https:/.../Modeling_polynomials_video_debrief-part-3.mp4

>> And so, what were the
different things that you think

that you introduced into this
lesson to help with their reasoning?

>> Honestly, I think
that even just providing the

little sentence frame that we
did allows, kind of walks them

down the path of you're going
to need to share your reasoning

about this. This isn't just
going to be an answer. And I

think also the turn and talk.
So hearing from someone else

allows them to build their own
argument, that mathematical

practice of critiquing the
reasoning of others. You're doing

that internally whether or not
you're asked to like rebut

at that moment. And I think
also the writing piece, the

individual writing piece allows for that.

>> And so, there were
some struggles like you said

about scaling the axes. Were
there other struggles that you

noticed as you were trying to
get them >>>> I know we were

short on time, but as you're
trying to get them to figure

out which model to use? So ...
>> Yeah. I didn't, honestly I

don't have a great sense of what
everyone used as their model

so I'd love to look at this,
this, because in the moment I

wasn't able to recognize who
was using quadratic and who

was using cubic. >> Oh right,
sort them by ... >> So maybe we

could just go through and look

at groups who did quadratic versus cubic.

So interesting.

>> Yeah. >> So, I was expecting
coming into the lesson that

100% of groups would use the
cubic function, but I think

that I had not even anticipated,
which is ridiculous that I

didn't anticipate, but I had
not anticipated there would

be an error in calculation.
>> Yeah. Right. >> And that's >>>> I

mean we're humans, of course
there might be an error. So,

because of that outlier maybe
that's me putting a reason in

where I don't know if that's
true or not but we have three

of the eight groups who chose
a quadratic to model the

data. >> Well only because it
fits a quadratic relatively

well. So, how do you think
that you would be able to help

these students see that the
quadratic model was actually a

better fit than the I'm sorry,
the cubic model was a better

fit than the quadratic?
>> Right. Well, I would have loved

to have the time to have. I had
the front table's Chromebook

queued up to try to share theirs, so.
>> And it was a

cubic? >> It was a cubic and it
had corrected the data. And

Vincent said to me, "When we
corrected this one point, the

cubic just fell right onto
it." I mean those weren't his,

those might've been his exact
words, but it's just so clear

… >> Right. >> … when you have
the correct data in there. So,

on this side of the lesson
I'm not surprised that some

students didn't get to the cubic
and I don't ... I'm thinking

about it, how might I have
done the lesson differently.

And I think, I wonder about
whether stopping earlier and

asking Vincent to share that
correction might have supported

everyone in getting a cubic.
But then again, to me that's

not really equal to success.
I'm not looking at this and

being like, "Oh, these kids got
quadratic instead of cubic.

They didn't understand the
lesson today." The lesson was

focused on multiple representations
of mathematics, and I

think that students had that opportunity.

And it was >>>>
another takeaway we wanted was

for students to do some sort
of deep thinking and building

an argument and revising that

argument as we moved through the lesson.

And I feel like we
see evidence of that.

>> And do you think then, that because
they've experienced this in a

completely different way from
just doing it on a piece of

paper that you'd be able to

return to it and revise the work today?

If a student was convinced
it was a quadratic would you

easily be able to readdress
it? >> I think so. Absolutely, right.

Not through my voice
though, through one of the

student’s voices, you know?