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Masterclass de Matemáticas Sesión (30 Septiembre - AM) Parte 1 — Transcript

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0:29Heh, heh. Hello, hello, very good
0:53morning. Welcome to a new masterclass
0:56session. Today our math masterclass
0:58with our teacher Patricia. Teacher,
1:00very good morning. How are you? Very
1:04good morning, Teacher Javier. Very
1:06happy to be back in a math session,
1:08already our 23rd session. Already at 23
1:13sessions, teacher, that's great. How
1:16time flies; today is the last day of
1:19September, October is coming, and our
1:22recess week. Reminding you that we
1:25won't have masterclasses during recess
1:27week either. We return super recharged
1:32starting October 13th, because the 12th
1:35is a holiday, so on October 13th we
1:38return to have a session to start
1:41wrapping up this 2026 masterclass
1:44season in October. Juan David, our
1:48master, good morning, how are you? Good
1:52morning, teacher. Javi, teacher, happy
1:55to join you in a new math session, and
1:58also October is starting, a very cool
2:01month and getting closer and closer for
2:04our 11 th-grade students to graduate.
2:09Congratulations, guys and girls, I hope
2:10you do very well.
2:13>> That is correct, Juana. Thank you very
2:15much. Reminding you that tomorrow we
2:18have a natural sciences masterclass and
2:20on Friday we have an English session.
2:23Let's quickly say hello to everyone who
2:25is logging in, to those who have
2:26already written to us. Ana María, very
2:28good morning. To Clarismar Contreras,
2:30good morning. To Zambrano, good morning
2:32. Aaron, good morning. Daniela, good
2:35morning. Uh, Mariana Páez, very good
2:38morning. Brigit Méndez, good morning.
2:42Gabriela Urbano, good morning. Uh, Dana
2:44López, good morning. Hm hm. Isabela
2:49Giraldo, very good morning. Taliana,
2:51good morning. Ángel, very good morning
2:54. Alejandro, good morning. And Lady
2:56Camila, good morning. The vast majority
2:58from the Juan Lozano school. We hope
3:01you have an excellent session today
3:03because teacher Cata is going to talk
3:06to us about something very important
3:09and we are going to continue analyzing
3:11processes through data. Yes, but right
3:16now you are going to be like
3:17investigators, okay? And in this
3:21session you will be investigators and
3:23you will have to solve several
3:24mysteries that teacher Catalina is
3:26going to give us today. So be super,
3:29hyper, mega attentive to all the
3:32processes. Well, for those who haven't
3:35written to us, haven't said hello, well
3:37, say hello here, so we can say, "Hello
3:39, hello, how are you?" And that's it.
3:42And yes, I said, teacher, I said,
3:44teacher Cata, sorry, it's teacher
3:46Patricia, I woke up sleepy today. Sorry
3:49, sorry. Well, thank goodness they tell
3:53you here internally too, hey, getting
3:55it wrong, sorry. Things that happen on
4:00live streams, so you believe that we
4:02are truly live, that we got up super
4:05early in the cold, said, said teacher
4:08Patricia, I'm in Mosquera and it's cold
4:11, so it kind of affected my neurons.
4:15Sorry, teacher.
4:18>> Ready, teacher Javi, thank you very
4:20much for the introduction.
4:21>> Forgive me, forgive me. Yes,
4:23>> don't worry,
4:24>> I won't do it again. I won't make a
4:26mistake again. I'll eat you again. A
4:29hug for you, teacher, for you too who
4:31is there being super attentive.
4:35>> Uh, we are here, uh, super excited for
4:38today's session. A hug for you, teacher
4:41, for you.
4:41>> Well, thank you very much, teacher. J
4:43Bonito
4:44>> thank you.
4:45>> Well, well, let's begin. Things that
4:48usually happen, right? We also forget
4:51little things here and there sometimes.
4:53Okay. So, very good morning. I know
4:56teacher Javier already greeted you,
4:58however, well, I always make it a habit
4:59to greet those who connect. Very good
5:02morning, Ana María. Very good morning,
5:05Clarism Joes. Very good morning, Aarón
5:09, Daniela, Mariana, Juan José,
5:11Gabriela, Jusp, Isabela, Taliana,
5:14Teacheril, very good morning. Uh, very
5:19good morning, Alejandro, very good
5:21morning, Lady, very good morning,
5:23Fernanda, very good morning, Valentina,
5:25or very good morning, Catherine.
