Teaching mathematics to English Language Learners (ELLs) is a dynamic and rewarding endeavor that requires a strategic blend of content instruction and language support. The goal is not to dilute the mathematics but to make it accessible and rigorous for students who are still developing academic English proficiency. Effective math instruction for ELLs leverages students' prior knowledge, uses visual and hands-on learning, and explicitly teaches the language of math. This guide outlines high-leverage practices that empower educators to build classroom environments where ELLs can thrive both mathematically and linguistically.

Create a Language-Rich Mathematics Classroom

The foundation of success for ELLs in math is a classroom culture that values and supports language development as a core component of learning. Mathematics is not a universal language; it has its own specific vocabulary, sentence structures, and discourse norms. Building a language-rich environment helps demystify these elements and allows ELLs to engage with mathematical concepts more deeply.

The Critical Role of Academic Language

Math instruction relies heavily on a specialized academic register. Students must understand terms like sum, product, quotient, and coefficient, as well as functional language used in problem-solving, such as compare, analyze, justify, and construct. For ELLs, these words can be significant barriers. Colorín Colorado, a premier resource for ELL educators, emphasizes that explicit vocabulary instruction is not just a reading strategy; it is a math strategy. Teachers must treat vocabulary as a central part of the lesson, not an afterthought. This involves pre-teaching terms, posting them on a word wall with visual examples, and providing multiple opportunities for students to use them in context.

Fostering Mathematical Discourse

Encouraging "math talk" is one of the most powerful ways to build both language and conceptual understanding. When students talk about math, they process ideas more deeply and learn from each other. However, ELLs may be hesitant to speak spontaneously. Providing structured opportunities and language frames can make discourse accessible. Use routines like Think-Pair-Share or Number Talks. Provide sentence starters such as:

  • "My strategy was different because..."
  • "I agree with your answer, and I want to add that..."
  • "Could you explain how you got that step?"

These frames reduce the cognitive load of formulating language, allowing students to focus on the mathematical reasoning. The National Council of Teachers of Mathematics (NCTM) identifies mathematical discourse as a core teaching practice, and for ELLs, it is a dual-purpose tool for learning content and language.

Leverage Visuals and Hands-On Learning

Visual and tactile representations are powerful equalizers in a diverse classroom. They transcend language barriers by providing a common, concrete reference point for abstract ideas. Moving from concrete to abstract in a systematic way is essential for ELLs.

The Concrete-Representational-Abstract (CRA) Approach

The CRA framework is a research-backed strategy for teaching mathematics. It involves teaching concepts in a specific sequence:

  1. Concrete: Students use physical objects (counters, base-ten blocks, fraction tiles, algebra tiles) to model the problem. This allows them to explore a concept without the immediate pressure of language.
  2. Representational: Students draw pictures or diagrams that represent the concrete objects they used. This bridges the physical and the symbolic.
  3. Abstract: Students solve problems using only numbers and symbols.

For ELLs, spending adequate time in the concrete and representational phases is critical. It ensures that the mathematical concept is firmly established before the student is expected to navigate the language-heavy symbolic notation. For example, when teaching subtraction with regrouping, students should first trade ten blocks, then draw the exchange, and finally write the algorithm.

Graphic Organizers as Universal Supports

Graphic organizers are exceptional tools for reducing language load and organizing thinking. They provide a visual structure for problem-solving. Consider using:

  • Problem-solving templates: Frames like "What do I know? What do I need to find? What is my plan? What is my answer?" help students systematically approach word problems.
  • Place value charts: These are essential for understanding number sense and operations with large numbers or decimals.
  • Venn diagrams and T-charts: Ideal for comparing geometric shapes or sorting numbers.
  • Frayer models: Excellent for deep vocabulary work (discussed in the next section).

By providing these visual scaffolds, teachers reduce the cognitive load associated with language and organization, freeing up mental energy for pure mathematical thinking.

Implement Systematic Vocabulary Instruction

ELLs need more than just a glossary; they need deep, contextualized instruction in the language of mathematics. Effective vocabulary instruction is active, visual, and requires repeated exposure.

