1 00:00:00,000 --> 00:00:12,180 I'd like to show you a short video of some classroom activities with some student interviews. 2 00:00:12,180 --> 00:00:18,440 And then I'm going to integrate a few fun activities that some of you might be interested 3 00:00:18,440 --> 00:00:24,520 in if you happen to have the opportunity to teach math or science at, let's say, a middle 4 00:00:24,520 --> 00:00:26,900 school level. 5 00:00:26,900 --> 00:00:32,420 Some things that anyone can do if you've gone through the normal curriculum that you would 6 00:00:32,420 --> 00:00:34,980 have in science in any high school. 7 00:00:34,980 --> 00:00:39,820 So I wanted to give you some things that you could actually perhaps use if you do have 8 00:00:39,820 --> 00:00:49,660 this opportunity, even if you don't have any specific scientific background. 9 00:00:49,660 --> 00:00:54,900 Due to a series of events that I won't get into because it's kind of a long story, I 10 00:00:54,900 --> 00:00:59,700 was asked to work with middle school students, third year middle school students, that is 11 00:00:59,700 --> 00:01:03,940 students of approximately 13 to 14 years of age, in the middle school that happens to 12 00:01:03,940 --> 00:01:05,800 be in front of my house. 13 00:01:05,800 --> 00:01:09,220 So that's how it all started. 14 00:01:09,220 --> 00:01:13,820 After a year or two, I decided, after two years actually, I decided that it would be 15 00:01:13,820 --> 00:01:19,900 interesting to introduce a science lesson into the program, to the normal language program. 16 00:01:19,900 --> 00:01:21,340 I had no idea of what CLIL was. 17 00:01:21,340 --> 00:01:25,860 I had no idea of what content-based language was. 18 00:01:25,860 --> 00:01:32,700 I just simply thought it would be a good idea to teach one subject or one lesson in science 19 00:01:32,700 --> 00:01:36,780 just to see how the students would accept it because it seemed like a logical thing 20 00:01:36,780 --> 00:01:41,920 to do, to show them how what they've learned in school can actually be applied. 21 00:01:41,920 --> 00:01:44,980 Because students are used to learning English to do their exercises. 22 00:01:44,980 --> 00:01:47,580 They're used to learning English to write letters. 23 00:01:47,580 --> 00:01:52,100 They're not used to using English for practical purposes. 24 00:01:52,100 --> 00:01:53,100 Can you hear me now? 25 00:01:53,100 --> 00:01:54,100 Is it too loud? 26 00:01:54,100 --> 00:01:55,100 Too loud? 27 00:01:55,100 --> 00:01:56,100 No? 28 00:01:56,100 --> 00:02:02,620 All right, so our first lesson was on the cell. 29 00:02:02,620 --> 00:02:07,340 It was a normal science lesson with multiple choice answers afterwards. 30 00:02:07,340 --> 00:02:09,780 Students were encouraged to ask some questions. 31 00:02:09,780 --> 00:02:16,220 And since the students were very enthusiastic about having applied what they know, I asked 32 00:02:16,220 --> 00:02:23,340 the principal, the headmaster of the school, if it would be possible perhaps to continue 33 00:02:23,340 --> 00:02:25,980 this experience. 34 00:02:25,980 --> 00:02:27,580 And she seemed to be very happy about it. 35 00:02:27,580 --> 00:02:30,660 In fact, she told me immediately, ah, this is CLIL. 36 00:02:30,660 --> 00:02:35,700 And that was the first time I'd ever heard CLIL, the abbreviation. 37 00:02:35,700 --> 00:02:44,020 So at that point, I started to look into it and I started to become familiar with the 38 00:02:44,020 --> 00:02:45,020 program. 39 00:02:45,020 --> 00:02:50,700 And over the years, what was initially simply content-based teaching, science, basically 40 00:02:50,700 --> 00:02:55,980 science lessons in English, slowly came to be science and math lessons that were taught 41 00:02:55,980 --> 00:03:03,500 in English but were integrated also with grammar, vocabulary, and language skills in general. 42 00:03:03,500 --> 00:03:07,020 Our first lesson was on the cell, as I've told you. 43 00:03:07,020 --> 00:03:10,740 One of the things that I had to do was to develop the materials. 44 00:03:11,020 --> 00:03:17,660 So the first thing I did was go into the archives of the school, where they have all the textbooks 45 00:03:17,660 --> 00:03:21,980 that sales representatives leave to the school. 46 00:03:21,980 --> 00:03:24,180 They leave several copies of things. 47 00:03:24,180 --> 00:03:28,180 So I took a look at them to see exactly what students would be learning in their third 48 00:03:28,180 --> 00:03:30,300 year of middle school. 49 00:03:30,300 --> 00:03:37,460 From that point on, I decided that it would not be a good idea to overlap too much with 50 00:03:37,580 --> 00:03:41,660 what was normally being done by the core subject teachers. 51 00:03:41,660 --> 00:03:43,180 Why? 52 00:03:43,180 --> 00:03:52,820 Because as maybe some of you have noticed, sometimes the presence of a CLIL teacher can 53 00:03:52,820 --> 00:03:56,300 be a little bit intrusive. 54 00:03:56,300 --> 00:04:00,900 The core subject teacher might feel a little bit uncomfortable with a third person coming 55 00:04:00,900 --> 00:04:07,260 in and not only teaching their subject, but teaching their subject in another language. 56 00:04:07,260 --> 00:04:12,460 So I thought it would be a good idea to avoid overlapping my course too much, to avoid 57 00:04:12,460 --> 00:04:19,220 any tension between the core subject teacher, not that I had had any particular evidence 58 00:04:19,220 --> 00:04:23,340 of this, but I thought it would probably be a good idea not to overlap too much. 59 00:04:23,340 --> 00:04:28,820 So at that point, when I was sure of what they were doing, I chose subjects that I thought 60 00:04:28,820 --> 00:04:35,580 would be complementary to those that they were doing at school and useful also in the 61 00:04:35,580 --> 00:04:36,580 following year. 62 00:04:36,580 --> 00:04:42,100 In Italy, they go into high school after the third year of middle school. 63 00:04:42,100 --> 00:04:47,500 I chose the subjects and then during a trip to the United States, I picked up all kinds 64 00:04:47,500 --> 00:04:51,660 of materials that I thought would be useful for preparing lessons. 65 00:04:51,660 --> 00:04:55,900 These materials were materials for mother tongue students of English. 66 00:04:55,900 --> 00:05:02,380 They weren't materials for CLIL specifically or for teaching English as a second language. 67 00:05:02,380 --> 00:05:09,020 They were normal science and math materials. 68 00:05:09,020 --> 00:05:11,620 Over the years, the program increased. 69 00:05:11,620 --> 00:05:17,980 Now what we have is a non-mandatory program that students choose to do. 70 00:05:17,980 --> 00:05:23,460 They choose to come after school and stay an hour and 15 minutes or an hour and a half 71 00:05:23,460 --> 00:05:32,660 once a week from November to early April in order to attend CLIL lessons. 72 00:05:32,660 --> 00:05:34,180 This has been very positive. 73 00:05:34,180 --> 00:05:42,300 At the beginning, we had a few problems because naturally, parents tend to interfere. 74 00:05:42,300 --> 00:05:47,700 Their children had to be the children to attend this course and that is not always the case. 75 00:05:47,700 --> 00:05:53,140 Not necessarily because these students were not particularly good students, but either 76 00:05:53,140 --> 00:05:57,180 they had problems with behavior, they didn't have a long enough attention span, and we 77 00:05:57,180 --> 00:06:03,020 all knew this because I had them also during my normal lessons during the day where I teach 78 00:06:03,020 --> 00:06:08,100 as a mother tongue teacher in the school, or they didn't have the language skills, or 79 00:06:08,100 --> 00:06:10,620 they just didn't want to. 80 00:06:10,620 --> 00:06:12,340 Some of those students were our better students. 81 00:06:12,340 --> 00:06:16,460 Maybe they play football and they knew that that was going to interfere with their sports 82 00:06:16,460 --> 00:06:17,460 schedule. 83 00:06:17,460 --> 00:06:18,980 They just didn't want to. 84 00:06:18,980 --> 00:06:19,980 Then what did we have? 85 00:06:19,980 --> 00:06:23,940 We also had a problem with students not wanting to be there. 86 00:06:23,940 --> 00:06:29,420 What we do now is make students responsible for their commitment to come. 87 00:06:29,420 --> 00:06:32,180 These are not always your best students. 