Literacy-based Summer Camp: Day 14
As an observer in the class, I was intrigued by the depth of interaction between her and the children. Asking children to think about their responses meant that even if they copied others’ responses, they had to explain their answers. This made them pause and reflect. In addition, through Tangram she got them to think about different kinds of shapes, angles, proportionality and make fun objects from it.
This is a combined post which included Dr. Jeenath and my reflections of the day.
Jeenath’s Reflections
As students were still entering the class, as a warm-up activity, I began by asking them some multiplication facts to check if they could multiply single-digit numbers like 7 and 8. A student responded immediately, 56. I realised maybe I should move to a double-digit number, and this time I specified which students should be responding. However, I noticed the student who was asked to respond was struggling to do the multiplication and almost gave up, when another student gave the correct answer. When I asked him to come to the blackboard and show his method, he was actually doing the column method mentally, e.g., if the number was 24✕7, the student computed the unit digit to be 8 as 4✕7 is 28 and further did 7✕2 and added the 2 to it, so got 168 in the process. It was basically following the procedural algorithm. I was expecting there could be some alternative method. So, I tried some other number this time, like 37✕4 and asked students to just raise their hands and not give away the answer. This time I asked a new student to respond, and he said 148. When I asked him to explain his process on the board, he said he broke 37 into 30 and 7 and then 30✕4, which is 120 and 7✕4 is 28, so the total came out to be 148. I really appreciated his method and said this is a very efficient method of grouping and regrouping numbers to do it easily. Next, I asked what 34✕5 would be, and although students could give the correct answer using the previous method, I also suggested there’s one more efficient method. If you half the number and multiply it by 10, because 5 is half of 10. I showed the entire operation on board and later also tried 2-3 more such multiplication facts, but students seemed not very confident with this method. So I left it, saying maybe this method will be clear with more exercise.
Jeenath’s Reflections
As students were still entering the class, as a warm-up activity, I began by asking them some multiplication facts to check if they could multiply single-digit numbers like 7 and 8. A student responded immediately, 56. I realised maybe I should move to a double-digit number, and this time I specified which students should be responding. However, I noticed the student who was asked to respond was struggling to do the multiplication and almost gave up, when another student gave the correct answer. When I asked him to come to the blackboard and show his method, he was actually doing the column method mentally, e.g., if the number was 24✕7, the student computed the unit digit to be 8 as 4✕7 is 28 and further did 7✕2 and added the 2 to it, so got 168 in the process. It was basically following the procedural algorithm. I was expecting there could be some alternative method. So, I tried some other number this time, like 37✕4 and asked students to just raise their hands and not give away the answer. This time I asked a new student to respond, and he said 148. When I asked him to explain his process on the board, he said he broke 37 into 30 and 7 and then 30✕4, which is 120 and 7✕4 is 28, so the total came out to be 148. I really appreciated his method and said this is a very efficient method of grouping and regrouping numbers to do it easily. Next, I asked what 34✕5 would be, and although students could give the correct answer using the previous method, I also suggested there’s one more efficient method. If you half the number and multiply it by 10, because 5 is half of 10. I showed the entire operation on board and later also tried 2-3 more such multiplication facts, but students seemed not very confident with this method. So I left it, saying maybe this method will be clear with more exercise.
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| Grouping and regrouping numbers |
Now that all the students had come to the class, I thought of doing the Tangram activity with the students. We first started by distributing the sheets to each student and made them sit in pairs so that students could support each other. Students were instructed to make Tangram pieces, and while making each piece, there was a discussion about different geometrical shapes. After students made all seven Tangram pieces, students were asked to rearrange them to get a square, a rectangle and a triangle. While they were able to get a square, they took a long time to get the rectangle and couldn’t figure out the arrangement for the triangle, but once they were shown the triangle arrangement, they were really amused and excited. Once this part was done we moved to measurements where students suggested the cost of the small square piece as a cake piece to be Rs.10 and then predicted the cost of the big square made out of the seven pieces to Rs. 70, 80, 100, but finally they calculated it to be Rs. 80. They tried with some more variations for the cost of the small square as Rs 30, Rs 150 and could compute the total cost to be Rs. 240 and Rs. 1200 respectively. We also tried this with potatoes costing Rs 20/Kg and buying 5 Kg, 10Kg etc for students to identify the multiplicative relation between units and the quantity. The session concouded.
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| Sahil is helping other children with Tangram activity |
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| Dr. Jeenath is helping children cut pieces of paper |
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| A rectangle from the tangram pieces of paper |
Engagement with Children: Other Observations
Throughout the activities, however, one interpersonal issue that continued to emerge was Sahil’s inability to restrain his responses, disrupt the process with his constant comments, overconfidence and lack of support for his peers. Mathematics is one of his favourite subjects, which he takes pride in. However, when he was asked to explain his mathematical thinking for his response, he often responded with complicated operations, which did not show any mathematical thought but rather memorisation of algebraic formulae. When Jeenath asked other students for responses on a similar task, who often had simpler strategies, and appreciated them, he often got uncomfortable, acted out and demanded that his method or response be recognised and accepted. I often spoke up and asked him to stop disturbing the class. At some point, he made fun of Dr Jeenath's pronunciation of a word, and I lost my cool. I asked him to behave and concentrate on learning from her rather than mocking her. Jeenath was a lot more patient with him
We continued to face disruption from him throughout the session. Repeated reminders, requests and stern enforcement of rules fell on deaf ears. In the end, I had to ask him to leave the classroom and take a walk, cool himself and then come back. It always makes me uncomfortable when I do that to him. However, sometimes he leaves no choice.
