Effective strategies for English language learners in mathematics

English Language Learners

Teachers can best support English language learners by presenting them with challenging mathematics, encouraging the use of graphic models and representations, and addressing mathematical language. The implementation of these strategies will create a supportive environment, giving English language learners the tools needed to be successful in the mathematics classroom.

According to the National Center for Education Statistics, children ages five to 17 who speak a language other than English at home rose from 10 to 21 percent of the population from 1980 to 2009 (NCES). As the number of English language learners rises in the United States, there is increasing concern about how to best address their needs in mathematics classrooms. 

While great instruction provides access to English language learners, there are additional strategies that are particularly helpful for these students. This article will focus on presenting English language learners with challenging mathematics, using graphic models and representations to encourage engagement, and enhancing comprehension of mathematical language.

Mathematics that Challenge the Student

As is necessary in all classrooms, teachers of English language learners must set high expectations. Educators are frequently hesitant to set high demands for English language learners in the classroom, perhaps sympathetic to the trials they face as they struggle to adapt to a new life, language, and culture. However, if teachers do not actively engage these students with challenging mathematics, English language learners will suffer in the short and long term. Language needs should not be confused with an inability to perform mathematically. As students wrestle with difficult mathematical concepts, teachers can use language supports and various questioning techniques to help facilitate student understanding, rather than weaken the mathematical level of difficulty. This may be accomplished by providing contextual supports for meaning through the use of simplified language, teacher modeling, visuals and graphics, cooperative learning, and hands-on learning.

Graphic Models and Representations

Graphic models and representations help English language learners at all stages of problem solving. When first presenting new mathematical concepts to English language learners, teachers can use diagrams to connect important ideas. English language learners also benefit from instruction structured from concrete to abstract. For example, an educator teaching perimeter may begin a lesson by providing visual examples of the concept. The teacher may then encourage students to find classroom examples and lead a discussion around these real-world figures. Students can take notes in their math journals, which sets the stage for continued exploration into the content.

Pairing Graphic Representations with Content Vocabulary

Graphic representations are also an excellent tool for aiding students as they learn vocabulary in mathematics. These pictures can become a mnemonic device to help students relate to the content. Teachers may use math journals, vocabulary cards, or graphic organizers to help students make connections. Students need not be required to write all of their notes in English, and some English language learners may benefit from using at least a portion of the notes to write thoughts and ideas in their native language.

Using Manipulatives

Manipulatives make mathematics concrete for students. The use of pattern blocks, paper money, tangrams, algebra tiles, or any other commercial or homemade manipulatives are excellent tools that give students opportunities to make connections between the concrete and the abstract. Because manipulatives turn math into something tangible that can be reshaped, reformed, and created, many students enjoy these experiences.

Mathematical Language

The importance of maintaining high expectations for English language learners, as with all students, extends to mathematical language. Instead of allowing students to use simple and sometimes incorrect vocabulary to discuss mathematics, teachers can provide English language learners with language tools and encourage them to use correct mathematical vocabulary. Before expecting students to share mathematical ideas with peers or in front of the class, it is essential for the teacher to model appropriate conversations using precise terminology. Students can then participate in activities, such as “Think-Pair-Share,” to practice precise language. Once English language learners are comfortable with the language, they are able to speak easily in front of larger groups of students. Throughout these different interactions, teachers should aid students who struggle to use correct vocabulary by restating answers and helping them to reform their previous responses. It is especially important to privately seek out those students who do not typically participate in class discussions or who are not as outspoken as others. Even though teachers must always model correct vocabulary in math, it is also important to note that students may use hand gestures, drawings, or other representations when they cannot fully verbalize their thoughts. Modeling will help them verbalize those thoughts. These high expectations will lead to the appropriate use and deeper understanding of math vocabulary.

Identifying Language Demands

Many teachers frequently mistake mathematics as a content area with limited language demands, lending itself with relative ease to English language learners. Research shows, however, that mathematics is an area that is linguistically complex and comprised of multiple language modalities and specialized vocabulary. The five main language modalities include reading, writing, listening, speaking, and representing. Students must use language in all of these areas in mathematics, creating, understanding, and using representations to make sense of and communicate about mathematical ideas. Since the language abilities of English language learners vary from one domain to the next, teachers can become overwhelmed when considering their language needs in the mathematics classroom. This information, however, should enrich classroom instruction. Figure 1 is an example of a tool that can be used to analyze language needs in the classroom. It gives teachers an opportunity to consider different aspects of instruction to determine whether students are given opportunities to use various modalities, as well as time to consider the best supports for their language needs. The language demands may include tasks such as reading, writing, speaking, listening or representing. The tool provides insight to focus teacher attention on the planning needed to deliver a rich experience for each student.

Taking Advantage of a Student’s First Language

A student’s native language can be a valuable asset when teaching English language learners new vocabulary in any content area. This is especially true of Spanish-speaking students, who can use their knowledge of cognates to identify and attach meaning to words in English. English words that are cognates with Spanish are commonly high-frequency words in Spanish and low-frequency in English, which provides a great advantage and powerful tool in mathematics. Sometimes students are unaware that they are already familiar with these words, and encouragement from teachers can help them develop the habit of looking for cognates in math vocabulary. The teacher may, for example, ask students to identify any mathematical vocabulary that may be familiar in Spanish, preparing their minds to look for these similarities.

Instructional tools exist that can help the English language learner find success in the mathematics classroom. Student expectations must always remain high, challenging students to stretch their mathematical abilities to new levels. Graphic models and representations help to develop a concrete foundation that will lead to abstract concepts, become mnemonic devices for math vocabulary, and give students hands-on experience with a variety of math concepts. It is important to model correct math vocabulary, analyze the different language modalities that will be involved in instruction and use that to best support students, and take advantage of the student’s first language. This combination of strategies will bridge the gap that many English language learners encounter in mathematics.

Roxanna Caceres is a bilingual math teacher for Think Through Math. She graduated with a B.S. in Psychology from Brigham Young University and a M.Ed. in Special Education from Texas Tech University.Rachel Burner is the Associate Math Director at Think Through Math. She graduated from the University of Pittsburgh with a dual B.A. in Communications and Philosophy and a M.A.T. for Elementary Education with a concentration in Mathematics. She is currently a member of several professional organizations including the National Council of Supervisors of Mathematics (NCSM) and the National Council for Teachers of Mathematics (NCTM).
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