88 00:06:32,180 --> 00:06:37,020 Those students who have at least passing marks in English, but not necessarily the best students. 89 00:06:37,020 --> 00:06:43,140 Some of these students who are not our best students are excelling in CLIL, in science 90 00:06:43,140 --> 00:06:45,840 and math taught through CLIL. 91 00:06:45,840 --> 00:06:49,580 Some of the students are even getting better in their core subject English course because 92 00:06:49,580 --> 00:06:55,100 they want to participate in the CLIL course in the afternoon, and they can't unless their 93 00:06:55,100 --> 00:07:01,460 English is reasonably decent, let's say, a passing mark in English, or a full passing 94 00:07:01,460 --> 00:07:04,260 mark in English. 95 00:07:04,260 --> 00:07:09,420 Anything I've forgotten? 96 00:07:09,420 --> 00:07:15,140 Now we have what our CLIL program includes is an introduction to mathematics in English, 97 00:07:15,140 --> 00:07:23,900 science, mostly chemistry, a little bit of biology, the cell, the human heart, et cetera. 98 00:07:23,900 --> 00:07:27,980 Since I'm not a mathematician, I'm a pharmacist, and the amount of mathematics that a pharmacist 99 00:07:27,980 --> 00:07:33,180 uses does not include things like geometry, et cetera. 100 00:07:33,180 --> 00:07:41,700 Most of the math course is actually based on simple mathematics or history of mathematics. 101 00:07:41,700 --> 00:07:48,900 The first thing I wanted to show you is where this course is taught. 102 00:07:48,900 --> 00:07:53,980 It's taught in a little bit of advertisement for the city of Urbino in central Italy. 103 00:07:53,980 --> 00:07:58,500 It's a beautiful Renaissance city with probably one of the most beautiful examples of Renaissance 104 00:07:58,500 --> 00:08:02,580 architecture in the world. 105 00:08:02,580 --> 00:08:07,300 So I'm going to lower this just a moment if I can, I'm not quite sure how, but I will 106 00:08:07,300 --> 00:08:19,860 figure it out. 107 00:08:19,860 --> 00:08:22,460 It's not the end of the presentation, but I'll just lower it like this. 108 00:08:22,460 --> 00:08:24,740 Okay, I want to show you this brief film. 109 00:08:24,740 --> 00:08:28,780 I hope you know it's a classroom setting, so the audio is not fantastic. 110 00:08:28,780 --> 00:08:36,340 What you're going to be seeing is pieces of lessons and student interviews. 111 00:08:36,380 --> 00:08:40,740 It's very hard to make any kind of a film, and I imagine it is here at that age because 112 00:08:40,740 --> 00:08:46,540 you need permission from the parents to film their children. 113 00:08:46,540 --> 00:08:50,500 Students naturally forgot to bring their permission several times, it snowed. 114 00:08:50,500 --> 00:08:55,500 So the lessons that I had prepared, the ones that maybe I'd wanted you to see may not be 115 00:08:55,500 --> 00:08:56,500 in this film. 116 00:08:56,500 --> 00:09:00,100 In fact, these are rather traditional lessons, and what we're going to be doing today is 117 00:09:00,100 --> 00:09:04,500 talking about those elements that you can add to a CLIL course to make it a little more 118 00:09:04,500 --> 00:09:05,780 fun. 119 00:09:05,780 --> 00:09:08,140 Something that makes them want to come back. 120 00:09:08,140 --> 00:09:11,620 Not just a traditional science lesson, but something that makes it a little bit more 121 00:09:11,620 --> 00:09:12,620 attractive to younger students. 122 00:09:12,620 --> 00:09:26,100 Okay, so I'm going to let you see this video, I hope it will be clear enough. 123 00:09:26,100 --> 00:09:49,300 There's one girl who's a multi-tongue speaker of English, another girl who speaks Dutch, 124 00:09:49,300 --> 00:09:52,300 and naturally her English is quite good. 125 00:09:52,500 --> 00:09:55,500 And then there's a mixture of other students. 126 00:09:55,700 --> 00:09:58,700 There we go. 127 00:09:58,700 --> 00:10:01,700 Just a minute. 128 00:10:01,700 --> 00:10:04,700 Technical problems. 129 00:10:04,900 --> 00:10:07,900 There we go. 130 00:10:07,900 --> 00:10:10,900 Just a minute. 131 00:10:10,900 --> 00:10:13,900 Technical problems. 132 00:10:13,900 --> 00:10:16,900 There we go. 133 00:10:17,100 --> 00:10:20,100 There we go. 134 00:10:20,100 --> 00:10:23,100 Just a minute. 135 00:10:23,100 --> 00:10:26,100 Technical problems. 136 00:10:26,300 --> 00:10:29,300 Technical problems. 137 00:10:29,300 --> 00:10:32,300 There we go. 138 00:10:32,300 --> 00:10:35,300 Technical problems with English. 139 00:10:35,300 --> 00:10:37,300 Language. 140 00:10:37,300 --> 00:10:40,300 Time integrated learning. 141 00:10:40,300 --> 00:10:52,300 It's a course that you learn English and like for science, chemistry, biology, or photography. 142 00:10:52,500 --> 00:10:57,500 She's sick in English. 143 00:10:57,500 --> 00:11:00,500 Michael is not here. 144 00:11:00,500 --> 00:11:03,500 Anyone who's not eating? 145 00:11:03,500 --> 00:11:06,500 Okay. 146 00:11:06,500 --> 00:11:09,500 Someone who didn't really want to come? 147 00:11:09,500 --> 00:11:12,500 Someone who didn't want to come? 148 00:11:12,500 --> 00:11:15,500 There it is. 149 00:11:15,500 --> 00:11:18,500 Can she eat? 150 00:11:18,700 --> 00:11:21,700 Who's that? 151 00:11:21,700 --> 00:11:24,700 What is the question? 152 00:11:24,700 --> 00:11:27,700 Who's that? 153 00:11:27,700 --> 00:11:30,700 Who's that? 154 00:11:30,700 --> 00:11:33,700 Let me get that. 155 00:11:33,700 --> 00:11:36,700 Who's that? 156 00:11:36,700 --> 00:11:39,700 Who's that? 157 00:11:39,700 --> 00:11:42,700 Who's that? 158 00:11:42,700 --> 00:11:45,700 Who's that? 159 00:11:45,900 --> 00:11:48,900 Eat. 160 00:11:48,900 --> 00:11:51,900 I said, who are you? 161 00:11:51,900 --> 00:11:54,900 What? 162 00:11:54,900 --> 00:11:57,900 You're 70. 163 00:11:57,900 --> 00:12:00,900 You're a bit too young. 164 00:12:00,900 --> 00:12:03,900 You're a scientist. 165 00:12:03,900 --> 00:12:04,900 Scientist. 166 00:12:04,900 --> 00:12:05,900 Scientist. 167 00:12:05,900 --> 00:12:06,900 Century. 168 00:12:06,900 --> 00:12:07,900 Century. 169 00:12:07,900 --> 00:12:08,900 You produce. 170 00:12:08,900 --> 00:12:09,900 You produce. 171 00:12:09,900 --> 00:12:10,900 You produce. 172 00:12:10,900 --> 00:12:11,900 You produce. 173 00:12:11,900 --> 00:12:12,900 You produce. 174 00:12:12,900 --> 00:12:13,900 You produce. 175 00:12:13,900 --> 00:12:14,900 You produce. 176 00:12:15,100 --> 00:12:17,100 Who's that? 177 00:12:17,100 --> 00:12:18,100 Who's that? 178 00:12:18,100 --> 00:12:19,100 Next. 179 00:12:19,100 --> 00:12:20,100 Next. 180 00:12:20,100 --> 00:12:21,100 Here you go. 181 00:12:21,100 --> 00:12:22,100 Function. 182 00:12:22,100 --> 00:12:23,100 No, here. 183 00:12:23,100 --> 00:12:24,100 Set. 184 00:12:24,100 --> 00:12:25,100 Function. 185 00:12:25,100 --> 00:12:26,100 Function. 186 00:12:26,100 --> 00:12:27,100 Very good. 187 00:12:27,100 --> 00:12:28,100 Fundamental. 188 00:12:28,100 --> 00:12:29,100 Fundamental. 189 00:12:29,100 --> 00:12:30,100 You do. 190 00:12:30,100 --> 00:12:31,100 Structural. 191 00:12:31,100 --> 00:12:32,100 Structural. 192 00:12:32,100 --> 00:12:33,100 Structural. 193 00:12:33,100 --> 00:12:34,100 Structure. 194 00:12:34,100 --> 00:12:35,100 Okay. 195 00:12:35,100 --> 00:12:36,100 Structural. 196 00:12:36,100 --> 00:12:37,100 Special. 197 00:12:37,100 --> 00:12:38,100 Special. 198 00:12:38,100 --> 00:12:39,100 Special. 199 00:12:39,100 --> 00:12:40,100 Special. 200 00:12:40,100 --> 00:12:41,100 Special. 201 00:12:41,100 --> 00:12:42,100 Special. 202 00:12:42,100 --> 00:12:43,100 Special. 203 00:12:43,100 --> 00:12:44,100 Special. 204 00:12:44,300 --> 00:12:45,300 Thank you. 205 00:12:45,300 --> 00:12:46,300 Thanks. 206 00:12:46,300 --> 00:12:49,300 Where did you go? 207 00:12:50,300 --> 00:12:51,300 Matteo? 208 00:12:51,300 --> 00:12:52,300 Science. 209 00:12:52,300 --> 00:12:55,300 Can you tell me what you study? 210 00:12:55,300 --> 00:12:56,300 Yes. 211 00:12:56,300 --> 00:13:04,300 We study biology, chemistry, philosophy, and... 212 00:13:04,300 --> 00:13:05,300 What did you study? 213 00:13:05,300 --> 00:13:06,300 What did you study? 214 00:13:06,300 --> 00:13:08,300 The chemistry. 215 00:13:08,500 --> 00:13:19,500 I studied algebra, mathematics, geography, philosophy. 216 00:13:49,700 --> 00:13:54,700 You know the advertising methodology for Xinjiang, right? 217 00:13:54,700 --> 00:13:55,700 No martini. 