(‘A Math Problem’ is an investigative series on the unprecedented education crisis caused by the pandemic-induced school closures. The Indian Express sat in through five weeks of mathematics lessons in a Delhi government school to track how a class recovers its Covid learning losses. You can read all four parts here.)
“Close your eyes and think… is there any time of your day that mathematics is not around you?” The children shift in their seats, their impatient eyes dart behind their shut eyelids as they attempt to conjure up math images.
Thus begin two months of an unprecedented assignment for Neha Sharma, class teacher of 5A of the Delhi government’s Veer Savarkar Sarvodaya Kanya Vidyalaya, and her class of 38 who are back in school after two years of the pandemic.
While the CBSE Class 5 curriculum prescribes word problems with addition, subtraction, multiplication and division, angles and degrees, perimeter and area, fractions, factors and multiples with LCM and HCF, measuring volume of cuboids, and expressing tenths and hundredths in decimal points, after two years of disrupted learning, Neha’s class is hardly equipped to tackle any of these. In mid-March Sharma had assessed the children and the results were dispiriting: many struggle with foundational mathematics that are taught in Class 3 or earlier: two-digit subtraction, division with remainder, even identifying numbers from 1-99.
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As schools reopened, to full capacity, on April 1, the Delhi government’s Education Department decided that until mid-June, classes 3 to 9 would focus on the basics of reading, writing and maths through the tools provided by the government’s Mission Buniyaad, a foundational learning programme which, in normal circumstances, is only for children identified as being behind their grade level.
The Indian Express tracked Class 5A as its teacher Neha Sharma navigated them through five weeks of their bridge classes.
Work plan: Neha hopes to take the class through a rigorous round of counting practice, before moving on to two-digit addition.
A little game to get things started: Neha asks the children to speak out odd numbers. It kicks off with Kashif saying “1”, moves on to Apurva who calls out “3”, before Gunjan stumbles by saying “6”. Several others struggle: Pranjal calls out “10” after “7”. Once they reach 51, Neha gets them to do the same activity in reverse.
Neha notices a few students lagging behind, and quickly intervenes. Harish is made to sit between best friends and “active students” Arshna and Janani. She also gets the class to clap for Siddharth’s little triumphs.
In a prior assessment, Harish had failed to do two-digit subtraction and identify single digits — he was a ‘beginner’. Siddharth had, with a little coaxing, identified two-digit numbers, but failed to do division or subtraction — he was behind a lot of children in class. Neha has put him in ‘10-99’ category.
Wednesday is fun day: Neha divides the class into groups and asks them to name an everyday item that is a circle. The answers flow in thick and fast — “coin… laddoo… roti… Earth… Sun…” Rectangles? “School van… TV… desk… window… lunchbox…” Square? That makes them think a little harder: “Whiteboard… cardboard box!”. Triangles? “Samosa, pizza slice, pastry, sandwich, triangle paratha…” “Wow, you all are so smart! I could only think of samosa and pizza,” she tells them.
Later, Neha says, “Siddharth needs a lot of support, but I do think he will get by with love and care. It’s Harish that I worry about. There’s no point trying to get him to do addition if he can’t even recognise numbers. I will need some time with him after school. I’m afraid he might end up dropping out if he doesn’t get what’s happening in class.”
Assessment 1: April 4
*Total students 38
Can do simple division 27
Cannot do simple division, can do 2-digit subtraction 1
Cannot do subtraction, can count and identify numbers 10-99 3
Cannot identify single digit numbers, beginner 1
* Not everyone is present for the assessments
l There has been considerable progress from the mid-March assessment. Everyone in the class, with the exception of Harish, can identify numbers and tackle different counting activities. Vismaya, who could not do subtraction before school started, solved the subtraction and division sums Neha gave.
Work plan: Introduce multiplication tables, and brush up on subtraction
On Monday, Neha asks Rohan to recite the tables of 3 which he manages to with some difficulty. Next is Kashif, a student who had given up on his subtraction sums in the last assessment. He painstakingly makes his way through the tables of 4. Neha makes the class clap for him before telling the class, “All of you must practise the tables every day.”
Neha now wants to get the children to do some subtraction and work on their speed. She is fairly confident: in last week’s assessment, 28 out of 32 students were able to do two-digit subtraction. She writes down 10 subtraction sums, all of them involving borrowing, and asks them to solve these. But to her dismay, five minutes in, most of the students are still copying down the sums. “You are no longer little children, you need to be faster,” she coaxes them.
Twenty minutes later, Neha solves the sums on the board and asks the children to check if they have done them correctly. Sonam, whom Neha counts among her “bright” students, has got all sums wrong. This flusters her, “There is a huge difference between what I saw today and the impression I had from previous assessment, when I gave them just two sums at a time,” she said.
Her dismay deepens when she corrects their homework the next morning — most children have got their subtraction sums wrong.
