Mathematics education and the classroom: teacher versus facilitator

I have been working with children on the subject of mathematics for nearly 21 years. During the first seven (7) years of this period, I taught mathematics to children in the same manner as it is generally taught in traditional classrooms. In other words, it is assumed that the teacher’s job is to teach and the children’s job is to learn. During this period, I was a part of traditional schools and coaching classes, and I continued to teach mathematics with the help of prevailing and conventional methods.

After working in this manner for seven years, I began working on mathematics with non-governmental organizations (NGOs) engaged in education. For the last 14 years, the manner in which I have been involved in mathematics education with children has been one in which the process of learning and teaching is not one-sided but two-sided. That is, I am also learning from children, and children are also learning from me.

One thing that I have come to understand much better during these 14 years is that, as a facilitator, we do not have to teach; we have to learn. Throughout this journey of learning mathematics with children, and through discussions, conversations, and work with my colleagues, I have learned a great deal. And this process of learning is still continuing. Whatever I have learned, or am learning, I continuously try to incorporate into my work. In this article, I am sharing my learning experiences and the reflections that have emerged from them in the hope that they may prove helpful to fellow practitioners.

Mathematics teaching in the light of educational documents

India’s new National Education Policy has clearly stated that the purpose of education is to nurture good human beings who are curious and endowed with logical abilities, who possess the qualities of patience and empathy, courage and resilience, scientific temper, creative imagination, and ethical values. Only such citizens will be capable of building the kind of society envisioned by the Constitution of India.

In this context, if we talk about mathematics education, the “Position Paper on Mathematics Education (2005)” states that the primary objective of mathematics education in schools is to mathematize children’s thinking. It further states that mathematics education at the elementary level should prepare children to face the challenges that they will encounter later in life.

This Position Paper on Mathematics also discusses the conditions under which mathematics should be learned. It emphasizes six key points:

1. Children should learn to enjoy mathematics.

2. Children should learn important mathematics.

3. Mathematics should become a part of children’s lived experiences, something they can talk about.

4. Children should pose meaningful problems and seek their solutions.

5. Children should use abstract ideas to develop an understanding of relationships and structures.

6. Children should understand the fundamental structure of mathematics, and teachers are expected to ensure that every child remains connected with the processes taking place in the classroom.

When we view mathematics education and the mathematics classroom in the light of these two important documents, certain experiences and ideas become particularly relevant. Incorporating these into our teaching and instructional planning may prove helpful.

Can we connect the mathematics of our lives with the mathematics of textbooks?

I believe that yes, this can be done. There is a great deal in the life of an ordinary person that can be connected with the mathematics found in textbooks. Let us try to understand this with the help of a few examples.

The first example: Praveen, a child studying in Class 6, has a father who borrowed ₹10,000 from a moneylender for agricultural work. He took this loan at an interest rate of three (3) percent per month. This means that he pays three rupees (₹3) per month as interest on every ₹100 borrowed, ₹30 per month on ₹1,000, and ₹300 per month on ₹10,000 to the moneylender. The loan has been running for eight (8) months. So far, he has paid ₹2,400 as interest. The principal amount is still outstanding. In many places, the interest charged every month ranges from five (5) percent to 10 percent. This single example from the real world presents enormous possibilities for working with children on a variety of concepts included in textbook mathematics, such as simple interest, compound interest, principal, profit, loss, monthly rate, annual rate, and the quantitative understanding of numbers.

This example contains several questions that can be discussed with children, such as: Why does the need for a loan arise? Why is there a need to borrow specifically from a moneylender? Is it not possible to obtain a loan from a bank? What difficulties arise in obtaining a loan from a bank? What does an interest rate of three percent per month amount to on an annual basis? What is the current rate of interest in banks? How much difference would there be in the interest paid on the same loan if it were taken from a bank instead of a moneylender? Are there any other ways of obtaining credit, such as borrowing through self-help groups? What is the interest rate in such arrangements? How many people in the village borrow from the moneylender? How much income might the moneylender earn every month and over the entire year through interest payments?

The second example: In a small village with about 200 households, most parents say that they do not have enough money for their children’s education. In fact, they often do not have enough money even to meet small needs such as notebooks, pencils, and similar items. Most of the parents in the village are agricultural laborers. Those who own land have very little of it. There is also a shortage of water. In this same village, children studying in Classes four to eight came together to collect some information.

For example, one glass of liquor costs ₹15. At one location, approximately 30 glasses of liquor are sold every day. This means that about ₹450 worth of liquor is sold daily. There are eight (8) such locations in the village where liquor is sold. This means that liquor sales amount to approximately ₹3,600 every day. In some places, sales are even higher.

Throughout this entire process, the children reflected and deliberated on many issues, and several questions emerged from them. They observed that a great deal of money was being spent on alcohol every day. If this money could be saved, it could be used for the welfare of their families. They also noted that if so much money was being spent on alcohol in their small village, then the amount would be much greater if the expenditure of all 165 villages in the development block were added together.

