Masterclass de Matemáticas (Sesión 30 Septiembre - AM) Parte 2 — Transcript

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1. 0:00for students and in this way be able to
2. 0:04continue. Ready? Perfect. So, when it
3. 0:10comes to practice, well, here we are
4. 0:12going to do it, we have planned it
5. 0:14differently. However, well, we are
6. 0:19going to continue and we have a problem
7. 0:25here at the moment, which is that the
8. 0:27same educational institution wants to
9. 0:30know the expectations of 11th grade
10. 0:32students regarding their future, but it
11. 0:35cannot ask all the young people in the
12. 0:37country. Yes, because it is quite clear
13. 0:42that the institution does not possess
14. 0:44this database, meaning it lacks the
15. 0:47data for all of the institutions
16. 0:49involved, does it not? Only the one for
17. 0:53its institution. So, in this case, what
18. 0:57the institution can do is conduct the
19. 1:02survey, apply that survey as such to
20. 1:05those people who correspond to 11th
21. 1:08grade. Yes. So, well, Juan, tell me. If
22. 1:15you worked in an educational
23. 1:16institution and wanted to know what
24. 1:18expectations 11th grade students have
25. 1:20regarding their future, what types of
26. 1:25questions could you ask?
27. 1:35>> What types of questions could I ask?
28. 1:37>> Yes. If you wanted to know what
29. 1:42expectations 11th graders have, tell me
30. 1:44what you would think of asking, like,
31. 1:48>> what sectors they like, what they've
32. 1:50seen themselves in after leaving school
33. 1:53. I would also ask them, what trends
34. 2:02they've seen on social media regarding
35. 2:05jobs, regarding places they'd like to
36. 2:07go to work or study. For example, in my
37. 2:11case, my generation is very much into
38. 2:14going to Canada or those countries to
39. 2:16also learn French and English. So, I
40. 2:20would focus more on those questions to
41. 2:22find out what they see themselves in,
42. 2:24if they see themselves as entrepreneurs
43. 2:25, if they see themselves in projects
44. 2:29together. That's the general rule,
45. 2:31teacher.
46. 2:33>> Okay, Juan, thank you very much. Indeed
47. 2:36, so here we have several questions
48. 2:44that we had raised here. The first one
49. 2:52is, what is your main option when you
50. 2:55finish school? So, Juan, we always have
51. 2:58, well, the 11th graders always have
52. 3:00that question, and at one point, we
53. 3:02also experienced that exact same doubt.
54. 3:05What options do we have after finishing
55. 3:07high school? Right? I finish high
56. 3:09school and now what do I do? Right? So,
57. 3:12the first question here is, what is
58. 3:14your main option after finishing high
59. 3:17school? So, continue university studies
60. 3:20, pursue technical or technological
61. 3:22studies, work, start a business, study
62. 3:25and work. Or I haven't decided yet.
63. 3:29Tell me, Juan, when you finished 11th
64. 3:31grade, which was your main option out
65. 3:34of the ones we're discussing here? Out
66. 3:37of the ones I'm showing? Tell me.
67. 3:43>> Uh, do you know what they're there,
68. 3:44teacher? What character? Uh, my main
69. 3:47option was engineering. You can't
70. 3:51>> see what I'm projecting, Juan. Oh, wait
71. 3:56. Now yes.
72. 3:58>> Ready. So, the first one is, what is
73. 3:59your main option after finishing high
74. 4:01school? So, tell us which ones were
75. 4:03yours, or which ones those were.
76. 4:06>> Mine was to continue university studies
77. 4:10, teacher.
78. 4:12>> Okay. Well, let us remember that mine
79. 4:16was the same, however, there are some
80. 4:18kids in this current era, is that not
81. 4:21true? The topic of entrepreneurship has
82. 4:24been popular, right? Because many of
83. 4:28them want to, as you mentioned, the
84. 4:31trends on social media right now are
85. 4:34about entrepreneurship, like
86. 4:37influencers, like YouTubers, right? So
87. 4:42it can also be entrepreneurship.