5:28Welcome to this math session number 23.
5:32Time flies pretty fast, 23 sessions
5:35already. Uh, very good morning,
5:39Catherine Vanessa, welcome. Also, a
5:43greeting to those who will connect in
5:46the afternoon to watch this session as
5:48a recording. Very good morning. Very
5:54good morning, teacher Diego. Uh, okay.
5:59Very good morning, Diego. How are you?
6:02Uh, okay. Well, then let's start this
6:05session with our agenda for today. Uh,
6:10we have our initial question, our
6:11introduction, our development, our
6:13practice, our closing, and subsequently
6:15our closing question. Uh, a huge favor
6:20for today's session. It turns out that
6:25today, uh, well in fact, uh, we are
6:28going to have, as teacher Javier said,
6:30uh, we are going to investigate, we are
6:33going to take on the role of
6:35researchers and for this we are going
6:37to do some surveys, right? very small
6:40ones among us. Uh, which means that at
6:45some points we will have to disconnect
6:47for a moment because I know that if you
6:50are on your mobile device, uh, you must
6:52disconnect from YouTube for a few
6:54moments, right?,to enter the form and
6:57fill it out and then reconnect. So, I
7:01ask you not to disconnect 100%at those
7:05moments, but please come back. Ready?
7:11So, at this moment let's remember that,
7:17uh, indeed, good morning, Sebastián,
7:20welcome, that the component of today's
7:23session is random, right? And our
7:28learning goal is to be able to describe
7:30a population or sample, right?,based on
7:33concepts of descriptive and inferential
7:35statistics. And additionally, to reach
7:39this learning goal, we are going to use
7:41statistical instruments and tools to be
7:43able to build that information, right?
7:47And be able to characterize a certain
7:49population. So, at this moment we are
7:52going to Laura Daniela, good morning.
7:55Uh, we are going to enter the initial
7:57questionnaire part. Remember that it is
8:00only one question. So, thumbs up,
8:03please, when, uh, you have already
8:06filled out this form, remember that it
8:09is very important, since the
8:11traceability we do is extremely
8:14important to know what knowledge you
8:17had before the session and at the end
8:20of the session, okay? So, quickly our
8:25master already did us the favor of, uh,
8:31as such sharing the link with us. So,
8:37please, one minute for the answers.
8:40Ready? Quickly. Well, we have two
9:12answers. Very, very good morning,
9:15Sergio. Welcome. Ana María, excellent.
9:18Thumbs up. Thank you very much. Santi,
9:20excellent. Thank you very much. So we
9:24continue. Who else said me? Alejandro
9:32Ramos, thank you very much. Catherine
9:36Vanessa, excellent. Very good to those
9:41who have already filled out the form.
9:51>> Very good morning, Sofía, welcome.
9:55Professor Ángel, thank you very much.
10:00Aarón, excellent. Thank you very much.
10:05Valentina Guevara, excellent. Here the
10:13little names of those who are filling
10:15it out appear. Ana María Rieta.
10:20Perfect. Very well. I thank those who
10:24are missing to please hurry so we can
10:25start. in this session it will be a
10:28little more interactive, so yes we are
10:30going to we are going to be, uh, quite
10:35attentive. Lady, thank you very much.
10:44Perfect. Okay, thank you very much.
11:05Perfect. Ready. Okay. Well, so the idea
11:17is, uh, well, to invite you. Uh, we
11:21completed seven responses, however, the
11:23idea is that more are completed during
11:25the session. So there you have the link
11:29so please stay tuned. Well, Karen
11:34Torres, welcome, very good morning. All
11:37right, so let's start with our
11:39introduction, shall we? So, right now,
11:43let's, uh, Daniela, uh, thank you very
11:46much, your response has also been
11:49recorded. Ready, so we are going to
11:52introduce ourselves a bit today into
11:54the world of statistics. Right, it
11:59turns out that many things, many topics
12:03, yes, uh many topics depend these days
12:06, uh, on what corresponds to statistics
12:10. It turns out that currently all, uh,
12:19all social topics, right? all, uh,
12:25social topics and so on are being, uh,
12:32developed based on statistics, because
12:35first I must know what problems a
12:38certain population has, right, before
12:41intervening. So, we are just going to
12:46find out. So, pay attention here, we
12:49have a situation, a context as always,
12:52right? We have it in every session. It
12:55turns out we are going to focus on the
12:58institution. Very good morning, Gerson.
