Mathematics and the Bilingual Brain
Two plus two equals dos mas dos
Language is an inseparable part of mathematics. Some of the first lessons that parents teach their toddlers are the words to count the chubby little fingers on their hands. From there, children progress to the basics of elementary school arithmetic— addition, subtraction, multiplication and division.
For educators and scientists who are fascinated with the brain and its cognitive powers, the idea of mathematical computation has set off lively discussions and ponderous research. When bilingual children recite multiplication tables in their heads, what language are they using? What language do bilingual adults use when they are balancing their checkbooks or calculating their income taxes?
This is not just idle curiosity. The answers to those questions have potentially important implications for school systems and educational programs, according to Nicole Y.Y. Wicha, Ph.D., assistant professor of biology at UTSA.
“One in five kids in the United States is bilingual,” she said. “We are trying to understand how that influences the cognitive processes in the brain.”
Good research is the foundation for effective teaching programs, both for children who are not native English speakers and for English speakers who learn a second language.
The conventional view has been that people access mathematical concepts, such as multiplication tables, more efficiently in the language in which these were learned. So, for example, immigrants who spoke Spanish first and learned basic math in their native language as children will turn to that language to calculate math later in life, even if they have become proficient in another language. This view raises the question of whether bilingual individuals will be at a disadvantage when they have to process math problems in their other language. Dr. Wicha hypothesized that the picture was more complex.
“The mathematicians argue that the language in which you learn mathematical concepts is the language in which those concepts are better remembered. We wanted to see if that holds true for a lifetime.”
Given its proximity to Mexico, San Antonio is a living laboratory for researchers like Dr. Wicha who are interested in how the brain remembers and accesses language. The city is rich in people who have had diverse life experiences with language. There are first-generation Americans whose first language in the home was Spanish and who learned English in elementary school. There are immigrants who moved into the country when they were older, arriving with varying degrees of English proficiency. The UTSA campus, with its regional focus on serving the population of South Texas, draws many of these young adults to campus, providing Wicha and others with ample study subjects.
Wicha has funding from the National Institutes of Health to explore some of her questions about how the bilingual brain handles the language of math. For recent studies, she turned to a basic math skill that every child learns by heart in grade school—simple multiplication tables.
“Every 7- or 8-year-old in school learns multiplication tables in one language,” she said. “We wanted to know if bilingual adults are still accessing that information in the language in which they first learned it.”
In these latest studies, Wicha was able to use electroencephalograms, which monitor electrical activity in the brain. She “watched” while the brains of 22 young adult bilingual volunteers performed basic multiplication calculations. All the volunteers were college-age students who were native Spanish speakers as small children but were proficient in English by the age of 15. Each of the volunteers had learned multiplication tables in either Spanish or English but not both.
In the experiments, simple math problems were presented in digits and in words. The word problems were presented in both Spanish and English. Wicha said the initial analysis of the data seemed to uphold the conventional view that basic math “was hard-wired in the brain in the language in which it was learned.
The first study results were published in June in the journal Psychological Science.
But the encephalograms showed that math problems presented as words, not digits, activated differently in some individuals. It suggested that some people respond faster to math problems that are presented in the language that they are using regularly, rather than the language in which they initially learned a math concept.
“It makes the story more complex but more true to what everyone else has discovered,” Wicha said. “Bilingualism is very dynamic. There are a lot of individual differences in the way individuals use their bilingual ability.”
She repeated these same experiments with teachers who work in bilingual education programs and teach math concepts to native Spanish-speaking students in South Texas. Some of the teachers are native English speakers who learned their math concepts in English when they were children. Some of the teachers first spoke Spanish as children and learned their elementary math in Spanish.
With that as a backdrop, Wicha has found that the teachers are exceptionally fast with responses, regardless of the language in which a word problem is presented. But their brains appear to respond quicker to problems presented in the language that they are teaching, not the language in which they first learned their mathematical concepts.
“What we are showing is that your language experience does affect the way you access your mathematical concepts,” Wicha said. “It is not as hard-wired into your brain as people in the math world have proposed.”
Wicha plans to run these same experiments with bilingual elementary school children to understand how math concepts are accessed in each language during the early stages of learning arithmetic.
Overall, the big picture is that cognition research shows that everything people do is often affected by the medium of language, Dr. Wicha said. New technology offers great insights into showing the brain at work and shows the advantages that bilingualism carries into other areas of cognition.
“There is still a lot of stigma associated with being bilingual in U.S. schools. This data shows that bilinguals can access math concepts in both of their languages and therefore are not necessarily at a disadvantage relative to their monolingual peers.
“In other words, this is saying that it is OK to be bilingual early in life,” she said.