88. 4:44Regarding studying and working, many
89. 4:46have also had that option, right? They
90. 4:49study during the day, they study at
91. 4:51night and work during the day or the
92. 4:54other way around, they study during the
93. 4:56day and work at night or they still
94. 5:01haven't decided, right? Many people
95. 5:04haven't decided this in 11th grade. And
96. 5:08here's another interesting question, as
97. 5:11such, which area of training interests
98. 5:14you the most. Yes. So here's what you
99. 5:19mentioned, Juan, and it was about what
100. 5:21branch or sector you wanted to focus on
101. 5:23. So, health sciences, engineering and
102. 5:28technology, economic and administrative
103. 5:31sciences, art, design and communication
104. 5:33, education, they haven't decided yet.
105. 5:37And another one right now, Juan, if you
106. 5:39knew that educational institutions have
107. 5:42something called vocational guidance.
108. 5:48Yes, my teacher Pati, yes, I knew that
109. 5:51they had, uh, the partnership, the
110. 5:53socio-occupational guidance as a
111. 5:56strategy.
112. 5:57>> Exactly. Yes, in fact I know that in
113. 6:00the rotating talks here, uh, within
114. 6:03this same, uh, masterclass experience,
115. 6:06they have also, uh, addressed those
116. 6:09topics. So, yes, it is very important
117. 6:11because many kids still haven't decided
118. 6:14. So this would also be a very good
119. 6:17question to, uh, be able to give, uh,
120. 6:20continuity to that study that the
121. 6:22educational institution wants to do
122. 6:25that is presented in the initial
123. 6:27situation, which corresponds, uh, as
124. 6:30such, to know what expectations those
125. 6:3311th grade kids have, right? when they
126. 6:36leave school. Now, Juan, when you were
127. 6:40you, how prepared did you feel to make
128. 6:43those decisions about your future? Not
129. 6:45at all prepared, not very prepared,
130. 6:48moderately prepared, prepared, or very
131. 6:51prepared? Uh, I felt very prepared,
132. 6:57teacher, because I started the exercise
133. 7:00since tenth grade, in my case.
134. 7:04>> Okay, Juan, interesting. Yes, well, let
135. 7:07us say that our previous generations
136. 7:09perhaps did have a little bit more of
137. 7:11that vision. I am not entirely sure if
138. 7:16young people today truly possess that
139. 7:19vision of feeling either very prepared
140. 7:22or only moderately prepared, which also
141. 7:25corresponds to understanding what
142. 7:27expectations they hold and what those
143. 7:30young people feel as individuals. Back
144. 7:35then, how many hours did you dedicate
145. 7:38to activities related to preparing
146. 7:40yourself for the future? 0 hours, 1 or
147. 7:442 hours, 3 to 5 hours, 6 to 8 hours, or
148. 7:47more than 8 hours. Teacher, I think it
149. 7:52was 1 to 2 hours when I was in 11th
150. 7:54grade at that time.
151. 7:57>> Okay. Juan, it
152. 8:00>> was more like learning about the degree
153. 8:02, reinforcing the basics of mathematics
154. 8:03, since engineering has a lot of
155. 8:05mathematics,
156. 8:07>> but it wasn't like that all the time.
157. 8:11>> Okay, Juan. Well, currently, some
158. 8:14educational institutions have the Sena
159. 8:16agreement, right? Which goes on
160. 8:19preparing the students for that future
161. 8:25after they finish school, bringing them
162. 8:28a bit closer to what corresponds to a
163. 8:30technical or a professional career path
164. 8:32. Well, then, taking this into account,
165. 8:36our survey would respond to the
166. 8:41situation of the institution, which
167. 8:44wants to effectively find out what the
168. 8:48expectations of children are when they
169. 8:51finish grade 11. Yes. Okay, so let's
170. 8:55continue. Ready. So, here we have to
171. 9:07effectively analyze several questions,
172. 9:10right? How are they here? Well, here we
173. 9:18have already collected the information.
