Mathematics is sometimes regarded as a “universal language,” as it is grounded in abstract concepts such as numbers and shapes. And there is some truth to that! After all, two people who speak different languages may still be able to solve the same math problem and get the same solution. However, language is nevertheless essential for teaching math, as mathematics is inextricably linked to the language in which it is taught.

Proficiency in any language relies on two factors: **language comprehension** and **language production**. When it comes to teaching math to ELL students, we can look closely across lessons and consider, “What is the language load at this moment? Comprehension or production?” Then we can leverage targeted strategies to promote academic language development while also deepening mathematical understanding.

Students learning English carry a different cognitive load when they are also learning mathematics. What follows are ELL strategies for math that lighten the students' cognitive load so that they can show mathematical understanding while you maintain rigor in the lesson.

A note on language: we employ the common phrase *English language learner*, along with the acronym ELL, but we also recognize that this is imperfect nomenclature. Students who are learning English do not fit neatly into a single label.

## ELL Strategies for Math: Language Comprehension

### 1: Use Routines That Break Down Word Problems

Word problems present an especially tough problem to students learning English. They’re hard enough for students who are further along in their English language development! Word problems demand that the reader parse plenty of non-mathematical vocabulary such as names, objects, jobs, and places.

Mathematics instruction will always include word problems, as that is how to articulate complex mathematical situations. Strategies like **Three Reads**, **Stronger and Clearer Each Time**, and **Compare and Connect** help break down the context of a problem and guide students in focusing on one aspect of the language at a time.

### 2: Focus on Mathematical Vocabulary

Learning mathematics is *so* much more than learning mathematical vocabulary. Spend time on the words.

For multilingual learners, vocabulary can sometimes be an entryway into the math. Students may have existing notions about words such as *product, times, *and *one, *for example, and by discussing them, you are connecting about ideas on both language and mathematics. Your students will help you learn other languages as you help them learn math, a symbiotic relationship.

Provide vocabulary instruction upfront both for mathematical vocabulary and non-mathematical vocabulary that appears in word problems students will confront in the lesson. Vocabulary instruction involves more than just reviewing definitions. It can include playing vocabulary games, reading math readers, and using tools such as word banks.

**3: ****Connect with Familiar Contexts**

What would engage your students, regardless of language? Think about what sports they play, music they listen to, TV shows they watch, food they eat, or holidays they celebrate (to name a few). If you can draw on your students’ cultural knowledge, you can open paths to engage them even when language serves as a temporary barrier.

Look for ways to modify contexts of word problems and possible bridges between math that they understand and the content you’re trying to teach. Position your students as mathematically competent regardless of how well they can articulate their reasoning in English. If you can, let them make up their own word problems! Then you learn more about what is familiar to them.

**ELL Strategies for Math: Language Production**

**4: Use Sentence Frames**

Sentence frames allow students to practice speaking but may help them feel less intimidated. They offer a scaffold to students who understand mathematical ideas but get caught up in English grammar. The scaffold extends to students whose first language is English but nevertheless struggle to articulate mathematical ideas.

By employing sentence frames in your classroom, you also support learning vocabulary (see Strategy 2: Focus on Mathematical Vocabulary). It gives students clear contexts in which to practice the vocabulary, and the vocabulary itself can be part of the sentence frame, for example “This polygon (is/is not) a quadrilateral because _____.”

Seek out sentence frames that are both lesson-specific and content-agnostic. HMH math professional learning includes a treasure trove of examples like the ones below:

- A _____ (is/is not) a _____ because _____.
- I can conclude that _____.
- While a _____ and a _____ both have a _____, they are different because _____.
- If _____, then _____ will _____.
- A _____ is a polygon because _____ and _____.

### 5: Create a Low-Stakes Conversation Space

It is important that students can test out ideas aloud in a low-stakes environment before being asked to share with the whole class. Look for ways that students who don’t participate much yet can join the conversation. For example:

- Ask questions that students can answer using gestures or drawings.
- Provide students with sentence frames to help them express their ideas in English.
- Have students practice sharing their ideas in lower-stakes partner or small group discussions before being asked to share out with the whole class.

There is no need to reduce the complexity of a math lesson even when you must think about the complexity of language. Incorporate routines and structures that equip students to participate in discussions and share their ideas. As you plan instruction, ask yourself questions like the examples below to help promote student participation along the way:

- Whose ideas will I record?
- How will students express their ideas?
- What visual models can students use to express their ideas?
- When will I provide sentence frames?
- When is there time in the lesson for students to think independently and discuss with a partner or small group?

When possible, encourage students to think, write, and enter math conversations in any language available to them. It’s unreasonable to task you with picking up another language, but long gone are the days where you have to look everything word by word in the dictionary. Translate letters using Google Translate or, if your school has the option, look for learning software that’s available in multiple languages.

**6: Use Tools, Visual Models, and Manipulatives**

It is important to remember that the barrier is language, *not* necessarily knowledge. These strategies aren't just good practice for multilingual learners. All learners who have working eyesight benefit from visual learning, and the same applies to physical learning with manipulatives. Math is unique in how often and how flexibly it can make use of visual and physical models. Yet when the learner is multilingual, models can go from best practice to critical mathematical scaffolds.

When learning is digital, the line between visual and physical models becomes blurred. For many students, in fact, digital models are *especially* helpful. Some learners feel more comfortable using tools when they can do so independently, and potentially anonymously.

When it comes to arithmetic in particular, students may draw calculations using algorithms and models that work but are new to you. Arithmetic falls into this gray area between procedural math and conceptual math, and as such is prone to regional differences. Just look at how division "looks" to a Venezuelan, U.S., and French student:

In general, have students show you what they know. And lean into the differences! There is rich discourse to be had when comparing different ways to divide (or multiply or add or subtract) numbers, along with other possible cultural differences such as how to notate numbers or draw graphs.

**7: Collaborate with Colleagues**

This strategy is possibly the biggest one of all and transcends simply helping with language production. It helps with comprehension too; in fact, it helps with practically everything! Only you know the roles within your community, school, or district. Are there translation services? School-community liaisons? Dedicated English language development teachers? Ask your colleagues what is available, and use it!

Don’t forget about ELA instructors either. It doesn’t matter what grade you teach. If you are teaching in English, then it is impossible to fully separate math content from English content. We don’t have a “left brain” and a “right brain,” we just have brains. The skills that come from learning to read and write in a language improve one’s math ability, too, and in this way, the ELA educators in your school or district could become valuable contributors to your classroom.

**How to Support ELL Students in Math**

When supporting English language learners in math class, we often don’t know if the problem stems from a language need or a math need. Yet it is important to think constantly in terms of assets, not deficits. A class that collectively speaks multiple languages is a cultural gold mine!

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*With Spanish language components, multilingual family letters, and ELL activity guides, HMH mathematics solutions are** designed with the multilingual learner in mind.*

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