Scientists from India and the US have found that the arithmetic skills of Indian schoolchildren do not transfer between applied and academic mathematics. Schoolchildren who work in the marketplace were poor at solving abstract school arithmetic problems, but were good at solving applied problems of similar complexity. And schoolchildren who did not work were good at solving abstract problems, but could not solve applied problems. The study was published in Nature.
School math lessons are designed to help children acquire skills that are useful both in everyday life and for future mastery of higher mathematics. However, people are not always able to apply the knowledge they learn in school in everyday life. For example, early research has shown that a large number of Americans do not have the mathematical skills needed for everyday calculations. Perhaps this situation could be improved by studying mathematics in real-world contexts. According to some studies, this helps develop more generalizable and flexible arithmetic skills — and even makes it easier to learn 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 the markets of Kolkata and Delhi, and about 500 non-working children studying in nearby schools. Most of the working children also went to school: they spent part of the day there and part at the market. These children were asked to calculate the weight of a customer who asked for, say, 1.4 kilograms of onions and 0.8 kilograms of potatoes. For the non-working schoolchildren, the tasks were the same, only for them the scientists created a game market.
Most of the children selling in the Calcutta market were good at calculating prices without using paper and pen or a calculator. More than 80 percent of the children did it on the first try, and by the second attempt, the proportion had risen to 97 percent. Just over half of the children were able to calculate the price of an unfamiliar product with an unfamiliar price, again without using a calculator or pen and paper. However, the children were less successful at simple abstract division and subtraction tasks. Only 32 percent of the Calcutta children and 15 percent of the Delhi children 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 school rules, but only a small proportion of them left school before the end of grade 4, where division is taught.
When researchers presented working children in Delhi with hypothetical market problems similar to those they solve every day, about 90 percent of the children solved them. But not everyone could 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 rather than per kilogram), only 61 percent of the children solved the task. In addition, 41 percent of the children used pen and paper to solve problems of this complexity.
In contrast, the unemployed students from Delhi were better at solving abstract problems: 56 percent of the children solved the written part. Also, more than 90 percent of the unemployed children solved the hypothetical market problems presented in writing in two attempts. But they did not do so well in the play market: only 60 percent of them were able to correctly calculate the buyers, even though they had the opportunity to use pen and paper. Interestingly, the unemployed students did rely significantly more often on written calculations, and sometimes these calculations were redundant. For example, they often added the same numbers together instead of multiplying them, and often repeated the same operation.
The experiment showed that the mathematical skills acquired by children at school and in the market do not translate well into each other. Those who have learned to solve abstract problems cannot always apply their knowledge in everyday life, and working children are not accustomed to the abstract nature of school problems. The authors concluded that in Indian schools, children are not taught to form connections between intuitive and formal understanding of mathematics, and this requires the development of new curricula. It is worth noting that similar studies in other countries may give different results due to differences in the school curriculum.
Previously, scientists found that children who are taught to count before school perform better in both mathematics and language.