218 00:13:55,700 --> 00:13:56,700 That's right. 219 00:13:58,700 --> 00:14:02,700 George Clooney has a bottle of champagne with a bottle. 220 00:14:02,700 --> 00:14:05,700 He says, no martini, no product. 221 00:14:05,700 --> 00:14:06,700 Why? 222 00:14:06,700 --> 00:14:07,700 That's what you think. 223 00:14:07,700 --> 00:14:08,700 But he has... 224 00:14:08,700 --> 00:14:09,700 It's made of cardboard. 225 00:14:09,700 --> 00:14:10,700 Do you have... 226 00:14:10,700 --> 00:14:11,700 Yes. 227 00:14:11,700 --> 00:14:12,700 I learned that... 228 00:14:13,400 --> 00:14:17,400 Wood is better than other materials and different polymer. 229 00:14:17,400 --> 00:14:21,400 The wood is better than other different materials and different polymer. 230 00:14:21,400 --> 00:14:25,400 The gas is better than other different materials and different polymer. 231 00:14:25,400 --> 00:14:29,400 A plasma is better than other different chemicals and other different polymer. 232 00:14:29,400 --> 00:14:30,400 And... 233 00:14:40,400 --> 00:14:42,400 The next one is we're going to learn English. 234 00:14:43,100 --> 00:14:45,100 Do you think wood is a good way to learn English? 235 00:14:45,100 --> 00:14:51,100 Yes, I think wood is a very good way to learn English because the teacher speaks all the time in English. 236 00:14:51,100 --> 00:14:55,100 And she gives us a lot of explanation that we need. 237 00:14:56,100 --> 00:14:57,100 Anybody else? 238 00:14:57,100 --> 00:15:07,100 I think wood is a very good way to learn English because it helps us to understand another way of English. 239 00:15:07,800 --> 00:15:08,800 Anyone else? 240 00:15:09,800 --> 00:15:16,800 Yes, because learning a subject in a foreign language helps to learn the subject but also the language. 241 00:15:18,800 --> 00:15:21,800 Do you think that wood is a good way to learn English? 242 00:15:21,800 --> 00:15:23,800 Yes, I think that... 243 00:15:23,800 --> 00:15:33,800 I think wood is a good way of learning English because it's probably more interesting than the traditional way of learning. 244 00:15:34,500 --> 00:15:35,500 Thank you. 245 00:15:42,500 --> 00:15:44,500 Just to get you to... 246 00:15:44,500 --> 00:15:45,500 Could you hear it enough? 247 00:15:45,500 --> 00:15:46,500 Could you hear it at all? 248 00:15:46,500 --> 00:15:47,500 Was it clear enough? 249 00:15:47,500 --> 00:15:49,500 I know a classroom setting is not the best thing. 250 00:15:49,500 --> 00:15:50,500 Some of those students... 251 00:15:50,500 --> 00:15:55,500 For example, the boy with the scarf, the checkered traditional keffiyeh, I think it's called. 252 00:15:55,500 --> 00:15:56,500 He's not considered... 253 00:15:56,500 --> 00:16:00,500 He's a very bright boy but he's not your traditionally good student. 254 00:16:00,500 --> 00:16:03,500 And he decided that he wanted to take this course. 255 00:16:04,200 --> 00:16:05,200 Actually, he's quite good. 256 00:16:05,200 --> 00:16:11,200 I have to admit that I had not coached them but I had given them questions that I would ask. 257 00:16:11,200 --> 00:16:15,200 Because naturally, the stage fright I thought might kick in. 258 00:16:15,200 --> 00:16:18,200 So I thought I'd give them the questions beforehand. 259 00:16:18,200 --> 00:16:19,200 I'm sorry. 260 00:16:19,200 --> 00:16:28,200 I thought I'd give them the questions beforehand so that they could take a look at them and maybe prepare just a little bit so that they wouldn't get scared in being filmed. 261 00:16:29,200 --> 00:16:31,200 So let's go on with the presentation. 262 00:16:34,200 --> 00:16:38,200 Here are the first pages of part of our science module. 263 00:16:38,200 --> 00:16:40,200 The first is naturally, what is matter? 264 00:16:40,200 --> 00:16:43,200 The second is the smallest part of matter, the atom. 265 00:16:43,200 --> 00:16:48,200 As you can see, some of the words are highlighted in red or written in red. 266 00:16:48,200 --> 00:17:02,200 And I've also included maybe a cognate or some language that they would understand to help them to be able to understand the words that I thought they might not know or probably would not know. 267 00:17:02,900 --> 00:17:03,900 Tiny, for example. 268 00:17:03,900 --> 00:17:09,900 If you say minute, an Italian speaker would automatically know what that is. 269 00:17:10,900 --> 00:17:13,900 So these were our first two lessons. 270 00:17:14,900 --> 00:17:20,900 The third lesson was a short history of atomic theory with the different models of the atom over time. 271 00:17:20,900 --> 00:17:24,900 And then we have a lesson on elements and the periodic table of the elements. 272 00:17:25,600 --> 00:17:31,600 Here I usually introduce a little bit of an activity. 273 00:17:31,600 --> 00:17:33,600 Two activities, actually. 274 00:17:33,600 --> 00:17:45,600 Two things that help students to become familiar because in the third year of middle school, most Italian or our Italian students in this particular school don't get a lot of background in chemistry. 275 00:17:45,600 --> 00:17:47,600 They just get a little bit, perhaps. 276 00:17:48,300 --> 00:18:02,300 So what I did was I wanted them just to simply get to know the periodic table of the elements and be able to deal with it, to become familiar with it so that they wouldn't be, I don't know, a little bit intimidated by it when they got to it in high school. 277 00:18:02,300 --> 00:18:04,300 So now I'm going to give you an activity. 278 00:18:04,300 --> 00:18:10,300 I'm going to give you a periodic table of the elements, which you may not have seen for a long time. 279 00:18:10,300 --> 00:18:11,300 Okay? 280 00:18:11,300 --> 00:18:12,300 I'll pass them around. 281 00:18:13,000 --> 00:18:14,000 Okay? 282 00:18:14,000 --> 00:18:19,000 So even if you haven't found a lot, there are lots of them in there, but this is just to give you an idea. 283 00:18:19,000 --> 00:18:22,000 Can anyone tell me any of the names that they found? 284 00:18:22,000 --> 00:18:26,000 Name something, an element named after a famous person, a famous scientist. 285 00:18:28,000 --> 00:18:29,000 Einsteinium and? 286 00:18:31,000 --> 00:18:32,000 Fermium. 287 00:18:32,000 --> 00:18:33,000 Enrico Fermi. 288 00:18:33,000 --> 00:18:34,000 Okay. 289 00:18:34,700 --> 00:18:35,700 Excuse me. 290 00:18:37,700 --> 00:18:38,700 Yes. 291 00:18:38,700 --> 00:18:39,700 Mendeleev. 292 00:18:39,700 --> 00:18:40,700 No. 293 00:18:40,700 --> 00:18:41,700 Any other ones? 294 00:18:41,700 --> 00:18:42,700 Excuse me. 295 00:18:42,700 --> 00:18:43,700 Yes. 296 00:18:43,700 --> 00:18:44,700 Famous nuclear physicist, if I'm not mistaken. 297 00:18:44,700 --> 00:18:45,700 Okay. 298 00:18:45,700 --> 00:18:46,700 Okay. 299 00:18:46,700 --> 00:18:47,700 Okay. 300 00:18:47,700 --> 00:18:48,700 Okay. 301 00:18:48,700 --> 00:18:49,700 Okay. 302 00:18:49,700 --> 00:18:50,700 Okay. 303 00:18:50,700 --> 00:18:51,700 Okay. 304 00:18:51,700 --> 00:18:52,700 Okay. 305 00:18:52,700 --> 00:18:53,700 Okay. 306 00:18:53,700 --> 00:18:54,700 Okay. 307 00:18:54,700 --> 00:18:55,700 Okay. 308 00:18:55,700 --> 00:18:56,700 Okay. 309 00:18:56,700 --> 00:18:57,700 Okay. 310 00:18:57,700 --> 00:18:58,700 Okay. 311 00:18:58,700 --> 00:18:59,700 Okay. 312 00:18:59,700 --> 00:19:00,700 Okay. 313 00:19:00,700 --> 00:19:01,700 Okay. 314 00:19:01,700 --> 00:19:02,700 Okay. 315 00:19:02,700 --> 00:19:03,700 Okay. 316 00:19:04,400 --> 00:19:05,400 Yeah. 317 00:19:05,400 --> 00:19:06,400 Yeah. 318 00:19:06,400 --> 00:19:07,400 You find them, if I'm not mistaken. 319 00:19:07,400 --> 00:19:08,400 Any other ones? 320 00:19:10,400 --> 00:19:11,400 Curium. 321 00:19:11,400 --> 00:19:12,400 Madame Curie and her brother. 322 00:19:12,400 --> 00:19:13,400 Excuse me. 323 00:19:13,400 --> 00:19:14,400 Nobelium. 324 00:19:14,400 --> 00:19:15,400 Yeah, Nobelium, absolutely. 325 00:19:15,400 --> 00:19:24,400 Then from Greek mythology, we have one named Tantalum, named after Tantalus from Greg mythology. 326 00:19:26,400 --> 00:19:28,400 Iridium, Iris from Greek mythology. 327 00:19:29,400 --> 00:19:31,400 Any others planets? 328 00:19:32,400 --> 00:19:33,400 No. 329 00:19:34,100 --> 00:19:36,100 Plutonium. 330 00:19:38,100 --> 00:19:40,100 Neptunium, I believe. 331 00:19:40,100 --> 00:19:41,100 No. 332 00:19:42,100 --> 00:19:45,100 Helium, the sun, actually. 