Cabana analyzes a group's work in terms of logical flow and carefulness of organization, trying to make a guess about what they really understand.
00:02 ¿Qué estan haciendo, la e?
What are you doing, E?
00:07 Yo pienso que, que tengo que hacer, ah, es como 0 menos 1 por 0 menos 4…
I think that, what I have to do, uh, is like 0 minus 1 times 0 minus 4.
00:13 Muy bien. Aja, ok.
Very good. A ha. Ok.
00:31 ¿Les interrumpo? Sigue trabajando.
Can I interrupt? Keep working.
00:37 Edgar, lo que has hecho aqui es totalmente correcto. La manera que es mas alto para el procedimiento. Totalmente claro.
Edgar, what you've done here is totally correct. The best way for the procedure. Totally clear.
00:42 La factorizacion aqui, el problema original era de este, ¿verdad? Y esta respuesta, ¿de donde vino?
The factoring here, the original problem was for this one, right? And this answer, where did it come from?
00:48 Esta bien.
00:49 Aqui, no mas que lo puse.
Here, I just put it.
00:51 ¿Lo hiciste todo esto? ¿Lo hiciste en tu cabeza? Wow. Ok.
Did you do all this? You did it all in your head? Wow. Ok.
00:56 ¿Por qué, por qué multiplicaste estos factores?
Why, why did you multiply these factors?
01:00 ¿Por qué las multiplicaron?
Why did you multiply them?
01:01 ¿Estos dos?
01:04 ¿Para qué sirve este resultado aquí?
What is the result here for?
01:07 Se sigue para…
You follow it for...
01:09 No no no. Esta linea aquí encima, que no fue parte del problema original, ¿para qué sirve?
No no no. This line here on top, that wasn't part of the original problem, what's it for?
01:13 Es para comprobar este.
It's to prove this.
01:16 ¿Para nada?
01:17 Para nada—me pase que es para nada. El 4 y el 1 vino 2 factores, ¿verdad?
For nothing. It seems like it's for nothing. The 4 and the 1 came 2 factors, right?
01:23 Y aquí lo has usado tambien la forma factorizada para el y-intercept. Asi que este es todo correcto, ni este no es tan mal.
And here you've also used the factoring approach for the y-intercept. So this is all correct, and this isn't so bad.
01:30 En este caso. Ya lo encontraron lo que es necesario. Ok. Resto es todo correcto.
In this case, you already found what is necessary. Ok. The rest is all correct.
01:38 ¿Lo de arriba tambien esta bien?
That part above is also fine?
01:41 So, uh huh.
01:44 All right, very good, Eduardo.
01:48 All this is fine, I was confused right here about this +3 on both sides.
01:53 I don't know, I was trying to, like, you know, add this, so it would be, like the x equals 3, for like…
02:01 What are you trying to solve here?
02:02 The x, right? To get the x.
02:04 Oh! I see what you're saying! You meant that you're doing this, as an algebra problem in your head. Oh, I get it. Okay, I see. Never mind.
02:12 It, on some of them you'll need to do that, because it won't be a mental math problem. But then show the work, like, separately.
02:18 Right below the equation, show the work. But that, I see, I understand now, that's good.
02:21 The only thing, if I'm being nit-picky, like here, you put this in parentheses.
02:27 Yeah, I was thinking about, ah…
02:30 But if you put in..
02:31 Like right here, see, I scribbled them out.
02:33 Este en el cuadrito?
This is in the square?
02:35 If you wanted to, but then it would become a zero. Oh!
02:41 Oh, I'm glad that, there's a mistake! Mmm hmm.
02:54 You wrote them backwards. You did it on all of them. Hey, calm down.
02:51 You have that this is an x-intercept, right?
02:53 Yeah, but.
02:54 You made it a y.
02:57 Well, but this tells you, this tells you that x is 3.
03:00 So don't put it in the y. Okay, so.
03:05 No puede…
03:06 Here? This is an A+. And here, this is like a D.
03:11 No, porque dijo, ‘mano!
No, because I said it, man!
