In India, numerous children employed in retail markets exhibit strong numeracy skills: They can swiftly carry out various calculations to finalize transactions. However, as a recent study indicates, these children frequently perform significantly worse on equivalent types of problems encountered in the educational environment. This occurs even though many of these students are currently attending school or have attended school until the 7th or 8th grades.
On the other hand, the research also reveals that Indian students who remain enrolled in school and lack employment perform better on traditional academic math problems, yet they often struggle with the types of calculations encountered in market scenarios.
In summary, both the “market children” and the “school children” find difficulties in the methods where the other group excels, sparking inquiries about how to assist both demographics in developing a more holistic understanding of mathematics.
“For the school children, they tend to perform poorly when transitioning from an abstract problem to a concrete problem,” states MIT economist Esther Duflo, who co-authored a new paper elucidating the study’s outcomes. “Conversely, it’s the opposite for the market children.”
Indeed, according to Abhijit Banerjee, an economist at MIT and another co-author of the paper, the children with jobs who also attend school “underperform even though they are remarkably adept at mental math.” “That, for me, was always the eye-opener, that one doesn’t directly relate to the other.”
The paper, “Children’s arithmetic skills do not transfer between applied and academic math,” is released today in Nature. The authors include Banerjee, the Ford Professor of Economics at MIT; Swati Bhattacharjee from the newspaper Ananda Bazar Patrika, in Kolkata, India; Raghabendra Chattopadhyay from the Indian Institute of Management in Kolkata; Duflo, the Abdul Latif Jameel Professor of Poverty Alleviation and Development Economics at MIT; Alejandro J. Ganimian, a professor of applied psychology and economics at New York University; Kailash Rajaha, a doctoral candidate in economics at MIT; and Elizabeth S. Spelke, a professor of psychology at Harvard University.
Duflo and Banerjee shared the Nobel Prize in Economics in 2019 and are co-founders of MIT’s Jameel Abdul Latif Poverty Action Lab (J-PAL), a global frontrunner in development economics.
Three experiments
The study primarily comprises three data-collection exercises incorporating some embedded experiments. The initial one reveals that 201 children working in markets in Kolkata possess solid math skills. For example, a researcher pretending to be a regular customer would inquire about the cost of 800 grams of potatoes sold at 20 rupees per kilogram, followed by a request for the cost of 1.4 kilograms of onions priced at 15 rupees per kilogram. They would seek the total answer — 37 rupees — before giving the market worker a 200 rupee note and reclaiming 163 rupees in change. In total, the children engaged in market work solved this kind of problem correctly between 95 and 98 percent of the time by the second attempt.
However, when the employed children were taken aside (with their parents’ consent) and given a standardized Indian national math exam, a mere 32 percent managed to accurately divide a three-digit number by a single-digit number, and only 54 percent were able to subtract one two-digit number from another two-digit number correctly two times. Clearly, the children’s capabilities were not translating into satisfactory classroom performance.
The researchers then conducted a second investigation involving 400 market-working children in Delhi, reproducing the findings: Working children exhibited a strong aptitude for market transactions, yet only around 15 percent of those who were also in school achieved average math proficiency.
In the second part of the study, researchers also reversed the inquiry: How do academically successful students perform on market math challenges? With 200 students from 17 Delhi schools who are not employed in markets, it was found that 96 percent could solve standard problems with pencil, paper, unlimited time, and one occasion to self-correct. However, when the same students were asked to tackle the problems in a simulated “market” environment, that number dropped to just 60 percent. The students had unlimited time and access to paper and pencil, suggesting that this figure may overstate their actual performance in a real market context.
Finally, in a third study involving over 200 children in Delhi, the researchers once again compared the performance of both “market” and “school” children across various math problems under different conditions. While 85 percent of the working children provided the correct answer to a market transaction question, only 10 percent of nonworking students answered a similarly challenging problem correctly when faced with time constraints and without supports like pencil and paper. In contrast, given identical division and subtraction questions, yet with the aid of pencil and paper, 59 percent of nonworking children answered correctly, compared to 45 percent of market workers.
To further assess the capabilities of market children versus school children on an equitable basis, the researchers then presented both groups with a word problem involving a boy visiting the market to buy two vegetables. Approximately one-third of the market children could solve this without any assistance, whereas less than 1 percent of the school children were able to do so.
What could account for the decline in performance of nonworking students when faced with market-related problems?
“They have learned an algorithm but don’t comprehend it,” Banerjee explains.
In contrast, the market children seem to employ specific strategies for managing retail transactions. For example, they tend to use rounding effectively. Take a problem such as 43 times 11. To approach this intuitively, you might calculate 43 times 10, and then add 43 for a final result of 473. This seems to be their method.
“The market children are adept at leveraging base 10, so they perform better on base 10 problems,” Duflo remarks. “The school children are oblivious to this. It has no relevance for them. The market children may possess additional strategies of this nature that we did not observe.” Conversely, the school children demonstrated a stronger understanding of formal written methods such as division, subtraction, and more.
Advancing academically
The findings underscore a significant point regarding student proficiency and educational advancement. While the capability of children with market jobs to generate rapid responses is commendable, it would likely be more beneficial for their long-term prospects if they also excelled academically and obtained a high school diploma or higher. Identifying a method to bridge the gap between informal and formal approaches to solving math problems could significantly benefit some Indian students.
The existence of such a divide indicates that new methods could be explored in academic settings.
Banerjee, for example, conjectures that part of the challenge lies in classroom processes that suggest there is only one valid method to arrive at an arithmetic solution. Instead, he believes, following the insights of co-author Spelke, that assisting students in reasoning towards an approximation of the correct answer can facilitate a genuine understanding of what is required to resolve such problems.
Nonetheless, Duflo adds, “We do not wish to hold teachers accountable. It’s not their fault. They are provided a rigid curriculum to adhere to, along with stringent methods to follow.”
This still leaves the question of what specific changes to implement in the classroom. Interestingly, this is a topic the research group is currently evaluating as they consider new experiments that might address this issue directly. The current findings, however, make it evident that progress would be advantageous.
“These findings emphasize the necessity of educational frameworks that bridge the divide between intuitive and formal mathematics,” the authors assert in their paper.
Support for this research was partially provided by the Abdul Latif Jameel Poverty Action Lab’s Post-Primary Education Initiative, the Foundation Blaise Pascal, and the AXA Research Fund.