Literacy-based Summer Camp: Day 15
On the second day of the Mathematics workshop with Dr Jeenath, children engaged in grouping-based activities, an embodied mathematics task that involved the use of their bodies and a graph. Children also made a pinwheel and other designs with paper. A session with teachers was also organised later in the day.Dr Jeenath's Reflections: Session with students
The session began with the Nim game. Since the students were fewer in number, two groups were made with 3 in each group. The rules of the game were explained to the students. This included that each group can start with either 1 or 2 numbers, and the next group can add either 1 or 2 to the number given by the previous group. The winning number given was 10; that is, the group that reaches 10 first wins the game. A table was made on the blackboard to record the score of each of the groups (teams).
Team-1 consisted of Shweta and two young boys, and Team-2 consisted of Salim, his brother Mohammed and one more boy. We first started with Shweta’s group (team-1), with her saying the first number as 1, and as the game progressed, Team 2 called out 7, after which no matter what team-1 said, team-2 won the game. For the next round, we started with Team 2, and then the game progressed, but this time again, Team 2 managed to reach 7 and again managed to win the game. Although members in team 2 had figured out that reaching 7 would lead to winning.
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| Team 1 and Team 2 engaged in Nim Game with Jeenath |
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| Jeenath explaining the winning strategy of the Nim game to children |
I tried to make this clear to team-1 to notice the same, and in fact wrote it on the board to notice. I tried to encourage students to think of the number before this so that they could reach 7, but students were not able to predict it. One new student entered the class, and he was asked to join Team 1 as Team 1 was losing, and he was encouraged to help them win. We played one more round with the same gameplay. There was a point when team 2 said number 5, but team 1 ended up choosing 6 instead of 7, which in turn could have helped them win, and this time again, team 1 lost to team 2. To break this chain, instead of repeating the winning strategy, I changed the winning number from 10 to 15 this time. It was team 2 turn to say the first number and interestingly, we noticed that they started with 1 and team-1 added one to it to make it two, and the process of adding one continued till team 1 reached the number 6, for which team two made it 7 and the team-1 said 8, but this time team-2 said 10 instead of 9 by adding 1, and team-1 member though called 11, but Shweta asked them to pause and said 12 instead to take the winning move and this time team-2 lost. We played one more round, and the students noticed 12 is the winning move. After further encouraging them to do the reverse thinking, they finally predicted the winning moves for 15 to be 12, 9, 6, 3.
I was personally happy that, unlike yesterday, when I did this game with teachers, where teachers couldn’t reach the winning strategy, with students, we managed to achieve the winning strategy. I also asked students to predict the winning strategy for 10, and this time, they could predict that they need to subtract 3 and the winning moves will be 7, 4, 1 for 10. We concluded the game here.
For the next activity, I decided to address what Ekta told me the day before, where she said that, the students need activities that can help them build their visualisation with body and body movements. The best activity I could think of is drawing from the LOGO turtle activity. I first started by asking students to show me the right angle, for which students started saying “L” and showed the right angle through their hands and palms. So next, I drew two axes on the floor with chalk and discussed what would be 0, 90, 180, 270, 360 and 45 degrees. Next, I introduced the initial position as the origin (where the two axes cut each other), facing towards the top of the vertical axis. Then I introduced three commands forward as (fd), which means moving forward, and right-turn as (rt), which is turning towards the right and left-turn as (lt), which is turning towards the left. Since the floor already has square tiles. I asked students to imagine themselves as a point (bindu) and then move 1 unit of a square tile as fd 1 and moving 2 units as fd 2. Further rt 90 means turning towards the right by 90 degrees. Students immediately got the instruction, and when I first wrote 3 sets of instructions, fd 2, rt 90, fd 1, two students came and tried those commands.