Dr Jeenath continued to engage him after the class and discussed other queries. She continued to question and challenge his mathematical knowledge. As a child, he found it difficult to acknowledge his own limitations. Nevertheless, one hopes that the interaction makes him, as well as us, question his behaviour and find alternative ways to deal with the situation without putting a stop to learning.
Given that children were used to playing various physical games during the camp, they continued to ask for them throughout the session. The math-based engagement in itself did not seem like a game enough for them. This makes me wonder if, if children were engaged in similar educational activities, their perceptions might change. Also, I continued to think about all the games children played by themselves, which were social in nature, required physical interaction and relationships. The ones that we engaged them in were cognitively demanding and required intellectual competition.
Overall, given that Dr Jeenath involved all children in the classroom to speak and participate, it was amazing to see how everyone was able to contribute and share their mathematical thoughts. For me, it displayed how each one of us is capable of some form of mathematical operations, since we all use it in our day-to-day life.
Afternoon Session with Teachers
The session with teachers began around 2 pm. Teachers had been canvassing through the community for admissions on one of the hottest days, which left them tired. Nevertheless, teachers of all subjects and grades sat in the classroom, listening and occasionally participating.
Afternoon Session with Teachers
The session with teachers began around 2 pm. Teachers had been canvassing through the community for admissions on one of the hottest days, which left them tired. Nevertheless, teachers of all subjects and grades sat in the classroom, listening and occasionally participating.
Jeenath's Reflections
The presence of the majority of teachers at the beginning of the session, 21, gave a positive impression as a facilitator. I begin with the Nim game, dividing all the teachers into two groups. As the teachers were sitting in two rows in pairs in the classroom. For convenience, we decided to make the groups based on how they were sitting, so each row represented one group. The left row mainly had all the female teachers, and the right row had all the male teachers, but two to three female teachers were sitting at the back of the right row. After making the two groups, I explained the game.
Each group can select 1 or 2 as a number, and they have to keep adding either 1 or 2 to the number that the other group suggested, and the one who reaches 10 first wins the game. In the first round, we played the game. The first number was suggested by the left row of teachers as 2, the second group on the right added 1 to it to get 3, then the one on the left added 2 to it to get 5. Then the group on the right added 2 after some thoughts to get 7, and then the group on the left realised they would lose the game whether they add 1 or 2 to 7, so they added 1 and then the next group won. I highlighted that reaching 7 is the winning trick here, but I also wanted them to think about whether the game is dependent on who starts the game first. So this time I asked the right group to suggest the first number, and this time again the right group managed to reach 7, and the left group again lost the game. There was visible excitement after winning or losing the game between the teachers. I was trying to get their attention to the winning strategy and to think of what numbers give an advantage in this game. I asked them to think about reaching 7, what should be the previous number, they said 5 or 6, then asked them to think what number would lead to 5 or 6, for which, after some thinking, they said 4. I also pushed them to think of the numbers before 4 to win, and whether it has advantages or disadvantages for the player who starts the game.
The teachers were not responding, nor were they discussing this among themselves. So I asked if the first player says 1, what should the next player be saying? For this, again, there was no response, so I told them they can either make it 2 or 3 and not 4, so the second player may lose in this case. If the first player says 2, then the second player can win by making it 4. I was also writing them on the board, but I saw
less engagement while discussing this. Secondly, I said we can make different variations of this game, we can decide the final number to be 15 instead of 10 and play the game one more time. Interestingly, this time, once the right group reached 10, a teacher from the left group first said 11 by adding 1, but then another teacher said no, we should make it 12 by adding 2 and got visibly excited as they already predicted that they would win the game this time.
less engagement while discussing this. Secondly, I said we can make different variations of this game, we can decide the final number to be 15 instead of 10 and play the game one more time. Interestingly, this time, once the right group reached 10, a teacher from the left group first said 11 by adding 1, but then another teacher said no, we should make it 12 by adding 2 and got visibly excited as they already predicted that they would win the game this time.
