Counting bricks is an important activity during our sessions at the brick kiln. The children have made much progress in learning mathematics due to this activity. Their parents have to count bricks to keep track of their payment. Hence, counting bricks is a meaningful task for these children. Also, they don’t have to sit at one place to complete this task. They have to move and run around, which is akin to their basic nature. All of them are always ready to count bricks. Whenever I realize that they are getting bored of sitting at one place and reading, I ask them, “Shall we count bricks?” and a sudden wave of enthusiasm engulfs them!
In the beginning, they would count the bricks one by one. But now, they can count in multiples of two, four, twenty five and hundred. The reason is, one ghoda (stack of bricks at the kiln) is of 25 bricks. They stack up 12 layers of 2 bricks each, and keep a single brick on top. The children can count the bricks in such a ghoda in twos. Bigger stacks of 55 bricks are structured as follows: 13 layers of 4 bricks each, and 3 single bricks on top. The children make use of these structures for counting. They also use their own strategies for counting. See this video, in which Rahul is answering the question – “how many total bricks in 3 ghodas of 55 bricks each?”
Kishor and I decided to push the children a little more. Our friend Arun had accompanied us today to see our class. He is a teacher himself. He joined us in teaching and took detailed notes of our efforts. There were many ghodas of raw bricks outside Amit’s house. We started our math class over there. Rahul also came with Amit. Our conversation went like this:
I: How many bricks in one ghoda?
Amit: Twenty five
I: So, how many bricks in these 2 ghodas?
Amit spent a lot of time mumbling to himself and using his fingers to count. Arun’s patience ran out and he prodded Amit.
Arun: How many bricks in the ghoda on this side?
Amit: Twenty five
Arun: Then say quickly how many bricks in two ghodas.
Amit started counting bricks one by one. Now Arun couldn’t hold back himself. He explained to Amit that if he counted in fours, he would be able to count faster. Amit followed this, and counted 50 bricks. I smiled at Arun. He realized that he needn’t have rushed Amit this way. He could have allowed Amit to count one by one, and then brought it to his attention that he could count in fours to save time. We realized that the principle of not interfering with children’s thought processes sounds quite simple, but is actually quite difficult in practice. I took over the conversation from this point onwards.
I: If there are 50 bricks in two ghodas, how many bricks in four ghodas?
Amit: A hundred (This reply came rather promptly)
I: How many bricks in this entire haaroli? (Haaroli is a long row of ghodas)
This was my attempt to push Rahul and Amit. They started counting the ghodas by touching each ghoda. “A hundred and hundred makes two hundred… another hundred makes three hundred…”. But they would miss a ghoda in between or count a ghoda twice. When they’d realize their mistake, they would start counting from scratch. I suggested a trick – when they complete counting 100 bricks, they should put a blade of grass on that ghoda. This trick worked very well, and Amit and Rahul started moving forward.
After some time, Rahul said, “Ten hundred”. Arun didn’t like that. He asked, “How much is ten hundred?” Rahul got a little confused. I intervened and asked him to continue counting. Arun realized that it’s not necessary to insist on using the word ‘hazaar’ – it can hinder the children’s process. The children completed counting till “Twelve hundred bricks”. I decided to challenge them further.
I asked them, “Can you tell me how many bricks are there in all these haarolis?” Promptly, the boys climbed to the top of the haaroli and started counting. Now, they were using many different strategies for counting. For example, when they had to add 3600 and 1200, Amit said, “Thirty six hundred plus twelve hundred, right? So, thirty six hundred and ten hundred…. that’s forty six hundred… add the remaining two hundred… that makes…. forty eight hundred!!” Using such strategies, they counted “Eighty four hundred bricks in seven haarolis” and climbed down.
I decided to represent this count in the form of a table. But we didn’t have a paper and pen, so we squatted next to the haaroli and prepared a table on the sand, with the help of the boys. While preparing the table, the boys were counting mentally, and at times they were looking at the bricks and counting physically. They went through the whole process of counting once again, albeit quite quickly.
We have noticed while working with these children that they face a problem with number-names. In Marathi and some North Indian languages, the number-names are a little peculiar. These children can say “80 and 4” quite easily. But they find ‘chauryanshi’ (चौंऱ्यांशी ) confusing. Actually, we can express ‘chauryanshi’as ‘ainshi chaar’ or ‘panchahattar’ as ‘sattar paach’. But this practice is not prevalent in Marathi. Rahul and Amit can count “Eighty four hundred bricks in seven haarolis” but get confused with number-names upto 100.
Prof. Manohar Railkar has written a detailed article about this issue. The influence of Sanskrit on Marathi and North Indian languages has resulted in making the number-names upto 100 quite complicated. Children who come from families where there is a regular practice of using numbers and learning tables by heart, may not find it very problematic. But we will have to work quite hard to help our brick kiln children master these number-names. However, if we look back at where we had started from, it seems that we have made quite a lot of progress. Kishor and I are feeling quite happy about it!