For the next activity, I decided to address what Ekta told me the day before, where she said that, the students need activities that can help them build their visualisation with body and body movements. The best activity I could think of is drawing from the LOGO turtle activity. I first started by asking students to show me the right angle, for which students started saying “L” and showed the right angle through their hands and palms. So next, I drew two axes on the floor with chalk and discussed what would be 0, 90, 180, 270, 360 and 45 degrees. Next, I introduced the initial position as the origin (where the two axes cut each other), facing towards the top of the vertical axis. Then I introduced three commands forward as (fd), which means moving forward, and right-turn as (rt), which is turning towards the right and left-turn as (lt), which is turning towards the left. Since the floor already has square tiles. I asked students to imagine themselves as a point (bindu) and then move 1 unit of a square tile as fd 1 and moving 2 units as fd 2. Further rt 90 means turning towards the right by 90 degrees. Students immediately got the instruction, and when I first wrote 3 sets of instructions, fd 2, rt 90, fd 1, two students came and tried those commands.
Next, I asked students only to come and make the set of instructions on the board, and one girl came and wrote the instructions as fd 3 rt 90 lt 45. One student came and moved according to the commands on the floor where the axes were made, starting from the origin. Since for this set of commands, for the last two, the position doesn’t change, I added an additional command of fd 2 after the second command. Students could follow the instructions and could turn according to the angle. One more boy came and wrote the set of instructions, and the students tried moving according to that. Next, I asked the students that I was going to give them a slightly different task, where I asked them what set of instructions they had to follow to make a square. The chalk was fading every time students stepped on it. Thus, we decided to give them the graph sheet instead and asked them to draw similar axes on it and then predict the set of commands to make a square.
2 very young students couldn’t follow the task, also asked for graph paper, and we gave them graph paper and asked them to make a square and a rectangle on it. Later, they were also shown what the unit length on a graph paper is and were asked to draw 3 units and 2 units. Later, one could also show me 5 units on the graph sheet. First, Shweta and 2 very young students came with her set of commands, which was
fd 2, rt 90, fd 2, rt 9, fd 2, rt 90, fd 2
Shweta also showed it by actually walking on the floor where the axes were drawn. Later, the other boys could also write the commands for making the square. Once most could do the square, I asked them to make a triangle and find the commands for it. Again, after taking some time, Shweta showed me the commands and also through her actions, she said she did rt45 fd 3 rt90 fd 3 rt 135 fd 6. I praised her effort, but I also showed her the diagonal unit and the side unit and asked her which is bigger, for which she said the diagonal unit is bigger than the side unit. Thus, I suggested to her that for the diagonal length, maybe we can use “du” to refer to diagonal units as different from the regular units. Later, I just checked other students' work and concluded the discussion.
Since tomorrow was an exhibition and students also seemed to need a break from the activity, we moved to some craft activities of making designs through paper cuttings. We also made a pinwheel to display for the exhibition.
Engagement with Children: Observations
As an observer, I (Ekta) observed the Nim game and the joy of children in competing with each other. I was also struck by the way they broke away from their regular classroom arrangement and often sat on benches while participating or stood up on the bench to see the blackboard when Jeenath wrote something on the blackboard. The freedom of movement meant that children's participation was not just verbal but could be seen through their bodies, gaze and movement in the classroom.
The number of children in the camp has been slowly decreasing over the week. I continue to feel disappointed that so many children are missing the rich Math engagement that Jeenath created. One way to alleviate this disappointment is to teach participating children to teach other children after we are gone.
The graph-based activity involved a series of instructions that took a while. I was worried that children might get bored and not engage. However, to my surprise, they took to it instantly and began to work with their graph and the graph on the floor, with each complementing their understanding. The possibility of group work also created peer learning opportunities. In fact, seeing Shweta engage and participate enthusiastically meant that other children also came forward to each task that Jeenath provided them. As someone who really liked math but never had good math teachers, I wished to be a child again and have a teacher like Jeenath in my classroom. I wondered what kind of career I would have if that were the case?