13:01Welcome. We are going to place
13:04ourselves in the educational
13:06institution where each one is at this
13:08moment, whether in the role of teacher
13:11or in the role of student, okay? or
13:14perhaps there are parents, well also in
13:16the role of parents or guardians. It
13:20turns out that here they indicate to us
13:22that in your educational institution,
13:24they want to improve well-being
13:26activities like sports, art, mental
13:28health, recreation, nutrition, among
13:30others. Yes, for this, a survey will be
13:35applied to the students, right? to know
13:39which are those well-being activities
13:41they are most interested in. Yes. And
13:45the idea today is to be able to learn
13:48how to analyze and how to represent
13:51this data once we have it. Yes? So,
13:56here is a question we always start with
13:59, right? We always start with a
14:03question and today's question for you
14:05to answer in the chat is, how could we
14:08know which well-being activities are
14:10really important for students? What do
14:13you think? Tell me. Remember that in
14:18this session it is very important to
14:20participate, right? We know that your
14:24contribution is totally important, it
14:27is essential to be able to continue the
14:29session. So, please, in the chat
14:34quickly, let's see who is the first to
14:38comment. Watch the question: how could
14:42we know which well-being activities are
14:44really important for students? Let's
14:47see, who said me? Let's see, who is the
14:50first one to write? Let's see, let's
14:52see, let's see, let's see, let's see
14:59over here. Well, let's see who writes
15:04in first. Let's see, let's see, I see a
15:14comment here already. Okay, Ana María,
15:16excellent. Very good. I love your
15:20participation as always, Ana María
15:22says, "Interviewing and surveying the
15:24students." Okay, right. Remember that
15:28these two that Ana María just
15:30mentioned, right? Are data collection
15:39techniques. Yes. To have that data
15:45collection as such, right? There are
15:50several tools and techniques that we
15:52can use. So, surveys, questionnaires,
15:56interviews, yes? Through observation.
15:59Yes. So, these two that Ana María just
16:02mentioned are data collection
16:04techniques. So, look, we already have
16:08two concepts that we are handling in
16:10today's session. Well, and only Ana
16:13María is present, right? I know there
16:14are many connected. So, who else said
16:17me? Aaron. I don't see Aaron responding
16:20here, who always participates,
16:22Professor Ángel. Let's see, who else?
16:24Tell me, please, how else could we know
16:29what wellness activities are really
16:31important for the students? Tell me,
16:33please. Well, I have another one here
16:48from Professor Ángel. Very good. A
16:50data collection process for the
16:52community to be able to analyze the
16:54trends. Very good, Professor Ángel.
16:56And very good, Ana María. I hope that
16:59now the others will be encouraged and
17:01we can have many comments as we always
17:04have in our math sessions. Well, let's
17:08stick with these uh three techniques.
17:12So, clearly, Ana María indicates two
17:14data collection techniques, interviews,
17:16surveys. Professor Ángel tells us that
17:20indeed uh we must start a data
17:23collection process, right? That starts
17:27effectively by knowing which technique
17:29I am going to apply. Ready? So, to be
17:37able to to be able to at this moment be
17:46clear, right, about what I am going to
17:48analyze, consult, and investigate
17:51starting from a data collection
17:53technique, such as the survey. Also,
17:57first I have to take into account what
17:59I understand by wellness, what is it
18:01that I really want to know and find out
18:03about the students, what do I want to
18:05reach. Yes? So, what is the idea here?
18:12Let's say that here we are going to
18:14take into account, yes, the data. Watch
18:18out, when I am going to ask a question,
18:21right? It can be open-ended or it can
18:25be closed-ended. Yes. So, open-ended
18:30means I allow the person answering to,
18:35right? Not choose, not pick an option,
18:40but for the person to actually answer
18:43me according to the question. And when
18:48I make it closed-ended, which is how we
18:50are going to do it in this case, right?
18:53Here I honestly depend on the options,
18:56that is, the person must choose, the
18:58respondent must choose one of the
19:01options I present to them. Yeah? Now,
19:05several things are defined here. Yes.
