A mathematics class is going on in a middle school class in the Nalanda district in Bihar.
Today we are working on how to make word problems. This is a new activity for children. They know how to answer questions but have not had any experience of formulating problems. The teacher says, "Here is a problem: I have Rs. 40 and I want to divide it equally among 8 children. How much will each child get?" Immediately the children shout, "Five". Then the teacher asks, "If I did not say that the money has to be divided equally, then what would happen?" One boy from the middle of the class says, "Then there would be a problem in the calculation!" Such conversations continue and the class moves forward.
There are three boys at the back of the class — Ravi, Rakesh and Rupesh. They are watching but not participating. Other children raise their hands and want to discuss what they are thinking. But these three boys are silent. After a lot of debate over word problems, the teacher says, "Think hard and write down your own problem. Let's see what you come up with." The class starts writing but the three boys just sit and watch. Ravi looks around the class. Rakesh fidgets. Rupesh gazes out of the open window at the fields outside.
I lean over to Ravi and ask him, "Do you know what to do? Can you understand what the teacher is asking you to do?" Ravi's brows are furrowed. He looks at me but does not reply. "Okay," I say, "how many people are there in your family?" He replies immediately, "Five". "Suppose your uncle visits you and he brings a box of 20 laddoos. Let's say that everyone in your family eats an equal number of laddoos, how many laddoos will each one eat?" Ravi doesn't say anything and looks at me seriously. I repeat the problem. From his eyes I can see that he is starting to catch what I am saying. Softly I hear him replying, "Four". Now, we try another problem. And he can answer it. This makes him smile — a shy smile.
"I asked you two questions. Now you ask me one." Smilingly, Ravi asks a question that must have been bothering him since the class started. "But why can't you keep asking me and I will answer? I can answer. Why do I have to ask you a question?" he says. "How about if you think about this as a game. We can take turns. It will be fun if both of us can play the game," I cajole him. Ravi thinks some more and then asks me a question and then another one and then another one. The first one comes out slowly and is similar to the one I had asked him. But the next two are different. One after the other, the questions flow and now they are not taking long to frame.
Rakesh has been watching and listening. He has the classic look of a naughty boy. His face is mischievous; his hair cropped very short. A few buttons are missing on his shirt. When I turn my attention to him, he says emphatically, "I don't want to write." I can see that his notebook is blank. He has tried to write a bit but it looks like a scribble. "Fine, you don't have to write. But you have to ask me a question. You have to make up your own problem. Rakesh looks relieved but hesitates in saying anything aloud. I take his notebook and write in it. "From one tree we picked 100 mangoes..." I could hear him reading what I wrote. He reads the words slowly, sounding out each word carefully. "All the mangoes had to be divided equally between two brothers. How many mangoes will each get?" Rakesh continues to read with great concentration. Then he lifts up his head and says, "Fifty, of course." "Excellent," I say and pat him on the back. He looks amused. We continue, "Okay now can you ask me a question? Think, think, think," I say.
Ravi has been listening with great interest. In this short time, he has become an expert. He puts in his question quickly. "There are 40 toffees and 10 children. Divide the toffees equally. How much would each child get?" Rakesh scratches his head and then his back, rubs his nose, looks around at others and then finally out comes a question.
Through all of this Rupesh has been silent. I cannot tell if he has been listening. It seems as if he is not interested. I try to talk to him individually, like I did with Ravi and Rakesh, but it does not work. He simply does not want to be a part of this activity. By this time the class has moved to the next step. Now there is going to be a contest. The children sitting on the benches on the left side of the class constitute group one and those on the right side make up group two. Each group has to ask a division word problem that they have made to the other group. Groups will be marked not only for correct answers but also for making good problems. Children are raring to go. Everyone loves competitions in classrooms. Questions fly back and forth. There is no issue with the answers but there are arguments about whether the question was properly formulated. Marks to each group are being added up on the blackboard. Suddenly Rupesh stands up. It is the first time this morning that we have heard him speak. In a clear voice he says, "A pen costs R6. How much will 15 pens cost?" Children shout, "This is not a problem where things have to be divided." I am very relieved. Rupesh has spoken. He is with us. The door has opened. Once the door is open, then walking in is easy.
The class is over for the day. I bid goodbye to my three special boys. I will, of course, remember them — the three Rs. But what I am also taking away with me is that if children at the back of the class — the backbenchers — can be understood, much of the challenges of teaching and learning can be solved.
(Rukmini Banerji is with Pratham and Assessment Survey Evaluation Research (Aser) Centre)
The views expressed by the author are personal