Researchers studying the mathematical skills of working children (under 16 years of age) in India recently went around markets in Kolkata buying vegetables, fruits, stationery and other goods from 201 children and teenagers employed there, assessing the skills of each.
Some 90% of the children got the calculations for the transactions right in their first attempt and on their own. And nearly all of them got the answers right after being given a chance to correct mistakes, without the help of pen or paper. But when 117 of them participated in a written test, their performance dipped dramatically. They struggled with the addition, subtraction, multiplication and division that they had used effortlessly in the market transactions, or “street mathematics”, when these were presented as “school arithmetic” – abstract numbers without any context and with only a set of rules or algorithms to solve them. Here, their performance matched the findings of large-scale learning assessments such as the Annual Status of Education Report. The annual survey has consistently reported low achievement in mathematics.
“Consistent with prior studies, we found that most children in our sample were unable to solve arithmetic problems as typically presented in school,” the researchers said in their working paper, titled The Untapped Math Skills of Working Children in India: Evidence, Possible Explanations and Implications. About a third (32.2%) of the children could divide and 21.4% could subtract. Of the 201 children, 70% were enrolled in school, 98% had had some schooling and 53% had completed primary school.
The paper is authored by Abhijit V Banerjee of the Massachusetts Institute of Technology, journalist Swati Bhattacharjee, Raghabendra Chattopadhyay of the Indian Institute of Management, Calcutta, and Alejandro J Ganimian of New York University. The institutions are affiliated to the Abdul Latif Jameel Poverty Action Lab, a research centre based in the Massachusetts Institute of Technology.
On August 31, Ganimian tweeted a summary of the findings of the survey:
The gap between the mathematical skills children possess and what they demonstrate in an exam raises questions about the effectiveness of current teaching methods and utility of tests as a measure of learning.
This not the first time the gap has been studied in India. Educationist Anitha Rampal said it was noticed during the government’s Literacy Campaign – which was launched in the late 1980s and was aimed at educating 80 million adults in the 15-35 age group. The National Curriculum Framework of 2005, which provides a framework for syllabi, textbooks and school teaching practices, also recognised it. And in 2007, the National Council of Educational Research and Training re-designed mathematics textbooks with it in mind.
But that effort has been undermined by factors such as large classes and the absence of training for teachers to be more effective educators. The government also continues to stress on large-scale testing despite doubts about its efficacy in assessing learning. It has recommended educational reforms that involve frequent tests for schools in Uttar Pradesh while Delhi adopted such a system in 2016.
Street maths is easier
According to Rampal, children showed greater mathematics skills in the market because they could “match a concrete context with the abstract notion of a number” – the numbers represented quantities of goods or the value of currency. But in classrooms, a number is just that and children are confounded by rules of calculation that hold no meaning for them.
Anil Teotia, a resource person for mathematics in the Delhi State Council of Educational Research and Training, said that over time, this inability to relate to numbers leads to a fear of mathematics and the notion that it is only for the gifted.
The working paper suggests turning all mathematical exercises in schools into “market transactions”. Education researcher Chanchal Yadav did exactly that in 2015, as part of her research in a Delhi government school. She had a group of Class 8 students of mixed abilities study the implementation of the mid-day meal programme – a government initiative that provides free lunches to schoolchildren. “Even just tabulating data on students and quantities and representing it graphically enhanced mathematical skills,” she said. The group later computed sex ratios (the number of girls per 1,000 boys) and also explored the gender wage gap.
Similarly, in an East Delhi school, Rajinder Goel used voting figures from municipal elections to teach mathematics.
Yadav explained: “Data needs context. A child must understand what a mean [average] means when it is not just some formula.”
Yet, a large number of children struggle to relate to mathematics early on, become more alienated as they grow older, perform poorly in tests and, as government school teacher Jyoti Sethi said, drop it altogether after Class 10.
Teaching methods are partly to blame for this. Teachers are reluctant to abandon traditional ways of teaching in which there is one approach and solution to a problem.
Yadav explained how children approach classroom mathematics and street mathematics and why they find the second easier:
“To add 25 with 58 in class, you first add 8 and 5. From 13, you write 3 and carry over one and so on. The child must memorise this procedure. But placed in a context a child can relate to – such as prices of two notebooks – they naturally think of different ways to solve a genuine problem. They may add 20 with 50 and five and eight separately and then put 70 and 13 together to get 83. My Class 2 students count in currency denominations.”
But, Rampal pointed out that “teachers think this is not mathematics”. She said, “They do not get that the algorithm must be closer to the [child’s] own sense of meaning.”
According to the educationists, children must develop a sense for numbers and what they represent before they make the leap to working with complex algorithms. But that is not how mathematics is taught in schools and the result is rote learning.
“Children do not know the difference between three and third,” explained Teotia. “They will count till 100 but may not know where to find 41.”
‘Maths is for the gifted’
Generations of teachers warning children to work hard in order to excel in mathematics has not helped. “There is a very strong public belief about mathematics,” said Sethi. “The poor abandon it because they cannot afford the private tuition they assume is necessary.”
In many schools, adverse pupil-teacher ratios make it difficult to take innovative approaches to teaching. Said Yadav, “Teachers must have time but most are weighed down by clerical duties.”
In Delhi, Teotia and mathematics mentor teachers – who are advisors to regular teachers – are trying to change the way the subject is taught by adding context.
Goel, who is a mentor, said, “We have designed model test papers for Classes 6 to 8 that are all word problems drawn from situations familiar to children.”
Tests tell you nothing
However, frequent, large-scale testing discourages innovation and change. A Delhi government school teacher said that till last year, she had the freedom to be creative about how she taught her students – within the resource constraints of public schooling. “Now we are forced to use traditional methods otherwise they will do badly in tests and further policies are based on them,” said the teacher, who did not wish to be identified.
In 2016, the Delhi government introduced its education reform policy, which involved frequent centralised tests and centrally-planned interventions based on them. The Central government also stresses on fixed “learning outcomes”, or class and subject-wise minimum learning benchmarks.
But according to Yadav, “Large-scale assessments can only tell [you] how the system is doing overall.” She said that to know how each child is performing, classroom assessment works best.
Added Rampal, “It helps you understand the challenges children face.”
Pointing to the inadequacies of tests, the Delhi school teacher explained, “Some standard tests assume children who know single digits are at a lower level than those who know double digit numbers. But children do not progress in a linear fashion. A child may recognise 100 or 50 because of bank notes and not the number 9. Children who follow cricket learn to quantify and count to 100 long before the textbook gets to three digits.”