19:09If the question, well, it's belongs to
19:13a qualitative or quantitative variable,
19:14which is what we will see right now.
19:17Yes. So, first of all, the first thing
19:21I really have to do is choose the data
19:24collection technique. Once I choose it,
19:29then I must focus on what I want to
19:32find out. In this case, the educational
19:34institution wants to find out, intends
19:37to find out about wellness activities,
19:39right? for the students. So, to keep
19:44them very much in mind. Fine, ready. It
19:53turns out that here we have a path to
19:56be able to conduct research based on
19:59statistics. So, the first one, as I was
20:02indicating, is to ask, right? Through
20:04that data collection technique. Next, I
20:09collect those data, organize them,
20:12represent them, analyze them, and
20:15finally I interpret them and find the
20:19conclusions derived from the results
20:22obtained in that data collection. Ready
20:28? Fine. So, up to here we already have
20:34a context, right? the context being our
20:38educational institution and that this
20:41institution wants to collect which
20:43wellness activities the students enjoy
20:45the most, right? So far so good. We
20:49already have a path, we already know
20:52that effectively our uh our technique
20:56as such uh corresponds our technique
21:02corresponds, doesn't it? Our collection
21:05technique corresponds to a survey. Now
21:09we enter this part, now we go to our
21:12development part, where we are going to
21:15see some key concepts that will serve
21:17us and that we will contextualize
21:20according to the situation we just saw.
21:24Ready? So we are going to start our
21:28development part. Ready? In this part,
21:36by means of this infographic that I am
21:38going to show you, we are going to
21:40define several concepts. Ready? So, we
21:47have three concepts here. Population,
21:52sample, and variable. It turns out that
21:56here my population, watch out, in this
21:58case is the educational institution.
22:01Ready? the entire educational
22:04institution. Well, now it says, it is
22:07the total group of people about whom we
22:09want to obtain information. So, here we
22:12have the whole institution, and it
22:14turns out that the sample is a subset
22:17of the population, right? Uh, that you
22:22select, let's say, to conduct the
22:24survey. In this context, if the
22:27educational institution is the
22:28population, what would the sample be in
22:31this case? Tell me, please, what could
22:36the sample be, what could be a sample
22:38of that population, who would become
22:44the sample, I mean, the population
22:47itself is the entire educational
22:50institution, right? And if it turns out
22:55that, uh, I am not going to survey
23:00everyone, then who would be the sample?
23:02Who could potentially be the sample?
23:04Tell me, please, in the chat quickly.
23:18Well, how wonderful, I have two
23:20comments. Excellent. Aaron tells me, "
23:23The students surveyed." Very good,
23:25Aaron. Indeed. Yes, Ana Maria, a part
23:28of the population would be the sample.
23:30Very good. That is to say, the students
23:32, the sample would be half of the
23:33population. Okay. Well, here are
23:35several little things. First of all,
23:38thanks to Aaron, Ana Maria, and Vale
23:40for participating. I love it. Now,
23:44indeed, as you indicated, the students
23:48surveyed will be that sample because,
23:52well, let's say there are times when
23:56the population is quite large and it is
24:01more complex to ask everyone exactly.
24:05So, in that case, I choose a
24:07representative sample. Yes? What do you
24:11mean by representative? If the
24:13educational institution has 1,000
24:16students, I can't just pick three
24:18students and assume that this sample
24:21represents the whole educational
24:23institution. Yes, but I do choose a
24:27representative sample, or for example,
24:31I choose only the 11th grade, or I
24:34choose, uh, grades, one grade per
24:37educational level. So, one from primary
24:41, one from secondary, and one from high
24:42school, for example. Yes, it doesn't
24:46necessarily have to be half; however,
24:50as I am indicating to you, the idea is
24:53for it to be a representative sample.
24:57Okay. Good. Good morning, Angelica
25:00Maria. Welcome. So, we are now clear on
25:07both the definition of the concept and
25:10the contextualization of, in this case,
25:14our situation, the population, and the
25:18sample, right? So, let's say, always
25:22remember that the sample is a part or a
25:25subset of the entire population. Yes.
