When I was 12, my family lived adjacent to a small farm. Though I was not old enough to work, the farm’s owner, Mr. Hall, hired me to man his roadside stand on weekends. Mr. Hall had one rule: no calculators. Technology wasn’t his vibe.
Math was my strong suit in school, but I struggled to tally the sums in my head. I weighed odd amounts of tomatoes, zucchini and peppers on a scale and frantically scribbled calculations on a notepad. When it got busy, customers lined up waiting for me to multiply and add. I’m sure I mischarged them.
I was thinking about my old job as I read a quirky math study published this month in the journal Nature. Nobel Prize winning economists Abhijit Banerjee and Esther Duflo, a husband and wife research team at MIT, documented how teenage street sellers who were excellent at mental arithmetic weren’t good at rudimentary classroom math. Meanwhile, strong math students their same age couldn’t calculate nearly as well as impoverished street sellers.
“When you spend a lot of time in India, what is striking is that these market kids seem to be able to count very well,” said Duflo, whose primary work in India involves alleviating poverty and raising the educational achievement of poor children. “But they are really not able to go from street math to formal math and vice versa.”
In a series of experiments, Duflo’s field staff in India pretended to be ordinary shoppers and purposely bought unusual quantities of items from more than 1,400 child street sellers in Delhi and Kolkata. A purchase might be 800 grams of potatoes at 20 rupees per kilogram and 1.4 kilograms of onions at 15 rupees per kilogram. Most of the child sellers quoted the correct price of 37 rupees and gave the correct change from a 200 rupee note without using a calculator or pencil and paper. The odd quantities were to make sure the children hadn’t simply memorized the price of common purchases. They were actually making calculations.
However, these same children, the majority of whom were 14 or 15 years old, struggled to solve much simpler school math problems, such as basic division. (After making the purchases, the undercover shoppers revealed their identities and asked the sellers to participate in the study and complete a set of abstract math exercises.)
The market sellers had some formal education. Most were attending school part time, or had previously been in school for years.
Duflo doesn’t know how the young street sellers learned to calculate so quickly in their heads. That would take a longer anthropological study to observe them over time. But Duflo was able to glean some of their strategies, such as rounding. For example, instead of multiplying 490 by 20, the street sellers might multiply 500 by 20 and then remove 10 of the 20s, or 200. Schoolchildren, by contrast, are prone to making lengthy pencil and paper calculations using an algorithm for multiplication. They often don’t see a more efficient way to solve a problem.
Lessons from this research on the other side of the world might be relevant here in the United States. Some cognitive psychologists theorize that learning math in a real-world context can help children absorb abstract math and apply it in different situations. However, this Indian study shows that this type of knowledge transfer probably won’t happen automatically or easily for most students. Educators need to figure out how to better leverage the math skills that students already have, Duflo said. Easier said than done, I suspect.
Duflo says her study is not an argument for either applied or abstract math. “It would be a mistake to conclude that we should switch to doing only concrete problems because we also see that kids who are extremely good at concrete problems are unable to solve an abstract problem,” she said. “And in life, at least in school life, you’re going to need both.” Many of the market children ultimately drop out of school altogether.
Back at my neighborhood farmstand, I remember how I magically got the hang of it and rarely needed pencil and paper after a few months. Sadly, the Hall farm is no longer there for the town’s children to practice mental math. It’s now been replaced by a suburban subdivision of fancy houses.
This story about applied math was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for Proof Points and other Hechinger newsletters.
Nobel economists show how knowledge doesn’t easily transfer between applied and abstract math in studies of street sellers in India. MindShift
