Demystifying Mathematics – Finding Joy in Numbers

In our education system the teaching and learning of mathematics, is more often than not, abstract and procedural. Students seldom gain conceptual clarity. The fear of math is accentuated by notions like it is alright to not be good at the subject or it is not useful in life. In this article, we discuss the experiences, approaches, and struggles of organizations working on improving mathematics education in India, and the various techniques and materials they use to make learning math joyful for children.

Aavishkaar – Palampur

Aavishkaar is one such organization. The Aavishkaar team is aware that students, struggle to understand the fundamentals of mathematics. Sandhya Gupta, co-founder of Aavishkaar shared that their work focuses on facilitating educators and young learners to adopt a creative, curious, and critical thinking approach to education as the present system does little to hone children’s curiosity and fails to provide them with safe spaces to make mistakes and learn.

They use teaching-learning materials and techniques that make learning math a visual, relevant, contextual, and engaging experience. They work in the public schools of Himachal Pradesh, Telangana, and Assam. They also closely collaborate with grassroots organizations across the country. The Aavishkaar team conducts training courses for teachers who are capacitated with the required knowledge, skills, and mindset.

Aavishkaar runs a learning center for students from first to tenth grades in Palampur. They also frequently hold online and residential camps for students where they deep-dive into particular themes. The team uses a framework that helps children participate in sessions and critically engage with concepts. Their five-step framework includes introducing the concept in a fun activity, working on a problem in groups and arriving at solutions, discussing their selection in the class, engaging on extensions of the problem, and finally reflecting on the essence of the concept.

The team begins each session with what they call ‘Ganit Charchaa’, where they generate a discussion in the classroom. The aim of this introductory activity is to encourage children to participate in the lesson without any inhibitions and reinforce that there can be numerous ways of solving a problem. Sandhya shares, “For instance, in ‘Ganit Charchaa’, the activity can be asking children to count certain items arranged in an order. The children use different ways to arrive at the total number of items. Children count the items by grouping them into different shapes such as a triangle, square, etc. This exercise allows children to arrive at the solution using their own rationales. Activities like these instill confidence amongst children as they realize that there are varied ways to look at something. Children also learn to acknowledge and respect each other’s opinions.”

Dispelling notions of fear against, or inability to enjoy, mathematics is consciously undertaken by Aavishkaar’s educators. They have observed that children and teachers both share this uneasiness. The educators are encouraged to discuss experiences of mathematicians that drive home the point that learning math the right way can be fun.

Aavishkaar’s educators often explore a real-life problem in small groups. For instance, to explain linear equations, children can be given a problem in which a local shopkeeper has to procure a particular item such as pens from a wholesaler. The wholesalers charge different costs for the item and are located at varying distances. Questions such as which is the best deal, writing a general equation for finding the cost of procuring that item, representing the deals on a graph, etc. are then posed to the children.

Children work in groups to answer certain questions. They are later requested to explain the rationale behind their solutions to the larger group and they are nudged by the facilitators to use mathematical reasoning to arrive at those answers. Teachers are encouraged to discuss extensions of the problems raised by students in the session and some that they themselves deem to be relevant. The students are then made to reflect on the essence of the concept through individual and group discussions.

Sandhya added, “These children tell us that since the educators allow them to make mistakes and not scold them for it, they enjoy participating in the sessions. We need to make them feel safe in a classroom and the progress they show will be remarkable.” The Aavishkaar team hopes to reignite curiosity and passion for mathematics in each child.

Palakneeti Parivar

Palakneeti Parivar was set up in 1996. It works on social parenting and providing holistic education to children living in a slum of Pune. Khelghar is a project started by Palakneeti Parivar with the aim of reaching out to the underprivileged. There are about two hundred children from the Laxminagar slum of Kothrud in Pune participating in the activities at Palakneeti’s learning centers. The parents of these children work at construction sites. They hail from areas facing droughts in Maharashtra, and from neighboring states of Karnataka, Telangana and Andhra Pradesh.

These children do not get the required learning support in their schools or families. The Palakneeti team, through play-based activities, attempts to correlate conceptual learning with the experiences of these children. Their focus is on increasing children’s proficiency in mathematics, Marathi and life skills. Based on the grades they are in, and their learning levels, children are divided into eight groups. They have two hours of sessions daily at the learning centers run by the team. The focus remains to engage closely with children in primary grades.

