Scientists from India and the United States found that the arithmetic skills of Indian schoolchildren do not transfer between applied and academic mathematics. Students employed in the marketplace performed poorly on abstract arithmetic problems, but were able to solve applied problems of similar complexity. Meanwhile, students who were unemployed performed well on abstract problems but were unable to solve applied problems. The study was published in Nature.
School mathematics lessons are designed to help children acquire skills useful both in everyday life and for future mastery of higher mathematics. However, people are not always able to apply the knowledge they acquire in school in everyday life. For example, early studies have shown that a large number of Americans lack the mathematical skills necessary for everyday calculations. Perhaps teaching mathematics in real-world contexts could improve this situation. According to some studies, this promotes the development of more generalizable and flexible arithmetic skills—and even facilitates the learning of abstract mathematics.
To test this, Abhijit Banerjee of the Massachusetts Institute of Technology and his colleagues from India and the United States tested nearly 1,500 schoolchildren working in markets in Kolkata and Delhi, and about 500 non-working children studying in nearby schools. Most of the working children also attended school, spending part of the day there and the other part at the market. These children were asked to calculate the weight of a customer who asked for, for example, 1.4 kilograms of onions and 0.8 kilograms of potatoes. The tasks were the same for the non-working schoolchildren, but the scientists created a playful market for them.
Most children selling goods at a Kolkata market were good at calculating prices without using paper, pen, or a calculator. Over 80 percent of children succeeded on the first try, and by the second, this percentage had risen to 97 percent. Just over half of the children were able to calculate the price of an unfamiliar item with an unfamiliar price—again, without using a calculator, pen, or paper. However, the children were less successful with simple abstract division and subtraction tasks. Only 32 percent of children from Kolkata and 15 percent of children from Delhi were able to divide a three-digit number by a one-digit number, and half were able to subtract one two-digit number from another. This could be explained by the fact that some of these children had dropped out of school and forgotten the rules, but only a small number of them left school before the end of fourth grade, which is where division is taught.
When scientists presented working children in Delhi with hypothetical market problems similar to those they solve every day, about 90 percent of the children solved them. However, not everyone was able to solve more complex problems. When the problems were supplemented with new products at new prices and an unfamiliar pricing scheme (for example, price per unit instead of per kilogram), only 61 percent of the children solved the task. Furthermore, 41 percent of the children used pen and paper to solve these complex problems.
In contrast, unemployed schoolchildren from Delhi were better at solving abstract problems: 56 percent of children solved the written portion. More than 90 percent of unemployed children also solved hypothetical market problems presented in writing within two attempts. However, they fared less well in the simulated market: only 60 percent were able to correctly calculate the number of buyers, even with pen and paper. Interestingly, unemployed students did rely significantly more on written calculations, and sometimes these calculations were unnecessary. For example, they often added identical numbers together instead of multiplying them, and often repeated the same operation.
The experiment showed that the mathematical skills acquired by children in school and in the marketplace transfer poorly. Those who have learned to solve abstract problems are not always able to apply their knowledge in everyday life, while working children are unaccustomed to the abstract nature of school problems. The authors concluded that Indian schools fail to teach children to form connections between intuitive and formal understanding of mathematics, requiring the development of new curricula. It is worth noting that similar studies in other countries may yield different results due to differences in school curricula.
Previously, scientists found that children who are taught to count before school perform better in both mathematics and language.