Tiered Vocabulary and Word Analysis

Understanding the three tiers of vocabulary helps teachers prioritize their instruction:

  • Tier 1 (Basic): Everyday words (e.g., count, big, small). These may need quick support but are not the focus.
  • Tier 2 (Cross-curricular/Academic): Words like compare, contrast, determine, calculate, and justify. These are vital for understanding instructions and demonstrating reasoning across subjects.
  • Tier 3 (Domain-Specific): Words unique to math, such as isosceles, denominator, polynomial, and asymptote.

Focus intensive instruction on Tier 2 and Tier 3 words. Teach students to recognize root words, prefixes, and suffixes. For example, teaching that tri- means three helps with triangle, trinomial, and tripod. Recognizing cognates (words that sound similar in English and other languages, like polygon/polígono) can be a huge asset for Spanish-speaking ELLs.

Active Vocabulary Routines

Move beyond look-up-and-define exercises. Use routines that force students to interact with the word:

  • Word Walls: Create a dedicated space for math vocabulary. Include the word, a visual, a student-friendly definition, and a non-example. Reference it constantly.
  • Frayer Models: A four-square graphic organizer where students define the word, list characteristics, provide examples, and list non-examples. For the word polygon, a student might write: Definition: "A closed 2D shape with straight sides." Characteristics: "Closed, straight sides, 2D." Examples: "Triangle, rectangle." Non-examples: "Circle, cube."
  • Interactive Notebooks: Have students keep a math journal where they record new vocabulary, draw visual representations, and write sentences using the terms.

Scaffold Instruction and Use Formative Assessment

Scaffolding is a temporary support structure designed to help students achieve a task they could not do alone. For ELLs, this means breaking down complex problems and instructions into manageable steps and providing language support until they gain independence.

Clear, Structured Instructions

Complex linguistic instructions can derail an ELL's ability to show their math knowledge. Follow the SIOP (Sheltered Instruction Observation Protocol) model by clearly stating content and language objectives at the start of the lesson. For instructions:

  • Use short, simple sentences.
  • Number the steps.
  • Model the process ("I Do, We Do, You Do").
  • Include visual cues (e.g., a picture of a pencil next to "Write your answer").
  • Check for understanding frequently by asking students to repeat instructions in their own words, not just asking "Does everyone understand?"

Formative Assessment for Content, Not Language

Traditional math assessments often penalize students for language errors, masking their true mathematical ability. To get an accurate picture of what an ELL knows, use varied formative assessment strategies:

  • Quick Draws or Diagrams: Ask students to draw a model to represent a fraction or a geometric concept.
  • Native Language Support: Allow students to explain their reasoning in their home language or use a bilingual dictionary for key terms.
  • Observational Checklists: Note how students use manipulatives or interact in group work. This can be more informative than a written quiz.
  • Exit Tickets with Sentence Frames: Provide a structure like "The main idea of today's lesson was..." or "One strategy I learned for solving [problem type] is..."

WIDA provides Can Do Descriptors that can help teachers understand what students can reasonably be expected to do at different levels of English proficiency, allowing for more targeted and fair assessment.

Foster Peer Collaboration and Diverse Language Use

Collaborative learning provides ELLs with a low-stakes environment to practice both math and language. When structured effectively, group work can be one of the most productive parts of the math lesson.

Structured Group Work

Simply placing ELLs in a group is not enough. The interaction must be structured to ensure participation. Use strategies like:

  • Jigsaw: Each student in a group becomes an "expert" on one part of a problem or concept and teaches it to the others. This gives them a defined, achievable role.
  • Reciprocal Teaching for Math: Students take on roles like "Questioner" (asks clarifying questions), "Summarizer" (restates the problem), "Clarifier" (explains vocabulary), and "Predictor" (guesses the next step).
  • Math Talk Partners: Pair students strategically, sometimes with a same-language partner to allow for deep conceptual discussion in their native language.

Translanguaging as a Pedagogical Resource

Rather than enforcing an "English-only" policy, research increasingly supports translanguaging—the strategic use of students' full linguistic repertoire to learn. This does not mean students never use English; it means they can leverage their home language to access complex content. For example, a group of Spanish-speaking students might solve a difficult word problem by first discussing it in Spanish, then working on the math, and finally reporting their answer in English. This deepens understanding and validates students' identities. The TESOL International Association advocates for creating inclusive classrooms that respect and build upon students' linguistic resources.

