Classroom Strategies, Materials Adaptation, Tools and Resources

Developing the Math Language Routines

Foster Student Participation Through Building Math Language, Practices, and Content

For many years, math teachers have been thirsty for resources that help them to make math more inclusive of the diversity of learners in their classrooms. The Math Language Routines (MLRs) provide teachers with ways to foster student participation while building math language, practices, and content simultaneously. The MLRs were developed by a team of math and language specialists working together at Understanding Language (UL), a research center at Stanford University. The benefits of having an interdisciplinary team working together were tremendous! In this blog, we share the backstory of how the MLRs were developed.

Embedding Language Routines into Math Instruction

UL entered into partnership with a national math content developer who invited us into its curriculum design and writing process for the purpose of strengthening language supports for English learners (ELs). It is common to get requests from publishers to layer on EL modifications during the curriculum refining process, but this offer to join while the curriculum was still in development presented a unique and exciting opportunity to help create challenging, engaging, grade-level learning opportunities for ELs. Our aim was clear: design a math curriculum that acknowledged, embraced, and built on the language variability that exists in classrooms. We felt that in doing this, all learners, including ELs, would benefit. The UL team proposed this challenge to the content development team: Could we embed language supports into the materials in ways that were central to the lesson architecture, instead of as notes in the margin?

Over several months, we developed a theory of action reflective of assumptions we shared about math learning:

  1. Language learning and content learning should happen simultaneously;
  2. Student agency is central in mathematical sense-making and language learning;
  3. Strategic scaffolding should foster student participation in high-challenge, high-support learning; and
  4. Instructional responsiveness to students’ language and mathematical needs is imperative.

From this theory of action, we developed four design principles that undergirded the routines:

1. Support sense-making Routines should help students make sense of the language, the skills, and the math. Amplifying the language (rather than simplifying) supports students in acquiring sophisticated concepts and terms.
2. Optimize output Routines should help students get progressively better at expressing their thinking when writing and speaking about math.
3. Cultivate conversation Routines should help students have rich interactions to help fill in knowledge gaps, make mistakes and collectively correct mistakes, and provide a low-stakes way for them to strengthen mathematical thinking and language use.
4. Maximize meta-awareness Routines should help students to organize thinking, apply concepts across contexts, and reflect on their use of math language.

 Developing the MLRs

Once we’d named our design principles, we studied the curriculum to develop a shared understanding of the language features and the language demands in the lessons (for example, some lessons focused on the language of generalization, for every x, etc.) We asked ourselves, “What is the mathematical work that students are asked to do, and what are the language expectations embedded in the lessons and assessments?” We noticed that the more sophisticated and conceptual the mathematics, the greater the language demands. While the prompts in lesson activities were mathematically and linguistically juicy, there was no “on-ramp” for the students who were still developing the skills for participating in sophisticated mathematical discourse. We concluded that it was one thing to ask and expect students to discuss their ideas in math, and it was quite another to explicitly and systematically build their language skills over time.

We needed a set of routines that were clear in purpose and structure, applicable across math topics, and flexible enough for teachers to adapt with their own students that would increase student opportunities to speak, write, and listen to mathematics in service of improving student understanding of mathematics. In some of those meetings, the language and math specialists worked on the math tasks together, building a shared understanding of how to develop math and language simultaneously. We pushed against the usual practice of sprinkling in a few English Language Development strategies, as these don’t target specific mathematical language demands or progressively build math language. From there the eight MLRs were created.

Math Routine 1: Stronger and Clearer Each Time
Math Routine 2: Collect and Display
Math Routine 3: Clarify, Critique and Correct
Math Routine 4: Information Gap
Math Routine 5: Co-Craft Questions and Problems
Math Routine 6: Three Reads
Math Routine 7: Compare and Connect
Math Routine 8: Discussion Supports

As two authors of this publication, we are thrilled to see MLRs appearing in math classrooms and curricula nationwide. We love hearing the stories of teachers learning and implementing the MLRs, and about the impact these practices have with all of their students, and especially their ELs. The MLRs were designed to give teachers practical strategies and the support they need to make rigorous mathematics content accessible for all learners, and we encourage others who are finding success with them to share their stories.

3 thoughts on “Developing the Math Language Routines

  1. Thank you, Jack and Renae, for bringing this important work into the public. I am a math coach and we have jumped “all in” to promoting the MLRs as complementary to the:
    SMPs (
    5 Practices (,
    8 instructional routines (
    Talk Moves (

    The MLRs are critical to fostering high levels of student discourse around “sticky” problem-solving, the exact environment that produces collaborative, critical thinkers. I agree wholeheartedly with the language routines and challenge all educators reading this to begin embedding these routines into their practice immediately.

  2. This is fabulous! As an English Learner specialist supporting teachers around our state, it is imperative that we curriculum and lesson writers realize that language supports belong in the lesson architecture and not in the afterthoughts. They are a foundational piece to the understanding of content for all students, especially ELs. Thank you for prioritizing the importance.

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About the Author: Jack is currently the director of research at youcubed at Stanford. He began his career as a high school math teacher in Texas, where he worked with many multilingual learners. His research centers around the development of language for mathematical purposes. He consults internationally on math teaching and learning. He also teachers in the Stanford Teacher Education Program (STEP).

About the Author: Renae Skarin is the Director of Curriculum Review Process where she leads EL experts in reviewing and providing feedback to curriculum developers on the strength of supports for ELs. Previously, she worked at Stanford, where she was a researcher, professional development facilitator, and curriculum developer, for projects specializing in issues of equity and accessibility for diverse learners. Renae has a strong background in second language teaching and teacher education. She is currently completing her doctoral dissertation in Educational Linguistics.