UDL Guidelines in Practice: Grade 1 Mathematics

Today we´re going to be looking at a first grade classroom
and the teacher will be teaching math concepts,
and so we´ll have an opportunity to see her in practice
and we´ll have an opportunity to think about UDL
related to her practice.
So let´s take a look.
Great.
And if you look on your paper and up here at the top,
it says what-- right here, read it with me.
"My guess."
There´s a line there.
So when you look at the bag without counting,
you´re gonna guess how many cubes do you think are in there.
And then our captain is going to sort them out
and put them into, what?
Tens.
And?
Ones.
Ones, and then you´re gonna find the real answer
and see how close you are.
We´re gonna do this three different times,
but the first time we´re gonna do it together, okay?
So I´m gonna use this table right here to help me with this activity, okay?
So I´m gonna pass this bag around, and take a quick look,
pass it to the next person.
Take a quick look, how many do you think are in there?
Alright, Jayden, what do you think?
How many cubes do you think are in here?
Forty.
Forty, okay, come on up.
He´s gonna come.
Can you write--can you reach way up here?
Use your marker here and you´re gonna write your guess right up there.
You think it´s gonna be 40.
Okay, perfect, thank you.
And I´m gonna take all my cubes out of the bag
and I´m gonna start putting 10 of them together so that they´re in 10
so we can count them a little bit easier.
How many do I have there?
Seven.
How many more do I need to make ten?
Let´s count, two, four, six...seven.
How many more do I need to make ten?
Three.
Excellent, will you do that for me?
How many do we actually have?
Let´s all count them together, let´s start by tens.
Ten, twenty, thirty, thirty-one.
Thirty-one.
You were really close, weren´t you?
That was a great guess.
Any questions about wh-- `cause you´re gonna--
you´re gonna have your turn next.
Everyone should have written what we just did on their paper
and you´re going to do the next three
with your captain at your table.
And Ms. McCubrey and I will walk around and help you.
So if you´re having a problem and you have question,
raise your hand and we´ll come over and help your table.
In looking at this film, one of the things
that I noticed is that in introducing the lesson, the activity,
she´s really modeling what she wants the students to do.
And she´s very clear and she models it
with a small group of students, and you know, identifies herself
as taking on a specific role that they will be taking,
and then she sets the whole learning activity up
so that now it will be their turn.
So it seems like she´s moved from modeling
to providing some guided practice,
which is a very nice structure in a classroom.
Well, I was just going to say that´s highlighting the structure
of everything.
She´s doing--
Sometimes in the guidelines when it talks about
highlighting or clarifying syntax, but it´s really the underlying
structure of things.
So making the structure of a lesson explicit,
making the structure of what we´re doing
is something that is very necessary for some students
and is a good sort of meta-skill for even the most advanced of students.
Specifically within the guidelines, she does a gradual release--
that is, when she says, ‟We´re gonna do it three times.
I´m gonna do it with you the first time” and so on.
So she´s, um, both modeling and gradually releasing that
so that they can do it on their own.
And she also elicited feedback from them as a group
after she completed her modeling, which is a good check-in
to make sure that they really have the idea
before they all start doing it in their smaller groups.
Alright, let´s continue and see what else we can see.
Remember, pass the bag around first, let everyone take an idea,
and write your guess down on the top line.
Did everyone take an estimate over here,
take a guess-- how many you think?
Alright, and the caps--okay.
Now the captains should start sorting the blocks out
into tens and ones so we can get an actual number.
These things keep breaking.
Two, three, four...
Ten.
How many do you have?
Seven.
Seven, so you need how many more to make a group of ten?
Seven plus what equals ten?
Three.
Three.
Ms. McCubrey, we have two left.
Okay.
Ah, 31.
Alright, so you have three groups of ten and how many ones left over?
Three.
Three!
Okay, so you´re gonna put three in the tens place
`cause there´s one, two, three groups of ten
and three in the ones place because there´s three...ones.
So what´s your number?
You know what´s interesting, I was just thinking about
the use of the blocks and the nature of the classroom.
In our observation of this classroom, there are 30 students
and there are 11 different languages represented.
So the fact that they're using manipulatives and visual graphics
is not making the language as such a barrier.
So, how do we get to the goal of the lesson
is to understand the tens and ones or that concept.
And yet they were doing it with something
that was very concrete and not bound by language.
So I think she did a nice job of trying to get around
those language areas and those potential barriers that could exist.
Right.
You know, I was also struck by something that I think
might cause people to pause when they look at our guidelines
in terms of illustrating key concepts non-linguistically.
I mean, she was using the words and the language
and then she provided the cubes.
And I think that´s really even more critical in math
than a lot of subjects because it´s not just that you´re providing
an alternate representation, it´s that students need to understand
the relationship between the physical and the symbolic.
And so she was doing a nice job of using
physical manipulatives with the students,
but also then using the language of math so that they can
make the connections between the two.
So it is sort of both, a cross-linguistic
but also a non-linguistic representation,
and multiple representations are what we´re talking about here.
Eight...nine...ten.
There were groups of students who were working in small groups
and there were children working independently on computers.
There were two teachers in the classroom
and one teacher was actually working with a group supporting them.
So many different methods were going on at that point.
There are multiple ways they're acting on numbers
and acting on objects to count and all of those
so that they´re not all the same.
There´s a good deal of variety in the ways in which
a student can engage in the mathematics
that she´s concerned about.
I´m struck by the use of white boards.
They are just everywhere in classrooms today.
She really seems to use that not only as an instructional tool,
but as a tool to help support students' learning
so they´re getting to use it.
So that, again, is a really-- can be a very engaging
new technology that´s in our classrooms.
And she uses the groups with, um,
to provide different levels, like she´s working
with one group of students that, um,
probably need more specific guidance from her again
on understanding this concept of place values
and the tens and ones.
So she´s really structuring the activities and working with them.
This is what we used today in our lesson, right?
This is exactly what we used.
So we´re gonna use it again.
Who remembers which side the tens are on?
Everybody remembers?
Then what happens on the smart board
and the computers is a program where the students
are putting up their groups of tens and ones
and the computer itself is telling them how many they´ve put up there.
So it´s reinforcing them.
So it´s kind of a step away from the teacher guidance.
And then there are more activities that are totally independent,
like the matching game where they´re reading the numbers off
and trying to find matches of two-digit numbers.
Right.
And I think when we go back to the guidelines,
that that´s such a great example
when we think of sustaining effort and persistence.
And one of the check points under there is to vary
the levels of challenge and support, and there you go,
that´s such a great example of showing lots of different levels
of challenge and support within the same classroom.
And also closing with an assessment,
and it´s not a formal assessment.
It really is just kind of touching base with, you know,
what did you learn, one thing that you learned.
Which is, again, a very nice closing point
that it doesn´t have to be the formal paper and pencil task
showing me what you learned, but let´s just get a general sense
of where you are.
Okay, who can tell me one thing they learned today?
Sophia, what did you learn?
We learned about numbers to put them in tens and ones.
Excellent, good, Sophia.
Julia, what did you learn?
Sometimes I think the class will end and then students are off
to the next lesson or into-- you know, going to gym or to art,
and they don´t really get a chance to really reflect on what they learned.
So I think it was just nice that you could tell
she clearly ended the lesson five minutes early
so that they students really did have that time to reflect.
And Grace, like you were saying, it is a great example
of developing those self-assessment and reflection skills
that the teacher really built it into the lesson
to give them time to think about what they´ve learned
in the past hour.