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>>Mrs. Diekmann: ...displayed up on the screen. Who can read the standard?
I want you to read just the standard. Tatiana.
>>Tatiana: Construct viable argu-arguments and critique the reasoning of others.
>>Mrs. Diekmann: Alright. Good. So let's look at that. Construct viable arguments
and critique the reasoning of others.
So this standard is telling me what am I going to have to do or be able to do to
to demonstrate that I understand how to use mathematical practice 3.
And we're going to look at it a little bit closer. That's just the standard.
Now here is our mathematician friend. What is she saying here?
So in order for kids to be able to be successful at the content standards
they need the mathematical practice standards because the two standards work
in tandem. The mathematical practices teach kids to work and think like mathematicians
so it makes accessing the content standards a lot easier.
No mathematicians that are using mathematical practice 3 they have some thinking
habits that help them. What are some thinking habits of a mathematician who's using
mathematical practice 3? Cordell.
So today was the first exposure that the kids had to SMP 3. We've worked on SMP 1
and 6 prior to this so they do have some understanding about what the mathematical
practices are but this was the first time they saw this one.
Um, that direct instruction is really important because you need to break
that standard down so kids understand exactly what they are expected to be able
to do to show that they have mastery of that standard later.
Alright, so let's kind of break that down a little bit. I can explain my thinking.
If I am constructing a viable argument. That's what I am doing, right?
I am explaining my thinking to others.
And respond to the mathematical thinking of others. That's the same as critiquing
the reasoning of others. Right? If I'm going to respond to someone else's
mathematical thinking, I'm going to critique them or give them some feedback.
Turn and face your face partner please. Take just about a minute to talk to each other
and explain if you know what it means to construct a viable argument and what it means
to critique the reasoning of others. Lean forward and talk to your face partner.
So in the beginning for this first lesson, my role as the teacher is really just to
kind of continue to repeatedly break down that standard and keep going back to what
is the standard actually say. So the first lesson is really my instruction and I'm
leading everything to make sure that they understand what the standard's actually
asking them to do.
Um, Melanie, can you read us the problem very quickly please?
>>Melanie: There are 3 rows of pictures on the wall, each row has 6 pictures
how many pictures are on the wall?
>>Ms. Diekmann: So as soon as I read that I'm thinking to myself ummm, definitely sounds
low level.
When you're choosing problems to practice the standards, you really want to look
at problems that actually lends themselves to whatever that standard is.
So I want to choose problems that are really going to give kids opportunities to
explain their mathematical thinking. So I want to make sure that they're challenging
enough that gives them an opportunity to do that. And then also so that when they're
giving feedback and critiquing each other, it needs to be a problem that actually lends
itself to it. Not something that's super straight forward but that really lends
itself to those mathematical conversations.
When I say go, all I want you to do is begin solving. You're going to work in shoulder
partners and as I'm coming around I'm really just going to be listening to see if I
hear any of that mathematical language that's going to let me know you're
constructing viable arguments or critiquing the reasoning of others.
I think the part about constructing viable arguments, explaining their own thinking,
they're pretty good at. But when it comes to critiquing others and asking the questions,
they need a lot of practice with what kind of questions am I going to ask.
So Haley is going to model really quickly a little bit about how their conversation went.
And when I was listening to them, I could tell, hmmm, I think they're beginning to
understand what SMP 3 says. So let's give them our attention.
>>Haley: I think we should do an array of 3 rows and 6 in each row.
>>Ms. Diekmann: OK, so Jocelyn, Haley is making a what?
>>Jocelyn: A plan.
>>Ms. Diekmann: A plan. I want you to give Haley some feedback or critique her reasoning.
I want you to let Haley know what you think about her mathematical reasoning.
>>Ms. Diekmann: Okay, eyes on me. So let's think about what we just saw...
...Standard 3
>>class: Construct viable arguments and critique the reasoning of others.
>>Ms. Diekmann: Alright. Standard 3 is the standard that we are going to be focusing
on today. So if you could, open up the first window there for math practice 3.
Alright. Standard 3 says construct viable arguments and critique the reasoning of others.
