Posted by: degarcia | November 24, 2008

Language Issues in Mathematics

“Isn’t English a Trip?”

I thought it would be easier

when math class started.

Because that’s just about numbers,

and circles,

and things like that,


Was I in for a surprise!

When Mrs. Jones started talking about addition,

she used the word plus

like 2 plus 2 equals 4.

Sounds good to me.

But last week she mentioned the word combine,

And she said that meant addition too.

“What, Mrs. Jones?

Could you please repeat your question?

What’s the sum of all the elephants?”


What did Julia tell me sum meant?

Is that the same as some,

like “when some of the kids tease me”?

 –José Franco (2005)

This poem expresses a common experience second-language learners and language-impoverished children have. As teachers, we need to be acutely aware of the irregularities of math vocabulary.



In order to understand how to help second language students, you must first understand the two levels of language proficiency: basic interpersonal communication skills (BICS) and cognitive academic language proficiency (CALP).

Click here to find out about BICS and CALP.


Math is NOT language free:

Contrary to popular belief, math is not language free or culture free.

In “UnLATCHing Mathematics Instruction for English Learners” (2006, 14), Leslie Garrison, Olga Amaral, and Greg Ponce write:


Part of the reason English learners struggle in mathematics is that rather than being language free, mathematics uses language that is a highly compressed form of communication where each word or symbol often represents an entire concept or idea. In a literature text, readers can comprehend a passage if they are familiar with 85%–90% of the words. The other words and their meanings can often be gleaned through context. Mathematics problems, on the other hand, generally require the student to understand nearly every word as there is seldom enough context provided with the problem to assist with unfamiliar words or concepts. Another problem that English learners encounter is that sometimes they recognize a word, but the meaning they know for the word is different from the intended meaning and therefore does not help them understand the problem.

Rusty Bresser’s 10 strategies for helping English-language learners:

1. Ask questions and use prompts

2. Practice wait time

3. Modify teacher talk

4. Recast (interchange) mathematical ideas and terms

5. Pose problems that have familiar contexts

6. Connect symbols with words

7. Reduce the stress level in the room

8. Use “think-pair-shares”

9. Use “English experts”

10. Encourage students to “retell”


Related Links:

Who is Rusty Bresser?


Ideas for Helping Second-language Students in the Classroom:


( Ideas taken from Elementary Mathematics is Anything but Anything)

1.     Classroom talk needs to emphasize precision in mathematical language by you and the students.

2.     Students need to read, write and speak mathematically using words and symbols to develop fluency.

3.     You need to be modeling a range of vocabulary, as well as demanding its use by the students.

4.     When new vocabulary or symbols are discussed, they should be written on the board or added to a math language wall that can be accessed easily by all students during math time.

·        Vocabulary should not just have a definition but should be accompanied by a pictorial and a numerical example.

5.     Teach all students to use voices loud enough for all to hear, as well as to try to clarify their thoughts as much as possible. Students should talk one at a time and not interrupt one another.

6.     If necessary, rephrase what other students are saying in simpler or more precise speech, but beware of restating students too often. Students with language needs can grow dependent on your support and may never learn to listen to their peers.

7.     Have a student sit next to you during whole group discussions so that you can whisper some information into his ear that may scaffold his understanding of what is being discussed.

8.     Because it is common to interchange words that mean the same idea as a way of developing vocabulary, it is important that you point out that these different words mean the same thing; otherwise, you may cause confusion.

9.     If certain students are missing key vocabulary, then perhaps small-group lessons need to focus on developing that missing vocabulary, and perhaps the concepts behind that vocabulary, before entering a unit that would demand understanding of such ideas.



Click below to find links to each of the following:

ESL Lesson Plans and Resources

Special Needs of Second Language Kids

Helping English Langauge Learners make sense of math word problems

Helping ELL students develop computational fluency

Math Lessons ( 


Bahr, D. and L.A. de Garcia (2010).  Chapter 12. Elementary Mathematics is

       Anything but Anything. Boston: Houghton Mifflin

Garrison, L. Amaral, O. & Ponce, G. (2006). UnLATCHing mathematics instruction for

        English learners. NCSM Journal of Mathematics Education Leadership, 9 (1), 14.


Franco, J. 2005. Isn’t English a trip? In Changing the faces of mathematics:

           Perspectives on Latinos, 21– 22. Reston, VA: National Council of Teachers

           of Mathematics.

Bresser, R. 2003. Helping English-language learners develop computational fluency.

                Teaching Children Mathematics 9(6):294–298.




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