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This website provides several ways that a teacher can use to help teach math to their english language learner students. This was published by Dr. Jim Ewing and it has a lot of useful tips hidden inside of it. One way that I thought would be helpful within my future classroom is that students need to be comfortable in order for them to learn the subject better.

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How to Teach Math to ELLs by Dr. Jim EwingThe first step to teaching math to ELLs is to change their positive math mindset (Boaler, 2016; Ewing, 2020). 7-Strategies to Develop Math Mindsets for ELLs 1. We can facilitate students…

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This website has multiple adaptations and modifications that a teacher can use to help accomodate their instruction for english language learners that need a better understanding of the content subject, Math. Some of the ways that are listed on how a teacher can accomodate her instruction are using the frayer model, word walls, and manipulatives. There are also several examples under these accomodations that provide a better knowledge on how to use them.

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Presentation on how to teach Math to ELLs

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Presentation on how to teach Math to ELLs

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This is an hour long presentation lead by Gladis Kersaint and Denisse R. Thompson that discusses the importance behind teaching math to english language learners. I only listened to half of the presentation, but in my opinion I think that they discussed a lot of useful information in relation to teaching a   content subject that a future teacher should have.

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Teaching Mathematics to English Language Learners - National Council of Teachers of Mathematics

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This presentation will give straightforward advice on how to teach mathematics to ELLs. The speakers will describe strategies for facilitating classrooms discussions, helping ELLs read and interpret mathematics textbooks, and helping them tackle word problems.

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Within this article, there are several ways on what a teach can do to support an english language learner. In my opinion, I think this is very useful to have as a future teacher because there can be some students who get frustrated and will need additional help to learn Math. This article includes instructional strategies and also has additional ones located at the bottom.

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This is a sixteen page article from the state of New Jersey explaining how to teach emergent bilinguals math using the SIOP model. One thing that interested me the most was that there was a list of materials that a teacher could use including vocabulary cards, graphic organizers, or word problems.

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This website describes how a teacher can face many challenges while they try to teach math to their english language learner students. One thing that surprised me within this text is that students tend to not understand the language that is needed to understand the math instruction.

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Many educators share the misconception that because it uses symbols, mathematics is not associated with any language or culture and is ideal for facilitating the transition of recent immigrant students into English instruction. To the contrary, language plays an important role in learning mathematics. Teachers use language to explain mathematical concepts and carry out math procedures. While solving problems in mathematics, we often use specialized technical vocabulary ( addition, subtraction, addend, sum). And researchers of mathematical learning have found that students can deepen their understanding of mathematics by using language to communicate and reflect on their ideas and cement their understandings. Classroom talk can cause misconceptions to surface, helping teachers recognize what students do and do not understand. When students talk about their mathematical thinking, it can help them improve their ability to reason logically.

The challenge of teaching math to English learners lies not only in making math lessons comprehensible to students but also in ensuring that students have the language needed to understand instruction and express their grasp of math concepts both orally and with written language.

The challenge of teaching math to English learners lies not only in making math lessons comprehensible to students but also in ensuring that students have the language needed to understand instruction and express their grasp of math concepts both orally and with written language. ELLs have the dual task of learning a second language and content simultaneously. For this reason, "it is critical to set both content and language objectives for ELLs. Just as language cannot occur if we only focus on subject matter, content knowledge cannot grow if we only focus on learning the English language" (Hill and Flynn 2006, 22).

English language learners are faced with some common obstacles when learning math. One challenge they face is unknown or misunderstood vocabulary. For example, they can become confused during a discussion if the mathematics vocabulary has different meanings in everyday usage, as with even, odd, and function. They also may be confused if the same mathematical operation can be signaled with a variety of mathematics terms, such as add, and, plus, sum, and combine. A word such as left-as in "How many are left?"-can be confusing when the directional meaning of the word is most commonly used in everyday English. The words sum and whole also can cause confusion because they have nonmathematical homonyms ( some and hole).

A second obstacle is with an incomplete understanding of syntax and grammar. For example, math questions are often embedded in language that makes the problems unclear or difficult to comprehend.

Consider the following problem:

Samuel bought three bags of oranges with seven oranges in each bag.
How many oranges did he buy?

This word problem uses both the past and present tense of the irregular verb to buy in one question, which may cause difficulty for an English language learner, depending on the student's English language proficiency.

