Students work together in a group, clarifying each other's process and thinking. The female students clarify accurate steps for the male student.

9th - 12th Grade - Newcomer ELL Algebra - Graphing Quadratics*Carlos Cabana, San Leandro High School, San Leandro Unified School District, San Leandro, California*

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00:00 ¿El cero? Y pones esto.

Zero? And put this one.

00:06 Igual…igual a esto.

The same—the same as this.

00:08 Paréntesis…

Parentheses…

00:12 ¿A cuál vamos a poner paréntesis?

Which one are we going to put parentheses on?

00:13 ¿Cuál?

Which?

00:16 No, no, esto.

No, no, this one.

00:18 Pero puedes hacer parentesis... es lo mismo, mas que. no mas que convertirlas en cero.

But you can put parentheses, it's the same, you don't have to, you don't have to do more than convert them to zero.

00:24 Pero pon el parentesis.

But put the parenthesis.

00:36 Lo bajas, los bajas, pero sin los parentesis.

You bring it down, you bring it down, but without the parentheses.

00:45 Ya trae otro...

You already bring another...

00:50 Ok.

Ok.

00:51 Y ahora, lleves el ...

And now, you bring the...

00:56 Igual a cero.

Equals zero.

00:58 Cual es? No mas los tres.

Which is it? No, 3.

01:00 Aqui.

Here.

01:02 Igual a cero. Es el mismo.

Equal to zero. It's the same.

01:06 Los dos, mas dos son cero.

2 plus 2 is zero.

01:08 Dos, mas dos, ponlo aca! Dos mas dos..

Two, plus two, put it here? 2 + 2...

01:11 Es cero.

Is zero.

01:14 Dos mas dos son cero.

Two plus two is zero.

01:20 Ahora pone...

Now put...

01:23 ... el x mas tres.

The x + 3.

01:26 El 3, y aca x, x igual a menos 2.

The 3, and here x, x equal to -2.

01:32 X igual a menos dos.

x equal to -2.

01:34 Ok.

Ok.

01:35 Circula la respuesta para que..

Circle the answer so that...

01:42 Despues vamos a 3 en el cero, verdad?

Then we go to 3 in the zero, right?

01:44 No, menos cuatro. Ya esta, verdad?

No, -4. And that's it, right?

01:50 En la dos, si.

In 2, yes.

01:51 En la dos. So tenemos que encontrar el cuadro aqui, verdad?

In the 2. So we have to find the square here, right?

01:54 No sabe que.

Don't know.

01:56 Aqui, aqui va a estar el cuadro? Va a ser cuadro?

Here, here is going to be the square? It's going to be the square?

02:01 Si, pero tenemos que acabar el trabajo

Yes, but we have to finish the work.

02:05 Cual, el cero, pues.

Which, the zero, then.

02:06 Luego tenemos que hacer eso?

Then we have to do that?

02:13 Y luego como pusiste?

And then how did you put it?

02:15 El cero y la x.

The 0 and the x.

02:17 Si, ya lo puse. Sin todas las x.

Yes, I already put it. Without all the x.

02:21 Y ya lo voy..

And I'm already going.

02:24 Entonces y, igual a que? Cero? a cero?

So, y, equal to what? To 0? To 0?

02:31 Cero menos cero,

0 minus 0.

02:33 Cero menos cero, igual, menos 7.

0 minus 0, equal, -7.

02:36 Asi? Y despues que sigue? Llego a menos 7, verdad?

Like this? And then what comes next? I get -7, right?

02:44 No no no, te equivocaste.

No, no, you made a mistake.

02:48 Cero mas x, no y.

0 plus x, not y.

02:53 Que escribes?

What did you write?

03:01 Menos? 6, 0.

Minus 6, 0.

03:07 No, menos 7.

No, -7.

03:10 No, tienes que poner igual a menos 7.

No, you have to put equals -7.

03:12 No mas ponlo menos 7... menos 7.

Just put -7. -7.

03:17 Cual es la diferencia?

What's the difference?

In my students' group discussions, I'm pushing for higher order of thinking that can advance the conversation somehow. Part of that has to do with who's the audience for the answer. Is it the teacher? Is it the group if it's a small group conversation, or is it the whole class? I want the audience to get that a student responding is a learner and has both questions and insights regardless of their status. I want the answer to model what mathematical thinking should look and sound like. It should have reasons, it should maybe point the way towards the generalization or trajectory or a strategy to be in the service of some mathematics that's a little bit bigger.

This group is super interesting to me because if I'm remembering right, one of these students' papers were always a struggle. They were full of things that made no sense whatsoever, just the function of her lack of background before. This is the kid who could have reacted to all that random stuff on her paper just by quitting, and she doesn't. The fact that she's taking it upon herself to take what she's understanding and share it with her partner is super interesting to me, and really spoke to the kind of human being that she is, I think. I notice the number of times when she just told him what to write, but was trying to make sure that it was sort of written correctly, which I think is her own way of trying to make sense of mathematics, giving reasons for her thinking.