There was resistance from one male teacher, they said 11 first, but I intervened that they said 12 finally, so now you can add to 12, one of the female teacher on the right row also got amused that no matter what
she adds, their group is going to lose, but she still excitedly added 1 and said the total to be 13, but then the left group called out 15 by adding 2 to 13 and won the game. This was an interesting turn, as the left group won the game for the first time after the right group won it twice. I also encouraged them to think about how the winning strategy changed when the final winning number was changed from 10 to 15. I also highlighted how 12 was the winning point for the left group and encouraged them to think about the number previous to 12 that may be advantageous; it was definitely not 10 this time. Teachers said it will be 9, and then 6, and then 3. I ended the discussion by sharing that there are more variations possible to this game by changing the options from 1 or 2 to 1, 2 or 3 to 1 to 10 and also by changing the final number from 10 to 15 to 100.
she adds, their group is going to lose, but she still excitedly added 1 and said the total to be 13, but then the left group called out 15 by adding 2 to 13 and won the game. This was an interesting turn, as the left group won the game for the first time after the right group won it twice. I also encouraged them to think about how the winning strategy changed when the final winning number was changed from 10 to 15. I also highlighted how 12 was the winning point for the left group and encouraged them to think about the number previous to 12 that may be advantageous; it was definitely not 10 this time. Teachers said it will be 9, and then 6, and then 3. I ended the discussion by sharing that there are more variations possible to this game by changing the options from 1 or 2 to 1, 2 or 3 to 1 to 10 and also by changing the final number from 10 to 15 to 100.
For the next task of the workshop, we discussed and noted down some mathematics topics on the blackboard and asked teachers to sit in groups of 4-5 to work around making a small teaching unit or lesson plan by choosing one topic from the board or any other mathematical topic of their choice. Few teachers seemed reluctant, but after giving them some prompt questions, they started writing them on the chart paper. They were given around 20-30 mins to work on it. Teachers' groups took up topics like fractions, Geometry, and measurement. A few teachers were also moving out in between the sessions. When teachers were asked to present their unit, they were very reluctant to come and present. Then a male teacher came in front of the class and agreed to present his lesson on fractions. Using that as a cue, we discussed some interesting things about fractions. After that, a female math teacher presented her lesson on Shapes, 2D and 3D shapes. We discussed around making the definition of 2D and 3D shapes, which is both mathematically correct and appropriate for students to access. After this, there were two groups left, but none of the members came forward to present; in fact, on insistence, they gave their chart to the female math teacher to present. The female math teacher read out the lesson for measurement, and while doing that, she herself added examples for each measurement unit. For the last lesson on Triangles, which the female math teacher was asked to read, was basically definitions for types of triangles based on sides and angles. Assuming this is very factual and lacks any imagination, I asked her to stop and again asked the group if they had thought of any activity around it, for which the teacher couldn’t say much, and she said the male teacher in the group made the lesson, and he can only explain this well. There were still some 15 mins left to end the session, and the teacher suggested that instead of starting a new session, let's have the session the next day. So at the end, we had a general discussion about what grade and subject the teachers were teaching, and we noticed that, except for one female math teacher, most tried to dissociate with math, as they were either teaching primary grades or teaching subjects like Hindi, GK, Telugu, etc.
Engagement with Children: Other Observations
I (Ekta) personally was upset with the fact that not many teachers responded to Jeenath's interesting activities and repeated requests for presentations. However, Jeenath also mentioned her experience with other teachers in alternative contexts who sometimes did not even care and were often absent from school. In comparison to that, the teachers' participation here, as limited as it was, was vastly positive, despite many being from non mathematics background. Perhaps one needs to consider the subject matter, the administrative demands on teachers (they were canvassing for admissions throughout the day), and the support system around them, which created the atmosphere for their relaxed learning and engagement.
Throughout the session, teachers (male teachers) went in and out of the classroom. Since many of them were not from mathematics, they also felt that they did not need to contribute or participate. In fact, when Jeenath asked teachers to present, the female teachers gave their activity sheets to the Math teachers and asked her to present on their behalf. The female teachers lacked much confidence compared to their male counterparts.
Many of them used their phones to look for activities. I was not sure if this would be productive and meaningful. However, Jeenath pointed out that it is hard for teachers to think of activities; the activities on the phone can be an additional resource. However, she insisted that they contextualise it to children’s lives with examples and things that children find around. This helped, as teachers in their presentation used local foods or products as exemplars.
Throughout the session, teachers (male teachers) went in and out of the classroom. Since many of them were not from mathematics, they also felt that they did not need to contribute or participate. In fact, when Jeenath asked teachers to present, the female teachers gave their activity sheets to the Math teachers and asked her to present on their behalf. The female teachers lacked much confidence compared to their male counterparts.
Many of them used their phones to look for activities. I was not sure if this would be productive and meaningful. However, Jeenath pointed out that it is hard for teachers to think of activities; the activities on the phone can be an additional resource. However, she insisted that they contextualise it to children’s lives with examples and things that children find around. This helped, as teachers in their presentation used local foods or products as exemplars.
Teachers in the school did not have much teacher professional development. Overall, I felt that even if they did not participate in the activities, they continued to be intellectually challenged with Jeenath's deep and pointed questions that they really appreciated. Teachers are hardly challenged on subject matter and are almost an authority in their field; however, having a subject matter expert engage with them has a tremendous effect and the quality of discussion as an observer was very revealing.
(A joint post by Ekta Singla & Dr. Jeenath Rahaman)


















































