For decades, educators have assumed that learning arithmetic in school helps students solve real-world problems. Yet, a new study published in Nature by a team of researchers including Nobel laureates Abhijit Banerjee and Esther Duflo, challenges this belief. Their research in India shows that children adept at performing arithmetic in market settings struggle with classroom-style math — and schoolchildren proficient in textbook math fail at simple market transactions.
The problem, the study suggests, is that there’s no bridge between math learned in school and math encountered in real-life situations.
Despite great economic progress in the past 20 years, many areas of India still struggle with poverty. In some parts of the country, it’s not uncommon to see children working in retail markets, selling various goods. Their work involves mental calculations, performed without pen and paper. These calculations often involve multiplication, addition, subtraction, and division — often with multi-digit numbers.
The study surveyed over 1,400 children in Kolkata and Delhi, India, who work in local markets. These children, some as young as eight, routinely perform complex arithmetic to calculate costs, make change, and adjust prices. Yet they fail when presented with similar arithmetic problems in the abstract format used in schools.
Similarly, researchers tested 471 children who were enrolled in local schools but had no market-selling experience. These students performed well on classroom-style problems. However, when asked to solve a simple market math problem — like calculating the total price for multiple items at different rates — only 1% of them succeeded. In contrast, more than a third of the market-working children got it right.
“For the school kids, they do worse when you go from an abstract problem to a concrete problem,” says MIT economist Esther Duflo, co-author of a new paper detailing the study’s results. “For the market kids, it’s the opposite.”
School math is not market math
The researchers first wanted to ensure that the market-working children’s success wasn’t due to memorization. They deliberately tested them with unusual quantities and unfamiliar pricing to rule out rote learning. Yet, the children still solved these problems quickly and accurately.
They would ask, for instance, how much is 800 grams of potatoes sold at 20 rupees and 1.4 kilograms of onions sold at 15 rupees per kilo. They asked how much change the buyer would get when handing a 200 rupee note (163 rupees). These are rather unusual and specific quantities, yet the market kids managed to solve this type of problem remarkably well. Over 90% got it right the first time very quickly, and 95 to 98% of the time by the second try.
Then, researchers asked the kids in the market (with their parent’s permission) to do some standard school math tests. They asked them to divide a three-digit number by a one-digit number, and less than a third of the kids got it right. Even when they were asked to subtract a two-digit number from another two-digit number, just 54% of them got it right. This is far easier than the onion/potato task.
In another experiment, researchers tested kids who do well in school on various market-type problems. These were students who could solve problems like the one above with 96% accuracy. When the kids had to solve “market” type problems, even with unlimited access to time and paper and pencil, only 60% got it right. In a market setting, without pen and paper, they would likely fare even worse.
So what gives?
Different mental strategies
They used efficient, non-conventional mental strategies not typically taught in schools. Many broke down complex multiplications into easier steps. For instance, instead of calculating 11 × 43 directly, they would solve it as (10 × 43) + 43, leveraging their intuitive understanding of numbers. They also rounded prices to make calculations easier, adjusting them back afterward.
In contrast, school children followed rigid, inefficient methods. Their calculations were slow and often involved unnecessarily complex steps. Many students relied on written addition instead of multiplication — for example, solving 24 × 8 by adding 24 eight times. Others used tally marks instead of direct numerical operations.
While they could solve problems given unlimited time and paper, their methods were impractical in real-world settings. Their math skills, though technically correct, were far too slow to be useful in business or daily transactions. They also lacked transferability to the real world.
It’s not that one group of kids knew math better than the other; they just had different approaches. Yet what’s so striking is that neither group of children transferred their skills to the other domain. Market-working children, despite their strong arithmetic abilities, could not solve simple abstract problems presented in school format. Likewise, school-going children, despite their training, could not apply their math knowledge outside the classroom.
Schools should bridge the gap to the real world
Children don’t really learn universal principles. They compartmentalize knowledge based on context. If they learn math in a particular format — either through market experiences or school exercises — they struggle to recognize the same principles when presented differently.
For market children, school-style problems lacked meaning. Numbers were stripped of the context they were used to, making calculations harder. For school children, market problems involved unfamiliar real-world reasoning that their education had not prepared them for.
This is a systemic problem.
Researchers tried to compensate for potential factors that could influence the results. Some children were given positive encouragement before testing, a measure known to reduce stress — this had no effect on test scores. They created school-friendly versions of a market math problem, using a word system familiar to students, which also didn’t change results by much. They even tried to give some children financial rewards for correct answers, but even this didn’t influence performance.
At the end of the day, schools need to do better.
Instead of teaching abstract symbols first, math curricula should introduce concepts through familiar, practical scenarios. This could mean using games, financial literacy activities, or even small business simulations. Students should be encouraged to explore different ways to solve problems. Instead of enforcing step-by-step algorithms, teachers should introduce strategies like mental estimation, rounding, and decomposition — methods already used by market-working children.
It’s also important to do this early, the researchers conclude.
“We conclude that by the time they reach adolescence, the cognitive differences between working and non-working children are not easily overturned.”
The study was published in Nature.