Sumitra Marathe, who leads the mathematics program at Khelghar, along with two other volunteers, shared that the children often find the math taught in class to be crude. She added, “We try to dispel these fears about mathematics by making the children understand the foundational concepts and visualize their lessons. Our two-step pedagogy learnt from Navnirmiti involves using objects to introduce concepts. Then we continue to help them understand the numbers and symbols. The problem is that children can count the numbers from one to two hundred but when you say twenty-three then they do not understand what twenty three means. We give them sticks or some pebbles or pseudo currency notes and ask them to represent twenty-three objects.”

Using games to make children understand concepts makes the learning experience joyful for children. The team uses a lot of tools to break down, what may seem as, complex concepts for children. They organize games around shopping where children are given objects and then asked to add or subtract based on the prices and quantity of each object. They have three by three meters snakes and ladders games printed, where the children play using mathematical operations. Sumitra adds, “It is heartening to see the children enjoy these games. They can play them for hours. We simultaneously ensure that they are able to relate these activities with the operations taught at school.”

The team also uses calendars as a tool to teach children. They are inspired by the work of Arvind Gupta, an educator who has worked on using toys to teach science and math to children. In his videos, he shows how the calendar with just numbers one to thirty can be innovatively used for improving children’s understanding.

The team, through the usage of relevant materials, ensures that children visualize what they are learning. They use dotted sheets and notebooks with squares in them and tell children to visually perform each operation. For instance, if three and two need to be added, then children would be asked to represent these with distinct colors and their sum in another color.

To introduce concepts related to measurement to children, the team asked children to map all the taps and the broken taps near their homes. The children were asked to calculate how much water might be available in all the taps and how much water must be wasted in one minute through the taps that were leaking. The older children went ahead to repair the taps that were leaking. The Palakneeti Parivaar team understands that children’s learning abilities vary across groups, and they provide three levels of worksheets.

The education system fails to provide adequate time and appropriate methods to students to learn the foundations of mathematics. Working with a pedagogy that incorporates games and activities to strengthen math concepts, the Palakneeti Parivaar team believes that each child can rediscover the joy of learning mathematics.

Better Education Lifestyle and Environment Foundation

Better Education Lifestyle and Environment Foundation (BELIEF) is a non-profit based in Pune city that works to address issues in education, health, and the environment by creating replicable models of sustainable development by providing services and capacity enhancement of relevant stakeholders.

With the vision of improving primary and elementary education, BELIEF has initiated its Early Childhood Education (ECE) program with fifty-four anganwadis in Pune. The families in the area have migrated from drought-stricken regions of Maharashtra – Latur, Solapur, Marathwada and Western Maharashtra – and the surrounding states of Karnataka, Telangana, and Andhra Pradesh. They work in the vicinity of construction sites.

Most of the stakeholders in our education system including educators, policy makers, and parents have been taught mathematics using mechanical processes that have had limited real-life applications.

In ECE, anganwadis play a pivotal role in delivering pre-school education to children aged three to six years. Anganwadis are preschool centers running across the country under the Integrated Child Development Scheme (ICDS). The workers at these centers are also tasked with collaborating with other stakeholders such as Accredited Social Health Activists (ASHA), and Auxiliary Nurse Midwife (ANM), among others, to monitor and support the health and nutrition of children and expecting and lactating mothers.

The anganwadi workers are responsible for various services such as immunization, delivering supplementary nutrition and supporting other services. Inadequate handholding and contextual training to anganwadi workers on ECE and lack of support from parents results in compromised learning experiences of young children.

The BELIEF team tries to overcome gaps in implementation by envisioning the institutionalization of change. Atul from the team says, “We believe in bringing in sustainable change by strengthening the system. The role of each stakeholder becomes especially important in this context. For instance, in the case of ECE, we believe that everyone, from Child Development Project Officer (CDPO) to parents, should have a basic orientation of ECE. Presently, the team has prioritized working with Anganwadi workers and parents.”

They conduct training for anganwadi workers every fortnight. These two-hourlong sessions expose the participants to appropriate pedagogy and teaching-learning materials suited for young children. They initially focused on perspective-building where the workers were made to understand their role, its importance in the development of children, etc. After every four to five months, BELIEF conducts in-person training for them as well. The workers remain connected through a WhatsApp group.

The BELIEF team extensively uses teaching learning materials for children as they believe that these materials enrich their learning experience. To understand how to identify which object is greater in number, the team told workers to place three books and five pencils in front of children and request them to tell them the object that is greater in number.

Some children end up responding that books are more than pencils as they tend to get confused between two criteria of comparing area and number of objects. The workers are then asked to count the two items together (applying one-to-one correspondence) to help children understand which object is greater in quantity. Archana from the BELIEF team, who conducts training for anganwadi workers, shared that the material need not be expensive and anything readily available can be used for creating learning opportunities for children. For instance, to help children learn about patterns, the team suggested that the workers identify patterns in their surroundings using objects such as leaves, pebbles, flowers, etc. and discuss the same with children. This activity helps to build observational skills and increase understanding of patterns in children. After a few days, the children excitedly challenged their peers and anganwadi workers to identify the patterns they made. These activities expose children to the freedom and joy of exploration in education.