174. 9:22Yes, we have already had all the
175. 9:24questions, we analyzed each question.
176. 9:31Now, we were able to review them.
177. 9:38Remember the route. So, we have already
178. 9:40analyzed the questions, we have already
179. 9:42collected the information, right? Now,
180. 9:49something very important comes, which
181. 9:53is organizing the information. Okay, in
182. 9:59this case, we were able to do it in the
183. 10:03development section. Yes. However, I
184. 10:08will take the data again here, the
185. 10:11absolute frequency; specifically, how
186. 10:14many people choose each one of the
187. 10:19available options presented here? Yes.
188. 10:22When I organize that information again,
189. 10:26yes, as we did in the development
190. 10:29section, what we can do is try to
191. 10:37represent that information and for that
192. 10:40we build the graphs. So, we've already
193. 10:43seen how to build them. Yes, we can
194. 10:46build them using tools like Excel. Yes,
195. 10:53we can build them using the Google
196. 10:55Forms application, which already shows
197. 10:58them to us and places the specific
198. 11:01emphasis as such. For every single
199. 11:06question, it shows us a pie chart that
200. 11:09indicates the percentage which
201. 11:12corresponds to each of the questions
202. 11:14that we have asked as such in our
203. 11:17survey. Remember that it is very
204. 11:22important to identify what each graph
205. 11:24is for and what type of graph it
206. 11:29requires. Not all graphs represent the
207. 11:31same thing. What types of graphs do you
208. 11:35know, Juan? Tell us. Professor, Pati, I
209. 11:44know the box plot, the scatter plot,
210. 11:56the bar plot, and there are some graph
211. 11:58styles that are used when you do linear
212. 12:01regressions or logistic regressions,
213. 12:06>> which are also where you generate those
214. 12:08types of graphs, such as trigonometric
215. 12:10functions. Hm. What other graphs? There
216. 12:15are several, professor. There are many
217. 12:16with whiskers, all sorts of things.
218. 12:19>> Okay, perfect, thank you very much.
219. 12:22>> Yes, depending on the type of field,
220. 12:23there are several.
221. 12:26>> Yes, of course. What you say is very
222. 12:28true. Indeed, each individual graph
223. 12:31does generate a specific need in
224. 12:33accordance with what I am looking to
225. 12:36find out. So, in this case, since what
226. 12:41we want to find out are the
227. 12:43expectations that the students have,
228. 12:46yes, indeed, the closest are the bar
229. 12:48graph and the pie chart or circular
230. 12:51graph, right? Which is the one that
231. 12:55represents the percentages in terms of
232. 12:58circular graphs. and in the bar graph,
233. 13:02it is like such a comparison between
234. 13:05the different categories that we have
235. 13:08so that the educational institution can
236. 13:11make the decision to implement, let's
237. 13:15say, this orientation in case, for
238. 13:18example, the most voted option or the
239. 13:23most frequent action option could be
240. 13:25that it is not so prepared. So, let's
241. 13:28say that in these graphs when I
242. 13:31represent the information, yes, many
243. 13:34times it is much better represented
244. 13:38visually and we can see it, let's say,
245. 13:41in different contexts, in this case, in
246. 13:45the situation. Yes. And let's also say
247. 13:51that these statistics are useful not
248. 13:53only to do a survey and so on and have
249. 13:56some data and that's it, but that's not
250. 13:58where the usefulness ends as such, but
251. 14:01that's where that process begins, that
252. 14:03development that I can have regarding
253. 14:09making a very wise decision. Yes, Juan.
