February 11, 2004

Prof: Diversity helps with math

Daniel Orey sees a bonus benefit in California’s immigrant population – it may help its students with math.

Comparable populations worldwide have fewer problems with mathematics than students in the United States, says Orey, a professor in the teacher education department and Learning Skills Center. He suggests it’s because American children often think there’s only one way to solve problems.

“The way people look at language in the United States is echoed in math,” he says. “We tend to think there’s only one language to learn.” But math is a language with its own culture and norms, and children who learn more than one language find it easier to learn math, he says.

For the past several years, Orey has been a proponent of ethnomathematics, which identifies the techniques and practices used by members of distinct cultural groups. In addition to working with local immigrant populations, he regularly travels to Brazil, a world center of ethnomathematics research. “It’s the out-of-school application of math, the day-to-day uses,” he says.

For example, almost all cultures do some sorts of grouping. In the United States, a dozen is universally understood to be 12 similar objects. In Guatemala, a mano or handful means five of a kind.

To demonstrate the value of ethnomathematics, Orey has developed the Algorithm Collection Project to give his CSUS students, many of whom are future teachers, a sense of how math works in other countries. It was created as a way to understand the relationship between language and algorithms – methods such as addition or subtraction for solving certain kinds of problems.

Orey also says the project is a way to take advantage of immigration. “Northern California is one of very few places with this much diversity,” Orey says.

Part of the project involved making a vocabulary “wall” on Orey’s website (www.csus.edu/indiv/o/oreyd). Orey’s students interview newly arrived immigrants and compile a list of words used for common mathematical functions – addition, subtraction, multiplication, division – in the new arrivals’ countries of origin as well as visual examples of how they carry out the function.

It’s grown into a collection representing more than 21 languages currently spoken in the Sacramento region and confirms that other countries do the same basic things mathematically but often using different patterns. Common day-to-day algorithms differ by culture and by national origin. Orey says there are at least four major patterns used for long division by immigrants in this region, which he has named: North American, Franco-Brazilian, Indo-Pakistani and Russo-Soviet.

There are subtle differences linked to linguistics. For example, Latin-based countries put the modifier after the noun when speaking while North Americans put the modifier first. So, when Latin-based countries do long division they don’t have to do the mental reversing North Americans do – they already think “four into 20” rather than “20 divided by four.”

Each indicates there’s more than one way to solve a problem.

Another aspect of the project looks at how people with varying degrees of language acquisition – monolingual, bilingual and multilingual – interact with their algorithms. For example, he’s found many people in Sacramento from the former Soviet Union know at least three languages. At the same time, they’re more flexible when given a problem and have less of a tendency to stop trying. To them, Orey says, algebra is just one more language.

By looking at how other countries do math, Orey has also determined that the way it is taught in the United States is designed – unintentionally or not – often holds some people back. He suggests that the United States treats math in an elitist fashion, breaking it up into categories and, eventually, filtering people out. He opts for Brazil’s more holistic approach. They don’t divide math into algebra, trigonometry and calculus.

“Calculus is where it all comes together,” he says. “If people never make it to calculus, it’s like building a car, but never getting to drive it.”

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