03:14 It was just a mistake!
03:15 No, but…
03:16 Que vamos a hacer…
What are we going to do...
03:17 Hold on. No, no no.
03:19 Apenas de ver, aprendan ustedes… acuerdate que el objetivo es un A+ sketch. ¿ok?
You just saw -- you're learning -- you all, remember that the objective is an A+ sketch. Ok?
03:26 So para un A+ sketch, asi estan procediendo correcto.
So for an A+ sketch, you're proceeding correctly.
03:30 Por eso es importante, porque si van a calificar estos puntos, les va a salir mal.
But this is important, because if these points are going to be graded, you're going to do poorly.
03:33 Pero aqui, a ver.
But here, let's see.
03:34 Ahora vamos a ver, le va a tocar. I think you messed up the other ones, too. At least you're consistent. All right.
Now let's see, what you're getting. I think you messed up the other ones, too. At least you're consistent. All right.
03:40 You know what? You showed your work carefully enough, that when we went to find your mistake, you realized what it was.
03:50 What was the original problem?
03:55 It was this one, right?
03:58 Okay, so, first you factored, put in 0, those are correct, and then, what's this?
04:09 ¿Por qué x?
04:10 No es una buena… es un paso…
That's not good, it's a step.
04:15 Okay, then that's correct. And you have that right. Ok, good.
04:18 So, what I want to know, though, Melina, es ¿por qué lo tuviste factorizar?
So what I want to know, though, Melina, is, why did you have to factor it?
04:25 A sacar el y…
To get the y….
04:27 Gracias, Melina.
Thank you, Melina.
04:29 Para sacar el…
To get the...
04:32 ¿Para sacar qué? Come on. ¿Para qué lo tuviste que factorizar? Tenemos… wait, wait. Si tenemos este problema aquí,
To get what? Come on. Why did you have to factor it? We have to, wait, wait. If we have this problem here,
04:39 ¿Por qué hay que factorizarlo?
Why do you have to factor it?
04:41 Es para sacarlos de….como…
It's to get the... how...
04:43 ¿Los factores? ¿O los dimensiones?
The factors? Or the dimensions?
04:45 En este sacarlo.
In this, to get it.
04:48 ¿Para sacar qué?
To get what?
04:48 Primero lo de x, y luego lo de…
First the one for x and then the one for...
04:50 Aja. Lo de x. Los x-intercepts. Good.
A ha. The one for x. The x-intercepts. Good.
04:55 Edgar, lo haz el tuyo. Ya lo califiqué? Sí.
Edgar, do yours. Did I grade it already? Yes.
04:57 ¿Alfonso, tienes uno listo para calificar? ¿No? Sigue trabajando. Sigue en el… a ver.
Alfonso, do you have one ready to grade? No? Keep working. Keep going ... let's see.
05:05 Ya lo sabes hacer, ¿verdad?
You already know how to do it, right?
05:10 So, 2a, cual es el ….
So, 2a, which is the
05:11 La d.
05:14 Muy bien. Muy bien. Very good, ok.
Very good, very good. Very good, ok.
05:20 Ok. Pueden dejarlo allí. Ya me recuenten lo que estan haciendo. Sigan con el problema de atras.
Ok, you can leave it there. So tell me once more what you're doing. Keep going with the problem on the back.
I wanted to help them see the conceptual whole, based on their work and the thing I wanted to help them attend to.
As I was watching these I kept thinking, "Why am I focusing so much on whether their work is done correctly or not? Why am I not asking them as many questions that I usually do about reasoning and the big picture?" Based on this clip, I think what was in my head is that this is where they were, gathering enough insight into the bits and pieces, that the next day's lesson they'd have enough under their belts that we could come back to the big picture on the next day and think about reasons and common mistakes and the connections.
In their handout, the equation of a parabola is written in different ways that would help them see why factoring is useful for helping make a sketch. They need to be making decisions about "When do I plug in zero and why, and when do I factor or not?" Their papers are going to be complicated. There's going to be a lot of stuff on there, which I think is why I was paying so much attention to the details.