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New research shows a lack of language skills can hamstring a student鈥檚 ability to understand basic concepts in mathematics.
A series of studies led by Susan Goldin-Meadow, a psychology professor at the University of Chicago, found that profoundly deaf adults in Nicaragua who had not learned a formal sign language could not accurately describe or understand numbers greater than three. While hearing adults and those who used formal sign language easily counted and distinguished groups of objects, those who used only self-created 鈥渉omesigning鈥� gestures could not consistently extend the proper number of fingers to count more than three objects at a time, nor could they match the number of objects in one set to those in another set.
The study, while not conducted on children, offers new insight into the link between language and mathematics development in children, because it focuses on adults who have grown up without language and numeracy, said Laura-Ann Petitto, a professor of cognitive neuroscience and the director of the Genes, Mind and fNIRS [Functional Near Infrared Spectroscopy] Brain Imaging Laboratory for Language, Bilingualism, and Child Development at the University of Toronto, St. George. Such populations are difficult to find in modern society; the study includes only four subjects.
Prior studies focused on primitive hunter-gatherer tribes that had few words for numbers in their language, but unlike the homesigners also had few demands for numbers higher than three in their daily lives.
Even taking into account its tiny sample size, Ms. Petitto said the study links more directly to math and language learning in modern societies and 鈥減rovides tantalizing corroboration for child developmental work, which oftentimes finds that young children with particular types of language disorders also have concomitant disorders in math and numeracy.鈥�
Words to Numbers
Ms. Petitto and Elizabet Spaepen, a postdoctoral psychology fellow at the University of Chicago and co-author of the study, agreed that the results could suggest that students with early math problems could need language-based interventions, too.
鈥淎ll of this fits in with the same idea 鈥� that the way we conceive of numbers evolves from language,鈥� Ms. Spaepen said. 鈥淐hildren learn this stuff before they learn to read, before word problems become a problem.鈥�
鈥淚f you can鈥檛 understand what [five] means, you can鈥檛 add, you can鈥檛 do basic math,鈥� she said.
Children start counting everything in sight as soon as they begin to speak, but research shows they do not immediately attach abstract meaning to the numbers. They first learn numbers below three or four, which can be understood visually. For more than three items, people learn to perceive sets of items. The cardinal number principle鈥攊n other words, the understanding that the number 鈥渟even鈥� represents a set of seven items鈥攇enerally develops when a child is 2陆 to 4陆 years old.
Early childhood educators might see this development by asking a preschooler how many blocks are in a stack of seven on the table; a child who has not developed cardinal number understanding would be able to count the blocks one by one, but not able to answer if asked, 鈥淗ow many is that?鈥�
The Nicaraguan homesigners , but could not tell if seven was more or less than nine. If one block was removed from a set of blocks in a box, they could tell that the amount had changed, but not whether there were more or fewer blocks left in the box.
鈥淚t鈥檚 not slower for you to count to nine or five,鈥� Ms. Goldin-Meadow said. 鈥淲hen we say the number 鈥榮even,鈥� we mean seven items; it鈥檚 one word for a set. When [homesigners] put their fingers up, it鈥檚 1+1+1+1+1+1+1. It鈥檚 seven ones. So it actually is harder to remember nine than it is for seven.鈥�
Hidden Problems
Yet researchers found the homesigners鈥� lack of math skills remained mostly hidden from their families and community. Nicaraguan money differs by color and shape, and the homesigners could make basic currency transactions, though they could not translate monetary value to numbers or exchange coins into bills consistently.
鈥淭hey have this whole system, but they can鈥檛 generalize from it, and it鈥檚 very context dependent,鈥� Ms. Goldin-Meadow said.
The findings provide more evidence for the link between early literacy and numeracy suggested by other recent research. One published in the journal Developmental Psychology by fellow University of Chicago psychologist Susan C. Levine found toddlers whose parents spoke with them frequently about numbers were more likely to understand the cardinal number principle by preschool age than students who had heard fewer number words. Another study, published in 2001 in the Journal of Experimental Psychology, compared the brains of English- and Chinese-speaking students doing basic math problems. English speakers鈥� brains showed more activity in language centers, while Chinese-speaking students鈥� brains showed more activity in the visual and spatial areas of the brain. It was theorized that numbers in Chinese language might be easier to conceptualize because they follow the base-10 model more directly; for example, the Chinese word for 13 translates to 10-three, rather than the new word 鈥渢hirteen.鈥�
鈥淥ne educational issue that this research brings up is that young children being educated in a language not their own may be at a disadvantage in the early years of mathematics instruction,鈥� wrote Keith J. Devlin, the executive director of the Human-Sciences and Technologies Advanced Research Institute at Stanford University, and author of a 2000 book on the evolution of mathematical thinking.
The findings also may suggest the need to use number lines instead of finger-counting in early grades, Ms. Goldin-Meadow said.
The University of Chicago team plans to continue work with the homesigners to determine what part of language development is most crucial for math understanding and if there are ways to help those with low language skills learn numeric concepts more easily.