333 00:19:47,100 --> 00:19:52,100 And if you want a list of these, if you do decide to... Mercury, naturally. 334 00:19:52,100 --> 00:19:54,100 No, we may not have thought of him. 335 00:19:54,100 --> 00:20:03,100 You can easily find on Wikipedia a list of all the names of the elements that have been named after famous people, places, or things. 336 00:20:03,800 --> 00:20:05,800 And there are some interesting stories, too. 337 00:20:05,800 --> 00:20:13,800 Another thing that you can do to have students become familiar with the periodic table of the elements is this exercise. 338 00:20:14,800 --> 00:20:31,800 In their booklets, they have the more serious clue lesson that divides elements, gives a, what would you call it, a concept map of the table of the elements, of matter and the elements. 339 00:20:32,500 --> 00:20:45,500 So matter made of one kind of element, the elements, 118 known or predicted, 90 formed by nature, 25 created in the laboratory, three are missing because when I did this, three had been predicted but not found. 340 00:20:45,500 --> 00:20:50,500 One has been found in the meantime, so I'm going to have to change my numbers a little bit. 341 00:20:50,500 --> 00:20:53,500 These are classified in the periodic table of the elements. 342 00:20:53,500 --> 00:20:57,500 They're written as symbols, arranged by atomic number, and divided by properties. 343 00:20:57,500 --> 00:21:00,500 What I'd like to look at now is how they're written as symbols. 344 00:21:01,200 --> 00:21:03,200 They're written in symbols, usually with one or two letters. 345 00:21:03,200 --> 00:21:05,200 Some of them have three, some of the newer ones. 346 00:21:07,200 --> 00:21:11,200 The first letter is capitalized, and the second letter is in lowercase. 347 00:21:12,200 --> 00:21:18,200 And it's usually the second letter, the third letter, depending on what's already been used. 348 00:21:21,200 --> 00:21:28,200 The question is, imagine that you are a great scientist and the scientific world wants to dedicate a newly discovered element to you. 349 00:21:28,200 --> 00:21:30,200 What would your atomic symbol be? 350 00:21:30,900 --> 00:21:32,900 So, I have a great name for this. 351 00:21:32,900 --> 00:21:34,900 It's absolutely perfect. 352 00:21:35,900 --> 00:21:37,900 My name is Carducci. 353 00:21:38,900 --> 00:21:40,900 So, I want to be Carduccium. 354 00:21:43,900 --> 00:21:46,900 C, the first letter of my name. 355 00:21:47,900 --> 00:21:49,900 That's no good because it's carbon. 356 00:21:49,900 --> 00:21:54,900 I can't be CA, the first and the second letter, because that's calcium. 357 00:21:56,900 --> 00:21:57,900 CR? 358 00:21:58,600 --> 00:22:02,600 I can't be CR because it's already been taken. 359 00:22:02,600 --> 00:22:04,600 It's chromium. 360 00:22:04,600 --> 00:22:06,600 CD, maybe? 361 00:22:06,600 --> 00:22:07,600 No. 362 00:22:07,600 --> 00:22:08,600 Cadmium. 363 00:22:08,600 --> 00:22:09,600 No good. 364 00:22:10,600 --> 00:22:12,600 CU? 365 00:22:12,600 --> 00:22:14,600 Oh, copper. 366 00:22:14,600 --> 00:22:16,600 It's already been taken. 367 00:22:20,600 --> 00:22:22,600 There are only two possibilities left. 368 00:22:23,600 --> 00:22:25,600 CC, but... 369 00:22:26,300 --> 00:22:30,300 None of the other elements have two letters that are the same. 370 00:22:30,300 --> 00:22:32,300 No? So... 371 00:22:33,300 --> 00:22:35,300 What about CI? 372 00:22:36,300 --> 00:22:39,300 Would be the famous Carduccium. 373 00:22:41,300 --> 00:22:43,300 So, what would your symbol be? 374 00:22:43,300 --> 00:22:53,300 What you can do in the classroom is ask students to write their surnames and go through the periodic table trying to find what their symbol would be. 375 00:22:54,000 --> 00:23:02,000 In this way, they're forced to go methodically, element by element, and see which one could be appropriate for them. 376 00:23:04,000 --> 00:23:06,000 So, what would your symbol be? 377 00:23:07,000 --> 00:23:12,000 I was going to ask you maybe to do this, but I think maybe we should go on and do something a little bit different, okay? 378 00:23:14,000 --> 00:23:16,000 Science, the cell. 379 00:23:17,000 --> 00:23:19,000 This is our formal, traditional lesson on the cell. 380 00:23:19,000 --> 00:23:21,000 What is a cell in biology? 381 00:23:21,700 --> 00:23:27,700 A cell is the basic, living, functional, and structural unit of all organisms, and the usual science lesson. 382 00:23:27,700 --> 00:23:30,700 A little bit of history about the microscope. 383 00:23:31,700 --> 00:23:33,700 Then, we have an activity. 384 00:23:33,700 --> 00:23:43,700 How many of you have looked under a microscope, and your professor has told you that there are differences between one slide and another, and in looking at it, they all look totally the same? 385 00:23:44,400 --> 00:23:52,400 Usually, you look at them and you say, I don't know, you say it's a leukocyte, but I really can't tell the difference from any of the other cells you're showing me. 386 00:23:53,400 --> 00:24:00,400 So, we have an exercise in increasing your observation skills. 387 00:24:01,400 --> 00:24:03,400 So, this is what I do. 388 00:24:05,400 --> 00:24:07,400 I give the students a specimen. 389 00:24:08,400 --> 00:24:10,400 I give them a peanut. 390 00:24:11,100 --> 00:24:13,100 I give them a piece of paper, which is this. 391 00:24:18,100 --> 00:24:21,100 I don't know, we're probably not, do I have some volunteers? 392 00:24:21,100 --> 00:24:25,100 Can I have a little group of a few people that would be willing to do this? 393 00:24:25,100 --> 00:24:26,100 Would you come up, please? 394 00:24:26,100 --> 00:24:28,100 I need about five or six people. 395 00:24:29,100 --> 00:24:30,100 Oh, come on. 396 00:24:30,100 --> 00:24:34,100 It's not anything I'm not going to, no magic tricks, no. 397 00:24:37,100 --> 00:24:38,100 Good. 398 00:24:38,100 --> 00:24:39,100 Thank you. 399 00:24:39,800 --> 00:24:40,800 One, two, a few more. 400 00:24:41,800 --> 00:24:44,800 Okay, one, two, three, four, five seats. 401 00:24:44,800 --> 00:24:46,800 Just pull up a chair and sit over here. 402 00:24:48,800 --> 00:24:49,800 Yes, over here. 403 00:24:49,800 --> 00:24:53,800 I'm going to give them what you see there. 404 00:24:54,800 --> 00:24:57,800 It's a photocopy with a circle on it. 405 00:25:01,800 --> 00:25:03,800 Thank you for participating. 406 00:25:04,800 --> 00:25:06,800 Now, what I'm going to do is give you your specimen. 407 00:25:06,800 --> 00:25:08,800 You're not allowed to touch it. 408 00:25:09,800 --> 00:25:10,800 Thank you. 409 00:25:17,800 --> 00:25:19,800 I'm having some technical trouble here. 410 00:25:20,800 --> 00:25:21,800 I'm afraid it might explode. 411 00:25:23,800 --> 00:25:24,800 Yes, please. 412 00:25:24,800 --> 00:25:25,800 You need a man for this. 413 00:25:27,800 --> 00:25:28,800 Okay, we need a man. 414 00:25:32,800 --> 00:25:33,800 There we go. 415 00:25:33,800 --> 00:25:34,800 There we go. 416 00:25:36,800 --> 00:25:37,800 Thank you. 417 00:25:38,500 --> 00:25:40,500 It's the famous, what they call, the Lord of Colombo. 418 00:25:41,500 --> 00:25:42,500 Columbus' egg. 419 00:25:42,500 --> 00:25:44,500 It was probably Brunelleschi's egg. 420 00:25:45,500 --> 00:25:46,500 I'm going to give you a specimen. 421 00:25:47,500 --> 00:25:49,500 And I want you to describe it very, very carefully. 422 00:25:49,500 --> 00:25:50,500 I want you to make a picture of it. 423 00:25:51,500 --> 00:25:52,500 All right? 424 00:25:52,500 --> 00:25:53,500 You have to memorize your specimen. 425 00:25:57,500 --> 00:25:58,500 Okay? 426 00:25:58,500 --> 00:26:00,500 Draw a picture of it carefully and quickly, hopefully. 427 00:26:01,500 --> 00:26:03,500 And then I want you to be able to describe it 428 00:26:03,500 --> 00:26:06,500 using some of the vocabulary that you'll find. 429 00:26:07,200 --> 00:26:09,200 I want you to use some of the vocabulary that you'll find here. 430 00:26:10,200 --> 00:26:12,200 For example, some useful vocabulary. 431 00:26:13,200 --> 00:26:17,200 A hole, a filament, a spot, a discoloration, a crack, 432 00:26:18,200 --> 00:26:19,200 an indentation, a protuberance. 433 00:26:20,200 --> 00:26:24,200 Positional words, center, extremity, opposite extremity, 434 00:26:25,200 --> 00:26:26,200 for color, light, and dark. 435 00:26:27,200 --> 00:26:28,200 Okay? 436 00:26:28,200 --> 00:26:30,200 And we're going to let them work on that now for a little bit. 437 00:26:30,200 --> 00:26:32,200 I'll give you a few minutes to work on your peanuts. 