Routines With Roots: Unlocking the ‘Why’ Behind Math Language Routines

The answer we landed on—published in 2017 as Principles for the Design of Mathematics Curricula: Promoting Language and Content Development—rested on four design principles meant to guide curriculum development, lesson planning, and the in-the-moment decisions teachers make every day.

The Four Principles Behind the Math Language Routines

• Support sense-making: Scaffolding tasks and amplifying language so students can make their own meaning.
• Optimize output: Strengthening how students describe their mathematical thinking orally, visually, and in writing.
• Cultivate conversation: Structuring constructive mathematical talk in pairs, small groups, and whole class settings.
• Maximize meta-awareness: Connecting and making distinctions among mathematical ideas, reasoning, and language.

Alongside these research-backed principles, we created eight Mathematical Language Routines (MLRs) to serve as classroom-ready features.

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

The MLRs were designed as concrete expressions of the four design principles, classroom-ready structures that, taken together with the principles, would help better serve MLLs language and math needs. The MLRs were never meant to stand alone.

Today, MLRs are widely adopted in math curricula across the U.S. We didn't fully anticipate how far those routines would travel. Open many of these programs and you'll find Stronger and Clearer or Three Reads built directly into the lesson architecture. That kind of reach is something to celebrate. The MLRs have become part of a shared vocabulary across the field.

But adoption is not the same as integrity in use. MLRs only deliver on their promise when their research-backed foundations, or “the principles,” remain intact. 

From principles to materials specifications

The “principles,” written by the UL team, defined what strong instruction looks like, but publishers needed to know how to build it lesson by lesson. ELSF stepped in to provide that specificity through our Guidelines for Improving Math Materials. 

Several of us who had been on the UL team—including Jack Dieckmann, James Malamut, and myself—joined a broader group of MLL experts and practitioners to take the MLR principles to the next level.

The continuity wasn't accidental. We carried the UL theory of action with us: that math and language develop interdependently, that students are agents in their own sense-making, that scaffolding should foster autonomy rather than dependency, and that instruction must be responsive to what students actually say and do.

Think of it as an evolution of theory into practice:

• The UL Principles are the why. They define the classroom-facing vision, the philosophy.
• ELSF Guidelines are the what. Define the design specifications, the blueprint, that curriculum must be built from for teachers to succeed.
• The MLRs are part of the how. They are practices that operationalize the vision and curriculum in the classroom.

What ELSF added was specificity for the people building the materials. The UL principles informed ELSF’s five “Areas of Focus,” fifteen “Guidelines,” and more granular “Specifications.” Where the UL principle said Support Sense-making, ELSF gave publishers concrete guidance on multiple representations, anticipated the language demands of the unit, and helped make scaffolds in teacher materials more responsive. Where the UL principle said Cultivate Conversation, ELSF identified the lesson-level features that must be present for those conversations to happen effectively.

Why grounding matters

Routines without principles are procedures. And procedures, however well-intentioned, are easy to implement in a flattened manner.

For example, Stronger and Clearer can be reduced to "have students share with two partners and revise their responses," rather than the rich back-and-forth interaction requiring the listener to ask questions for clarity and reasoning, request details and examples, and give feedback relevant to the language and content objectives. Collect and Display might become a static word wall posted on a Monday after one discussion, and it would be rarely referenced again. Neither of those implementations is technically wrong. But both of them strip the routines of the very thing that made them effective in the first place: their grounding in the design principles.  

Once the principles behind the routine are understood, every choice a curriculum developer makes when embedding that routine in lessons becomes more intentional. Where might the students need more support to meet the lesson's language demands? Which routine will best support students in developing the specific language named in the language objective at that point in the activity or lesson? Does the routine need to be modified in any way for it to work at that moment of the lesson? The routine is the visible structure; the principle is the design logic that makes the structure work. ELSF Guidelines show curriculum developers how to extend that logic into the design of the materials themselves. 

What this means for the field

For curriculum developers 

The message is simple: if you are building with the MLRs, build with the intentions behind what you’re trying to accomplish for student learning. The MLRs are not bolt-ons or compliance features, so you can check off that language support was included. They are the visible expression of a coherent design system. Used inside that system, they are powerful. Used outside it, they are decoration.

For education leaders selecting curriculum

The essential question shifts from "Does this program use MLRs?" to whether the program reflects essential features of a quality design that support language and math development. 

To help with this, ELSF developed the Math Must-Haves , which evolved from the Guidelines and support the inclusion of the MLRs. The three questions to ask include:

1. Mapping language and math content: How does disciplinary language develop across the unit, in support of understanding of key mathematical ideas? 
2. Monitoring language and content development: Are language and math development intentionally scaffolded and paired with formative assessment guidance to ensure the objectives are met?  
3. Making connections through student collaboration and conversations: Are there significant and meaningful opportunities for student collaboration and conversation, such as student talk routines that progressively support development rather than just a bolt-on activity?

For curriculum leaders and professional learning providers 

The through-line is an invitation to provide curriculum literacy for teachers and leaders. Language routines are most powerful when teachers understand the rationale, the principal, and the outcome each one is designed to enact. Providing this professional learning ensures that educators are equipped to implement these supports with a deep understanding of how language and content develop interdependently, giving them the freedom to adapt—to select heavier or lighter scaffolds, to lean into the meta-awareness moves, to amplify rather than simplify the language of a task—because they know what the routine is intended to support.

The MLRs have spread further than many of us imagined when we first authored them at Stanford. That reach is a gift. The work in front of us now is to make sure the rationale for learning travels with them so that every multilingual learner who encounters a Three Reads or a Stronger and Clearer encounter not just a routine, but the design philosophy that empowers them to thrive. 
‍

Interested in building the capacity to identify, adopt or implement instructional materials that are responsive to the language and content needs of MLLs? Contact us at ELSF to set up a call to explore ways we can support your goals to improve academic outcomes for multilingual learners.