Teaching practices in India fail to teach school students strategies to do mathematics in real-world settings, according to findings from a study titled Children’s arithmetic skills do not transfer between applied and academic math, published in the journal Nature on Wednesday (February 5, 2025). The study was done by a team of researchers led by Nobel Prize-winning economists Abhijit Banerjee and Esther Duflo.
The study divided into three sub-studies recruited 1,436 working children from vegetable markets across Delhi and Kolkata, as well as 471 children with no market-selling experience enrolled in nearby schools, approximately aged between 13 to 15 years.
Speaking to The Hindu about the study, Ms. Duflo said that the idea germinated during one of her visits to India, while on a grocery run she noticed that working children perform complex mental mathematical calculations while selling vegetables in markets with ease, and decided to investigate whether, in the urban Indian context, the arithmetic skills that are used in the markets transfer to the more abstract mathematics skills taught in school.
In the first sub-study, 201 children who sold vegetables were approached by undercover enumerators who purchased unusual quantities like 800 grams of potatoes at ₹20 per kilo, and 1.4 kg of onions at ₹15 per kilo. They would ask for total cost and hand a ₹200 rupee note. They also posed a complete set of abstract math exercises, which 95%, 97%, and 98% were able to answer correctly without need of pen and paper. These children were also presented with hypothetical working transactions based on market-based scenarios with unfamiliar goods, prices and units and 52% of them solved these transactions without help of calculators, pen or paper.
While working children solved practical mental math problems of higher complexity with ease, lesser working children, about 32% could solve the division of a three-digit number by a one-digit number, and just 54% of children could solve two subtractions of one two-digit number from another, when presented in pen and paper school format in the Annual State of Education Report (ASER) test proforma, Ms. Duflo explained.
Researchers found in the second sub-study of 400 working children across 39 markets that like their Kolkata counterparts, they calculated the amount due and change correctly on the three successive market problems, with 96%, 99% and 97%, succeeding by their second try. However, only 15% could correctly perform division on the written ASER test.
To check if proficiency of maths in schools transfer to real-world situations, the study also tested 200 Delhi school children attending 17 public schools from same zones as markets, where they were given same written, verbal math problems, and a play-based market was created where school children sold items to enumerators. “Around 56% of school children completed division-level ASER tests, as compared to 15% working children. But they performed poorly in market-based scenarios. 63%, 51% and 69% of school children performed first, second and third transactions correctly despite using pen and paper and all the time they wanted,” the study notes.
“In a subsequent study, we raised the complexity level of real-life math problems and only 10% of school children were able to solve for these,” Ms. Duflo said.
In addition to this, a concrete word problem was presented to both school going and working children and mimicked the activity that working children perform, that if a boy who goes to the market with ₹200 and buys some quantities of two vegetables, with a question as to how much money is he left with. “36% working children answered correctly, compared to just 1% non-working school children,” Ms. Duflo added.
The study concludes that the pedagogy in place does not teach school students strategies to do math in real-world settings. It also does not take advantage of the fact that market children have developed such strategies on their own. “For instance, if you were to ask a working child too subtract 19 from 27 in an abstract way he may not be able to do it, but if you were to ask how many tomatoes remain if you take away 19 tomatoes from 27, he will perform the task quicker,” Ms. Duflo said.
The study says that these findings call for a mathematical pedagogy that addresses translational challenges through a curricula that connects abstract math symbols and concepts to intuitively meaningful contexts and problems.
“It also calls for changes in how math is introduced to children, and that pairing intuitive and abstract maths in pre-school, kindergarten and first grade in playway method through group games has durable impact,” Ms. Duflo explains.
Published - February 05, 2025 11:51 pm IST
