By Vanessa Cerrahoglu, Jennifer Wilson, and Liz Ramirez

We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful opportunities for students to engage in sense-making and use language to negotiate meaning with their peers. This calls for a language-rich environment where there’s space for all students to participate in argumentation and explanation.

What do these conversations look like now that we are no longer sharing physical space together? And how do we support our multilingual students who are gaining proficiency with English?

In this series of posts, we continue to consider how to “strengthen the opportunities and supports for helping students to describe clearly their mathematical thinking to others, orally, visually, and in writing” by looking at three Math Language Routines (MLRs). The posts in the series have been about enhancing access, MLR 3 (Clarify, Critique, Connect), and MLR 5 (Co-Craft Questions). You can learn more about the MLRs here

In this post we will explore MLR 7 Compare and Connect.

#### MLR 7 Compare and Connect

In the Compare and Connect routine (MLR 7), students make sense of mathematical strategies by relating and connecting other approaches to their own. This routine can be used to support discourse around a problem that can be approached and solved using multiple strategies or representations. Let’s explore this routine through the lens of the following activity from Algebra 1 Unit 4 Lesson 18.

As they solve the prompt, students will have to make assumptions about the context in order to model it. The goal of the discussion will be making these assumptions visible. We look to the structure of this routine to prepare students to engage in a conversation centered on making connections and comparing approaches in order to recognize the role assumptions play in reaching a mathematical solution. Students will prepare displays of their work, compare their reasoning with the reasoning of others, and use language to connect the representations.

Here is the support for English Language Learners provided for this activity.

#### What might this look like during distance learning?

Here’s how it happened recently with a group of Algebra I students in Duarte, CA.

First, students prepared displays of their work, showing how they made sense of the problem and why their solution makes sense. Some opted to use the tools of the video conferencing application while others chose to use paper and pencil.

#### Compare

During a synchronous video meeting, students examined each others’ work. It turned out that two students, Eduardo and Nuri, had a similar approach.

Eduardo exclaimed “Nuri did it like me!” The teacher pushed: “Can you say more? How can you tell that you both had a similar approach?”

As Eduardo explained, he highlighted pieces on Nuri’s work that were similar to his.

“Nuri and I both showed the numbers 10, 20, and 10 along the side.”

“What do those numbers represent?” the teacher asked.

“The change in the time,” Eduardo continued. “It’s 10 minutes to get from 11:00 to 11:10, and 20 minutes to get from 11:10 to 11:30.”

Eduardo also highlighted the equation $9 + 20 + 8 = 37$. “That’s the change in the percent charged. It went up $9 + 20 + 8$ or 37% in the 40 minutes from 11:00 to 11:40.”

The teacher paused. “Nuri, where is your work different from Eduardo’s?” The conversation continued with evidence from the student work.

#### Connect

Students looked for similarities and differences. Eduardo noticed that everyone tracked the change in percent charged—9, 20, 8. But there was something in Ameilia’s work that puzzled her classmates.

Ameilia’s Work

What puzzled the group was Ameilia’s sequence of: 9, 20, 8, 21, 7, 22,. . . This prompted Eduardo to ask, “How did you get 21, 7 and 22?” Ameilia described she noticed a downward trend in the nine and eight (9, 20, 8, …) and assumed an upward trend in the other numbers (9, 20, 8, 21, 7, 22…), “I followed the patterns,” she shared.

A collective, “ah!” could be heard by the group at this point.

#### Asynchronous Learning

In asynchronous settings, students should submit an image of their work, whether it’s a screen capture or a photo of paper and pencil work. The teacher then selects and prepares student work samples to focus the “compare” and “connect” conversation using a discussion board or shared electronic document.

#### Why use this routine?

Let’s go back to our question: What happens when we pay attention to language?

By focusing on language, the teacher created an opportunity for students to go beyond just describing their own process and answer. Students explored connections between their thinking and the thinking of others. Students used oral language to reflect on their reasoning, and comparisons between their work and the work of others. This allowed them to encode their thinking in a different way than just numerically or visually. Just as students benefit from examining multiple mathematical diagrams, linking these different language representations (oral, representational) increases sensemaking and also makes the learning stickier.

When students were asked about a new insight gained from the conversation, Eduardo said, ”a new insight I have is that everyone has a different style of thinking and how they solve problems. A lot of people have different ways of solving a problem so it’s cool to see how other people do their problems to get an answer.”

Special thanks to Ann Kim and her students for sharing their learning with us.

## Next Steps

Here’s an activity from each grade level that makes use of the Compare and Connect routine.

We would love to learn alongside you. How have you used MLR 7 with your students during distance learning? Share your Compare and Connect prompt, and, if possible, student work, at #LearnWithIM.

##### Jennifer Wilson
Jennifer enjoys learning alongside the Illustrative Mathematics community as a professional learning facilitator and writer. She is a Core Advocate and National Board Certified Teacher, and she has most recently taught and learned math with students and teachers in the Rankin County School District in Brandon, Mississippi. She is a recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (2011) and an instructor for TI’s Teachers Teaching with Technology program. Jennifer thinks a lot about how we might slow down and savor learning math through questions, collaboration, and connection, and so she blogs at Easing the Hurry Syndrome and The Slow Math Movement.
##### Liz Ramirez

As the Director of Access and Supports at Illustrative Mathematics, Liz’s goal is to develop quality resources and professional learning opportunities that empower teachers to meet the diverse needs of their students. Before joining IM, Liz devoted her career to teaching students and supporting educators in New York City Public Schools. She is passionate about improving the experience of learning mathematics for all students, especially those in underrepresented and underserved communities.

##### Vanessa Cerrahoglu

Vanessa Cerrahoglu started her journey as an educator, curriculum developer, and workshop facilitator over 20 years ago. She taught high school mathematics in Los Angeles and Orange County before joining her local county office as a math coordinator. She has developed a unique perspective to the problems we face every day, through her work with diverse learning communities: a site with predominantly English language learners in Title 1 schools, a math and science academy, and an academy grounded in the arts. She currently supports teachers, administrators, and varied stakeholders, grades K–12, to foster a love for learning mathematics! She tweets @mymathsoul.

## 2 thoughts on “English Learners and Distance Learning: Compare and Connect”

1. Barbara says:

I have been using IM in sixth grade since the beta version was being piloted. I am comfortable with using the routine in my classroom with students. I was excited to read “what this might look like during distance learning” as that is what I was struggling with this spring. This struggle will no doubt continue for me in the fall. What I read was – students used something of their choice to prepare a display of their work. Then I read – students examined each other’s work. The routine is well articulated, but not the part about how to execute it while distance learning. I am not alone in my looking for more regarding how to create success using distance learning tools. Where might I find more help with that?

1. Illustrative Mathematics says:

From the authors
Hello, Barbara! Thank you for your message. Our last blog post will have some more specific ideas for each MLR. Here are some for MLR7:

– Support students to use screencasting tools or send a picture of their work ahead of time so that you can select strategies for students to compare and connect.
– Synchronously or asynchronously, share selected pieces of student work and ask students to identify what is the same and what is different across the selected pieces of student work.
– In a synchronous setting, display selected student work so that students can identify where the same quantities or relationships are expressed in the different strategies.
– In an asynchronous environment, paste multiple strategies or representations based on student work into a document or discussion board for students to respond to.

We are glad to brainstorm with you given your specific situation. Do you meet with your students synchronously? Do you use a classroom management system such as Canvas or Blackboard? What digital tools do you and your students use?

Jennifer, Liz, and Vanessa