438 00:26:33,200 --> 00:26:34,200 And we'll go on with the course. 439 00:26:34,900 --> 00:26:35,900 Peanuts. 440 00:26:43,900 --> 00:26:44,900 Okay. 441 00:26:46,900 --> 00:26:49,900 Part of the course also deals with mathematics, 442 00:26:49,900 --> 00:26:51,900 although I'm not a mathematician. 443 00:26:52,900 --> 00:26:53,900 No? 444 00:26:53,900 --> 00:26:57,900 But one of the things that Italian students, 445 00:26:57,900 --> 00:27:00,900 and probably it's common also to other foreign students, 446 00:27:01,600 --> 00:27:04,600 is saying numbers, saying very large numbers, 447 00:27:04,600 --> 00:27:06,600 saying fractions, saying percentages, 448 00:27:06,600 --> 00:27:08,600 how they're to be said. 449 00:27:08,600 --> 00:27:09,600 They obviously know how to write them, 450 00:27:09,600 --> 00:27:11,600 but they don't know how to say them. 451 00:27:12,600 --> 00:27:17,600 For example, when talking about fractions, 452 00:27:17,600 --> 00:27:21,600 you can explain to them that when the numerator is singular, 453 00:27:21,600 --> 00:27:23,600 the denominator is also singular. 454 00:27:23,600 --> 00:27:26,600 When the numerator is plural, the denominator must be plural. 455 00:27:26,600 --> 00:27:29,600 Just like in English, one third, two thirds. 456 00:27:30,300 --> 00:27:31,300 No? 457 00:27:31,300 --> 00:27:33,300 So these are things that are very helpful. 458 00:27:34,300 --> 00:27:36,300 Then we talk about a classification of numbers. 459 00:27:36,300 --> 00:27:37,300 How different numbers... 460 00:27:37,300 --> 00:27:39,300 I'm sorry, I'm not over here a lot. 461 00:27:39,300 --> 00:27:40,300 How to classify numbers. 462 00:27:41,300 --> 00:27:42,300 Natural numbers. 463 00:27:42,300 --> 00:27:43,300 What are whole numbers? 464 00:27:43,300 --> 00:27:44,300 What are integers? 465 00:27:44,300 --> 00:27:46,300 What are rational numbers? 466 00:27:46,300 --> 00:27:47,300 What are real numbers? 467 00:27:48,300 --> 00:27:50,300 This is also very good for vocabulary building 468 00:27:50,300 --> 00:27:53,300 because we do an exercise on using these words 469 00:27:53,300 --> 00:27:56,300 in normal English, not just for mathematics. 470 00:27:57,300 --> 00:27:58,300 Someone can be irrational. 471 00:27:59,000 --> 00:28:00,000 Someone can be odd. 472 00:28:01,000 --> 00:28:02,000 Someone can be... 473 00:28:03,000 --> 00:28:06,000 Something can be absolutely fantastic. 474 00:28:07,000 --> 00:28:10,000 Many of these words that are used 475 00:28:11,000 --> 00:28:14,000 can also be applied to normal English, 476 00:28:14,000 --> 00:28:16,000 and that's exactly what we use them for. 477 00:28:17,000 --> 00:28:18,000 Some of them they may know, 478 00:28:18,000 --> 00:28:21,000 others they probably wouldn't normally. 479 00:28:21,000 --> 00:28:24,000 For example, to be even. 480 00:28:25,000 --> 00:28:27,000 I pay for the pizza, you pay for the drinks. 481 00:28:27,700 --> 00:28:28,700 Then we'll be even. 482 00:28:28,700 --> 00:28:30,700 So odd, meaning strange. 483 00:28:30,700 --> 00:28:33,700 And we have exercises also in English exercises 484 00:28:33,700 --> 00:28:35,700 using these words. 485 00:28:38,700 --> 00:28:41,700 In mathematics, we also do a short history of mathematics. 486 00:28:41,700 --> 00:28:43,700 We take an early look at mathematics 487 00:28:43,700 --> 00:28:46,700 from the Egyptians, the Greeks, the Chinese, 488 00:28:46,700 --> 00:28:49,700 the Hindus, the Babylonians, and the Mayas' point of view. 489 00:28:50,700 --> 00:28:53,700 We also do exercises on solving word problems 490 00:28:53,700 --> 00:28:55,700 with ratios, proportions, and rates. 491 00:28:56,400 --> 00:28:58,400 In doing this, I try to choose, perhaps, 492 00:28:58,400 --> 00:29:01,400 the vocabulary, things that they might not know. 493 00:29:01,400 --> 00:29:03,400 For example, different types of dogs, 494 00:29:03,400 --> 00:29:05,400 different types of flowers. 495 00:29:05,400 --> 00:29:08,400 The example here is the ratio of bulldogs to all the dogs. 496 00:29:09,400 --> 00:29:10,400 No? 497 00:29:11,400 --> 00:29:13,400 The ratio of basset hounds to all the dogs. 498 00:29:13,400 --> 00:29:14,400 No? 499 00:29:15,400 --> 00:29:17,400 This is also helpful in building vocabulary, 500 00:29:17,400 --> 00:29:19,400 because you can choose words that you think 501 00:29:19,400 --> 00:29:21,400 that they don't know 502 00:29:21,400 --> 00:29:23,400 and that they could learn rather easily like this. 503 00:29:24,100 --> 00:29:26,100 Let's go on to an early look at mathematics. 504 00:29:28,100 --> 00:29:30,100 One of the things that they enjoy doing 505 00:29:30,100 --> 00:29:34,100 is talking about Leonardo Fibonacci, 506 00:29:34,100 --> 00:29:36,100 because many of you have heard of him 507 00:29:36,100 --> 00:29:38,100 through the Da Vinci code. 508 00:29:38,100 --> 00:29:40,100 He's become rather popular. 509 00:29:40,100 --> 00:29:42,100 The Fibonacci sequence 510 00:29:42,100 --> 00:29:45,100 has become rather well-known in recent times. 511 00:29:47,100 --> 00:29:49,100 In the early 1200s, 512 00:29:49,100 --> 00:29:52,100 an influential Italian mathematician 513 00:29:52,800 --> 00:29:54,800 named Fibonacci was one of the strongest advocates 514 00:29:54,800 --> 00:29:56,800 – and these are the words that would be in green – 515 00:29:56,800 --> 00:29:58,800 for adopting the Hindu-Arabic 10-digit numbering system 516 00:29:58,800 --> 00:30:00,800 with place value. 517 00:30:00,800 --> 00:30:03,800 In 12002, he wrote a famous algebra text 518 00:30:03,800 --> 00:30:05,800 called Liber Abaci. 519 00:30:05,800 --> 00:30:07,800 This text was not only argued in favor 520 00:30:07,800 --> 00:30:09,800 of the Hindu-Arabic numbering system, 521 00:30:09,800 --> 00:30:12,800 but also included a popular word problem 522 00:30:12,800 --> 00:30:14,800 involving the Fibonacci sequence, 523 00:30:14,800 --> 00:30:17,800 a series of numbers with various interesting properties 524 00:30:17,800 --> 00:30:20,800 observed repeatedly in science and nature, 525 00:30:21,500 --> 00:30:23,500 including areas like plant growth and heredity. 526 00:30:25,500 --> 00:30:27,500 Shall we see how our peanut project is going? 527 00:30:28,200 --> 00:30:30,200 Okay. 528 00:30:33,200 --> 00:30:35,200 I need something. Just a moment. 529 00:30:39,200 --> 00:30:41,200 All right. 530 00:30:45,200 --> 00:30:47,200 You memorized your peanuts. 531 00:30:47,200 --> 00:30:49,200 You know them personally? 532 00:30:49,200 --> 00:30:51,200 Okay. 533 00:30:51,200 --> 00:30:53,200 Please put your peanut on this dish. 534 00:30:53,200 --> 00:30:55,200 Okay. 535 00:30:55,900 --> 00:30:57,900 All right. 536 00:30:57,900 --> 00:30:59,900 Now what we're going to do is take a small group. 537 00:30:59,900 --> 00:31:01,900 You can even take a larger group than this. 538 00:31:01,900 --> 00:31:03,900 And then you take their peanuts, 539 00:31:03,900 --> 00:31:05,900 and you take them and you mix them 540 00:31:05,900 --> 00:31:07,900 with approximately, I don't know, 541 00:31:07,900 --> 00:31:09,900 a bunch more? No? 542 00:31:09,900 --> 00:31:11,900 Then we mix them up. 543 00:31:11,900 --> 00:31:13,900 And I hope this is going to work. 544 00:31:13,900 --> 00:31:15,900 It is a bit like a magic act. 545 00:31:15,900 --> 00:31:17,900 I want you to find your peanut 546 00:31:17,900 --> 00:31:19,900 and tell me why it's yours. 547 00:31:19,900 --> 00:31:21,900 All right? 548 00:31:21,900 --> 00:31:23,900 Now you can touch them. 549 00:31:24,600 --> 00:31:26,600 Why is that peanut yours? 550 00:31:26,600 --> 00:31:28,600 I'm going to tell you why this peanut is mine. 551 00:31:28,600 --> 00:31:30,600 Okay. Good. Exactly. That's exactly what I want. 552 00:31:30,600 --> 00:31:32,600 This peanut is mine because right here 553 00:31:32,600 --> 00:31:34,600 I remember there were cracks. 554 00:31:34,600 --> 00:31:36,600 Uh-huh. Exactly. 555 00:31:36,600 --> 00:31:38,600 And right in the center 556 00:31:38,600 --> 00:31:40,600 there were several spots 557 00:31:40,600 --> 00:31:42,600 and then it had this little dippity thing. 558 00:31:42,600 --> 00:31:44,600 A dippity thing. All right. 