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 language.

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." (NCTM 2000).

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.

References
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 Laboratory.