Stanford University's Understanding Language: Teaching Resources for Mathematics

This resources is based on the premise that ELLs develop mathematical proficiency as well as the linguistic resources to express that proficiency by actively participating in mathematical  practices and rigorous mathematical reasoning that is well scaffolded by instruction.
Resource URL:
Author(s) Organizational Affiliation: 
Stanford University, Graduate School of Education
Product Type: 
Skill Level: 
NRS EFL 3--ABE Intermediate Low
NRS EFL 4--ABE Intermediate High
NRS EFL 2--ESL Low Beginning ESL
NRS EFL 3--ESL High Beginning ESL
NRS EFL 4--ESL Low Intermediate ESL
NRS EFL 5--ESL High Intermediate ESL
NRS EFL 6--Advanced ESL Literacy

Understanding Language, an initiative of Stanford University, Graduate School of Education, aims to heighten educator awareness of the critical role that language plays in the Common Core State Standards (CCSS). Understanding Language seeks to improve education for all students—especially English Language Learners (ELL). The available resources demonstrate ways in which students' English language proficiency and disciplinary knowledge can be developed simultaneously in the context of content instruction. 

Teaching resources that exemplify high-quality CCSS-aligned instruction for ELLs in mathematics are provided.


Benefits and Uses: 

This is a high-quality and well-organized resource that should help fill a much needed gap with respect to resources targeting ELLs. It offers a variety of tools that support teaching and learning aligned with the CCSS. 

In addition to the CCSS-aligned exemplar math tasks, Understanding Language offers resources to support teachers in learning how to use CCSS-aligned math tasks with ELLs. This includes guidelines for math instructional materials development and language of math task templates which can be used by teachers to design and write their own language-focused activities.

Four annotated math tasks present opportunities for students to develop skills called for in the Standards for Mathematical Practice and to work on grade-level appropriate mathematics, as defined in the CCSS. A focal point of this resource is the support provided to teachers with the goal of orchestrating mathematical discussions in which students describe relationships, make generalizations, and use a variety of representations to support claims. The materials are designed to extend beyond enhancing the mathematical vocabulary of students to actively engage students in mathematics reasoning about important mathematical topics.

The primary audience for this resource is teachers who provide CCR-aligned instruction to ELLs. Teachers working to implement the CCR standards may need to adapt the math tasks for use in their classrooms. For example:

  • The elementary-level math task, Roger’s Rabbits, aligns to Level C, CCR standards and may need adaptation for adult learners.
  • The middle school math task, Making Matchsticks, targets a Grade 8 CCSS for math that is not included in the CCR standards, so this task may not be as useful for adult education teachers.
  • The two high school math tasks, Creating Equations and Sidewalk Patterns, both address standards included in Level E of the CCR standards; however, each also addresses one or more CCSS standards that are not included in the CCR standards. 

Each of the four example tasks above also identifies anywhere from four to six Standards for Mathematical Practice as aligned to them. It may be challenging to effectively address this number of Practices within the context of a given task, so teachers may decide to focus their students’ work on a task to emphasize a smaller subset of the identified Practices.

Since reading and understanding word problems is such a challenging task for many adult learners, the math tools Understanding Language offers can also be used to support the learning of adult students who are not ELL.  

Professional developers and/or program administrators tasked with supporting teachers as they implement the CCR standards may also find these resources useful. While the materials can certainly be used directly by teachers, an effective use of the resources may be in long-term professional development or study group experiences. The math lesson units could serve as a model for discussion of quality lessons for ELLs that are aligned to CCR standards and of what is possible in the adult education realm. Teachers could work together to adapt these lesson for the adult education classroom.

All of the resources are useful for adult educators. In general, one of the most significant features of all of the resources is the attention paid to accommodating ELLs without sacrificing any of the rigor and high expectations for CCR standards. Whether teachers study those aspects or experience them along with their students, they will find this to be a useful set of materials.

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