559 00:31:48,600 --> 00:31:50,600 Perfect. Did you find your peanut? 560 00:31:50,600 --> 00:31:52,600 Let me see. Which one is it? 561 00:31:53,300 --> 00:31:55,300 Why is it yours? 562 00:31:55,300 --> 00:31:57,300 It has a long crack here 563 00:31:57,300 --> 00:31:59,300 and the center is discolored. 564 00:31:59,300 --> 00:32:01,300 Okay. Good. 565 00:32:01,300 --> 00:32:03,300 So that was what you determined. 566 00:32:03,300 --> 00:32:05,300 Did you find your peanut? 567 00:32:05,300 --> 00:32:07,300 Okay. I think this one here is mine 568 00:32:07,300 --> 00:32:09,300 because there's no peanut. 569 00:32:09,300 --> 00:32:11,300 It has no holes, no cracks, 570 00:32:11,300 --> 00:32:13,300 no discoloration. 571 00:32:13,300 --> 00:32:15,300 It's the perfect peanut. 572 00:32:15,300 --> 00:32:17,300 It's the perfect peanut. 573 00:32:17,300 --> 00:32:19,300 And yours? 574 00:32:19,300 --> 00:32:21,300 I know this is my peanut. 575 00:32:22,000 --> 00:32:24,000 Uh-huh. 576 00:32:28,000 --> 00:32:30,000 Perfect. See? 577 00:32:30,000 --> 00:32:32,000 So this is a fun activity that you can add 578 00:32:32,000 --> 00:32:34,000 once you've done some 579 00:32:34,000 --> 00:32:36,000 more serious activities. 580 00:32:36,000 --> 00:32:38,000 You can add this just to lighten things up a little bit. 581 00:32:38,000 --> 00:32:40,000 Thank you very much. 582 00:32:40,000 --> 00:32:42,000 Thank you. 583 00:32:48,000 --> 00:32:50,000 All right. Let's go back to our Fibonacci sequence. 584 00:32:50,700 --> 00:32:52,700 Are any of you familiar with the Fibonacci sequence? 585 00:32:52,700 --> 00:32:54,700 No? 586 00:32:54,700 --> 00:32:56,700 The Fibonacci sequence is a series of numbers. 587 00:32:56,700 --> 00:32:58,700 It's a sequence of numbers 588 00:32:58,700 --> 00:33:00,700 in which each number 589 00:33:00,700 --> 00:33:02,700 is the sum 590 00:33:02,700 --> 00:33:04,700 of the two numbers that precedes it. 591 00:33:04,700 --> 00:33:06,700 For example, 1, 2, 592 00:33:06,700 --> 00:33:08,700 1 plus 2, 3. 593 00:33:08,700 --> 00:33:10,700 Oop. Didn't want to do that. Sorry. 594 00:33:10,700 --> 00:33:12,700 You just touch it and it moves. 595 00:33:12,700 --> 00:33:14,700 1 and 2 596 00:33:14,700 --> 00:33:16,700 equal 3. 2 and 3, 597 00:33:16,700 --> 00:33:18,700 5. 3 and 5, 8. 598 00:33:19,400 --> 00:33:21,400 5 and 8, 13. 599 00:33:21,400 --> 00:33:23,400 8 and 13, 21, and so on. 600 00:33:23,400 --> 00:33:25,400 This is the Fibonacci sequence. 601 00:33:25,400 --> 00:33:27,400 Why is it 602 00:33:27,400 --> 00:33:29,400 particularly important? 603 00:33:29,400 --> 00:33:31,400 Because these are the 604 00:33:31,400 --> 00:33:33,400 proportions that we can 605 00:33:33,400 --> 00:33:35,400 find also in nature, 606 00:33:35,400 --> 00:33:37,400 in architecture, 607 00:33:37,400 --> 00:33:39,400 and in art. 608 00:33:39,400 --> 00:33:41,400 They're considered 609 00:33:41,400 --> 00:33:43,400 numbers of, let's say, 610 00:33:43,400 --> 00:33:45,400 beauty in proportions. 611 00:33:45,400 --> 00:33:47,400 No? 612 00:33:48,100 --> 00:33:50,100 The phalanges. 613 00:33:50,100 --> 00:33:52,100 There's a ruler up above. 614 00:33:52,100 --> 00:33:54,100 2, 3, 5, 8. 615 00:33:54,100 --> 00:33:56,100 Other examples? 616 00:33:56,100 --> 00:33:58,100 In normal plant growth, 617 00:33:58,100 --> 00:34:00,100 one stem that branches out 618 00:34:00,100 --> 00:34:02,100 into 2, 619 00:34:02,100 --> 00:34:04,100 3, 5, 620 00:34:04,100 --> 00:34:06,100 and 8. 621 00:34:06,100 --> 00:34:08,100 There are also some in the Last Supper, 622 00:34:08,100 --> 00:34:10,100 but I don't remember and you can't see 623 00:34:10,100 --> 00:34:12,100 the picture very well. 624 00:34:12,100 --> 00:34:14,100 But if you do look it up online, 625 00:34:14,100 --> 00:34:16,100 you'll find the different proportions. 626 00:34:16,800 --> 00:34:18,800 The proportion 627 00:34:18,800 --> 00:34:20,800 in the rectangle. 628 00:34:20,800 --> 00:34:22,800 The Vitruvian Man. 629 00:34:22,800 --> 00:34:24,800 This is also very good 630 00:34:24,800 --> 00:34:26,800 as an exercise. 631 00:34:26,800 --> 00:34:28,800 As you can see, if you get a perfectly proportioned 632 00:34:28,800 --> 00:34:30,800 photograph of the original, 633 00:34:30,800 --> 00:34:32,800 you can see Da Vinci's 634 00:34:32,800 --> 00:34:34,800 scale 635 00:34:34,800 --> 00:34:36,800 at the bottom. 636 00:34:36,800 --> 00:34:38,800 What I've done with students is give them a piece of cardboard, 637 00:34:38,800 --> 00:34:40,800 it has to be cut very precisely, 638 00:34:40,800 --> 00:34:42,800 and had them use this 639 00:34:42,800 --> 00:34:44,800 part of the scale that's nice and clear 640 00:34:45,500 --> 00:34:47,500 to make a sort of 641 00:34:47,500 --> 00:34:49,500 a ruler. 642 00:34:49,500 --> 00:34:51,500 When you use this ruler, you can actually see 643 00:34:51,500 --> 00:34:53,500 that the nose is exactly 1, 644 00:34:53,500 --> 00:34:55,500 the distance between the eyes is exactly 2, 645 00:34:55,500 --> 00:34:57,500 the mouth is exactly 1, 646 00:34:57,500 --> 00:34:59,500 the wrist, this is good for learning parts of the body 647 00:34:59,500 --> 00:35:01,500 that they might not know, 648 00:35:01,500 --> 00:35:03,500 the wrist, the ankle, waist, 649 00:35:03,500 --> 00:35:05,500 shoulders, 650 00:35:07,500 --> 00:35:09,500 etc. 651 00:35:11,500 --> 00:35:13,500 Expect middle school 652 00:35:14,200 --> 00:35:16,200 students, the first thing that they're going to measure 653 00:35:16,200 --> 00:35:18,200 will obviously be 1, 654 00:35:18,200 --> 00:35:20,200 and it is a perfect 1. 655 00:35:20,200 --> 00:35:22,200 This is 656 00:35:22,200 --> 00:35:24,200 the word problem, 657 00:35:24,200 --> 00:35:26,200 I don't know how much time we have, 658 00:35:26,200 --> 00:35:28,200 10 minutes? Ok, I'll try to hurry up. 659 00:35:28,200 --> 00:35:30,200 The Fibonacci sequence actually 660 00:35:30,200 --> 00:35:32,200 was expressed in Liber Abici under the form 661 00:35:32,200 --> 00:35:34,200 of a riddle. He didn't just write 662 00:35:34,200 --> 00:35:36,200 a mathematical problem, he wrote a riddle. 663 00:35:36,200 --> 00:35:38,200 It talked about 664 00:35:38,200 --> 00:35:40,200 rabbits, and it said exactly, 665 00:35:40,200 --> 00:35:42,200 I hope I have it here easily, 666 00:35:44,200 --> 00:35:46,200 It said, 667 00:35:46,200 --> 00:35:48,200 a certain man 668 00:35:48,200 --> 00:35:50,200 put a pair of rabbits 669 00:35:50,200 --> 00:35:52,200 in a place surrounded on all sides 670 00:35:52,200 --> 00:35:54,200 by a wall. 671 00:35:54,200 --> 00:35:56,200 How many pairs of rabbits can be produced 672 00:35:56,200 --> 00:35:58,200 from that pair in a year 673 00:35:58,200 --> 00:36:00,200 if it is supposed that every month 674 00:36:00,200 --> 00:36:02,200 each pair begets 675 00:36:02,200 --> 00:36:04,200 a new pair from which the second month on 676 00:36:04,200 --> 00:36:06,200 becomes productive? 677 00:36:06,200 --> 00:36:08,200 So what have we got? 678 00:36:08,200 --> 00:36:10,200 This is a pair 679 00:36:10,200 --> 00:36:12,200 of rabbits, 680 00:36:12,900 --> 00:36:14,900 this is our first month 681 00:36:14,900 --> 00:36:16,900 we have one pair, not one rabbit, 682 00:36:16,900 --> 00:36:18,900 a pair of adult rabbits. 683 00:36:18,900 --> 00:36:20,900 In the second month we have that same rabbit 684 00:36:20,900 --> 00:36:22,900 and it's one pair of offspring. 685 00:36:22,900 --> 00:36:24,900 In the third month 686 00:36:24,900 --> 00:36:26,900 I have the original rabbit plus the baby rabbit 687 00:36:26,900 --> 00:36:28,900 it has produced, plus this rabbit 688 00:36:28,900 --> 00:36:30,900 which has reached maturity. 689 00:36:30,900 --> 00:36:32,900 In the fourth month I will have my original rabbit 690 00:36:32,900 --> 00:36:34,900 plus the baby rabbit, plus this 691 00:36:34,900 --> 00:36:36,900 rabbit which has grown up, 692 00:36:36,900 --> 00:36:38,900 this rabbit who is here and has produced 693 00:36:38,900 --> 00:36:40,900 now a new pair of rabbits. 