The BELIEF team believes that sessions on numeracy should be looked at in conjunction with literacy. For instance, children are encouraged to frame full sentences to express their mathematical understanding. If books are greater in number, then they would be nudged to understand and use the statement, “Books are more than pencils.” If there are three balls in varied sizes, then to introduce the concept of comparing sizes of objects and expressing their findings properly, children can be asked “Which ball is bigger?” or “Which ball is the biggest?”

During the pandemic, the BELIEF team started reimagining the roles of parents in foundational numeracy. Over WhatsApp, the team shares activities with them through text and audio messages and the parents facilitate these activities for their children. These were activities that the children could do at any time of the day. These activities were created based on Aakar, the Maharashtra state curriculum for children between the ages of three to six years. The parents were required to engage with children for about thirty to forty minutes every day.

The team understands that the struggle to strengthen ECE is going to be long drawn out, as every stakeholder is used to the older system. They believe that if the practitioners and researchers work together, then meaningful interventions in ECE can be rolled out.

Swatantra Talim

Since 2013, Swatantra Talim, a non-profit, has been working to build a culture of creativity and questioning skills among rural children aged six to sixteen years. It runs two after-school learning centers in Lucknow and Sitapur districts and works with five government schools in Lucknow district. To facilitate social change, the organization envisions co-creating every village as a center of innovation and building every child into an innovator.

The children in the region come from families with low literacy levels, culturally rooted orthodox value systems, and deep social inequalities. The lack of contextual education that fails to incorporate their experiences and traditional knowledge pushes these children further away from the public education system.

Rahul Aggarwal, co-founder of Swatantra Talim shares, “Our activities’ focus is on making learning mathematics explorative and collaborative. We try picking problems that can be attempted differently. The idea that there is only one method of attempting a problem needs to be debunked.”

The team uses Khoj Dabbas for their sessions. These could be described as a Lab-in-a-Box that equips each school with lesson plans, easy-to-follow activities, and locally sourced low-cost materials. These Dabbas enable educators to explain science, mathematics, language, and social science in an integrated manner.

For example, if the operations of multiplication and division are being explained in the session, then the teacher could conduct operations using contextual materials such as wooden sticks and eventually move to notebooks. This activity helps children understand abstract concepts by using concrete objects.

Khoj-Yaan is an extension of Khoj Dabbas. This experiential learning program focuses on expression, exploring thoughts, scenarios, and feelings in a ‘fun and learn’ way. It integrates teaching language, mathematics and science through puppetry, creation, puzzles, and games. Children in grades one and two are encouraged to make and play with toys.

For instance, the team using the story of the hungry caterpillar asked children to make their own caterpillars and weave a story. The children in grade three could modify the game of snakes and ladders to caterpillars and ladders where the facilitator could introduce new set of rules that help the children apply basic mathematical operations and become problem-solvers.

The children in grades four and five could be given puzzles such as sudoku that help them hone their logical reasoning and engage with numbers. Rahul adds, “The sudoku puzzle of a five into five grid can be conducted using five different objects and each object is five in number. These objects can be locally available materials such as sticks, pebbles, etc. Children enjoy doing these puzzles. Using such engaging techniques and materials, their fear of math starts to disappear.”

To introduce the qualities of numbers, a game could be played in which a player can be asked to select a number and the other player must guess it. For instance, if a player selects any number between one to hundred, such as fifty, then the facilitator can nudge the other players to ask whether that number is odd or even or a multiple of any number.

The fear of math is accentuated by notions like it is alright to not be good at the subject or it is not useful in life.

The pedagogy of simulation and trying out different methods to solve puzzles and problems encourages children to keep track of, and reflect on, their performances. The Swatantra Talim team believes that developing robust foundational conceptual understanding and an environment of thinking and brainstorming, encouraging exposure to innovative ideas and thoughts, and real-life applications will give children a well-rounded understanding of mathematics.

In Conclusion

Most of the stakeholders in our education system including educators, policy makers, and parents have been taught mathematics using mechanical processes that have had limited real-life applications. Fear has traditionally been evoked to make them learn, and the essence of concepts was not expressed. An education landscape that adopts engaging, explorative, and contextual attitudes, curriculum, pedagogy, and teaching-learning materials can help children truly find the joy of learning mathematics.