Consider another problem:

Lisa gave a total of 12 treats to her cats.
She gave her large cat 2 more treats than she gave her small cat.
How many treats did she give to each cat?

Here, students need to understand or figure out the meanings of words such as total and treats. They also need to understand words that convey a mathematical relationship such as more . . . than. In addition, students need to infer that Lisa has only two cats.

English language learners typically experience difficulty understanding and therefore solving word problems, and this difficulty increases in the later grades of elementary school as the word problems become more linguistically and conceptually complex. Difficulty with grammar, syntax, and vocabulary lies in both understanding math instruction and having the ability to engage in discussions about math.

Many teachers use strategies to help students understand the content in their math lessons. Scaffolds for learning may include manipulatives, visuals, and graphics. These supports are all essential for building a cursory understanding of math concepts, but they may not provide students enough linguistic support for them to discuss their thinking, which would lead to a deeper understanding of content.

The challenge for teachers is to focus on math concepts and the academic language that is specific to mathematics.

For example, let's say that a student's understanding of polygons is based on a two-column chart with drawings that distinguish polygons from shapes that are not polygons. Once the chart is put away, the student may not have internalized enough of the linguistic elements of the lesson to be able to continue her learning in subsequent lessons on polygons. Having the language to talk about math concepts is crucial to developing an understanding of those concepts.

Classroom discussions about math have been shown to deepen students' conceptual understanding. These discussions are a critical aspect of the development of language and content, providing a setting for English language learners to negotiate meaning in daily instructional interactions. However, if the language needed to engage in these discussions is not made explicit, ELLs are less likely to benefit from mathematical discussions and can fall further behind their peers.

The challenge for teachers is to focus on math concepts and the academic language that is specific to mathematics. Teachers must be cognizant of the linguistic demands of their lessons and how they will address those demands explicitly during instruction so that ELLs can fully participate.
References:
Hill, Jane D., and Kathleen M. Flynn. 2006. Classroom Instruction That Works with English Language Learners. Alexandria, VA: Association of Supervision and Curriculum Development.

Rusty Bresser is a lecturer and supervisor of teacher education at the University of California at San Diego. He has been an educator for more than thirty-five years and is interested in issues of equity and social justice in the areas of mathematics and science education. Rusty is the author of numerous professional learning articles and books. He is a recipient of the Barbara and Paul Saltman Distinguished Teaching Award.
Need help addressing the needs of the ELL students in your school? Our new course, Supporting English Learners in Math, offers instructional support and a lesson design process that supports differentiation for the varied levels of English learners in classrooms. This post is excerpted from Supporting English Language Learners in Math Class, K-2 by Rusty Bresser, Kathy Melanese, and Christine Sphar.

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The Challenges of Teaching Math to English Learners

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Many educators share the misconception that because it uses symbols, mathematics is not associated with any language or culture and is ideal for facilitating the transition of recent immigrant students into English instruction. To the contrary, language plays an important role in learning mathematics. Teachers use language to explain mathematical concepts and carry out math procedures.

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This website describes eight ways that a teacher can teach math to english language learners. A way that stood out to me as I was reading this was to pre-teach math vocabulary which helps the learners grasp the topic better.