694 00:36:41,600 --> 00:36:43,600 Fifth month the same thing, the original rabbit 695 00:36:43,600 --> 00:36:45,600 baby rabbit, this one has grown up 696 00:36:45,600 --> 00:36:47,600 and if you go on you'll find 697 00:36:47,600 --> 00:36:49,600 all these numbers are Fibonacci 698 00:36:49,600 --> 00:36:51,600 numbers, one, two, three, 699 00:36:51,600 --> 00:36:53,600 five, eight, 700 00:36:53,600 --> 00:36:55,600 etc. 701 00:36:59,600 --> 00:37:01,600 A number in the Fibonacci sequence 702 00:37:01,600 --> 00:37:03,600 divided by the number that comes 703 00:37:03,600 --> 00:37:05,600 immediately before it results in 704 00:37:05,600 --> 00:37:07,600 a number very close to the golden ratio 705 00:37:07,600 --> 00:37:09,600 or phi. The higher number 706 00:37:10,300 --> 00:37:12,300 in the sequence, the closer the quotient is to the value 707 00:37:12,300 --> 00:37:14,300 of phi, an irrational number believed 708 00:37:14,300 --> 00:37:16,300 to have divine properties representing 709 00:37:16,300 --> 00:37:18,300 the word or signature in God in nature. 710 00:37:18,300 --> 00:37:20,300 Okay, I don't think we have too much 711 00:37:20,300 --> 00:37:22,300 time for this, but if you want to, something 712 00:37:22,300 --> 00:37:24,300 that's very, an interesting 713 00:37:24,300 --> 00:37:26,300 activity is to have students 714 00:37:26,300 --> 00:37:28,300 write 715 00:37:28,300 --> 00:37:30,300 on a piece of paper, do they have this? 716 00:37:30,300 --> 00:37:32,300 No? 717 00:37:32,300 --> 00:37:34,300 This other one? 718 00:37:36,300 --> 00:37:38,300 I don't know if we'll have time, but we'll try it 719 00:37:39,000 --> 00:37:41,000 anyway. You can do it at home if you don't have time here. 720 00:37:41,000 --> 00:37:43,000 What I want you to do is 721 00:37:43,000 --> 00:37:45,000 write on these lines 722 00:37:49,000 --> 00:37:51,000 These are 723 00:37:51,000 --> 00:37:53,000 examples of the divine proportion 724 00:37:53,000 --> 00:37:55,000 in art, 725 00:37:55,000 --> 00:37:57,000 the flagellation of Christ, 726 00:37:57,000 --> 00:37:59,000 Piero della Francesca, the Mona Lisa, 727 00:37:59,000 --> 00:38:01,000 we have a perfect 728 00:38:01,000 --> 00:38:03,000 golden triangle. 729 00:38:03,000 --> 00:38:05,000 I don't know if I can maybe explain that to you 730 00:38:05,000 --> 00:38:07,000 quickly. 731 00:38:07,700 --> 00:38:09,700 The golden triangle is based on the 732 00:38:09,700 --> 00:38:11,700 proportion 733 00:38:13,700 --> 00:38:15,700 based on a proportion of a line segment. 734 00:38:15,700 --> 00:38:17,700 A line segment 735 00:38:17,700 --> 00:38:19,700 divided so that A 736 00:38:19,700 --> 00:38:21,700 plus B is to A 737 00:38:21,700 --> 00:38:23,700 as A is to B. 738 00:38:23,700 --> 00:38:25,700 Simple as that. The number that 739 00:38:25,700 --> 00:38:27,700 we come up with when we express this proportion 740 00:38:27,700 --> 00:38:29,700 is a number, 741 00:38:29,700 --> 00:38:31,700 an irrational number like pi 742 00:38:31,700 --> 00:38:33,700 called phi. 743 00:38:34,400 --> 00:38:36,400 If we take a perfect 744 00:38:36,400 --> 00:38:38,400 square and divide 745 00:38:38,400 --> 00:38:40,400 it in half, 746 00:38:40,400 --> 00:38:42,400 exactly in half, 747 00:38:42,400 --> 00:38:44,400 and then draw a 748 00:38:44,400 --> 00:38:46,400 diagonal to the corner, 749 00:38:46,400 --> 00:38:48,400 and from this diagonal draw a 750 00:38:48,400 --> 00:38:50,400 circle, and then we 751 00:38:50,400 --> 00:38:52,400 bring this up 752 00:38:52,400 --> 00:38:54,400 to meet the 753 00:38:54,400 --> 00:38:56,400 circumference, we will 754 00:38:56,400 --> 00:38:58,400 have a perfect golden 755 00:38:58,400 --> 00:39:00,400 triangle. And this golden triangle 756 00:39:00,400 --> 00:39:02,400 can be found in art 757 00:39:03,100 --> 00:39:05,100 in architecture 758 00:39:05,100 --> 00:39:07,100 in nature, and just 759 00:39:07,100 --> 00:39:09,100 about everywhere. 760 00:39:09,100 --> 00:39:11,100 The Vitruvian Man, Piero della Francesca, 761 00:39:11,100 --> 00:39:13,100 divided exactly here, 762 00:39:13,100 --> 00:39:15,100 the face of the Mona Lisa, which is 763 00:39:15,100 --> 00:39:17,100 a golden rectangle 764 00:39:17,100 --> 00:39:19,100 dividing the face 765 00:39:19,100 --> 00:39:21,100 in perfect proportion. 766 00:39:21,100 --> 00:39:23,100 Seashells, 767 00:39:23,100 --> 00:39:25,100 golden rectangle, 768 00:39:25,100 --> 00:39:27,100 what happens here is 769 00:39:27,100 --> 00:39:29,100 if we take this golden rectangle 770 00:39:29,100 --> 00:39:31,100 and we 771 00:39:31,400 --> 00:39:33,400 find a 772 00:39:33,400 --> 00:39:35,400 perfect square, we will be 773 00:39:35,400 --> 00:39:37,400 left with another golden 774 00:39:37,400 --> 00:39:39,400 rectangle. 775 00:39:39,400 --> 00:39:41,400 If we take this golden rectangle 776 00:39:41,400 --> 00:39:43,400 and we take a square out of it, 777 00:39:43,400 --> 00:39:45,400 we will be left with another golden 778 00:39:45,400 --> 00:39:47,400 rectangle. If we take that 779 00:39:47,400 --> 00:39:49,400 golden rectangle and 780 00:39:49,400 --> 00:39:51,400 we take a square out of it, we will be left 781 00:39:51,400 --> 00:39:53,480 with another 782 00:39:53,480 --> 00:39:55,480 golden rectangle and this will go on 783 00:39:55,480 --> 00:39:57,480 and on and on to infinity. 784 00:39:57,480 --> 00:39:59,480 No? So 785 00:39:59,860 --> 00:40:01,860 I think I'm going to have to speed 786 00:40:01,860 --> 00:40:03,860 things up a bit. How much time have we got? 787 00:40:03,860 --> 00:40:05,860 Okay. Try this. 788 00:40:05,860 --> 00:40:07,860 Choose any two successive numbers 789 00:40:07,860 --> 00:40:09,860 in the Fibonacci sequence, the lower 790 00:40:09,860 --> 00:40:11,860 before the higher. For example, two 791 00:40:11,860 --> 00:40:13,860 and three 792 00:40:13,860 --> 00:40:15,860 or five and eight. 793 00:40:15,860 --> 00:40:17,860 They have to be low numbers because 794 00:40:17,860 --> 00:40:19,860 your calculators won't be able to do 795 00:40:19,860 --> 00:40:21,860 them otherwise. 796 00:40:23,860 --> 00:40:25,860 So choose two low numbers 797 00:40:25,860 --> 00:40:27,860 in the Fibonacci sequence 798 00:40:28,240 --> 00:40:30,240 and do this 799 00:40:30,240 --> 00:40:32,240 problem. Now, add these two numbers 800 00:40:32,240 --> 00:40:34,240 and put their sum on the third nine. 801 00:40:34,240 --> 00:40:36,240 So let's say I have five and eight. 802 00:40:36,240 --> 00:40:38,240 I add them and I put their sum on this line. 803 00:40:38,240 --> 00:40:40,240 Then I add this number to this number 804 00:40:40,240 --> 00:40:42,240 and I put that number here. 805 00:40:42,240 --> 00:40:44,240 The number before and then 806 00:40:44,240 --> 00:40:46,240 the number before added to the number 807 00:40:46,240 --> 00:40:48,240 that comes after it. 808 00:40:48,240 --> 00:40:50,240 Then, 809 00:40:50,240 --> 00:40:52,240 I have to do this twenty times. 810 00:40:52,240 --> 00:40:54,240 Do I have anyone who would be willing 811 00:40:54,240 --> 00:40:56,240 to do that quickly with a calculator? 812 00:40:56,620 --> 00:40:58,620 Anyone who would like 813 00:40:58,620 --> 00:41:00,620 to do a quick math problem? 814 00:41:00,620 --> 00:41:02,620 A vision? 815 00:41:03,000 --> 00:41:05,000 Anyone who would like 816 00:41:05,000 --> 00:41:07,000 to do a quick math problem? 817 00:41:07,000 --> 00:41:09,000 A vision? 818 00:41:33,000 --> 00:41:35,000 These are word analogies. 819 00:41:35,000 --> 00:41:37,000 We won't have time to do them today, 820 00:41:37,000 --> 00:41:39,000 but they're very, very useful. 821 00:41:39,000 --> 00:41:41,000 If you do want to look into them, 822 00:41:41,000 --> 00:41:43,000 it's very easy to find out 823 00:41:43,000 --> 00:41:45,000 what word analogies are 824 00:41:45,000 --> 00:41:47,000 and how are they related to, 825 00:41:47,000 --> 00:41:49,000 for example, a simple proportion. 826 00:41:49,000 --> 00:41:51,000 For example, five is to ten, 827 00:41:51,000 --> 00:41:53,000 is twenty-five is to fifty, 828 00:41:53,000 --> 00:41:55,000 is twenty-five to fifty, 829 00:41:55,000 --> 00:41:57,000 is twenty-five to fifty, 830 00:41:57,000 --> 00:41:59,000 is twenty-five to fifty, 831 00:41:59,000 --> 00:42:01,000 is twenty-five to fifty, 832 00:42:01,380 --> 00:42:03,380 is twenty-five is to fifty. 833 00:42:03,380 --> 00:42:05,380 We can also do word analogies, 834 00:42:05,380 --> 00:42:07,380 such as, bee is to buzz, 835 00:42:07,380 --> 00:42:09,380 as cow is to moo. 836 00:42:09,380 --> 00:42:11,380 Or, 837 00:42:11,380 --> 00:42:13,380 cabbage is to vegetable, 838 00:42:13,380 --> 00:42:15,380 as rose is to flower. 