In India, many children who work in retail markets have good math skills: they can quickly perform various calculations to complete transactions. But a new study shows that these children often perform much worse on the same problems they learn in the classroom. This is even though many of these students are still in school or have been in school until the seventh or eighth grade.
Conversely, the study also shows that Indian students who are still enrolled in school and unemployed perform better on school math problems, but often perform poorly on the types of problems encountered in the marketplace.
Overall, both “market kids” and “school kids” struggle with the approach that the other group masters, which raises questions about how to help both groups learn mathematics more comprehensively.
“For school kids, when you go from an abstract problem to a concrete one, they’re worse off,” says MIT economist Esther Duflo, one of the authors of a new paper describing the study’s findings. “For market kids, it’s the other way around.”
In fact, kids who have jobs and go to school “do poorly at mental math, even though they’re incredibly good at it,” says Abhijit Banerjee, an economist at MIT and another author of the paper. “It’s always been a revelation to me that one doesn’t translate to the other.”
The paper, “Children’s Arithmetic Skills Do Not Transfer Between Applied and Academic Mathematics,” is published today in Nature . The authors of the paper are Banerjee, the Ford Professor of Economics at MIT; Swati Bhattacharjee of the Ananda Bazar Patrika newspaper in Kolkata, India; Raghabendra Chattopadhyay of the Indian Institute of Management, Kolkata; Duflo, Abdul Latif Jameel Professor of Economics of Poverty Reduction and Development at MIT; Alejandro J. Ganimian, Professor of Applied Psychology and Economics at New York University; Kailash Rajaha, a doctoral candidate in economics at MIT; and Elizabeth S. Spelke, Professor of Psychology at Harvard University.
Duflo and Banerjee shared the 2019 Nobel Prize in Economics and are co-founders of MIT’s Jamil Abdul-Latif Poverty Action Lab (J-PAL), a global leader in development economics.
Three experiments
This study mainly consists of three data collection exercises with several experiments embedded in them. The first shows that 201 children working in markets in Kolkata have good mathematical skills. For example, a researcher posing as an ordinary shopkeeper asks for the price of 800 grams of potatoes sold at Rs 20 per kilogram, then asks for the price of 1.4 kilograms of onions sold at Rs 15 per kilogram. They would ask for a mixed answer – Rs 37 – then give a 200 rupee note to the market worker and get Rs 163 back. Overall, the children working in the market solved this type of problem correctly 95 to 98 percent of the time on the second attempt.
But when the children were pulled aside (with their parents’ permission) and tested on a nationally standardized Indian math test, only 32 percent could correctly divide a three-digit number by a single-digit number, and only 54 percent could correctly subtract a two-digit number from twice another two-digit number. It’s clear that the children’s skills are not being applied in the classroom.
The researchers then conducted a second study with 400 children working in markets in Delhi, which replicated the results: Working children had strong skills in market transactions, but only about 15 percent of children who went to school had average skills in math.
In a second study, researchers also asked this question: How do students who are doing well in school fare in math problems in the marketplace? Here, with 200 students from 17 non-market schools in Delhi, they found that 96 percent of students could solve typical problems with pencil, paper, unlimited time, and the opportunity to repeat. But when students were forced to solve problems in a simulated “marketplace” environment, that number dropped to just 60 percent. The students had unlimited time and access to paper and pencil, so this number may overestimate their performance in the marketplace.
Finally, in a third study, conducted in Delhi with more than 200 children, the researchers again compared the performance of “market” and “school” children on a variety of math problems under different conditions. While 85 percent of working children got the answer right on a market exchange problem, only 10 percent of non-working children answered a question of similar difficulty correctly when faced with limited time and without tools like pencil and paper. However, given the same division and subtraction problems but with pencil and paper, 59 percent of non-market children got them right, compared with 45 percent of market children.
To further assess the market children and the school children on the playground, the researchers presented each group with a word problem about a boy who goes to the market and buys two vegetables. Almost a third of the market children were able to solve the problem without any help, while less than 1 percent of the school children did so.
Why might the performance of non-working students decline in market conditions?
“They learned the algorithm, but they didn’t understand it,” says Banerjee.
Meanwhile, the market kids seem to be using specific tactics to close retail deals. For one thing, they seem to be good at rounding. Consider a problem like 43 times 11. To do it intuitively, you could multiply 43 times 10 and then add 43 to that to get a final answer of 473. That seems to be what they’re doing.
“The market kids can use base 10, so they do better on base 10 problems,” Duflo says. The school kids have no idea. It doesn’t matter to them. “The market kids may have other tricks like this that we haven’t seen.” The school kids, on the other hand, were better at understanding formal written methods for division, subtraction, and more.
Moving forward in school
The findings make an important point about students’ skills and academic performance. While it’s good for advantaged children to be skilled at providing quick answers, it’s probably better for the long term if they also do well in school and graduate with a high school diploma or better. Finding ways to bridge the gap between informal and formal ways of solving math problems could therefore be particularly useful for some Indian children.
The fact that such a gap exists also suggests that it would be possible to try some new approaches in the classroom.
Banerjee, for example, suspects that part of the problem is the classroom process in which there seems to be only one real way to fund arithmetic answers. Instead, he believes that, building on the work of co-author Spelke, helping students think through their way to the correct answer can help them truly understand what it takes to solve these types of problems.
But Duflo adds, “We don’t want to blame the teachers. It’s not their fault. They’re given a strict curriculum to follow and strict procedures to follow.”
This still leaves open the question of what needs to be changed in specific classroom situations. This is, by the way, something the research group is currently exploring as they consider new experiments that could directly address this. However, the current findings represent a clear advance that will be useful.
“These findings highlight the importance of educational curricula that bridge the gap between intuitive and formal mathematics,” the authors say in the paper.
Support for this research was provided in part by the Abdul Latif Jameel Poverty Action Lab Post-Primary Education Initiative, the Blaise Pascal Foundation, and the AXA Research Fund.
