The Mathematics of Language

In 2003, nearly 86 percent of fourth-grade English-language learners scored not proficient in math on the Massachusetts Comprehensive Assessment System (MCAS) test.  What isn’t represented in that statistic, says doctoral student Maria Martiniello, is that — for English-language learners — success on the math section of a standardized test may have little to do with numbers and more to do with words.

Inspired by the emphasis placed on students’ standardized test scores, Martiniello’s research examines whether math tests — like the one given as part of the MCAS — are equally valid for children not proficient in English, considering a majority of math questions are word problems.

While researching a large data set, which included all fourth graders who took the 2003 MCAS, Martiniello uncovered several math questions that seemed to disfavor English-language learners.  Her conclusion: Just because an English-language learner does poorly on the math section doesn’t necessarily mean he doesn’t know the math.

“The problem is confusing math mastery with language mastery,” she says. “It is possible that they haven’t mastered the math content measured by the item, but it is also possible that they have difficulties comprehending the English text; or it could be both.”

Martiniello’s other research on differential item functioning sheds light on this issue. When a math question is more linguistically complex, the probability of answering it correctly is lower for English-language learners than for non–English-language learners. The probability of answering correctly is about the same when the text is not linguistically complex.

In addition to her research based on large-scale testing data, Martiniello interviewed English-language learners using think-aloud protocols to gauge children’s interpretation and comprehension of the MCAS math items. The interviews further confirmed Martiniello’s hypothesis about a language barrier being a major hindrance. For example, Martiniello discovered that many English-language learners weren’t familiar with words like “chores,” “rake,” and “weed” which affected their ability to answer questions correctly.

“If you don’t speak English at home, then you may not know a word [like] ‘chores,’” she says. “A math problem [containing that word] then becomes relatively more difficult for English-language learners, so performance on that item has little to do with their math knowledge.”

At the root of Martiniello’s research is a quest for fairness and equity by questioning the validity of standardized math tests, given their significant implications on students’ lives.

“The pursuit of equity is the driving force of my work,” Martiniello says. “It is through methodologically rigorous research that we can address these issues of fairness in testing. I hope my research will inform and improve the math tests we use for assessing English-language learners.”