[MUSIC]
>> I got the this word problem that we did today, from like, about Christmas.
And it's the change unknown problem.
And it's right, where, we've been working on
>> Can you unpack what change unknown is in case the others [CROSSTALK]
>> Yeah.
I'm sorry.
So, like, instead of saying, instead of saying like, there are
five reindeer and he gets five more, how many are there now?
It's saying, the question is, there are 16 reindeer,
Santa gets some more and now he has 26.
So instead of trying to find the result,
they're trying to find how, what is changing [CROSSTALK]
>> So the unknown. [CROSSTALK]
>> Okay,
the unknown. >> Unknown, yep.
[CROSSTALK]
>> Great, thanks. >> Exactly.
And I, and I teach first grade ELL and so, and that's, that's a difficult thing
in the past has been change unknown because
they all automatically want to add or subtract.
But anyway, I'm sorry, off track.
>> No, actually that's really important, I think, to know that.
>> To be able to conceptualize that.
>> Yeah, and so this was our, our task
and so they do this independently for five minutes and
then they share in small groups their strategies.
And then we share as a large group their strategy
and then on the back they'll complete a second one.
But this time it was with higher numbers,
I'm sorry, the same, the same problem type,
and so just looking through these there's predictable
patterns about like, what the kids are doing.
Out of the 21 kids, four of them did not get the correct answer, and so
those four obviously, this for the, for whatever
reason this problem type was too difficult for them.
>> And what's, what kinds of errors did you notice?
>> The well for these, these four, not to make excuses.
>> Yes.
>> These four are my, are the pre-production
students in my class, and you know, they [CROSSTALK].
Language was the common denomination. >> Yes.
They don't, they don't, they don't speak any, you know, any English at all.
>> Right.
[COUGH] And I don't speak any other languages, so, I think looking
through that that seems a lot of what they're doing.
One girl in that four got the right answer
but then couldn't write an equation to sh- like
when she was writing an equation and so that
could mean, could show you know I didn't, she
didn't understand what an equation is or what equality
is saying 16 plus 26 equals ten instead of
16 plus ten equals 26 so that she could and then to the other one, just I think
they didn't understand. >> Right.
>> And then the rest of them, you can
kind of sort them by the strategy that they showed.
>> Mhm.
>> Is there anybody who got the answer right but the strategy was nowhere.
>> Yeah, there's two kids for the, for
the first one, no three kids, for the first
one who either it looks like they erased their
strategy or, I can't tell what their strategy was.
They got the right answer. This person just drew
with base ten blocks.
So, thinking she could have drawn the 16 and then added a ten.
But I don't know if she did that. So, I can't really tell what she did.
And then, the other ones kind of just erased theirs.
But they got the answer right, so you know that could be in there, for all
I know that could be they looked at their partner's and then wrote down the answer.
But you know, I don't really know.
>> How hard has it been with first graders to socialize them to the practice
of showing their work?
I mean, I think that's the way we talk about it,
but of making their thinking visible, have you struggled with that?
>> You know, we, we did last year on my, on my team we struggled a
lot but, this year it was kind of, we, we all started at the, at the beginning.
There's the first day and every day we give a word problem.
We don't, we give a task once a week which is all independent.
But we give a word problem every day and with
the emphasis of when we come back, and what's the answer?
Is the answer important?
No, it's not important.
What's most important is showing what you were thinking.
>> Mm-hm.
>> And so, I think just, instead of just saying,
great job, you got the answer and the, the work's okay.
We, we'd emphasize that, you know, showing
the answer is the important thing because it's
really showing what your, how you're solving this
problem instead of just, that you know it.
>> And you do that in the classroom discussions?
>> Yeah.
Yes, we would input.
For this one, it would be, after they solved
the first, they work, they sit at tables and
they did kind of a round robin share with each other.
>> Mm-hm.
>> How they solved it.
And then we, as they're doing that, I pick out the different strategies.
I walk around for them to show it and explain on the board for the whole group.
And then that way, when we go to the back, which is the same problem type with
different numbers, they kind of have different examples of
how other kids in the class solved it and.
>> [CROSSTALK] >> Strategies are still on the board?
>> Yeah, they're still on the board but of course it's different numbers.
>> Mm-hm. >> But and then also
the big, the biggest thing that also does is for the, for the
lower, the lower English level kids who
didn't understand what the problem was asking.
They can, after the discussion, they can say, oh, it wasn't asking me to add
them, it was asking me how many more do I need to get to this.
So that helps them to go, to go back on the backside to, to work their strategy.
>> We've been offering some elements of good
tasks, the things that we want to ask,
the things that we ask of our students. What are the, the markers of good tasks?
And I think in both cases we've hit on some of those.
But one certainly from what you're saying here, Micheal, is that it will allow for a
diversity of responses from students. And you did that intentionally.