Make Connections to Students' Lives

Math becomes far more accessible and engaging when it is clearly connected to students' real-world experiences and cultural backgrounds. This is a core principle of culturally responsive teaching.

Culturally Responsive Mathematics Teaching

This involves more than just "relatable" word problems. It means valuing the mathematical practices that exist in all cultures. For example:

  • Patterns and Geometry: Explore patterns in textiles, architecture, or tile work from students' home countries. This validates their heritage while teaching geometry.
  • Measurement and Currency: Use problems that involve converting between metric and imperial systems or different currencies.
  • Data Analysis: Have students collect data from their own communities—such as languages spoken, family sizes, or types of businesses—and create graphs and analyze trends.

Using Everyday Contexts

Use scenarios that are universally familiar across cultures, such as shopping, cooking, sports, and planning a trip. When teaching proportional reasoning, use recipes from different cuisines. When teaching percentages, use sales ads from local grocery stores. This not only builds relevance but also exposes students to practical, survival-level vocabulary in English. Real-world contexts provide a shared experience that helps ELLs grasp the purpose behind the math.

Differentiate Instruction Thoughtfully

ELLs are not a monolithic group. They come with varied educational backgrounds, varying levels of native language literacy, and different English proficiency levels. Effective instruction differentiates accordingly.

Differentiating by Proficiency Level

Adjust the language demands without lowering the mathematical expectations. A new arrival (Entering/Emerging) and a long-term ELL (Expanding/Bridging) will need different supports.

  • For newcomers: Focus on hands-on tasks, visual supports, and key vocabulary. Assessments might be pictorial or involve matching. Use native language resources when possible.
  • For intermediate students: Use complex sentence frames, work on academic vocabulary, and expect them to explain their reasoning in short written responses.
  • For advanced students: Focus on precision of language, justification of arguments, and tackling un-simplified word problems. They may still need support with Tier 2 academic vocabulary.

Flexible Grouping

Vary how you group students based on the task. Sometimes, group students by home language to allow for deep conceptual discussion. Other times, group them by math readiness for targeted instruction. Still other times, mix proficient English speakers with ELLs to provide strong language models. Flexible grouping ensures that ELLs are not isolated in one group all year and allows them to learn from diverse peers.

Integrate Technology with Purpose

Technology, when used strategically, can be a powerful support for ELLs in math. It can provide visual models, repetition, and individualized practice.

Apps and Platforms with Language Support

Many digital tools now offer built-in language supports:

  • Khan Academy: Offers full courses in Spanish and other languages. The practice exercises often have hints and worked examples that provide step-by-step models.
  • Desmos: A dynamic graphing calculator that is highly visual. Teachers can create activities with embedded notes, videos, and text-to-speech options. Desmos reduces the focus on calculation and allows students to explore relationships and see patterns.
  • IXL Math: Provides dictionary features for math terms and immediate feedback with explanations.

Edutopia regularly features articles on how teachers use these tools to create more accessible math lessons for multilingual learners.

Video for Frontloading and Flipped Learning

Video is an excellent tool for frontloading vocabulary and concepts. In a "flipped" model, students watch a short instructional video (often with closed captions) at home or independently. This allows them to hear the language multiple times, pause to look up words, and come to class with a basic understanding. The teacher can then use valuable class time for collaborative problem-solving and deep inquiry where they provide targeted support.

Conclusion

Teaching math to English Language Learners is not about simplifying content; it is about strategically scaffolding learning to build bridges between students' existing knowledge and challenging academic material. By creating a language-rich environment, leveraging visual and hands-on tools, explicitly teaching vocabulary, and implementing thoughtful differentiation, educators can create a classroom where ELLs are not just surviving but excelling. These strategies represent a shift in perspective from viewing language as a prerequisite for learning math to recognizing that learning math is learning language. With patience, intentional planning, and a commitment to asset-based pedagogy, teachers can empower every student to become a confident and capable mathematician.