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Classroom and ESL teachers often discuss difficulties they encounter when teaching math to English learners (ELs). The first step is to look at the challenges your students face when learning math in English. It's often said that "math is a universal language," but in my opinion, it's not. Teachers need to go beyond teaching students how to add, subtract, multiply, and divide. And even those simple calculations can be taught differently in other cultures. In fact, the cultural backgrounds of our students are rich resources from which mathematical concepts may be developed in English. Here are eight strategies for teaching math to ELs.
1. Validate ELs' Prior Mathematical Knowledge
For example, teachers of ELs from South America should know that students are taught to show their work when solving division problems in a different way than is taught in the United States. In some cultures, the emphasis is on mental calculations, and students are not taught to show the process they use to solve a problem. I encountered this when I taught students from Port-au-Prince, Haiti. Students from other countries may not learn math concepts in the same order as is taught in U.S. schools; a 4th grade student from another culture may have never studied geometry because it is taught at a higher grade. It's important to be aware of what your ELs know and what they have been taught when it comes to math so that you can validate that learning by building on it-rather than stumbling over it.
2. Provide Scaffolds to Support ELs' Understanding of Math Problems
Simplify the language of the math problem. Have students practice picking out key words and talk about what they mean using highlighters, Wiki Sticks, or sticky notes. Colored highlighters have been known to enhance memory performance. Highlighters and sticky notes also boost student engagement in the lesson you are teaching. One trick is to have ELs highlight the question they have to answer in a math problem or use a pen to eliminate unnecessary words. Wiki Sticks can also be used to underline key ideas in the math textbook, because they are not permanent and can be reused.
3. Use the Same Types of Scaffolds You Use for Other Content Areas
What scaffolds do you use when teaching English language arts and social studies? Use these same scaffolds when teaching math. Create vocabulary banks so that your students can turn-and-talk to classmates using mathematical terms. Access your ELs' prior knowledge and build on it. Modify teacher talk, provide adequate wait time, and use visuals to teach math concepts and language.
4. Preteach Math Vocabulary
Previewing and preteaching new math vocabulary words is an important scaffold necessary to help ELs understand mathematical concepts. Remember that your ELs are learning two new languages-English and the language of mathematics in English. We can't expect ELs to take a list of math vocabulary words from a chapter and look up the words in a dictionary. They require direct instruction of new math vocabulary and plenty of practice to develop math fluency in the concept.
5. Present Math Problems and Concepts Visually
I can't say enough about the importance of employing all kinds of visual supports when teaching ELs any content area. Use charts graphs, realia, diagrams, pictures, and graphic organizers. Word Walls should be used at all grade levels. Teach specifically the language of mathematics. Help students understand the different meanings of words such as table and how to use them correctly in a mathematical context.
6. Give Students Opportunities to Talk to Each Other
According to Kristina Robinson in an excellent article for Colorín Colorado, teachers should have ELs speak with other students in small groups or with a partner during whole class discussions. This may make them feel more comfortable trying out new vocabulary without the anxiety of speaking in front of the whole class. ELs will understand material better if they explain it to another student either in English or in their home language. Newcomers certainly benefit from hearing the explanation in their first language. Another way to help ELs talk about math is to ask for whole class, choral responses instead of calling on individual students.
7. Have ELs Create Their Own Math Notebook
A notebook dedicated to math vocabulary can be a boost for older math students in Grades 4-12. It can be set up to fit the age and needs of the students in your class. Words can include definitions in your ELs' own words and or in their own language. I've found that choral recitation can really increase ELs' oral participation in a lesson. If you provide a sentence frame similar to those used in other content areas, even beginning ELs will be able to write down responses and produce them orally.
8. Bridge the Gap Between Math and Real-World Issues
You may want to develop math projects that focus on themes or issues that are relevant to the cultural, racial, and linguistic composition of your classroom. Kwame Sarfo-Mensah, a middle school teacher in Boston, wrote in Edutopia that mathematics should not be taught in isolation. She finds that the best way to find a theme that your students will really care about is to ask them. Her students, for example, selected the topic of police brutality, which had impacted them personally in their community. Sarfo-Mensah also suggests that teachers check their state math standards to see what mathematical concepts would apply to the issue that their students have chosen.

What strategies and scaffolds have you found most useful when teaching math and mathematical language to ELs? What have you found particularly challenging? Please share in the comments, below.

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| 8 Strategies for Teaching Math to English Learners

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Classroom and ESL teachers often discuss difficulties they encounter when teaching math to English learners (ELs). The first step is to look at the challenges your students face when learning math in English. It's often said that "math is a universal language," but in my opinion, it's not.

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This article discusses ten ways that a teacher can help English Language Learner students succeed in the content subject math. One of the ways that are described within this article is considering language and math skills when grouping students together.

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Anne Formato collaborating on math lessons

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Anne Formato collaborating on math lessons

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This video describes how teacher Anne Formato had the opportunity to teach a content area class. Also, she collaborates with another teacher and talks about the differences between the ESL classroom and the content classroom.

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ELL Teacher Anne Formato: Collaborating on math lessons for ELL instruction

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This article describes a former student who struggled with math as an English Language Learner and a teacher Hillary Hansen who changed her instruction to help these students. There are a lot of useful tips for an ELL teacher wanting to teach a content subject including the important of language acquisition and building a background knowledge.

