When it comes to learning math, English language learners (ELLs) have a unique challenge. Unlike most English-speaking students, ELLs have the task of learning a second language and learning content simultaneously. Contrary to popular assumption, language plays a critical role not just in reading and writing, but in learning mathematics as well. As a teacher, you're challenged with making math lessons comprehensible and with ensuring that students have the language to understand instruction and express their grasp of math concepts orally and in writing. Our panel of experts share ten ways to teach ELLs their ABCs and their 123s.

1 Create Vocabulary Banks.
Charts that contain key math vocabulary words and phrases are helpful references for ELLs when discussing or writing about their math thinking, especially if the words are accompanied by illustrations.

2 Use manipulatives.
Manipulatives are important tools that make math content comprehensible. They give students ways to construct physical models of abstract mathematical ideas; they build students' confidence by giving them a way to test and confirm their reasoning; they are useful for solving problems; and they make learning math interesting and enjoyable.

3. Modify teacher talk and practice wait time.
It is important to give all students, especially English language learners, time to process questions and formulate responses. Speak slowly and use clear articulation. Reduce the amount of teacher talk and use a variety of words for the same idea. Exaggerate intonation and place more stress on important new concepts or questions. After asking a question, wait for a few moments before calling on a volunteer. Writing the question on the board will also help.

4. Elicit nonverbal responses, like a thumbs up or down.
Nonverbal responses will help you check for understanding without requiring students to produce language. ELLs can participate and show that they understand a concept, or agree or disagree with an idea, without having to talk. This is especially important for students whose comprehension of English is more advanced than their ability to speak the language.

5. Use sentence frames.
Math sentence frames serve a variety of purposes. They provide the support English language learners need in order to fully participate in math discussions; they contextualize and bring meaning to vocabulary; they provide a structure for practicing and extending English language skills; and they help students use the vocabulary they learn in grammatically correct and complete sentences. After sufficient practice with using the frames to express their mathematical thinking, students will be ready to use the frames for writing.

For example, the following frames support students at various language levels in their discussions about polygons.

Beginning Level
This is not a polygon. It is/has curves.

Intermediate Level
This is not a polygon because it has curves, and is open.

Advanced Level
This shape has four straight sides, four vertices, and is closed; therefore, it is a polygon.

6. Design questions and prompts for different proficiency levels.
Questioning students lets them reveal what they have learned. Answering questions lets students test, confirm, or modify their own understandings. None of these goals can be met unless the queries are structured in a way that allows students to produce a response. Here are some examples of questions and prompts used to support students at different proficiency levels.

Beginning Level
English language learners are not always able to answer the questions posed to them, especially when the questions are open-ended. Provide support for and improve the participation of students with lower levels of English proficiency by using a prompt that requires a physical response, like "Show me the circle" or "Touch the larger number."

You can also ask a question requiring a yes-or-no answer: "Is one number larger than the other?"

When asking short-answer questions, build the answer into the question for additional support: "Is this a triangle or a circle?" or "Is the line horizontal or vertical?" or "Should we add or subtract?"

Intermediate and Advanced Levels
Students with intermediate and advanced levels of proficiency need less support to understand and respond to questions, but carefully crafted queries can improve the quality of both their responses and their English. For example, instead of asking an intermediate-level student, "How did you solve the problem?" you might phrase the question this way: "What did you do first, second, and third to solve the problem?" This sort of question models the structure of a well-crafted answer: "First, I put the blocks in groups of ten. Second, I counted by tens. Third, I added the ones left over." Compare that with the response more likely to result from the first question: "I counted them."

Students with advanced fluency can respond to questions and prompts that are even more open-ended, such as "Describe to me the steps you used to solve the problem and explain how you used them."

7. Use prompts to support student responses.
Prompts can help English language learners get started when responding to a question. For example, begin with: "You figured it out by..." or "It is a polygon because..." or "First you put the hexagon on the table, and then...." If you encourage them toward an answer, they are more likely to follow your lead and respond with confidence.

8. Consider language and math skills when grouping students.
There are times when grouping students with similar abilities in math makes sense, especially when those students are all struggling with the same concept or skill. Most of the time, however, students benefit from working in groups where participants have varying skill levels in mathematics. Students also benefit from working in groups where participants have different levels of English language competence. However, it is important to monitor student talk to ensure that all students have the opportunity to engage in mathematical conversations.

9. Utilize partner talk.
For partner talk, ask a question and then give students a minute or two to put their thoughts into words with their nearest neighbor. Partner talk allows more students to participate in classroom discussions, and eliminates the pressure that comes with speaking alone in front of a large group. It also fosters positive peer collaboration; when students figure something out together, trust is built between them.

10. Ask for choral responses from students.
When you have students echo back a word or phrase, it exposes them to new vocabulary and serves as a model for correct pronunciation, syntax, and grammar.

Teacher Tips
Instructor readers share what works best for them.

"The more you use strong pictorial and manipulative backup, the easier it is for ELLs to learn math. In fact, even those who speak English as a first language greatly benefit from manipulatives and drawings. Not many learners grasp mathematical language effectively without a visual experience." -Lin Cazares

"Show and tell whenever possible through demonstration, role playing, and modeling. Use pictures and video during vocabulary and concept instruction. Finally, ask for help if you need it! Your district and/or school should have a specialist who is trained to assist you!" -Jenifer L. Moore

"Get the students up and active. They are by nature very kinesthetic; they clap their hands when learning to count by fives and tens, go on a "numbers hunt" by walking and searching around the room, or patrol the school to identify geometric shapes." -Nanette Avery

"Small groups allow ELL students to feel more comfortable and confident. They enjoy having a peer instead of asking questions in front of the whole class. Plus, circulating around the room allows me to stop and focus on their needs." -Sarah Wilson

"Give ELLs opportunities to work individually so they can progress at their own pace. During a difficult lesson, you might want to say something like: ‘Do as much of question 5 as you can in 10 minutes' or ‘Choose which question you want to start with.'" -Dorit Sasson

"Relate a concept to a personal experience a student has had in the past; that way they will have a greater chance of understanding the information taught. Try to introduce a concept by relating it to something from their country. For example, I have a student who came from Holland and I always ask her what they call a certain word in Dutch." -Pat Roth

"Have students keep journals to write about what they have learned and address questions they may have relating to a recent lesson. I read their entries and respond with answers and encouragement." -Nanette Avery

About the Book:
These strategies are brought to life in a new Math Solutions resource widely adopted by K-5 teacher preparation educators: Supporting English Language Learners in Math Class: A Multimedia Professional Learning Resource (Bresser et al., 2009). This tool was developed for teachers in regular or mainstream classrooms with one or more ELL students and includes three main components: a DVD of teachers and students in action, a two-book series for grades K-2 and 3-5, and a facilitator's guide to support implementation of effective strategies. Watch video clips of the authors using ELL strategies with students and find additional resources for ELLs online at www.mathsolutions.com/ELL.

Meet the Experts
Christine Willig
, Math Solutions' president and CEO, has worked for 25 years in education-focused leadership.
Rusty Bresser lectures and supervises teacher education at the University of California, San Diego (UCSD).
Kathy Melanese is a Distinguished Teacher in Residence (bilingual elementary) at UCSD.
Christine Sphar is a new-teacher support administrator in San Diego's Cajon Valley Union School District.
Carolyn Felux is the education director for Math Solutions.