254. 14:13You did know, speaking of making a
255. 14:17parenthesis here, that through
256. 14:21statistics, each of the mayors 'offices
257. 14:26of the different municipalities can
258. 14:30actually develop these social programs
259. 14:38and also approve these subsidies. Yes,
260. 14:41you knew about that. Juan, tell us a
261. 14:44little bit.
262. 14:48>> Hm. Profeipe, I didn't know about that,
263. 14:52but statistics do offer us various
264. 14:55applications and functionalities to
265. 14:57know who receives the subsidy. Also,
266. 15:01with statistics, you can review one
267. 15:03based on certain variables and make
268. 15:05decisions there. So, yes, Professor
269. 15:07Pati. Okay, Juan, thank you very much
270. 15:10for sharing your information with us.
271. 15:12Indeed, statistics play a very
272. 15:19important role. In fact, the National
273. 15:23Department of Statistics, yes, relies
274. 15:26on all the studies they do; Well, in
275. 15:30effect, they go to the Department of
276. 15:33Social Development and others, which is
277. 15:36the one that, with the information it
278. 15:39collects, can analyze it after
279. 15:47collecting the information and
280. 15:49effectively know who has or is entitled
281. 15:51to subsidies or not. Before the
282. 15:57pandemic, when they carried out
283. 15:58censuses, they would go to each home;
284. 16:01it was indeed through statistics that
285. 16:03this information was collected by
286. 16:05utilizing the survey technique, which
287. 16:07is the data gathering method that
288. 16:09allowed for making decisions based on
289. 16:11that information once the process was
290. 16:13completed. So, classify the different
291. 16:17households into different levels. Ready
292. 16:21? So, this entire process must be taken
293. 16:25into account, because even though we
294. 16:27may believe that conducting a survey is
295. 16:29very simple, we simply apply it and
296. 16:32that's it. It always has to have that
297. 16:35analysis, that representation, those
298. 16:38conclusions, that interpretation of the
299. 16:40data in the background, and knowing how
300. 16:42to effectively use the correct graph,
301. 16:44right? Uh, depending on the context in
302. 16:48which I'm working and, above all, what
303. 16:50I want to get to. Okay. Here, when I
304. 16:58analyze the results, which was what we
305. 17:00were talking about, there are several
306. 17:02questions here. So, which category has
307. 17:05the highest frequency? So there, in
308. 17:07that part, we analyze which category
309. 17:11really analyzes that part, which has
310. 17:14the lowest frequency, right? And what
311. 17:19percentage as such it represents, that
312. 17:22is, what percentage could that part
313. 17:28represent? So, for example, here the
314. 17:32general formula to find the percentage
315. 17:35it represents is the number of
316. 17:38responses in the category, that is, the
317. 17:41number of people who voted or who
318. 17:44marked that response option, right? And
319. 17:48the total number of respondents. So, as
320. 17:51we did in the development part, which
321. 17:53was a total of eight, then the total
322. 17:55number of respondents in this case
323. 17:57would be eight; and the number of
324. 17:59responses in the category, well, it's
325. 18:02already that of each of the data, and I
326. 18:04multiply that by 100 to finally know
327. 18:07which data, which percentage is the one
328. 18:09that corresponds. So, here we have that
329. 18:17part of results analysis. Ready? And
330. 18:29now, for the closing part, well, Juan,
331. 18:42tell me: what conclusion can we reach
332. 18:45in this case? Based on your experience
333. 18:49and what you've seen, what conclusion
334. 18:50can we reach about the level of
335. 18:51preparation that students feel for
336. 18:53their future? Do you think that at this
337. 18:57moment they feel prepared or not so
338. 19:00much? I think, teacher, not so much. I
339. 19:08would say, based on my experience,
340. 19:11including friends and acquaintances,
341. 19:14that 30%, teacher, are prepared and the
342. 19:17other 70%are like they don't know,
343. 19:19maybe they don't know about
344. 19:22alternatives, they're not sure, and I
345. 19:24feel that we need to reinforce more
346. 19:27support, not only in educational
347. 19:30institutions, but also from families.