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Math Instruction for English Language Learners

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Several years ago, I met a high school math teacher named Hillary Hansen who had just taught her first Basic Math course for English language learners (ELLs). She wanted so much to provide the students with the good foundation they needed, but she felt unable to engage them in her lessons. By the end of the year, she was exhausted and frustrated.That summer she had an opportunity to join a district Sheltered Instruction Observation Protocol (SIOP) cohort to receive professional development and support the needs of ELLs in content classes. She learned about the importance of language acquisition, building background knowledge, increasing student language production, and explicitly teaching academic language. She began the following school year with a new set of tools and a deeper understanding of the instructional scaffolding ELLs need in order to learn the content while also learning English.While Hillary still felt challenged and was working hard, the second year was much more successful for her and her students. She felt she was providing them with the foundation they needed not only to understand the mathematical concepts, but also to successfully interact within a math classroom in order to learn more advanced concepts.As a result of more effective instruction, her students:Understood the content better and were working together to find creative ways to learnIncreased their participation in discussions and learned how to use instructional supports in the classFelt more comfortable with math and asking questions to get the help they neededYou can learn more about some strategies that Hillary and other teachers recommend for teaching ELLs math in the information below, along with reflection tips and ideas for getting to know your students’ math backgrounds.ELL Math Resource CollectionThis resource collection features several ideas for teaching math to ELLs.Reflection QuestionsHow much math instruction have your ELLs received in their prior schooling?How much do their levels of math background vary?What are some of their strengths related to math?What are some of their challenges?What are some practical ways your ELLs are using math in their daily lives?What kinds of strategies have supported their success or engagement in other areas?What are some ways that collaboration or co-teaching might support your ELLs?What are some leadership opportunities you might give ELLs in pair work or small group work?Learn About Students’ Math BackgroundsTeaching ELLs: Tips for Math TeachersPrint PDF >It’s important to remember that ELLs’ math backgrounds may vary significantly. Some students may have had consistent schooling where they developed strong math skills. Others may have limited or no formal schooling, but may have practical skills related to time, money, or other daily topics. If possible, find out whether students have attended school regularly and what kind of experience they have had with math instruction and with math in general. Look for ways to tie instruction to student interests (like sports) and responsibilities at home that involve math, such as helping with family finances, working in family businesses, and holding other jobs. For example, students from migrant farmworker families may be using math related to agriculture, such as weighing or selling produce. Also keep in mind that students may use other numeric and measurement systems students, such as metric system, Celsius, military time, etc.In addition, Pennsylvania educators Sally Lopez and Erin Minick also encourage educators to:Look for leadership opportunities for all students in math classProvide students with opportunities to “teach” others, work together, and demonstrate what they know in multiple waysGroup students intentionally and with sensitivity, avoiding the designation of specific students as “needing more help” in their grouping, partner assignments, or placement in the classroom(Ms. Lopez and Ms. Minick conducted a book study focused on Teaching Math to Multilingual Students, which you can learn more about from their website.)Keep in mind that veteran educators of ELLs also stress the importance of getting to know students as a key part of supporting student success. For example, in this NCELA webinar, Dr. Haiwen Chu, a national expert on mathematics education for English Learners at WestEd, recalls that visiting his high school students’ neighborhoods provided valuable insights on their experiences and familiar topics.See additional ideas for getting to you know your ELLs in 10 Strategies for Building Relationships with ELLs.The Language of MathAlthough it is easy to assume that many ELLs will excel in math class because math is a “universal language” and students may have had prior educational experience that included mathematical instruction, that assumption can lead educators astray. While computational skills may transfer, ELLs may still need support with language-focused tasks, such as solving word problems, learning (and using) math vocabulary, and writing explanations. All of these skills require a language proficiency that sometimes exceeds our expectations. We tend to think of mathematics as a subject that does not require a strong command of language. In reality, however, mathematical reasoning and problem solving are closely linked to language and rely upon a firm understanding of basic math vocabulary (Dale & Cuevas, 1992; Jarret, 1999), especially when considered along with the demands of college- and career-ready