25:29Exactly, teacher. And in this case, yes
25:33, the idea is for it to be
25:36representative, not just three or two,
25:39right? Ready. Good. Uh, and we have
25:45something very important, another
25:47concept that comes in here, which is
25:49regarding the variable. Yes, it turns
25:53out that a variable is not only seen in
25:55the subject of functions and equations
25:58and such, but that variable also comes
26:00to life in the area of statistics, and
26:02in this area, it comes to life in the
26:04following way. It is the characteristic
26:07that one wants to measure, right?
26:09That's right, and in the population or
26:13sample, right? So, for example, in this
26:17case the variables end up being the
26:19preferred wellness activity, which are
26:22what? So, the data becomes sport, art
26:26and culture, emotional support,
26:28recreation, and healthy eating. Yes? So
26:32, it turns out that here uh, it is when
26:38we can verify effectively, yes, if
26:44those variables can be of the
26:46qualitative and quantitative type. Yes,
26:50qualitative is when they are
26:52characteristics, right? That's right,
26:56they are characteristics that are not
26:58measurable. Yes. And that they are not
27:01measurable in the sense that they
27:04cannot be quantified, meaning that the
27:06answer is not represented by a number;
27:09the answer is not numerical. Yes? For
27:13example, in this case, the data we are
27:16going to take into account regarding
27:19the wellness activities would be
27:22qualitative. Now, regarding
27:25quantitative, it is when the answer
27:28generates a numerical data point, for
27:31example, age, right? Uh, the number of
27:35times one participates, hm, the
27:37satisfaction score. Yes? So, all of
27:41this ends up being the types of
27:43qualitative and quantitative variables.
27:46Yes, we have already been looking at
27:52three concepts here: population, sample
27:54of a variable, and within variable,
27:57well, two types: qualitative and
27:59quantitative. Ready? Perfect. So, up to
28:04here we are doing well. Now, as I
28:11promised, a promise is a debt, and the
28:13idea is for us to verify how to conduct
28:16a survey and not just how to do it, but
28:19how to follow that process and that
28:22path in order to reach a conclusion
28:25after an analysis of a population. Okay
28:29, so right here at this moment we are
28:35going to do the following. Ready. Here,
28:53uh, our master is going to do us the
28:56favor of, uh, sharing that of sharing
29:02that link with us. That link will take
29:05us as such uh to a survey that I would
29:11like for us to please complete. That,
29:18uh, we are going to focus on the
29:21questions; they are three questions. It
29:24will ask for an email, enter any email,
29:27there's no problem. Uh, here we are
29:31going to focus on three questions, okay
29:34? What wellness activity? What wellness
29:46activity should be strengthened? How
29:48frequently would you participate? And
29:51what other activity would you propose?
29:53Ready? So, remember, I know you might
30:05need to disconnect a bit from the
30:07devices, uh, from the broadcast to
30:10access the link, but please come back
30:12so we can continue with the session.
30:15Well, don't disconnect and get lost
30:18somewhere out there. Well, I already
31:32have responses here, so let's project
31:34them. Sure. Ready, teacher, your screen
32:19is visible.
32:20>> Ready, my Juan. Thank you very much.
32:35Ready. So, here we can see, we already
32:38have five responses. Yes, I hope there
32:42will be quite a few more. Thank you
32:44very much. Okay. Here Teacher Angel,
32:50Valentina, Catherine Vega. Very good.
32:57One idea is that, please, there should
32:59be more. Well, here they are already.
33:14Well, so here, what can we see? Here we
33:19can see that effectively, well, we are
33:21going to work based on these three
33:23responses. Uh, I know it doesn't
33:28generate a significant sample, perhaps
33:31because many more people are missing,
33:33but we will do the exercise with these.
33:36Well, with seven. It turns out that
33:39this Google Forms form, what does it
33:40allow me to do? It allows me to collect
33:44responses, indeed. It also allows me,
33:49uh, to verify here, yes, in charts, in
33:52this case the circular or pie chart, as
33:55we call it. Here they are indicating,
34:00indeed, the behavior of those responses
34:04. So, here in this case, what can we
34:07see? Yes. Look, for example, here what
34:10we can be seeing. Here they are giving
34:13it to us by percentages. Right? So,
34:16here each one represents a color of the
34:20five we have. Right? So, tell me, tell
34:29me here what can we see in those charts
34:34so far. Tell me, please. Tell me what
34:56you see here. Well, we are going to do
34:59the following.

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