# Teaching Mathematics as a Learning Experience: A Bottom-up Approach

I used the pile of notebooks lying in the room to establish the same point for the ones who might not have understood. The time invested was more than what I would have done if I were a regular teacher but the outcome was that the girl who had earlier said that she dislikes mathematics, answered my recapitulation question, ‘why do we learn multiplication’ by saying that ‘it helps us add easily’.

### Back to the classroom: Context

It was the month of June in 2019 when I met 120 adolescent girls living in Dadri area of Uttar Pradesh (UP). The girls were enrolled in different govt. schools located in nearby villages. They had come to attend a six weeks long residential summer camp organized by NTPC (National Capital Power Station, NCPS) Dadri as part of their Corporate Social Responsibility initiative. I was representing Barefoot College, Tilonia, as an intern responsible to work towards the holistic development of these 120 girls under the ‘Girl Empowerment Mission’. The activities to be conducted during the program were designed by a team from Barefoot College and the camp site was provided by NTPC. This program was simultaneously organized across nine Indian states of Rajasthan, Madhya Pradesh, Uttar Pradesh, Himachal Pradesh, Bihar, Chhattisgarh, Orissa, West Bengal and Gujarat for 1500 rural girls in the age group 10 – 12 years.

I was one of the six interns who were selected from different parts of the country after a two-stage interview process for this particular site in UP. We went through a two-week virtual training program before we joined the rest of the team at the camp site. All the interns were trained for different curricular areas including literacy and numeracy, sciences, gender and equality-breaking stereotypes, menstrual health and hygiene, democratic leadership, environmental protection, creative arts, dancing, yoga and self-defence. It was only when we reached the site that the different ‘subjects’ were allotted to different interns based on their interest area.

### Know them before you teach them: Situation analysis precedes curriculum planning

Given my professional training and experience of teaching mathematics and social science to middle school students, I volunteered to take up mathematics and civic education with these girls. While the curriculum and pedagogy for civic education were broadly provided by the Barefoot College in the form of PowerPoint presentations, it was mathematics where I could innovate and experiment as I had to conduct the ASER test and design the plan keeping in mind the students’ performance in the same.

I corrected their ASER test and based on that I realized that the girls knew how to solve a problem but only the technical part and not the application part. I also realized the diversity of the group despite their apparently similar socio-economic background. When examined closely, I found out that the backgrounds were not so similar after all. While most of the students studied in the government schools there were many who were enrolled in nearby private schools. The diversity extended to the family background and parental involvement in their studies as well. The complexity of the group could then explain how some girls were able to solve complicated word problems, but others struggled to even identify numbers. An added layer to the problem was their different mediums of instruction at school. Some girls studied mathematics in Hindi while others were comfortable in doing it in English, as well. This explained why they were able to identify and express any number using Hindi but could not do the same when asked in English. There were a few who just could not identify a two-digit number in any language. Addressing these issues, in a month-long camp was going to be a challenge more because they were attending a ‘fun summer camp’.

I decided to design a month-long plan, but it had to be done in coordination with the other interns and the rest of the activities. I could only get a three hours slot per week to take up maths. Also, we were instructed to group the girls in three sections of forty children each. As an intern, I was facing multiple tasks. Firstly, I had to make a choice between having three homogenous or heterogeneous groups in a way that it did not create chaos for other people. Since English language was also an area of development, I consulted with the English teacher to form the heterogeneous groups. Secondly, I had to choose the topics I wanted the children to work at. Now, one might think that ASER test scores would have helped me and they did to a certain extent, but the real challenge was to keep the session engaging for everyone. Since the unitary method was not clear to the majority, I decided to work towards that direction by beginning with multiplication. Whether it was a useful strategy or not was to be found out at the end of the month. Lastly, I had to ensure that the subject remains fun for all of them because a) it was a summer camp and hence, meant to be a fun place and, b) as a child, I was scared of maths and could not make sense of it for the most part of my school life until I met a teacher who taught me how to play with numbers.

### Classification and framing: Curriculum, pedagogy and assessment

As soon as I entered the class on the first day, I was informed that it was a student’s birthday. So, I asked everyone to wish her and the children did so. Then, I drew a circle on the blackboard and said, ‘This is her birthday cake and all the 39 girls in this room will get 10 grams of this cake. How much should it weigh?’ After some thought, a girl said 400 grams. I asked why and she replied, ‘You will also eat, *na*?’ Fun part aside, there was this girl who was able to do most of these calculations mentally so, I asked her to explain the process. She was actually doing (30×10 + 9×10) for this but could not express this in words properly. I used this opportunity to introduce multiplication.

Some of the girls were able to solve the problem quickly but did not know that they were multiplying, others could multiply when I wrote in the numeric form and not as a word problem. Then, I asked them to think of the possibilities where people use multiplication. I gave the example of a shopkeeper packing sweets; they gave similar examples. Then, I forced them to think originally. So, they came up with responses such as how caterers in hostel who prepare food count children or teacher in classrooms count students (guided response but satisfactory).