standards.Co-Teaching and CollaborationFor many educators, the challenge of bringing language and math instruction together is a relatively new one. ELL teachers who hadn’t taught content areas previously are now being asked to lead or support instruction in the math classroom, and many math teachers who don’t see themselves as language instructors are now responsible for providing effective math instruction to ELLs. When educators collaborate, however, they can better understand each other’s expertise and combine their expertise for the benefit of students.For example, when planning a lesson, a math teacher and an ELL teacher could collaborate to identify both the target content, such as key standards, concepts, or specific topics, as well as key vocabulary, academic language, and the language-focused tasks students will need to complete the lesson. These tasks might include writing out a proof, reading a math problem, explaining how to solve a problem, or writing out numbers as words. The ELL specialist could walk the math teacher through this process several times so that it becomes a more integrated part of the math teacher’s planning over time. After the lesson, the teachers could identify other areas of focus or clarification needed and share these insights with their colleagues.Another tool content teachers can use is language objectives, which help target the language demands of the lesson. You can learn more about them in the videos featuring Mr. Jesus Ortiz below.Teaching Academic VocabularyVocabulary instruction is essential for effective math instruction. Not only does it include teaching math-specific terms such as “percent” or “decimal,” but it also includes understanding the difference between the mathematical definition of a word and other definitions of that word, as well as understanding the concept a vocabulary word describes.The following example, used in a presentation by Dr. Judit Moschkovich of the University of California at Santa Cruz, underscores why vocabulary must be introduced within the context of the content (Moschkovich, 2008): In this problem, the student is instructed to “find x.” The student obviously knew the meaning of the word “find” because they “found” it on the page and circled it. The student even put a note on the page to help the teacher in locating the lost “x”. The student understood the meaning of “find” in one context, but not in the appropriate mathematical context.I recently helped a math teacher create a sheltered lesson, and I was surprised to find that there were some vocabulary words that I didn’t understand. My lack of familiarity with the words hindered my ability to do the math problem and gave me a deeper empathy for ELLs who struggle in the same way with vocabulary and comprehending math assignments.Following is a list of tips for explicitly teaching mathematical academic vocabulary.Teach key academic vocabularyAfter you identify your target content, identify the academic vocabulary words that students will need to understand that content. Some of these key phrases or new vocabulary words may also be helpful to pre-teach in small groups or mini lessons. Think about:Academic vocabulary (equilateral)Words and phrases needed to solve a problem (less than, given, arrange)Common words needed to solve word problems (train station, dolphin, favorite)Homophones (eight/ate, plane/plain, one/won, two/to/too, four/for, some/sum)Words that students are likely to encounter in other settings (formula, prove)Words that represent a numerical value necessary for solving the problem, such as measurement words (foot, feet, meter, pounds, kilometers)After you identify the vocabulary you wish to teach, use scaffolds for academic vocabulary, such as: Visuals: These can include visual representations of concepts, photos, and illustrations of key vocabulary words, posters, and number lines.Realia (real objects) and manipulatives: These might include hands-on objects related to a topic or small items, such as coins or small blocks for counting, sorting, weighing, etc.Graphic organizers: Graphic organizers are tools that allow students to organize information in a visual or hands-on way.Anchor charts: Anchor charts are posters that students and teachers co-create to highlight key concepts and vocabulary that students will need for reference.Offer students the chance to work with objects and images in order to master vocabulary. If there aren’t enough items for each student, use manipulatives on the overhead or posted throughout the classroom, and demonstrate the vocabulary in front of the students. For example, Hillary created a Math Word Wall that has three parts: key vocabulary, “in your own words” definitions, and a variety of ways to portray a function. For example, multiplication is portrayed by the following symbols: x, *, and ( ).In addition, it can be helpful to ask students which strategies support their learning. Students often can provide valuable information on what is working for them!For examples of how vocabulary can impact students’ understanding of math problems, see the related video with ESL teacher Anne Formato below.Teach words with multiple meaningsDemonstrate that vocabulary can have multiple meanings. Help students understand the different meanings of words, as well as how to use them correctly in a mathematical context. This is also a good opportunity for using visuals and realia. Examples include:YardPlotTableProofAreaEvenPlanePlaceTimesBillQuarterChangeDraw on students’ home languagesUse cognates, which are related words in two languages. English and Spanish have many cognates within academic terms, like fraction/fracción.Use translated words or phrases strategically. For example, New York University has published bilingual glossaries for several topics.Allow (and encourage!) students to use their languages in group work to solve problems, brainstorm, and review material. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language.Increasing Student Language ProductionThe language demands of math are complex. Working with an ELL specialist can be a good starting point for identifying some of the math demands of the lessons you are teaching, as well as for planning how to teach and scaffold those language demands.As I’ve worked with content area teachers in my district to develop Sheltered Instruction lessons and activities to enhance ELL learning, I’ve told them, “If a student doesn’t say it in your class, they’re never going to say it.” This is a bit dramatic, but it’s true to some extent. When students learn new vocabulary, the opportunity to use it must be presented in class, because students are unlikely to try it out on their own — especially academic words like “parallelogram” or “function”!Here are some tips to increase student-to-student interaction with academic language in the math classroom:Have students translate symbols into words, and write the sentence out. Hillary used this strategy to check students’ comprehension of problems before they solved them. For example, 3x + 4 = 16 would be written out, “Three times X plus four equals sixteen.” This helps students process the operations involved in the question and gives them an opportunity to think through how to solve it. It also gives students a chance to familiarize themselves with important vocabulary words. Writing out the answer to a problem is a very important skill to develop because many state math tests require a constructed response to questions.Create a “sentence frame” and post it on the board. Write the format of the sentence you would like students to use in discussion and then hold them accountable for using it. For example, “The answer is _______ degrees because it is a _________ triangle. (Learn more in our sentence frame and sentence stems strategy.)Have students share problem-solving strategies. This involves asking a simple question, such as, “Did anyone else get the answer in a different way?” Then allow enough wait time so students can think through how their problem-solving process was similar or different to the one offered.Allow students to discuss how they are thinking about math. This is a way of redirecting the lesson from teacher-to-student to student-to-student. For example a student might ask a question, “How do you know what kind of triangle it is?” Instead of the teacher answering and going to the board and pointing out the names and different triangles, the teacher can simply ask, “Does someone have an answer? Or “Would someone like to offer help to Mario?” Allow students to share how they think about the math concept and any tips they have for remembering the information.Incorporate writing activities, such as entrance/exit tickets or math journals. This is an excellent way for students to process what they’ve learned and what questions they still have. The journal or exit/entrance ticket prompt could start with simple prompts such as, “One thing I learned today...” “One thing I still don’t understand…” “One way I can get the help I need…” “The answer to this problem is…” “Something that helped me was...“Challenge students to create their own math problems. This can be a fun activity if students create a problem similar to the ones you have used in class and they exchange problems with a partner. By creating the problem and checking the answer they are reinforcing their own learning.Teach students how to read, interpret, and summarize data. Provide students with explicit, step-by-step instructions in how to read charts, graphs, tables, and infographics, as well as how to describe what they observe in visual representations of data.Model the kinds of writing students are expected to complete (e.g., written explanations). Students need to see and understand what they are expected to do and produce, such as explaining how they solved a math problem. This is a great opportunity for the “gradual release” strategy -- I do, we do, you do.Try AI tools. Consider using AI tools to rewrite math problems for students at early levels of proficiency or to generate math problems with familiar vocabulary that achieve your target objective. Bilingual Glossaries in Content AreasNew York University has published several bilingual glossaries in multiple languages that cover different content areas, including elementary math, middle school math, Algebra 1 and 2, Calculus, and related math terms.Reading and Understanding Written Math ProblemsWritten word problems present a unique challenge to ELL students and teachers alike. In Reading and Understanding Written Math Problems, Brenda Krick-Morales writes, “Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation — ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered” (Bernardo, 2005).Teacher Xiao-lin Yin-Croft has encountered this pattern in her classroom of bilingual Chinese students in San Francisco. She has developed a very creative way to use her students’ background knowledge of math as a stepping stone for other language learning. She does this by accelerating math instruction at the beginning of the school year and then building on what students have learned in math in reading and other content areas. In Building Bridges for the Future, Xiao-lin explains her strategy:First, we read math word problems; I demonstrate the