839 00:42:15,380 --> 00:42:17,380 You can make up some simple multiple choice 840 00:42:17,380 --> 00:42:19,380 problems. 841 00:42:19,380 --> 00:42:21,380 All kinds of facts. 842 00:42:21,380 --> 00:42:23,380 George Washington is to first, 843 00:42:23,380 --> 00:42:25,380 as Abraham Lincoln is to sixteenth. 844 00:42:25,380 --> 00:42:27,380 And these work just very similar 845 00:42:27,380 --> 00:42:29,380 to do a proportion. 846 00:42:29,760 --> 00:42:31,760 The other as something else 847 00:42:31,760 --> 00:42:33,760 is to something else. 848 00:42:33,760 --> 00:42:35,760 Okay? 849 00:42:35,760 --> 00:42:37,760 I think I have to conclude. 850 00:42:37,760 --> 00:42:39,760 A little bit? Okay. 851 00:42:39,760 --> 00:42:41,760 Alright, the results of an anonymous questionnaire 852 00:42:41,760 --> 00:42:43,760 that I gave to my pupils. 853 00:42:43,760 --> 00:42:45,760 I had about 42 pupils, 854 00:42:45,760 --> 00:42:47,760 which is, I'd say, 855 00:42:47,760 --> 00:42:49,760 a good one-third of all the students 856 00:42:49,760 --> 00:42:51,760 that are in the third year. 857 00:42:51,760 --> 00:42:53,760 So it's a nice sample in two different classes. 858 00:42:53,760 --> 00:42:55,760 So 36 of them 859 00:42:55,760 --> 00:42:57,760 answered this questionnaire because they were at the lesson. 860 00:42:58,140 --> 00:43:00,140 And it was an anonymous 861 00:43:00,140 --> 00:43:02,140 questionnaire. 862 00:43:02,140 --> 00:43:04,140 I wanted them to give me honest 863 00:43:04,140 --> 00:43:06,140 answers to these questions. 864 00:43:06,140 --> 00:43:08,140 Students were asked 865 00:43:08,140 --> 00:43:10,140 to evaluate the difficulty of the course 866 00:43:10,140 --> 00:43:12,140 on a scale of 867 00:43:12,140 --> 00:43:14,140 extremely difficult, 868 00:43:14,140 --> 00:43:16,140 difficult, quite difficult, 869 00:43:16,140 --> 00:43:18,140 not so difficult, 870 00:43:18,140 --> 00:43:20,140 quite easy, very easy. 871 00:43:20,140 --> 00:43:22,140 No? 872 00:43:22,140 --> 00:43:24,140 I asked them how much easier it was to 873 00:43:24,140 --> 00:43:26,140 understand the lessons toward the end of the course 874 00:43:26,520 --> 00:43:28,520 as compared to the beginning. 875 00:43:28,520 --> 00:43:30,520 I asked them how positive or negative the experience 876 00:43:30,520 --> 00:43:32,520 was for them, which subject they 877 00:43:32,520 --> 00:43:34,520 enjoyed the most, math, science, or geography. 878 00:43:34,520 --> 00:43:36,520 I added a couple of geography lessons 879 00:43:36,520 --> 00:43:38,520 on the United States 880 00:43:38,520 --> 00:43:40,520 and Canada just to round the course 881 00:43:40,520 --> 00:43:42,520 out a bit. No? 882 00:43:42,520 --> 00:43:44,520 So there just wouldn't all 883 00:43:44,520 --> 00:43:46,520 be math and science. 884 00:43:46,520 --> 00:43:48,520 I asked how comfortable they would be with 885 00:43:48,520 --> 00:43:50,520 following courses involving CLIL methodology 886 00:43:50,520 --> 00:43:52,520 in the future because in Italy 887 00:43:52,520 --> 00:43:54,520 they're planning on introducing 888 00:43:54,900 --> 00:43:56,900 CLIL methodology 889 00:43:56,900 --> 00:43:58,900 in the high schools 890 00:43:58,900 --> 00:44:00,900 in a mandatory way. 891 00:44:02,900 --> 00:44:04,900 I asked if they would recommend the course 892 00:44:04,900 --> 00:44:06,900 to other kids their age 893 00:44:06,900 --> 00:44:08,900 and that if learning English with CLIL methodology 894 00:44:08,900 --> 00:44:10,900 seemed easier than with 895 00:44:10,900 --> 00:44:12,900 traditional methods, and if so, 896 00:44:12,900 --> 00:44:14,900 how much easier? 897 00:44:14,900 --> 00:44:16,900 I also asked them if any 898 00:44:16,900 --> 00:44:18,900 new things they learned, both in content 899 00:44:18,900 --> 00:44:20,900 and in language. I asked them simply, 900 00:44:20,900 --> 00:44:22,900 how much did you learn? 901 00:44:23,280 --> 00:44:25,280 Did you learn nothing? Something? 902 00:44:25,280 --> 00:44:27,280 A lot? 903 00:44:27,280 --> 00:44:29,280 Moltissimo? Which you can't translate 904 00:44:29,280 --> 00:44:31,280 very well into English. No? 905 00:44:33,280 --> 00:44:35,280 And these were our results. 906 00:44:35,280 --> 00:44:37,280 50% 907 00:44:37,280 --> 00:44:39,280 of the students approximately thought 908 00:44:39,280 --> 00:44:41,280 the course was difficult or quite difficult. 909 00:44:41,280 --> 00:44:43,280 50% approximately said it was 910 00:44:43,280 --> 00:44:45,280 easy. 911 00:44:45,280 --> 00:44:47,280 73% said that 912 00:44:47,280 --> 00:44:49,280 it was easier or much easier to understand 913 00:44:49,280 --> 00:44:51,280 the lessons by the end of the course. 914 00:44:53,280 --> 00:44:55,280 89% 915 00:44:55,280 --> 00:44:57,280 said the course was a positive or 916 00:44:57,280 --> 00:44:59,280 a very positive experience. 917 00:45:01,280 --> 00:45:03,280 43 liked science 918 00:45:03,280 --> 00:45:05,280 best. 43% liked science best. 919 00:45:05,280 --> 00:45:07,280 Math and geography approximately 920 00:45:07,280 --> 00:45:09,280 were even. 921 00:45:13,280 --> 00:45:15,280 100% said that they felt at least 922 00:45:15,280 --> 00:45:17,280 a little more comfortable about future CLIL 923 00:45:17,280 --> 00:45:19,280 experiences, and 64% 924 00:45:19,280 --> 00:45:21,280 said they were much 925 00:45:21,660 --> 00:45:23,660 more comfortable 926 00:45:23,660 --> 00:45:25,660 with future CLIL experiences. 927 00:45:27,660 --> 00:45:29,660 94% would recommend this course 928 00:45:29,660 --> 00:45:31,660 to other kids their age, and that was 929 00:45:31,660 --> 00:45:33,660 the one I was probably most proud of. 930 00:45:37,660 --> 00:45:39,660 75% said 931 00:45:39,660 --> 00:45:41,660 that learning English with CLIL was much easier 932 00:45:41,660 --> 00:45:43,660 or much easier 933 00:45:43,660 --> 00:45:45,660 than with traditional methods. 934 00:45:47,660 --> 00:45:49,660 64% said 935 00:45:50,040 --> 00:45:52,040 that they learned a lot of new things, 936 00:45:52,040 --> 00:45:54,040 and 100% said that they learned 937 00:45:54,040 --> 00:45:56,040 something new. 938 00:45:58,040 --> 00:46:00,040 The next question will now be 939 00:46:00,040 --> 00:46:02,040 I didn't put this on the questionnaire, 940 00:46:02,040 --> 00:46:04,040 but next year I will. 941 00:46:04,040 --> 00:46:06,040 Was it fun? 942 00:46:08,040 --> 00:46:10,040 I don't know if you didn't hand out any of those 943 00:46:10,040 --> 00:46:12,040 cards, but if anybody has any... 944 00:46:12,040 --> 00:46:14,040 The results. 945 00:46:14,040 --> 00:46:16,040 Did you come up with the results? 946 00:46:20,040 --> 00:46:22,040 What's the number? 947 00:46:24,040 --> 00:46:26,040 Okay, that's the final number 948 00:46:26,040 --> 00:46:28,040 on the 20th line. All right, now take that number, 949 00:46:28,040 --> 00:46:30,040 the final number, and divide it 950 00:46:30,040 --> 00:46:32,040 by the number that comes before it. 951 00:46:32,040 --> 00:46:34,040 And what did you get? 952 00:46:36,040 --> 00:46:38,040 It should be, 953 00:46:38,040 --> 00:46:40,040 if you did the calculation correctly... 954 00:46:46,040 --> 00:46:48,040 I'm sorry. 955 00:46:50,040 --> 00:46:52,040 I might have to do it. 956 00:47:08,040 --> 00:47:10,040 Come on. 957 00:47:14,040 --> 00:47:16,040 It's taking me a while. 958 00:47:16,040 --> 00:47:18,040 Oh well. 959 00:47:20,040 --> 00:47:22,040 Okay. 960 00:47:30,040 --> 00:47:32,040 It should be 961 00:47:32,040 --> 00:47:34,040 1.683. 962 00:47:34,040 --> 00:47:36,040 No? 963 00:47:36,040 --> 00:47:38,040 And be an infinite number. 964 00:47:38,040 --> 00:47:40,040 Is that the result you got? 965 00:47:40,040 --> 00:47:42,040 It should correspond 966 00:47:42,040 --> 00:47:44,040 exactly to the number 967 00:47:44,040 --> 00:47:46,040 5, which is... 968 00:47:46,040 --> 00:47:48,040 What number did you get? 969 00:47:48,420 --> 00:47:50,420 1.... 970 00:47:52,420 --> 00:47:54,420 16444. 971 00:47:54,420 --> 00:47:56,420 It should get very, very close 972 00:47:56,420 --> 00:47:58,420 to that number. 973 00:47:58,420 --> 00:48:00,420 I think that's about all. 974 00:48:00,420 --> 00:48:02,420 Is it about time 975 00:48:02,420 --> 00:48:04,420 that I'm supposed to finish?