The analysis carried out by the children raises many important questions. Through this analysis, they begin to understand the social and economic realities around them. They are no longer merely studying large numbers. Rather, they are attempting to understand the quantitative significance of those numbers. They begin to recognize the importance of these numbers in their own lives, because the numbers are no longer just numbers for them. Instead, they have become a part of their lived reality.

The third example: For several days, the class had been discussing percentages. One day, Ravina brought an empty packet of chips that cost ₹20 and had “20% Extra” printed on it. She said to me, “Bhaiya, it says 20 percent extra on the packet. But they are giving only 10 grams more chips.” We placed the packet in front of the children. We then asked everyone to discuss Ravina’s claim.

The children examined the packet carefully from all sides, talked among themselves, did the calculations, and concluded that Ravina was correct. Rahul and Ravina then explained the matter to the whole class. They pointed out that the packet normally contained 50 grams of chips. The company was offering 20 percent extra chips, which meant 20 percent of 50 grams, that is, an additional 10 grams. Thus, the packet had become a 60-gram packet.

I asked them, “If everyone’s calculations are giving the same answer, then where exactly is the problem?” In response, Ravina said that when she read “20% Extra” on the packet, it sounded as though the amount of additional chips was quite substantial, whereas in reality it was only 10 grams more. Whether this marketing practice was misleading or not was a separate issue. However, the discussion opened up many dimensions of thinking and conversation among the children.

After this discussion, the children spent several days finding out about discounts offered on different products. They discussed these in class as well as at home. A few days later, they began bringing empty packets, boxes, and old newspaper advertisements with them and shared their understanding with the rest of the class.

The children said that the information companies share about discounts on different products may be factually correct. However, it can also be misleading. When they were asked why it could be misleading, the children explained that it needed to be understood carefully. For example, in the case of the chips packet, ’20 percent extra’ meant only 10 grams of additional chips. Twenty percent sounds like a large amount, but in reality, it was quite small.

The children raised many questions about this issue. And debates and discussions on the topic continued in the classroom for several days.

During these discussions, we reflected on several questions, such as:

· How relevant is the concept of percentage that we learn in the classroom to our daily lives?

· How much truth and how much illusion are contained in the claims and statements made in advertisements?

· If it is said that a particular product is the first choice of 50 percent of Indians, what does that actually mean?

· If we assume India’s population to be 140 crores, does it mean that 70 crore people use that product?

· Why is a small asterisk placed next to claims made in advertisements, and why are the words ‘terms and conditions apply’ written underneath?

· Are such advertisements designed for specific groups of people?

· Are these claims made in relation to specific situations and contexts?

It is possible that many of the examples discussed above may not be relevant for every child. However, a facilitator can identify similar examples or points of discussion from the children’s own surroundings and contexts. Such examples, rooted in the realities of life, along with adequate opportunities for children to grapple with them and discuss them in the classroom, open up new dimensions of thinking for them.

This provides children with opportunities to apply the mathematics of textbooks to their own lives. As a result, they begin to understand that questions and numbers are not merely things found in books but are part of their everyday lives. Instead of viewing calculations and problem-solving simply as compulsory classroom exercises, they are able to understand the meanings embedded in them. This, in turn, strengthens their practical and social understanding. In this way, the statement found in our educational documents that mathematics should be used to solve problems arising in daily life can be seen taking shape in practice.

For a facilitator, it is not easy to carry out the kinds of activities described above within the constraints of the classroom, the curriculum, and time limitations. Alongside this, many people also believe that mathematics teaching conducted through such processes cannot really be considered mathematics. They also feel that teaching mathematics in this manner will not allow the formal mathematics prescribed in textbooks to be completed. And that it will slow down the pace of the curriculum and classroom learning.

However, in reality, such opportunities for learning and teaching enrich the classroom environment. Through these varied opportunities, children learn at their own pace. They develop their own ways of solving problems, make estimates, and use their own methods. They also analyze those methods, continuously expand their understanding, and attempt to view and understand the world around them from a mathematical perspective.

It is possible that such efforts at learning and teaching may slow down the pace of the classroom in the initial stages. However, once the process becomes established, it is certain that children will learn a variety of mathematical concepts more rapidly. Many facilitators use these approaches to mathematics teaching in their classrooms. And in such classrooms, children appear far more comfortable with mathematics.

Authorial note: The examples and discussions used in this article have been drawn from Mohalla Learning Activity Centers (MLACs). These have been operational under ‘Shiksha Ki Udaan’, a program of Eklavya. About 50 such centers are being run in Shahpur Block of Betul District and Berasia Block of Bhopal District. At these centers, children participate in learning and teaching processes with local facilitators before or after regular school hours. Financial support for this program is provided through IndiGo CSR – IndiGo Reach.

Editorial note: This article was originally published in Samuhik Pahal (vol. 2, issue 6), in Hindi, in February 2022. The first English draft of the translation was produced with the help of CoPilot, and it was subsequently copyedited by a member of the Samuhik Pahal Team.