Learning to Speak Math While Learning to Speak English

9/10/2009 10:51:00 pm

Multicultural Integral (sharpened)Image by dkuropatwa via Flickr

The other day I was talking to a teacher who works with EAL (English as an Additional Language) students. I was reminded of a summary of teaching tips I had assembled by scouring through a pile of research articles when my department was struggling with the issue of teaching a growing population of EAL students in our school. Unfortunately I've lost all the sources. This was originally designed to be shared with just my colleagues as a quick reference sheet.

It struck me that these tips are really good for all students.

By the way, that picture is an integral written using various languages and multilingual character sets. It makes perfect (mathematical) sense if you can decode all the numbers. Can you "read" it?

I hope other teachers find this helpful. Please add your own suggestions in the comments below.

Strategies for Teaching EAL Students Mathematics

The strategies below have been collated from a variety of resources. While all may be specifically geared towards assisting the EAL learner in math, these strategies are likely to prove effective in supporting the learning of all students.

The Language of Mathematics and Teacher’s Use of Language

"Command of mathematical language plays an important role in the development of mathematical ability"

  • Teach the language of the subject.
  • Be aware of vocabulary that has different meaning when used in mathematical contexts.
    • e.g. positive, negative, table, irrational, etc.
  • Mathematical operations signaled by several different words or phrases.
    • e.g. add, plus, sum, combine, increased by, etc.
  • Provide additional "wait time" for student responses to questions.
  • Be conscious of the vocabulary you use.
  • Simplify sentence structures and repeat sentences verbatim before trying to rephrase.
  • Rephrase idioms ("take a stab at it") or teach their meaning.
  • Clearly mark transitions during classroom activities.

Explanations and expectations need to be articulated explicitly and completely. Don't simply expect EAL students to "pick up on" assumptions, unstated premises, or subtle nuances of meaning.
  • Periodically check to ensure EAL students are understanding.

Create Language Supportive Classrooms

"Journal writing offers English Language Learners (ELLs) the opportunity to practice and develop their emerging mathematics discourse skills."

Some possible prompts for journal writing:

  1. Construct a word problem about [this] picture that can be solved mathematically. Share your problem with a partner and solve it.
  2. What is the most important idea you've learned in [algebra] this week and why?
  3. Write a paragraph containing as many of these words as possible: ..........
  4. List some things you must remember when answering this type of question or doing this type of problem.

Connect Mathematics to Students' Background and Experiences

  • Young people learn best from their own and not other peoples’ experiences.
  • Use students’ past experiences with mathematical terms to help give the terms meaning in a mathematical context.
  • The introduction of a new term should be carefully orchestrated through repetition in context and through saying it aloud and spelling it.
  • To learn mathematics successfully, many ESL students need a more multisensory approach to mathematics.
  • Relate mathematics instruction to the “out of school” life of students.
  • The implementation of “ethnomathematics” can help teachers relate mathematics to their students’ “out of school” lives.
  • Use teaching methodologies that “contextualize” the subject matter.
  • Be concerned about affective factors in the classroom.

Between the 10th and 15th year of teaching I discovered that what was needed for these children was not an emphasis on the academic but a meaningful interaction with mature adults. The relationship with a stable, mature adult is most important.

Vary Instructional Methods

"ELLs learn best when instructional methods and approaches match their individual abilities and learning styles."

  • Use a variety of methods tailored to students' needs including direct instruction, guided discovery, cooperative learning, computer assisted learning, etc.
  • Provide writing and other language development activities for EAL students.
  • Use cooperative learning strategies.
  • Encourage students to rephrase information or instructions orally.
  • Use peer tutoring.
  • Establish a "homework club".

Contextual Supports for Linguistic Development

  • Write key words on the board and other non-verbal cues, wherever possible, to present key ideas.
  • Provide written notes, summaries, instructions, and pre-reading.
  • Where possible, use the students' native language to check comprehension and clarify problems.
  • Communicate interest in students' linguistic development and set expectations.
  • Respond to students' language errors.
  • Establish a supportive environment for language learning.

In most subject areas, EAL students should be able to grasp essential concepts, if these are presented carefully, emphasized through repetition, and clearly distinguished from finer points that the students are less able to assimilate.

Assessing, Evaluating, and Reporting on Students' Progress

  • Use a diversity of measures including portfolios, observations, anecdotal records, interviews, checklists, criterion referenced tests, etc.
  • Design alternative assessment tasks including exhibits, dramatic renditions, interviews, writing samples, etc.
  • Include questions for small group discussion and individual writing.
  • Provide extra time on tests for EAL students to process the question in English, think about them in their first language, and respond in English.
  • Simplify directions in English and/or paraphrase in students' native language.
  • Permit students to use dictionaries or word lists.
  • Avoid heavy reliance on multiple-choice and true/false tests with EAL students (these involve a lot of reading and often depend on comprehension of subtle shades of meaning)

Functioning all day in a second language is exhausting and demanding. Homework can take these students two to three times longer to complete.

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  1. I find it very interesting that the tips and tools we learn for specific types of students or for specific school subjects work for many things. I just took a course on ELL (or EAL as you put it) students. Many of the things I learned in that class are things that I was able to use to help me with all of my new students. Especially the reading techniques I learned. Math would also go hand-in-hand because students need to visually see how things work. Interesting connection!

  2. Thanks for the list! I find these tips really useful for my teaching. There are simply things that you tend to forget every once in a while until you read it again in some article. I hope I can get more useful vocabulary drilled into my students while I tackle Maths with them.


  3. Excellent advice. I especially like the closing thought that homework can take 2 to 3 times longer to complete. Which is why I appreciate your suggestion of forming a homework club. *All* of my students can benefit from that.

  4. It is very refreshing to read this post. I teach language arts and reading, but next year i am going to be teaching math as well. I think integrating literacy activities and instruction is so essential in math. I like several of your ideas so much i am going to use them in my curriculum next year, such as discussion questions/groups, varied instructional strategies, written and verbal directions/notes, and alternate assessment options. Like you said these are great tips for all students!

    Amanda Lake