logical thinking process while translating words into pictures and, finally, into number sentences. Soon, they start to explain their own thinking after reading complicated word problems that involve several steps. They correct each other and argue about which number sentences they should use to arrive at the correct final results. As they sharpen their math skills, I capitalize on their enthusiasm to teach them how to extract the most important information from texts, and move them toward the oral and reading fluency they need to understand and discuss more challenging texts.Even if you aren’t accelerating math instruction, however, there are a number of ways to help students master word problems. Krick-Morales offers suggestions in the previously mentioned article, such as explicit instruction of key vocabulary, daily practice of problem solving, repeated readings of the word problem together as a class, and hands-on activities such as movement, experiments, or drawing to help students comprehend the problem. As students become more familiar with math vocabulary, they will be able to solve problems more easily.Identify key background knowledge in math problemsIt’s important to identify what kinds of background knowledge students will need to understand a math problem. For example, Ms. Lopez and Ms. Minick used this activity with a conference session: Ms. Lopez chose four math problems from her son’s math textbook and asked session attendees to brainstorm the kinds of background knowledge students might have questions about, some of which were relevant to solving the problem and some of which weren’t. Here are some things that attendees came up with:A math problem about a coupon and sales tax at a dog groomer: What is a dog groomer? Why do people take their dogs to get groomed? What is sales tax? What is a coupon? What is “deluxe”? What is an estimate and a discount?A math problem about people receiving a voucher for a free water bottle at a football game: Is football different from soccer? What is a voucher? Does the water bottle come with water inside it?A math problem about a fishing pole on sale: What is “percent off”? What is a sale? What is “regularly priced”? What steps have to be followed to solve this problem?A math problem about calculating a tip in a restaurant: What does “leave a tip” mean? What is a tip? Does the fact that there are four sisters (Emilia and three sisters) impact the outcome of the problem? Why aren’t they using an app like Venmo?As seen from the example above, this can be a powerful area in which math teachers and ELL teachers can collaborate.The Role of Background KnowledgeWhen it comes to background knowledge that impacts students’ understanding of new concepts, students may have relevant experiences to what you are teaching that just need to be drawn out (as in the vignette below). In other cases, students may not have the needed background knowledge. My colleague Hillary found that sometimes her students would get “lost” in a problem simply because they didn’t understand the context. Following are some tips to help in tapping into and building background knowledge of students.Identify connections to your students’ experiences. When planning the lesson, consider whether they might have relevant experiences, and as you introduce the lesson, find out what they know, giving them an opportunity to make connections. They may come up with connections you never had imagined!Modify the linguistic complexity of language and rephrase math problems. Students will understand the problem better if it is stated in shorter sentences and in language they understand. This may be an area in which you wish to experiment with AI tools that can rewrite problems.Guide students to cross out the unnecessary vocabulary in word problems. Doing so allows students to focus on the math function required. For example, one problem Hillary’s students came across referred to a “school assembly.” Even though the meaning of that phrase wasn’t important in the solving of the math problem, students didn’t know it wasn’t important, and the lack of understanding contributed to their confusion.Build knowledge from real world examples. Try to reinforce concepts with examples that students can picture and talk students through the situation. For example, if you need to paint a room, you need to know how much area will be covered so that you know how much paint to buy. Look for familiar ideas or props that can be used to engage students such as recipes, news stories about the economy, or discussion of personal spending habits.Use manipulatives purposefully. This is important at all grade levels. Hillary has found math cubes to be very useful in having students represent the numbers in the problems and then manipulate the cubes to get the answer. She used the cubes and the terms “hot” and “cold” numbers when teaching with the concept of negative numbers. Students would use the red cubes as “hot” or positive numbers and the blue cubes as “cold” or negative numbers. As students laid out the number of hot cubes and cold cubes represented, they could easily see if the answer would be a positive or negative number by which color had the most cubes. A problem such as -2 + 1 = -1 would look like this: The student then removed pairs of cubes — one red, one blue — until they could no longer remove any blocks. The remaining blocks represent the answer. Classroom vignette: A moment of humilityA middle school math teacher was trying to teach points on a grid and vertical/horizontal axis to her ESL students, three boys from Vietnam. She tried many approaches, including visuals, games, simulations, and manipulatives, and was just about to give up after very little progress. Suddenly, a student said, “Oh, I know — same same you drive a boat!” (“The same as you drive a boat!”) It turns out the child had helped his uncle use the stars to navigate a raft when they were fleeing Vietnam and trying to reach refugee camps in Thailand. He explained the concept to the other boys in Vietnamese with gestures and drawings on the board, who knew exactly what he was talking about. The teacher reflected, “I felt so humble. These boys knew a lot more about math than I had given them credit for. I had failed to activate their prior knowledge, and in the process had almost given up.