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Intuitively solving a problem like multiplying 43 by 11, they might first multiply 43 by 10, and then add 43, reaching the final answer of 473.
Being good at math on the go, as seen in Indian kids working in markets, does not often translate into classroom arithmetic, and vice versa, a study has shown, revealing how the curriculum can help bridge the gap between intuitive and formal styles.
Overall, both the groups -- market kids and school kids -- were found to struggle with the approach the other was fluent in, raising questions about how to help both groups learn math more comprehensively, the study, published in the journal Nature said.
Kids in retail markets are seen flexing their 'mental math;' skills while handling transactions.
However, some of these kids, who also attend school, 'underperform despite being extraordinarily good at mental math,' said co-author Abhijit Banerjee, an economist at the Massachusetts Institute of Technology, and one of the recipients of the Nobel Prize in Economics in 2019.
'That, for me, was always the revelation -- that one doesn't translate into the other,' Banerjee said.
The study also found that, conversely, school students who do not work in jobs perform better on academic math but often fare poorly with marketplace arithmetic.
'For the school kids, they do worse when you go from an abstract problem to a concrete one,' said co-author Esther Duflo, an MIT economist who shared the 2019 Nobel Prize with Banerjee.
Through experiments with 'school kids' and 'market kids' in Kolkata and Delhi, the researchers observed differences in their mathematical abilities.
For example, market kids appeared to be good at 'rounding' -- increasing or decreasing a value to reach the nearest whole number.
Intuitively solving a problem like multiplying 43 by 11, they might first multiply 43 by 10, and then add 43, reaching the final answer of 473.
This is what the researchers believe market kids are doing.
'The market kids are able to exploit base 10, so they do better on base 10 problems. The school kids have no idea. It makes no difference to them. The market kids may have additional tricks of this sort that we did not see,' Duflo said.
However, only a third of the 201 market kids in Kolkata could correctly divide a three-digit number by a one-digit number, while just over half could correctly subtract a two-digit number from another two-digit number twice.
'They were unable to solve arithmetic problems of equal or lesser complexity when presented in the abstract format typically used in school,' the authors wrote.
On the other hand, school kids were found to have a better grasp of formal written methods, including division and subtraction.
Sixty per cent of 200 students from Delhi (who did not work in markets) could solve such problems in a 'make-believe 'market' setting.'
Further, when the two groups of children were presented with a word problem depicting a real-world marketplace, 36 per cent of the market kids correctly answered the question, compared with just one per cent of the school kids.
'They learned an algorithm but didn't understand it,' Banerjee said about the school kids.
The question was: 'It is a story of a boy, Vishal, who goes to the market with 200 rupees and buys different quantities of two vegetables.
'The question is how much money Vishal has left,' the authors described.
The findings reveal a divide between the maths that finds its use in the real-world and the formal mathematical methods that one learns in higher secondary education (9th to 12th class), which would be 'better for the long-term futures' of the market kids, the authors said.
Feature Presentation: Ashish Narsale/Rediff.com