The Academic Language of Mathematics

In last week’s post, I presented some considerations for implementing the CCSS for Mathematics when instructing English language learners. In this week’s post, I want to follow up with a discussion of the role of academic language in that instruction. First, I will set the stage by sharing one expert's view of academic language for ELLs. Next, I will introduce you to a new book series from Corwin that focuses on theory as well as practical ideas for teaching ELLs the academic language of mathematics and English language arts. Finally, I’ll showcase some practical examples for teaching mathematics to ELLs in grade 2 from one of the book’s chapters.

One View of Academic Language

Dr. Debbie Zacarian is the director of the Center for English Language Education and Advancing Student Achievement at the Collaborative for Educational Services in Northampton, MA and author of Colorín Colorado's policy guide, Serving English Learners: Laws, Policies, and Regulations.

She is a contributor to the Corwin series listed below and also has her own new book out about academic language, Mastering Academic Language: A Framework for Supporting Student Achievement. She generously shared her insights on the importance of academic language for ELLs for this post:

A common means for designing programming for ELLs is analyzing their home languages, countries of origin, level of English language development and performance on high stakes tests.  While this is helpful information, the reality that ELLs are among the lowest performing subgroups in our nation and that a significant number fail or drop out should raise our level of urgency to shine a new light on how we design our programming.  Take a look at the federal definition of English proficiency:

  • The ability to meet the state’s proficient level of achievement on state assessments
  • The ability to successfully achieve in classrooms where the language of instruction is English; and
  • The opportunity to participate fully in society.

These skills and opportunities define academic language; however, many ELLs and vernacular speakers of English do not possess them.

That is, to be successful in school and beyond requires students to carry academic language to, in, and from school.  How can we remedy the gap?  We have to understand academic language learning as a four-prong process: a (1) sociocultural, (2) developmental, (3) academic, and (4) thinking-to-learn process.

Academic Language in Diverse Classrooms Book Series

Academic language is of increasing importance to educators as the Common Core State Standards, the new national anchor for curriculum, instruction, and assessment, have set a high bar of rigorous and challenging content, especially for ELLs.

A newImage seven-book series edited by Margo Gottlieb and Gisela Ernst-Slavit and published by Corwin presents the evolving theory behind the construct of academic language, a definition and examples of each of its components, and a template for direct classroom applicability. This book series offers guidance to educators in how to target academic language in planning for student learning as states undergo the implementation of the Common Core and corresponding English language development standards.

The series consists of six separate volumes for English Language Arts and Mathematics segmented according to grade band (K-2; 3-5; 6-8). A separate foundational text, entitled Academic Language in Diverse Classrooms: Definitions and Contexts complements the six volumes.

Each of the six books in the content series provides a detailed, comprehensive treatment of text-based academic language at each grade level and describes the process by which teachers can incorporate academic language into their instructional assessment practices. The first two volumes, Academic Language in Diverse Classrooms: Mathematics, Grades K-2 and  Academic Language in Diverse Classrooms: Mathematics, Grades 3-5 have recently been published, and the remainder of the books will be published later in 2013.

Mathematics Books Overview

The mathematics books build a curricular framework that integrates language and cultural supports with mathematics content during lesson planning, implementation, and reflection. The aim of the mathematics books is for readers to:

  • Understand the role of language within the math principles of the Common Core
  • Identify potential obstacles to understanding
  • Incorporate academic language into standards-referenced unit targets and lesson objectives
  • Collaborate with ELL specialists to help students access the curriculum

To that end, each grade-specific chapter models the types of interactions and learning experiences that help students master both math content and academic language. (On a side note, Dr. Ernst-Slavit and Dr. David Slavit just published an article in Language Magazine titled "Mathematically Speaking" that highlights different aspects of the language of mathematics and the fact that mathematics is not a universal language.)

Grade Two Examples of the Academic Language of Mathematics

In a chapter of the Grades K-2 mathematics book co-authored by second grade teacher Michael Silverstone and Debbie Zacarian, readers meet Mark Zimmerman, a general second grade teacher whose class of 23 students includes seven current or recently exited ELLs.  In one part of the chapter, Mr. Zimmerman teaches a CCSS-based mathematics unit on the concepts of odd and even. He bases his instruction on the following content and language targets:

Content target: Students will name and sort numbers as odd or even.

Language target: Students will explain how odd and even numbers are the same and how they are different.

He uses WIDA's 2012 Amplification of the ELD Standards to frame performance indicators for his ELLs at different levels of English language proficiency when speaking about the concepts of odd and even.


Mr. Zimmerman has observed that the ELLs and vernacular speakers of English in his class rarely, if ever, participate in class.  To help his students to be active leaders in mathematics, he  intentionally secured ways for them to understand and use the mathematics concepts by connecting them with their personal, cultural, social, and world knowledge and directly and explicitly teaching them based on their level of English language, mathematics, and thinking skill development. He knew that his students were well-versed in choosing two teams and in choosing a partner to work with and decided to build on his students’ strengths to teach them about odd and even.

To modPopsicleel the mathematical concepts of odd and even to ELLs at different levels of English language proficiency, Mr. Zimmerman wrote his students’ names on sticks and placed them in a can. He took random handfuls of sticks, and the students decided whether the sticks would divide into two even teams or two nearly even teams with unequal totals. He pointed out that an even number of students would make two exactly even teams – or, in an even number of students, everybody could have a partner and no one would be alone or in a group of three. With an odd number of students, there would be one student left out or in a group of three.

He then had his students use math terminology to offer proof and reasoning. For example, his students responded to questions such as:

  1. What happens when you add two even numbers? What happens when you add two odd numbers? What happens when you add an even and odd number?
  2. Is this true for any two even numbers? Is it true for any two odd numbers?
  3. Explain (or show) why this is true.

Mr. Zimmerman also gave partners prompts such as “Is this an even or odd number? How do you know?” He provided sentence starters so his students could answer these questions, such as:

  • An odd number has…
  • An even number has…
  • I know this is an even number because…
  • I know this is an odd number because…

For further discussion, I encourage you to take a deeper look at the practical books in this series to fill your toolkit with more ideas for teaching the complex academic language of the CCSS to ELLs.

Books on Academic Language

Corwin Series:

Additional books by Debbie Zacarian:

Colorín Colorado's Academic Language Resources

Colorín Colorado Academic Language Video

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