? 2032 01:39:08,990 --> 01:39:10,160 Did any of it stick? 2033 01:39:10,160 --> 01:39:12,920 And if none of it did, well, maybe you want to change what 2034 01:39:12,920 --> 01:39:13,350 you're doing. 2035 01:39:13,350 --> 01:39:16,654 AUDIENCE: Oh, but you cannot evaluate a 2036 01:39:16,654 --> 01:39:17,598 person every week, right? 2037 01:39:17,598 --> 01:39:21,106 And that's what drives students to copy solutions 2038 01:39:21,106 --> 01:39:25,360 because they care about the grade. 2039 01:39:25,360 --> 01:39:26,922 [INAUDIBLE]. 2040 01:39:26,922 --> 01:39:28,110 PROFESSOR: That's why distinguish 2041 01:39:28,110 --> 01:39:29,930 two senses of evaluate. 2042 01:39:29,930 --> 01:39:31,260 There's evaluate for the purpose 2043 01:39:31,260 --> 01:39:32,590 of helping the students. 2044 01:39:32,590 --> 01:39:34,570 And there's evaluate for the purpose of publishing their 2045 01:39:34,570 --> 01:39:36,900 grades elsewhere. 2046 01:39:36,900 --> 01:39:38,920 And it's the publishing their grades elsewhere 2047 01:39:38,920 --> 01:39:40,050 that worries them. 2048 01:39:40,050 --> 01:39:41,840 So you want to minimize that part. 2049 01:39:41,840 --> 01:39:44,620 And you want to do as much evaluation towards helping 2050 01:39:44,620 --> 01:39:45,620 them as possible. 2051 01:39:45,620 --> 01:39:48,140 So a solution set-- for example, one thing you can do 2052 01:39:48,140 --> 01:39:49,450 is say OK, here's the solution set. 2053 01:39:49,450 --> 01:39:52,170 Ask me about anything that's confusing. 2054 01:39:52,170 --> 01:39:54,430 And then you can put some of the responsibility for this 2055 01:39:54,430 --> 01:39:56,780 evaluation onto them so it's self evaluation. 2056 01:39:56,780 --> 01:39:59,830 But you're still using the homework for evaluation. 2057 01:39:59,830 --> 01:40:01,630 It's just you're not trying to say look, 2058 01:40:01,630 --> 01:40:02,290 that's the main thing. 2059 01:40:02,290 --> 01:40:04,370 I'm going to use that to tell everyone else about it. 2060 01:40:04,370 --> 01:40:06,050 That's what worries them and produces copying. 2061 01:40:06,050 --> 01:40:08,580 So you want to minimize that as much as possible. 2062 01:40:08,580 --> 01:40:09,510 And it's hard. 2063 01:40:09,510 --> 01:40:12,890 And that's the subject of the political obstacles to 2064 01:40:12,890 --> 01:40:15,430 educational change session that'll be in the 2065 01:40:15,430 --> 01:40:18,460 second-to-last lecture. 2066 01:40:18,460 --> 01:40:21,120 OK, so yeah, I don't pretend any of these have easy 2067 01:40:21,120 --> 01:40:24,370 answers, unfortunately. 2068 01:40:24,370 --> 01:40:26,640 Oh, there was another suggestion, which is that I 2069 01:40:26,640 --> 01:40:31,040 make a web forum where people can ask questions afterwards. 2070 01:40:31,040 --> 01:40:32,290 Because it's hard sometimes think of a 2071 01:40:32,290 --> 01:40:34,550 question on the fly. 2072 01:40:34,550 --> 01:40:35,160 And that's true. 2073 01:40:35,160 --> 01:40:38,300 And the problem is it's not easy to make web forms on the 2074 01:40:38,300 --> 01:40:40,700 MIT.edu site. 2075 01:40:40,700 --> 01:40:42,390 So I'll try to figure out a way to do that. 2076 01:40:42,390 --> 01:40:46,320 But for security reasons you can't really easily make web 2077 01:40:46,320 --> 01:40:50,460 forms that just append to a file or do something like 2078 01:40:50,460 --> 01:40:52,870 that, although I'm going to look into it and see what 2079 01:40:52,870 --> 01:40:54,210 workarounds I can find. 2080 01:40:54,210 --> 01:40:54,490 Yes? 2081 01:40:54,490 --> 01:40:56,033 AUDIENCE: [INAUDIBLE] 2082 01:40:56,033 --> 01:40:56,875 scripts? 2083 01:40:56,875 --> 01:40:59,370 PROFESSOR: Yeah, you can use scripts at MIT.edu. 2084 01:40:59,370 --> 01:41:02,540 So I have to figure out how to use that. 2085 01:41:02,540 --> 01:41:04,600 But yeah, I had that in the back of my mind. 2086 01:41:04,600 --> 01:41:05,830 But thanks for pointing that out. 2087 01:41:05,830 --> 01:41:06,090 Yeah? 2088 01:41:06,090 --> 01:41:06,990 AUDIENCE: What about forms? 2089 01:41:06,990 --> 01:41:08,300 PROFESSOR: Pardon? 2090 01:41:08,300 --> 01:41:08,820 AUDIENCE: Forms? 2091 01:41:08,820 --> 01:41:09,550 PROFESSOR: Forms? 2092 01:41:09,550 --> 01:41:11,588 AUDIENCE: [INAUDIBLE]? 2093 01:41:11,588 --> 01:41:13,440 PROFESSOR: Yeah, so then you get email. 2094 01:41:13,440 --> 01:41:16,110 So the only problem with that is that you get a ton of spam. 2095 01:41:16,110 --> 01:41:19,580 So there are all these spam bots that float around and 2096 01:41:19,580 --> 01:41:22,650 just fill out forms and send junk emails all the time. 2097 01:41:22,650 --> 01:41:27,880 So maybe that can be filtered out and it's not so bad. 2098 01:41:27,880 --> 01:41:31,350 So but yeah, that's one of the few things you can do on 2099 01:41:31,350 --> 01:41:35,150 MIT.edu, directly on the web.MIT.edu. 2100 01:41:35,150 --> 01:41:36,550 So there's a very solutions to it. 2101 01:41:36,550 --> 01:41:39,790 I'll try to think of something around that because it is a 2102 01:41:39,790 --> 01:41:41,790 good suggestion. 2103 01:41:41,790 --> 01:41:43,040 OK.