348. 19:36>> Yes, Juan, that's true. Indeed, we
349. 19:38don't all have the same options, right?
350. 19:42In terms of options such as whether to
351. 19:44continue or whether to enter the world
352. 19:46of work. So, yes, indeed, sometimes we
353. 19:50do not feel prepared enough to say, "
354. 19:53Well, I am finishing school here, and
355. 19:55then what happens after that exactly?"
356. 19:59So, yes, indeed, I also, from personal
357. 20:03experience, yes, I see that sometimes,
358. 20:06even though in this generation we have
359. 20:10a little more familiarity with
360. 20:13technology and AI, sometimes we don't
361. 20:19feel prepared, yes, to, well, students
362. 20:22don't feel prepared to face the world
363. 20:25and they don't take into account all
364. 20:28the options as such. Well, what do you
365. 20:40find most difficult about organizing
366. 20:43data,
367. 20:48>> teacher? When it's incomplete or also
368. 20:51when the data isn't standardized. For
369. 20:55example, in the case of students,
370. 20:58sometimes the names are misspelled or
371. 21:02have accents or periods, so all that
372. 21:05preparation and cleaning is the most
373. 21:08complicated thing for me. Then comes
374. 21:11the application of statistical tools.
375. 21:14There, it is easier when you already
376. 21:15have clean information, but the initial
377. 21:19part is always the hardest. Okay, Juan,
378. 21:23thank you very much. Yes, well, indeed,
379. 21:26when organizing data, many times the
380. 21:28data is incomplete or, for example,
381. 21:30when, as I was telling you at the
382. 21:32beginning, when it is an open question
383. 21:34that people may answer in their own way
384. 21:42. Many times these answers do not
385. 21:46coincide so much and I can get 80
386. 21:48different data points, so it is a
387. 21:50little more complicated to organize.
388. 21:54Additionally, when it is a fairly large
389. 21:57sample or population, that is when I
390. 22:00can organize them by intervals, right?
391. 22:03In other words, I no longer organize
392. 22:05them, they would no longer be grouped
393. 22:08data, but grouped data in which I have
394. 22:11generated another type of organization.
395. 22:15Yes. Juan, how do you think statistics
396. 22:18help us make a decision? It helps us,
397. 22:24teacher, to make decisions because, uh,
398. 22:27statistics shows how those confidence
399. 22:33levels, those confidence intervals, uh,
400. 22:36based on tests; If one can propose a
401. 22:39hypothesis test, whether that is true
402. 22:41or not, and then, based on...and those
403. 22:44are somewhat more advanced topics after
404. 22:46seeing how mean, median, and all that.
405. 22:50But, after applying all those
406. 22:53techniques, one is given values and,
407. 22:55with those values, one can make
408. 22:58decisions, whether to interpret natural
409. 23:01or social phenomena, or to give
410. 23:03subsidies to certain people. That is
411. 23:07how the power of statistics gives us
412. 23:09reliability based on data, because data
413. 23:13tells the story of the past.
414. 23:16>> Okay, Juan, thank you very much for
415. 23:17your contribution. Indeed, statistics
416. 23:20help us a lot to make decisions, right?