Tatiana, what does the mathematician say?
Okay, again, that will be the expectation today. I can explain my thinking and respond
to the mathematical thinking of others. I can explain my strategy using...Andrew...
At this point in the phase, I am still reviewing the mathematical practice that I want
them to focus on that day before I give them the problem. So we go over what are
the expectations of that standard and how are they are going to demonstrate
their understanding of that standard. I review that with them and then I present
them with the problem.
Louis, read me the solve and share problem please.
>>Louis: The solve and share problem says 24 divided by 4 is on the right side of the
balance below. What can you right on the left side that will have the same value as
the right side. Write five addition, multiplication, or division problems that will
keep the pens balanced.
>>Ms. Diekmann: Alright. 24 divided by 4 is on the right side of the balance below...
Today I had them work in pairs collaboratively on the problem.
My role while students were sharing with their partner was to ask some guiding
questions that would push their thinking and their conversation towards the expectations
of that standard. So I'm asking very targeted questions that I kind of have with me
that I carry around. Um that are going to elicit the kind of discussions that I want
the students to be having with each other.
Louis, tell Haley why you did that.
>>Louis: I did that to check the problem and I did...the inverse to multiplication.
>>Ms. Diekmann: Okay so that-the if I start with a division equation and I check with a
multiplication equation Louis just said you're using the what?
>>Haley: Inverse.
>>Ms. Diekmann: You're using the inverse operation. Okay. So talk to me using a little
bit of math vocabulary in your explanation. Start with the division equation.
>>Louis: Okay...
>>Ms. Diekmann: So I carry a clipboard with me that has um a square that is numbered
for each student in the class. And as I'm going around and facilitating and listening
in on the groups, I'm taking notes to myself about who's showing mastery, who isn't.
Maybe who's going to need to be pulled to a small group or have some reteaching.
And then the wheel on the clipboard has those guiding questions just to remind myself
what are the types of questions that I want to ask that are connected to the SMP
for that day.
Can you explain that equation to me using math vocabulary?
>>Haley: The 6 is the-a factor. The 6 is a factor and the 36 is the product.
>>Ms. Diekmann: Okay, so Louis, Haley said 6 and 6 are the two factors in that problem
and 36 is the product. Do you agree or disagree with Haley?
So after they finish sharing and working together in pairs, I called on specific
students to share their solution and then I called on other students to give them
feedback because part of that standard is to be able to critique the reasoning of others.
And so I wanted once one student shared their solution, I wanted another student
to critique their reasoning and then let them know whether they agreed or disagreed
with the solution that the student gave.
Uh, Vladamir, explain your and Michael's equation, using... math vocabulary.
I do try to connect other SMPs that they have learned. So so far students have learned
SMP 1, 6, 2, and 3. So today when students were sharing their answers and giving
feedback to other students I was really pressing for them to use math vocabulary
in their responses.
>>Vladamir: The 121 is the dividend, the 11 is the divisor and the quotient....is the
is the-11 is the quotient.
>>Ms. Diekmann: Okay, Anna Marie, do you agree or disagree with Vladamir?
>>Anna Marie: Um, Vladamir, I agree with your math vocabulary because uh, because
um 121 is the dividend, 11 is the divisor, and 11 is the quotient.
>>Ms. Diekmann: Okay, now tell Vladamir whether you agree with his calculation.
>>Anna Marie: Uh, and I also agree with your calculation because uh, well if you uh
do the inverse, like 11 times 11, it would be 21.
>>Ms. Diekmann: 11 times 11 will equal what?
>>Anna Marie: 2- 121.
>>Ms. Diekmann: 121. Um....
So I had them share in a variety of ways because I wanted them to have more
opportunities to work on um explaining their mathematical thinking and being
able to critique the reasoning of others. So after we did kind of a whole group
share out, I had them pair up with someone who was not working at their tables.
So with someone else in the room. And then they had a card that had sentence stems
on that that would-they would fill in their mathematical thinking but it was connected
right back to the standard. So um it's helping them work towards being able to do that
independently.
>>Tatania: When I started working I could tell my strategy was working because
if I checked my multiplication table, all my answers were right.
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