>> Yeah. >> That was your.
>> Okay.
>> Yeah.
Well, because we, we all, we always say that if everyone does
the same thing then we have nothing to talk about at the end.
>> Mm-hm.
>> And so but they, I, they a lot of times in,
because, because we talk about it with, with the kids on our team.
They intentionally.
>> Mm-hm. >> Do different things.
And a lot of them if you look through have done you know, two or three different.
>> Mm-hm.
>> Things so that way at the end, well mostly it's because as I go
around they know there's more chance of me choosing them, it's right on the board.
If they do something [CROSSTALK] if they do three or
four different things, [CROSSTALK] I mean, but if they do
three or four different things, it really shows
that they understand what the task is asking.
>> So what did they understand, or didn't they understand?
>> so.
It's, it's interesting to go through because
after you get through the ones that either
didn't get the answer correct, couldn't write
the equation, or didn't show a strategy, and
so I can't, and so when you're talking about what I want to know more,
it's those kids I really don't have a clear understanding of how they did this.
Or, or if the task
was too difficult then they didn't do anything, so
I have no understanding of what they can do.
>> Mm.
Mm-hm.
>> But as you look through the ones, that, that that did understand.
There's kind of a, there's a clear development.
Mm-hm.
>> Sequence of their, of their responses and how they solve the problems.
We have the, the kids that drew, you know, directly modeled with this.
Drew the 16 circles.
Drew until they had 26 and then counted the extra ones.
>> Mm-hm.
>> You know, and that's obviously on the back the question is up to 57.
>> Mm-hm.
>> And that's,
that's one of the not quite as advanced strategies, because it takes
so long and as you get higher and higher numbers it gets impractical.
>> Mm-hm.
>> You know, and then after that we have
the counting on strategies, which is what, is what
right now looking at this I was very, I was kind of surprised as how few did that.
Because that's something that we, that, that we kind of got stuck on
last year is they always wanted to count on, you know, they always wanted
to do whatever. But I only had one kid do that.
You know, you know what I mean by counting on beat.
>> Right, yes.
>> And then. >> Put in in their head.
>> Yeah, that kind of thing.
And then the rest of them used some sort of
base 10 strategy which is what we've been working on.
>> Okay.
>> So that's good to see.
Of course it was an easy one for this one but I guess I set it up for it to be easy.
>> What made it easy?
>> There's you know, 16 and 26 bits just adding one
10 and one of our standards is fluency with adding 10s.
So,
I mean usually, I would have, you know or other times I would have
if he had 16 and he got 10 more and hoping to make that connection.
But in this one they are seeing the start and the result.
And saying, oh, wait, 16, 26, a lot of them, a lot of them, use their hundred
chart, and they drew that by saying 16 and then drew a line, which means line down.
Uh-huh.
>> And then wrote 26, and then kind of, some of them
labeled it plus 10 so I can see exactly what they're thinking.
There
and then I also had some in, use I
guess like kind of an open number line type deal.
>> Okay.
>> But again, it's with, just adding one ten it
really doesn't show much but then if you go to the
back when they had to add 20 instead, they go
plus ten, plus ten, there was a couple they did that.
But if, if you can, you can sort of go through and
see which students understand base ten and, and applied it in this
new context because it wasn't, it wasn't like every problem I've been
giving for the last three weeks has been the answer of ten.
You know what I mean?
So what does this tell you in terms of what you need to do tomorrow?
Instruction,
what, what this the main thing that I did not see is no one used kind of a breaking
up strip what is the word but you know what I mean instead of going 16 + 10 = 26.
No one went 16 + 4 = 20 + 6 = 26.
Which is one that I expected to see. >> The composition.
>> Yeah, decomposition. Yeah.
>> So no one did that which means tomorrow, in kind
of our, and [INAUDIBLE] some way, I would want to somehow,
not, not like model, but kind of show how we show that.
>> Introduce.
>> Yeah. >> Mm-hm.
>> because, a lot of times they use strategies mentally in their brain.
Right.
>> And they don't know how to show it.
So, they automatically do something that they do know how to show.
>> Oh, that's interesting. >> Yeah.
>> Okay. >> That's a good point.
>> It is.
>> [CROSSTALK] But, I think, once you, once
you start modeling on the board this, how
you could show decomposition strategy, then they can
start actually showing the strategy that they used.
So that's one thing that I would want to focus on.
>> And are these first graders
comfortable with the multiple strategies idea?
>> Yeah.
I mean, again, it's starting from the, it's
almost December now, so they've just, they've just
gotten used to it and, I think, I mean, I really, I think it's, have been effective.
Like I said, it was not like this last year so as our, as our whole
first grade team we, we've noticed that, that
they're much more comfortably doing that this year.
>> You're really working toward making them comfortable with that.
>> Yeah, it's been.