“Every day I plan to move one step ahead but when I see your notebooks, I feel like I can’t do that. Bachchon, mai aage kaise badhoon?” she says, before spending the next 15 minutes revisiting the basics.
At the end of the class, Neha asks a few students to come up to the blackboard and solve a sum each. All of them get it right, except Siddharth.
The reversals of the last two days have left Neha disappointed.
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“When I went home yesterday, after getting my children to revise their tables, I thought they were doing fine. I hoped to move forward with word problems involving multiplication. But now that I have checked their homework, I think they will need more time. If they are stuck here, what will they do with other concepts?”
She has another problem: Extra time with Harish may not be possible. “I had called his parents about his low attendance and they said he is unwell. There is nothing I can really say to that,” she says.
ASSESSMENT 2: April 16
Can do division: Simple division, 23; division with remainder 8
Cannot do simple division, can do 2-digit subtraction 2
Cannot do subtraction, can count and identify numbers 10-99 4
Cannot identify single-digit numbers, beginner 1
l A few more have picked up division, but grasp of many on basic operations like subtraction is precarious. Harish still can’t identify single-digits.
Work plan: Get the class to be thorough with their tables
On Monday, the entire class recites the tables of 2 in a loud, sing-song chorus. By the time they get to the tables of 6, some of the voices drown out. “Start the tables of 6 again,” says Neha. This time they get it right, but by the time they get to the tables of 7, they fall out of step with one another.
Over the next few days, she tries different ways to get them to remember their tables: asking them to send videos of them practising at home, getting them to recite in class with their eyes closed, and so on.
On Wednesday, she gets students to test each other with multiplication sums, and applauds those who get it right. Some falter under pressure.
On Thursday, Neha gives them multiplication and subtraction sums, and is delighted that the entire class has got them right — Harish is absent.
With this confidence boost, she introduces division with remainders and subtraction with 3-digit sums. “When I was on my way home yesterday, it struck me that I had not yet taught them how to subtract with zeroes and that they might get stuck. These thoughts usually strike me when I am in the bed or in the Metro,” she laughs.
So on Wednesday, most of the subtraction sums involve numbers with a ‘0’.
At the end of the class, Neha is happy that about 80 per cent of her class are “average”. “Other classes have a lot of children lagging behind. In my class, there are two to three children to whom I have to pay extra attention. I think Siddharth is doing well with the push he is getting, but I have to pay more attention to Vismaya and Harish,” she says.
Assessment 3: April 23
Can do division: Simple division 11, with remainder 21
Cannot do simple division, can do 2-digit subtraction 3
Cannot identify 2-digit numbers, can count and identify numbers 1-9 1
Cannot identify single-digit numbers 0
🔴 After a rigorous session, more children can now do division with remainders. A big step forward.
WEEK 4 and 5
After the increased intensity of the last week, school timings have been curtailed to accommodate the Class 10 and 12 Board exams. So the junior classes begin at 7 am and the children line up to go home at 8.45 am. On most days, Neha has barely 20 minutes for her math class, so the days are spent revisiting what they have learnt so far.
Neha realises that most of her students keep getting stuck on division sums with remainder. So she sets aside Wednesday, Week 5, to tackle this problem.
Neha writes down 29/9 and asks Siddharth to recite the table of 9. He does it haltingly but makes it to 9×4. Neha tells him to stop there and says, “Look, it’s bigger than 29…” Siddharth picks up the cue and manages to crack the sum.
The next day she gives them a test with division sums. Some continue to make mistakes: writing 0 as remainder regardless of the rest of the operation. And then there are those who are still tripping on their tables.
“There are children in my class who know their tables but are not practising. That makes me very sad,” says Neha.
She gets all those who got their division sums wrong to line up and recite the tables. They line up, backs to the blackboard and mumble along. But Vismaya, who is part of the group, stands listlessly looking out of the window. Neha asks her to recite the table of 6. She looks down, shuffles her feet for a while before looking up and saying, “I only know it in Hindi.”
“You must not worry about that. Whether it is English, Hindi or Bengali, what matters to me is that you know it.”
Vismaya takes a breath and recites the tables of 6 — perfectly, in Hindi.
Chhaih ika chhaih; Chhaih duni baara
Chhaih tia athaara…
Neha smiles, Vismaya gets applause.
ASSESSMENT 4, May 7
Can do division: simple division, 10 with remainder 18
Cannot do simple division, can do 2-digit subtraction 2
Cannot identify single digit numbers, beginner 1
🔴 A lot of children didn’t turn up for this round of assessment. With some who did their division-with-remainder sums in the last assessment failing to do so this time, Neha also had to take the difficult decision of moving them back to the simple division level. Siddharth, who had been getting special attention from Neha, has made a lot of progress — from not being able to do subtraction sums to solving two simple division sums. Harish, however, remains a challenge. He still can’t identify single-digit numbers.
(Names changed to protect identities of children)
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