My first day in an American school started with good news: all clocks were in
Spanish! The bad news was devastating: I did not understand anything else.
Years later, I realized that numbers and many other symbols were in a
"language" that I could understand at that level, the academic language of
mathematics. English Language Learners (ELL) not only face a language barrier
in English, but also in the knowledge of the language of mathematics: its
syntax, semantics, grammar, vocabulary, and representation. Many
English-speaking students face a similar challenge.
What can educators do in mathematics classrooms to help students whose first
language is not English? How can we help them? The teaching strategies and
interventions described here are supported by research and best practices in
mathematics education and by my experience as a teacher of mathematics and as
an English Language Learner. They are also supported by my own teaching
philosophy: Every student must have an equal opportunity to be different.
Each student is different
Even when ELL share the same first
language and culture, they are different in many ways. Some come to our
schools with a strong academic background, while others have had deficient
schooling or none at all. For example, students from Latin America could be
Chileans or Salvadorians. Both groups speak Spanish and have grown up in
Hispanic countries. Yet, each have diverse experiences in their native
countries, such as academic, socioeconomic, urban or suburban experiences and
country-specific cultures, etc. They also may have diverse home conditions in
their new country.
In the recommendations that follow, we assume that mathematics classrooms are
comprised primarily of English-speaking students, along with a few ELL who are
in various stages of learning—both mathematics as well as English as a second
The role of the teacher
". . . all students need the
opportunity to learn challenging mathematics from a well-qualified teacher who
will make connections to the background, needs, and cultures of all learners."
The teacher is the most important factor in students' learning mathematics
and, as such, teachers must plan and implement lessons to accommodate
students' differences. The following teaching strategies are recommended for
ELL and also supported by the National Council of Teachers of Mathematics
Professional Teaching Standards (1992):
Have high expectations.
Implement a rigorous mathematics content.
Provide for a variety of learning styles, prior knowledge, experiences,
cultures, and all other differences.
Develop mathematics and language objectives in each lesson.
Use visuals, models, manipulatives, realia, technology, and other resources.
Describe mathematics using multiple representations.
Make creative groupings: whole class, small groups, pairs, and other grouping
that creates a non-threatening environment. Mathematics classrooms must
promote dialogues, not monologues.
Draw on others' strengths and use collaborative teaching with other
disciplines, including input from ELL programs and bilingual teachers.
Make use of creative tutoring, including speakers in the students' native
languages, such as other students and volunteers.
Focus on differences in algorithms. For example, in many countries students
solve division problems by writing the dividend, divisor, remainder, and
quotient in different places than what is taught in the United States.
Utilize a problem-solving approach to teaching, encouraging reflection,
discussion, and justification.
Focus on both concept development and procedures, not on mindless worksheets.
Life is full of complex problems, not exercises.
Select applications and real-world problems to which students can relate.
Learning is contextual, and what you learn depends on how you learn it.
To help develop correct use of the language of mathematics and English, demand
communication in the mathematics classroom: speak, write, read, and hear. "
To enable ELL to participate. . . to achieve [in] mathematics. . . the teacher
must help them develop language skills that go beyond mere social fluency
." (Peixotto 1999).
Learning is most efficient in the child's primary language (Khisty 1995).
English language fluency versus social English fluency takes many years.
Educators should use the first language whenever possible to teach the second
language, as well as the content knowledge (Garrison and Mora 1999).
You will likely find that successful strategies to help ELL in mathematics are
also effective strategies to use with all students. A focus on reasoning,
communication and problem solving in the mathematics classroom works for all
students, and, in particular, should be used for ELL. ". . . the
fundamental notion is not that [ELL] need mathematics different from. . .
'majority' students but rather. . . that effective instruction for all
children must be carried out on the basis of what is known about how children
learn with understanding." (Hernandez 1999). By implementing these
strategies and recommendations, we will be opening the doors of education and
success to all students.
Dr. Miriam Leiva has been a mathematics educator and teacher for over 35
years. She is president of
TODOS: Mathematics for ALL, an international organization affiliated with
the National Council of Teachers of Mathematics (NCTM). The mission of TODOS
is to advocate equitable and high-quality mathematics education for all
students, in particular Latino/Hispanic students, by advancing the
professional growth and equity awareness of educators.
De La Cruz, Y., N. Hernandez, L. Ortiz-Franco, and
W. Secada, eds. 1999. Changing the faces of mathematics: Perspectives on
Latinos. Reston, VA: NCTM.
Garrison L., and J. K. Mora 1999. Adapting mathematics instruction for ELL.
Changing faces of mathematics: Perspectives on Latinos. Reston, VA: NCTM.
Hernandez, N. 1999. The mathematics-bilingual-education connection: Two
lessons. Changing faces of mathematics: Perspectives on Latinos.
Reston, VA: NCTM.
Khisty, L. 1995. Making inequality: Issues of language and meanings in
mathematics teaching with Hispanic students. New agenda for equity in
mathematics education. NY: Cambridge University Press.
Leiva, M. 2005. "High expectations and success in mathematics for English
language learners." Keynote address delivered at the Success for All Children
Forum at Baylor University, Texas. TX: Baylor University.
National Council of Teachers of Mathematics (NCTM). 2000. Principles and
standards for school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). 1991. Professional
standards for teaching mathematics. Reston, VA: NCTM.
Peixotto, K. 1999. Preface to Teaching mathematics and science to
English-language learners. Portland, OR: NW Regional Educational