Latest / New Teacher Talk / Ep 231: Mathematical Language Routines

Transcript

Ep 231: Mathematical Language Routines · New Teacher Talk

Welcome back to New Teacher Talk, friends.
I'm Beth Wilkins,
and I am excited about today's conversation.
And I'm Anna Quinzio-Zafran.
Today's episode is one every math teacher, new or veteran,
is going to want to bookmark.
We're talking about mathematical language routines,
and our guest is exactly the right person to walk us
through it.
Helene, thank you so much for being here.
Let's talk about how language shapes math learning.
Welcome.
Are you looking for a new way to make solving math word
problems more engaging for your students,
no matter what grade or proficiency level?
Are you providing students opportunities to learn from each
other and not only from you?
Did you know that routines can strengthen these
opportunities for constructive sense-making and
communication?
Welcome.
My name is Helene Alalouf.
I am an instructional math and literacy coach.
Today,
I am going to talk about mathematical language routines.
You will leave with two routines you can use tomorrow,
and a resource of implementation supports,
as well as additional mathematical routines.
Grab paper and pencil so we can do math together using a
routine called the information gap.
I will present some information.
You will think of a question to ask me for more information
in order to be able to solve the problem.
But please be patient,
as I will ask you a question before answering.
Are you ready?
Here is the word problem.
What is the area of an exercise mat whose length is twice
the width?
What information do you need to know?
You might ask,
"What is the length of the mat?" Now remember,
my reply will be a question before I give you information,
so I'm going to ask about your rationale.
Why do you need to know that information?
You'll use your knowledge of math and reasoning to give me
your justification of how that particular specific
information will help you to solve this problem.
You might explain to me, "If I know the length, Helene,
I would know one dimension,
and I might be able to figure out the other dimension from
the information you've given me,
and then I could apply the formula to find the area."
The only way I can respond is the length is twice the
width.
Now, don't get frustrated with me.
Stay engaged with the thinking.
You do need to know the dimensions,
so what would your next question be?
You might ask about the width, and I'm going to say,
"Why would you need to know that?" And you would repeat
your reasoning, and I would have to reiterate,
I can only give you the information that the length is
twice the width.
I wouldn't reverse it and say the width is half the length.
So please ask a new question.
You might ask,
"What is the shape of the mat?" And my reply would be,
"Why do you need to know that information?" You could say,
"Uh, Helene,
if I do know the area formula is different for each figure.
If I know the shape,
I know which formula to apply to find the area." Great
thinking.
My reply would be rectangle.
Okay, so now you have some more information.
What's your next question?
You could ask me,
"What is the perimeter of the mat?" Do you remember how I
will reply?
Why do you need to know that information?
If I know the perimeter,
I could substitute the values for length and width in the
formula.
And since I know the shape is rectangle,
I can use the information about the perimeter to find the
length and the width by substituting those quantities and
the variables in the formula for area of a rectangle.
Bravo.
Love your thinking.
So I will tell you the perimeter is thirty-six feet.
Is there anything else you need to know or do you now have
enough information to solve?
Yes, I can solve the problem now.
Go ahead and do so.
And when you're ready,
continue to check your thinking and your solution.
Welcome back.
So you did your calculations.
So we know perimeter is thirty-six feet,
and we know perimeter area is twice the length plus twice
the width.
So since the length is twice the width,
we could set up an equation of P, perimeter,
thirty-six equals four W for the two lengths and two W for
the two widths, giving us six W.
So if thirty-six is six W,
thirty-six divided by six gives us the width of six and the
length of twelve.
So now we can apply the area formula of length times width,
twelve times six, seventy-two square feet.
Is that what you got?
How did this question and answer routine help you?
You can transform any mathematical question for whole class
discussion or paired learners in any grade and math
content.
Use this even once a week or so.
First, may I remind you, uh,
preparing students with norms for cooperative discourse,
similar daily routines like mystery number,
gentle reminder about explicit modeling for any new
procedure or content so students know how to ask and share
information.
And in the notes,
you'll find a link to implementation directions and the
information cards for your student partners.
So cultivating conversations like this and building
sense-making is one principle.
Another is optimizing output,
and that means strengthening the opportunities and supports
for helping students to describe clearly their mathematical
thinking to others, whether it's orally, visually,
or in writing.
So here's my second,
and it's my favorite mathematical language routine.
It is called Stronger and Clearer Each Time.
Helene, why is this your favorite?
I'm so glad you asked.
This interactive routine is one of my favorites because it
increases the quality of thinking and writing,
not only in mathematics,
but in all subjects across all grades.
In the resource of mathematical language routines,
the authors state, quote,
"The feedback enabled by these routines will help students
revise and refine not only the way they organize and
communicate their own ideas,
but also ask questions to clarify their understanding of
others' ideas."
So how does this routine work?
First, students complete the work independently,
and then they pair share.
One partner shows and tells,
while the listening partner observes and questions for
clarification and justification.
Example, how did you know?
Why did you do that?
How do you know your answer is reasonable?
Why did you draw that?
How does your visual representation match the problem
situation?
I thought it was this.
Why is it that?
And no copying is allowed.
The students talk.
The listener can make notes of what to change or add to his
or her work to make the work stronger or clearer.
And then they switch roles so that the other student has a
chance to showcase his work.
They thank each other,
and then they find new partners and repeat the routine,
asking and adding notes.
When they return to their seats,
this is a very important operation,
they need to revise their work and finally write a
reflection.
So once they have refined their work to make it stronger
and clearer, some reflection prompts might be,
what did I learn to make my work stronger and clearer?
What did I change or add to my work,
and why was that important to do?
What will I need to remember for next time?
In conclusion,
I modestly yet proudly share that employing the Stronger
and Clearer Each Time routine for only four months last
year raised grades three to five students' performance in
the New York State math and English tests from 48% to 61%.
Can you imagine if we had done it all year long and
consistently across the grades?
I am currently using the routines in advanced placement
history and science classes for students to refine their
document analysis responses.
Whatever you teach,
you and your students will enjoy these routines as
opportunities to build understanding,
promote collaboration,
and ultimately help them learn to transfer the knowledge
and skills into their independent work.
In the notes is a resource to support your implementation.
Teachers, thank you so much for listening.
I know that adding these routines will make your class so
much more engaging and effective.
Before we go,
remember to follow New Teacher Talk on Instagram and
BlueSky.
That's where you'll find our weekly Tuesday Teacher R
esource and our Thursday Thought,
two small boosts to help you through the week.
Remember to follow this channel on Apple Podcasts, Spotify,
or wherever you listen so you never miss an episode.
Please leave us a five-star review.
We're grateful that you're part of this community.
See you next time.