Malinda Evans spends about an hour and a half each day teaching mathematics to her 5th graders at Navajo Elementary School in the working-class South Valley neighborhood of Albuquerque, N.M. Whether the topic is basic division, geometry, or word problems, it is invariably also a lesson in the English language, which vexes many of her pupils more than any single equation ever could.
Spanish is the first language for more than half Ms. Evans鈥 students. As she and other teachers working with similar students have come to understand, translating the arcane terminology of math for English-language learners can be daunting.
Over the years, the sixth-year teacher has learned several tricks. She works on an overhead projector, writing out terms as she pronounces them. She avoids lengthy definitions. And she points out similarities in the roots of words in the two languages: Equilateral triangles, she tells students, can be remembered as igual and lado in Spanish, or 鈥渆qual鈥 and 鈥渟ide.鈥 Children with a strong command of English are encouraged to help their classmates, using whatever lingo will get the point across.
鈥淭hey come up with things I never would have dreamed of,鈥 Ms. Evans said. 鈥淭hey have made my own, personal understanding of math so much deeper.鈥
Similar strategies are being tested around the country. While math has long been regarded as a universal language because of its foundation in numbers, the subject poses nearly as many hurdles for students with limited English as lessons that rely more heavily on reading, many educators say.
That issue has gained renewed attention under the federal No Child Left Behind Act, which requires schools and districts to test students annually in both reading and math in grades 3-8 and one in high school and make yearly progress in those subjects.
In addition, the law requires schools and districts to report separately the scores of English-language learners, a provision that many observers say has brought new scrutiny to the needs of that population.
Calls for Commitment
A number of influential math organizations have also called during the past year for a greater commitment to helping English-language learners. The National Council of Teachers of Mathematics organized its annual meeting around the issue of diversity, particularly as it relates to improving the skills of poor, minority, and other students who may be disadvantaged.
And this summer, the National Council of Supervisors of Mathematics will begin work drafting what its leaders are calling 鈥渢he road map,鈥 a strategy for helping teachers and administrators address the math needs of students with limited English proficiency, said Linda M. Gojak, the president of the 3,000-member organization.
鈥淚 like to ask people: 鈥榊ou studied a language in high school? How would you like to learn algebra in that language?鈥 鈥 said Deborah Short, who directs a division of the Washington-based Center for Applied Linguistics that studies language development. 鈥淲ell, that鈥檚 what thousands of kids are doing, every day. 鈥 Language is a big piece of mathematics.鈥
The Language of Math
Some 5.5 million English-language learners attend public schools in the United States, making up roughly 11 percent of the overall public K-12 population, according to the U.S. Department of Education. Eighty percent of them speak Spanish as their first language. Fifty-seven percent of English-learners live in the West, federal estimates show, while 24 percent live in the South, 10 percent in the Northeast, and 9 percent in the Midwest.
Whether students鈥 first language is Spanish or another, they face several challenges in math. The academic language of the subject presents terms that almost never come up in everyday conversation, such as 鈥渜uotient鈥 and 鈥渆xponent.鈥 It also presents them with words that have double meanings, like 鈥渢able,鈥 and idiosyncratic English expressions, such as questions asking for the 鈥渄ifference鈥 between two numbers. Many students mistakenly take that as a cue to describe numbers鈥 different characteristics, rather than a call to perform subtraction.
69传媒 who began their formal math studies in another country may find that familiar symbols, expressions, and methods differ from those they encounter in U.S. classrooms. Those barriers become more pronounced as students delve into word and story problems that 鈥渃an be worded a thousand different ways,鈥 Ms. Evans said.
When taught effectively, math can provide an important bridge to improving English-language skills, because of the widespread similarities of number systems, researchers say.
But taking advantage of those connections requires skilled teaching, said Miriam A. Leiva, the president of TODOS: Mathematics for All, a nationwide association based in Tempe, Ariz., that is devoted to helping students with limited English skills in math, particularly Spanish-speakers.
Ms. Leiva moved from Cuba to the United States as a 13-year-old in 1954. She was one of only a few Spanish-speakers at her first school, in Miami, and only one subject offered material that was recognizable.
鈥淚 went from class to class not knowing what I was doing, until I got to math class,鈥 said Ms. Leiva, now a professor of mathematics at the University of North Carolina at Charlotte. While math helped her improve her English, she became convinced that many instructors needed help in figuring out the best ways to reach students from backgrounds similar to hers.
A critical challenge for many math teachers, Ms. Leiva notes, is finding a way to reach students with limited English skills without ignoring the needs of those already fluent in the language. At more than 60 percent of U.S. schools, English-language learners make up less than 1 percent of the overall population, according to federal estimates.
Even at Albuquerque鈥檚 Navajo Elementary School, where 90 percent of the students are Hispanic, teachers must be adept at working with children from a variety of backgrounds. Nine of the 20 pupils in Ms. Evans鈥 class are fluent in English.
The teacher believes the language exercises she uses help all students, even those whose first language is English, by encouraging proper sentence construction and grammar. She asks them to use verbs such as 鈥渁dded鈥 and not such nonstandard phrasing as 鈥淚 plused 2 and 2.鈥
鈥淭hat鈥檚 a disadvantage for them, on a state test, or in a book,鈥 Ms. Evans said of the use of slang.
Science, Too
In many parts of the country, the challenges are not limited to Spanish-speaking children. A research project in the 361,000-student Miami-Dade County, Fla., school district relies on a specially crafted curriculum and teacher-training model to build the English-language skills of both Latino and Haitian elementary pupils, most of whom speak Creole, through science lessons.
University of Miami researchers, supported by a five-year, $4.7 million grant from the National Science Foundation, offer some scientific vocabulary in three languages.
In addition, the researchers emphasize skills such as scientific inquiry and measurement that they believe cultivate students鈥 reading and math abilities. The strategy emphasizes the simultaneous development of language and content skills, as opposed to directing students to English-as-a-second-language classes, said Okhee Lee, a professor of science education and the director of the project.
So far, the researchers see results. Seven participating elementary schools made greater gains in reading and math on the Florida Comprehensive Assessment Test over the most recent testing cycle than other district schools serving Spanish- and Creole-speaking students.
鈥淜ids can learn science along with English,鈥 Ms. Lee said. 鈥淲e promote language-learning throughout.鈥