Eventually, I picked examples from the classroom where we were sitting, like if there are four tubelights in this room, then how many on the entire floor? In the end, I gave them a problem to solve along with a task to make five such word problems on their own. Meanwhile, they got their snacks *Parle G* and *Frooti*. I asked the person serving them to tell the number of biscuit packets in one carton and he used multiplication to do that. In short, my class went better than how I could have planned. Using the inductive approach to discussion helped as students learnt to make rules than follow them blindly. They understood the utility of knowing a concept which, I believe, matters a lot.

The next day, when I asked for word problems, only five of the entire group had done the homework. I was upset, obviously, but then, I gave a *smiley* on the notebooks of the ones who had done the work and asked them to share the questions one by one. Also, I told the five students that they could challenge anyone of their classmates to solve their questions. The end result was that some girls themselves said that they would also bring their questions the next day.

One of the girls had framed this question, ‘If a field (*khet*) can be irrigated in 19 hours then how many hours will it take to irrigate 17 such fields?’ I was really happy to see this application.

In the other class, when I entered and told them that I will take mathematics, immediately one girl said that mathematics is boring. So, I drew five emoticons (in their decreasing order of happiness – the last one crying) on the board and asked each one to pick the emoji that represented how they liked mathematics. There was only one girl in the class who was scared of mathematics; the others either liked it or were okay with it.

I said, ‘My aim of this class is to bring this one girl from the column of sad emoji to the column of *okay* emoji and if I can’t do it that would mean I have failed.’ Then I started the class by writing 4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4=?on the board. I called the girls in pairs and asked them to solve this as quickly as they could. They had to explain the mechanism also. The rest of them were doing it in their notebooks as well.

The end result was that I got to know that children were using multiple methods to solve it:

- Adding them all like one counts on the fingers.
- Counting the number of times 4 is written and multiplying it by 4.
- Making groups of 10 and then solving it. For example (4×10 + 4×10 + 4×6) if 4 is written 26 times.

I told them that all the methods are correct as long as logic is followed.

Then, I changed some digits in the equation and asked them if we can still use multiplication, they said no. I asked them why? A girl replied because the digits were bigger than 4. I erased and wrote 3, 2 and 1 instead of the previous digits. Then, I asked if we could now multiply. They said ‘no’ because the numbers are different, and the numbers have to be the same.

I used the pile of notebooks lying in the room to establish the same point for the ones who might not have understood. The time invested was more than what I would have done if I were a regular teacher but the outcome was that the girl who had earlier said that she dislikes mathematics, answered my recapitulation question, ‘why do we learn multiplication’ by saying that ‘it helps us add easily’.

Later, while taking the sessions on the unitary method, I used my laptop to show videos explaining how the unitary method works. But, since we did not have speakers, it wasn’t a very effective mode. So, I used role-play to explain the same concept again. Students participated enthusiastically and I had a great time. But I could see some students lagging behind and I had to do something about it. I decided to take two sets of lesson plans to the class. I would give the really difficult questions to the ones who understood the concept easily so that I could use concrete objects like sketch pens to explain the method for the ones who had not understood. It helped to some extent but again I felt guilty for not being able to do justice to all of them. I started questioning whether having heterogeneous groups was a good idea.

I knew that peer learning works wonders because I had attended *Nali Kali* sessions in a government school of the Gulbarga district in Karnataka. I just needed to work out a strategy that could incentivize collective learning.

I came up with an idea to have relay race in maths class. I regrouped children based on their abilities and assigned them a question to solve with a specific instruction that ‘one step of this problem will be solved by one student such that all have to understand and participate in order for the group to win’. They were expected to explain the problem to each other first before they could finish solving the problem on the blackboard. The strategy worked and I could notice the other qualities children had, including leadership, team-work, sensitivity and initiative. Of course, some of them were getting impatient as they really wanted to be the first to solve the problems but such experiences also help children learn the more abstract values. So, I found meaning in what was happening and the chaos that was created.

### What worked and what did not: A Reflection

My month-long engagement with these students was as fun as it could get for various reasons. I spent as much time thinking about what to do next before the class as much as during the class. What I did spontaneously gave me more satisfaction at times and rightly so as teaching is an interactive process. I just wonder if I could spend so much time on one concept if I were a regular teacher. And I know the answer is ‘no’.

There is a lot that goes on in a professional and structured space that hinders learning – both for students and for teachers. For instance, the ASER results at the end of the camp showed that some students still could not identify numbers and that revealed how my strategy to have heterogeneous groups had not worked for many. I should have conducted additional separate sessions with these students. But, being engaged with children from 6 am to 8 pm followed by group meetings that sometimes continued till 2 am, I do not know how I could have managed that. Also, for me, even if they could not identify numbers, they still learnt that mathematics is a fun and useful subject.

They learnt the possibilities of collaboration even while learning division. They learnt that helping each other learn and seeking help from peers is not a bad thing. And that is something which does not get assessed using standardised tests. I strongly feel that the system at large needs to acknowledge this subjective element to teaching and value teacher’s autonomy, experience and voices more often than not. After all, mathematics is fun because the experiences we gain while learning mathematics are fun.

### Author

Richa Pandey is a former student of Education with focus on School Organisation Leadership and Management from Azim Premji University, Bangalore. She has taught in several private schools in Delhi and is trained in the pedagogy of Maths and Economics as part of the B.Ed. program from Delhi University. Her areas of interest include alternative schooling, curriculum development, social-emotional learning and systemic change.