Friday, October 28, 2011

Mathematics for English Language Learners

When it comes to English language learners, mathematics can be very tricky. Many teachers make the mistake of thinking that "math is a universal language" or that "everyone understands numbers". This is simply not the case, and math may be just as tricky for your ELLs as science, social studies, or any other language-based subject.

Here are some things to think about when it comes to ELLs in the math classroom:
  • Even though the student may have been in third grade in his or her country, that does not mean that they should be able to pick right up in your classroom. Just as learning standards and objectives vary from state to state, they can often vary widely from country to country. The student may not possess the basic mathematical knowledge you expect your students to have. 
  • The flow of the problem may look different when working out the math. Some countries may also use different symbols to signify basic operations.
  • In some countries, they use commas when we use decimals, and they use decimals when we use commas. For example:
    • In the US, the number three thousand would be written 3,000. In other countries, it is often written 3.000. In the US, the number three and two tenths would be written 3.2 while in other countries it would be written 3,2. 
So, what does this mean for an instructor who has a math class full of ELLs?

Provide problem solving opportunities for your ELLs.
Coggins et. al (2007) remind us that problem solving is more than one or two step word problems, but more like "figuring out what to do when you don't know what to do" (p. 10). True problem solving requires not only critical thinking on the part of the student, but will also motivate them to communicate in English with their classmates in order to solve the problem. This can be beneficial for both their language learning and their mathematics learning. Furthermore, when you ask students to defend their reasoning, you have the opportunity to help them deepen their understanding. For lower level students, you can provide sentence frames to assist them in expressing their knowledge and ideas (for example, "I know the answer is __________ because......").

Provide opportunities for every student to speak and ask questions.
Often times as teachers, this can be the most difficult task. We must retrain ourselves to do several things. First, though the urge is strong, resist calling on the most eager students. Provide enough wait time that every student has a chance to think of the answer. I often tell my students to take one minute to think about the question without even raising their hands. After one minute, I repeat the question, and allow student to raise their hands. I work hard to make sure that each student has a chance to answer at least one question during a lesson. In larger, non-ESOL only classrooms, this may not be possible, but try to include as many students as possible during the lesson. The use of think-pair-share strategies and cooperative group activities allows each student a chance to discuss the topic (Coggins, et. al., 2007, p. 11).

Develop mathematical language in a way that increases understanding of the content.
In Language Arts, we often go over important vocabulary words before the lesson or the reading. However, in mathematics, this might not be the most effective way to present important academic vocabulary. According to Coggins et. al (2007), the concept that underlies a math vocabulary word must be systematically taught first by activating prior knowledge on the topic, experiencing the concept, and discussion using informal language. Once students understand the concept or idea, then the formal mathematical language can be taught. Coggins et. al (2007) also suggest that we not teach "key words" or phrases in word problems. The authors believe that this strategy causes students to focus less on the meaning of the story problem, and can lead to mistakes in choosing an operation when common phrases are used for different purposes. Instead, help students focus understanding the actions and mathematical concepts within the word problem.

Provide plenty of scaffolding.
Scaffolding occurs when the teacher provides a specific type of learning support, without reducing the complexity of the problem or telling the student exactly how to proceed. Begin by activating students' prior knowledge on a topic and relating it to something students are already familiar with in the "real-world". For example, when teaching money, you might relate it to the idea that students must pay the correct amount for their lunch each day. Cooperative groups or pair work is an excellent way to provide scaffolding opportunities for students- they can share ideas and ask questions with their peers, and build upon each person's understanding to improve their own understanding of the concept . Also provide visual, tactile, and auditory aids. A student might know what a penny is, but might not know the word. Providing a physical example will help that student solidify the concept (Coggins et. al, 2007).

Use concrete materials in the classroom to teach and reinforce concepts.
Concrete materials can help students to focus on a concept and the relevant vocabulary simultaneously. For example, using concrete manipulative to teach about hundreds and thousands can give the idea of "hundreds" meaning through tactile and visual experience, but you can also emphasize the relationship between hundreds and thousands much more easily using concrete materials. Also allowing students the opportunity to draw in order to solve a problem can be equally effective if manipulatives are not available.

I don't want to overwhelm you now, but I hope that some of these tips and suggestions can help you as you struggle to make mathematical learning comprehensible to your English language learners!! Please do not hesitate to pipe in with any questions!!


Coggins, D., Carroll, M., Coates, G. and Carroll M. (2007). English Language Learners in the Mathematics Classroom. Thousand Oaks: Corwin Press.

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