After the Math activity, I got the children to practise their narrations for each activity we did over the weeks and the charts associated with that. Shweta decided to have a shadow puppet show. Given that the number of children each day differed, I continued to be worried about the availability of children the next day for the exhibition. Getting children to feel ownership of the exhibition is crucial, so that their participation and engagement improve. Although it was not possible this time around, this is something that I need to figure out for the next year. This becomes even more difficult with the shifting and changing number of children each year.
After the session with the children, I had a series of tasks for the next day's exhibition and preparing for our departure immediately after the exhibition. Hence, I was unavailable for the teacher's session.
Dr Jeenath's Session with Teachers
For the teachers' session, which started at 3pm, initially, there were only female teachers. After requesting the support person to call the sirs (the male teachers), two male teachers joined. None of the male teachers who were present yesterday were there in today's session. But rather than waiting for long, I thought of starting the activity as a few of the teachers (the primary grade teachers) had to leave by 3:45pm for the canvassing.
For the teachers' session, which started at 3pm, initially, there were only female teachers. After requesting the support person to call the sirs (the male teachers), two male teachers joined. None of the male teachers who were present yesterday were there in today's session. But rather than waiting for long, I thought of starting the activity as a few of the teachers (the primary grade teachers) had to leave by 3:45pm for the canvassing.
I started by distributing sheets of paper to the teachers and then gave the instructions to make Tangram pieces. All the present teachers participated and made the pieces. However, due to the intensity of the wind caused by the ceiling fan, we couldn’t properly do the part where they had to make different shapes out of the tangram pieces. In fact, during this time, 2-3 male teachers who had arrived in-between the session left. One female teacher could still make the square shape and draw the arrangement on the board. This same teacher didn’t come for the presentation yesterday, but today she came in front of the classroom. So here again, rather than spending more time on this, I moved to the next activity of measurement.
In the next activity, we assigned the cost of a small square as 10, and teachers were asked to predict the cost of the full square. Initially, the teacher said Rs 70 and 90, but with further questions and asking for reasons, one teacher could eventually calculate the cost to Rs 80. When I asked if the cost of the small square is increased to Rs 20, one teacher immediately said it will be 160. The teacher started applying proportional reasoning, and in fact, when I gave the cost of a small square as 15, she predicted the cost to be 120. Later, when we thought of doing it through the pieces, we ended up getting 135, but later corrected it to 120. Some of the teachers had to leave for the canvassing for new admissions. So, at the end, only 5-6 female teachers were left. At the end, I gave them another task to find the boundary length of the whole square if the small square is 1 square unit. Although none of the teachers left, there were math teachers; one of the teachers predicted the side of the square to be 3. But then I asked, in that case, what will be the area of the square, but they said they don’t know the formula for the area of a square. But I still continued and tried to explain, and later also shared the Pythagoras theorem result that for any right triangle to show that the side of the big square will be 2√2 and thus the perimeter will be 8√2. We concluded our session with this.
Evening reflections
Jeenath and I discussed the behaviour of male teachers. We had noticed that they were often boisterous, showcased a sense of entitlement and superiority. In fact, the refusal to engage in the session was a reflection of one such behaviour. On the other hand, the female teachers reflected much underconfidence and often kept themselves away from the male teachers. As an observer in Jeenath's session, I also noticed that Jeenath's presence and expertise in Mathematics, where she pushed them to think beyond their current knowledge or made visible gaps in their own understanding, unsettled the male teachers. While I am sure this was the case with the female teachers, too, they did not have the agency to excuse themselves from the session, unlike the male teachers. The male teachers also did not engage much with us and kept themselves away from any discussion.
The other concern was the dwindling number of children in each session, which made it difficult for us to plan for any activities of the exhibition. This is something that we need to discuss with the school and perhaps find a solution together for the next year.
We spent much of our evening preparing posters, instructions, or material for the next day's exhibition. I was also grateful for Jeenath's presence and her efforts to support this exhibition. It kept me motivated and going.
(This is a joint post by Dr Jeenath Rahman and Ekta Singla)














