417. 23:24In several, well, I would say in all
418. 23:27contexts, uh, well, in the social
419. 23:29context, as Juan was telling us, as we
420. 23:32were talking about, and that is when
421. 23:35the decision is made to help, uh, with
422. 23:38a subsidy in the case of the government
423. 23:41, or also in the case when, uh, a
424. 23:43business, when a company is going to
425. 23:46launch a new product and so on, they
426. 23:49always, uh, generally, have a survey to
427. 23:52identify if that, if that product could
428. 23:56effectively enter the market or not,
429. 23:59right? If that product is viable to
430. 24:03sell, how many people approximately
431. 24:05would buy it? Yes. And, uh, as such,
432. 24:09how would that process be? Yes. And
433. 24:13then to make the decision if that
434. 24:16product is viable to launch it on the
435. 24:18market or not. And, well, let's say in
436. 24:22other branches, right? Also, for
437. 24:24example, in public receipts. For
438. 24:28example, regarding our Enelcensa
439. 24:31electricity bill, what could we observe
440. 24:36, Juan, if you have taken the time to
441. 24:38stop and review those graphs that we
442. 24:40are able to find on our electricity
443. 24:42bill? Tell us. Yes, I've checked them,
444. 24:47teacher, and it also shows a comparison
445. 24:49with respect to previous months and the
446. 24:51average amount that one spends. Exactly
447. 24:54. So, look, in this context it's also
448. 24:59very important because, of course, we
449. 25:01can make decisions. For example, in the
450. 25:05last few weeks, the government, let's
451. 25:08say, faced with the El Niño phenomenon
452. 25:11, what it did was launch this
453. 25:13initiative that if consumption rose, if
454. 25:16it reached a certain point, exceeded
455. 25:19the consumption limit, it would
456. 25:22generate a fine. But on the other hand,
457. 25:26if the minimum amount was spent, it
458. 25:29would receive a subsidy, a benefit. So,
459. 25:34look, we can indeed make real and very
460. 25:37wise decisions; because if we see that,
461. 25:41in comparison with previous months,
462. 25:44these consumption levels have increased
463. 25:48, then what can we do? I mean, what is
464. 25:52it that we can do about this situation?
465. 25:54Is, as such, make the decision, okay?
466. 26:07We can make the decision as such, in
467. 26:10this case, to generate strategies
468. 26:16within the family to be able to reduce
469. 26:19that level of consumption. For example,
470. 26:23leaving appliances unplugged at night.
471. 26:29Yes. For example, Juan, what strategies
472. 26:32do you apply with your family to
473. 26:34generate less consumption? To generate
474. 26:41less consumption. In the case, for
475. 26:44example, it was water or electricity.
476. 26:46>> The light.
477. 26:47>> Of the light. In the case of light,
478. 26:50well, we try to only have like one
479. 26:52light on and if, for example, we are
480. 26:55both in, I don't know, like in the same
481. 26:58space, that one is enough for us. Today
482. 27:02, too, when we stop using the
483. 27:04television, the computer, we turn them
484. 27:06off. There are also people who leave
485. 27:09their computers on all day,
486. 27:11>> and that generates a significant
487. 27:13expense in terms of electricity. That's
488. 27:17it, teacher, for you and for you.
489. 27:19>> Okay, Juan. In our case, we make it a
490. 27:21practice to leave every single
491. 27:23electronic device and appliance
492. 27:25unplugged throughout the night, with
493. 27:27the sole exception of the refrigerator.
494. 27:30But as for the rest, everything gets
495. 27:31disconnected because, aside from the
496. 27:33fact that it assists us with the matter
497. 27:38of saving money in economic terms, it
498. 27:42also serves to enable us to help the
499. 27:45planet and the environment by
500. 27:48generating a reduction in the total
501. 27:52consumption of electrical energy.
502. 27:57Therefore, we have been able to
503. 28:00evidence here that, in effect, these
504. 28:03statistics are useful to us not only
505. 28:06for analyzing graphs and such, but also
506. 28:12for the making of many decisions in a
507. 28:14wide variety of different contexts. So,
508. 28:18well, here we have reached the end of
509. 28:21this session. Thank you very much to
510. 28:29those who participated. Thank you very
511. 28:31much, Juan, for participating. Your
512. 28:35contributions were very valuable. We
513. 28:39will see each other in the next session
514. 28:42, and we hope to have the technical
515. 28:45issues improved by then. We will see
516. 28:49you in session number 24 later. Have a
517. 28:52great afternoon and to those who are
518. 28:56watching this video, greetings and a
519. 28:59thousand apologies.