We have been featuring pieces on how our education system as it exists today is failing us with several graduates unemployable in the industry. A new study throws some light on this focused on very basic math skills. What we learn in the classroom and what the real world teaches us seem distinctly apart.
This MIT paper by Nobel laureates Abhijit Banerjee and Esther Duflo, among others, titled ‘Children’s arithmetic skills do not transfer between applied and academic math’ involved three different studies comparing math skills of the not-so-fortunate kids who are forced to work in the markets to that of their privileged counterparts in school:
“The first one shows that 201 kids working in markets in Kolkata do have good math skills. For instance, a researcher, posing as an ordinary shopper, would ask for the cost of 800 grams of potatoes sold at 20 rupees per kilogram, then ask for the cost of 1.4 kilograms of onions sold at 15 rupees per kilo. They would request the combined answer — 37 rupees — then hand the market worker a 200 rupee note and collect 163 rupees back. All told, the kids working in markets correctly solved this kind of problem from 95 to 98 percent of the time by the second try.
However, when the working children were pulled aside (with their parents’ permission) and given a standardized Indian national math test, just 32 percent could correctly divide a three-digit number by a one-digit number, and just 54 percent could correctly subtract a two-digit number from another two-digit number two times. Clearly, the kids’ skills were not yielding classroom results.
The researchers then conducted a second study with 400 kids working in markets in Delhi, which replicated the results: Working kids had a strong ability to handle market transactions, but only about 15 percent of the ones also in school were at average proficiency in math.
In the second study, the researchers also asked the reverse question: How do students doing well in school fare at market math problems? Here, with 200 students from 17 Delhi schools who do not work in markets, they found that 96 percent of the students could solve typical problems with a pencil, paper, unlimited time, and one opportunity to self-correct. But when the students had to solve the problems in a make-believe “market” setting, that figure dropped to just 60 percent. The students had unlimited time and access to paper and pencil, so that figure may actually overestimate how they would fare in a market.”
A third study showed similar patterns.
“Why might the performance of the nonworking students decline when given a problem in market conditions?
“They learned an algorithm but didn’t understand it,” Banerjee says.
Meanwhile, the market kids seemed to use certain tactics to handle retail transactions. For one thing, they appear to use rounding well. Take a problem like 43 times 11. To handle that intuitively, you might multiply 43 times 10, and then add 43, for the final answer of 473. This appears to be what they are doing.
“The market kids are able to exploit base 10, so they do better on base 10 problems,” Duflo says. “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.” On the other hand, the school kids had a better grasp of formal written methods of division, subtraction, and more.”
What can be done to fix this?
“Banerjee, for one, suspects that part of the issue is a classroom process making it seem as if there is only one true route to funding an arithmetic answer. Instead, he believes, following the work of co-author Spelke, that helping students reason their way to an approximation of the right answer can help them truly get a handle on what is needed to solve these types of problems.”
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