“Source: This vignette is presented in Chapter 4 of Special Education Considerations for English Learners: Delivering a Continuum of Services. Using TechnologyTechnology can also be a powerful tool in math instruction for ELLs. Here are some ways you can play with technology in a math lesson:Look for educational resources that accompany your school’s technology tools and programs. There may be online or software programs available for teachers. For teachers who have an electronic whiteboard in the classroom, there are many resources available on links that can be easily accessed and brought into the classroom.Find out what’s available online. Both PBS Learning Media and Vital NY (Video Teaching and Learning for NYS Educators) on Teachers’ Domain offers an online library of free public media resources. Teachers’ Domain resources include video and audio segments, Flash interactives, images, documents, lesson plans for teachers, and student-oriented activities. (Free registration required.)If students are using a calculator or other device, ensure that they learn how to use it. Based on background and prior educational experience, students might not be familiar with how to use a calculator, graphing calculator, or math apps on devices such as phones or tablets. Give students a chance to practice solving problems with their calculators once you have reviewed different functions. Texas Instruments offers numerous activities and product tutorials in their educational materials.Learn more about how to use AI tools in math. AI tools can be used to generate, differentiate, or rewrite a math problem; create a summary of a lesson plan; and many other tasks. Keep in mind that AI-generated content always need a careful review and edit. (See more in Using AI in Math from Edutopia.)Look for interactive games that offer students a chance to practice their mathematical skills. Nintendo DS has an educational game called Brain Age, which is not language specific. The game provides excellent mathematical training for numbers and tracks results, showing student improvement over time.Books About Math and MathematiciansIn addition, there are lots of books about math and mathematicians that you can incorporate into your classroom and classroom library. You can see a wide range of titles for different ages in our Math Resource Collection.Closing ThoughtsEven if it doesn’t come easily at first, there are ways to get ELLs excited about math. By keeping their language skills and needs in mind when planning mathematical instruction (and by helping your colleagues do the same), you will be taking important steps in helping students master mathematical concepts and skills. You never know — your students may be the next generation of economists, rocket scientists, and math teachers just waiting for the tools they need! Note: I’d like to thank my Minnesota colleagues, Hillary Hansen at Burnsville Senior High School and Kim Olson at Hidden Valley Elementary, as well as Xiao-lin Yin-Croft from San Francisco, for providing many of the helpful math teaching tips in this article. It is inspiring to know that there are talented, creative teachers who are always finding better ways to teach and are willing to share the knowledge.Related VideosHow vocabulary can get in the way of solving a word problemELL Specialist Anne Formato talks about the trouble a student had in understanding a written math problem based on a vocabulary word. Teacher Alejandra Rojas: Why cognates are your “best friend” in math classElementary teacher Alejandra Rojas, who teaches in a dual-immersion program, explains why cognates support vocabulary development in her Spanish-language math class. Teacher Alejandra Rojas: When bilingual students translate for their parentsAlejandra Rojas, a teacher at a dual-immersion school in Arlington, VA, shares some of her experiences as a child and teenager translating for her mother. How to Write Language Objectives: Tips for ELL EducatorsIn this video from Syracuse, NY, Jesus Ortiz, a bilingual teacher, learns how to write a language objective from Areli Schermerhorn, a peer evaluator with expertise in ELL and bilingual education. Teacher Observation Cycle: A Math Lesson on PictographsThis video highlights Mr. Ortiz’s math lesson on pictographs. While the main topic of the video is teacher evaluation, numerous best practices and strategies related to math instruction for ELLs are mentioned in the video. Recommended ResourcesNCELA Teaching Practice Brief: Math (A related podcast is available as well)Supporting English Learners in Math and Science: Effective Instructional Practices and Examples from NCELA’s Teaching Briefs PBS Learning Media: Math LessonsEngageNY: Common Core and MathCommon Core Math and ELLs: Blog PostsDiscovery Education: PuzzlemakerCatherine Snow: Word Generation SMART Notebook Lesson ActivitiesTranslating Word ProblemsColorín Colorado Webcast: English Language Learners in Middle and High School