Uddalaka - Cheenta After-School for Thinkers and Doers

Uddalaka was born about 200 years before Gautama Buddha. He is regarded as one of the earliest philosophers and natural thinkers in the recorded history of humanity. Cheenta’s School for Mathematical Sciences is inspired by his work. A central feature of Uddalaka’s thought, as found in the Brihadaranyaka Upanishad and the Chandogya Upanishad, is enquiry driven by a burning sense of curiosity.

Cheenta’s after-school programme for thinkers and doers is presently open to children between the ages of 6 and 11. It is frugal by design and driven by mathematical sciences and creativity.

As of August 2026, students engage with our faculty team twice a week. The faculty members at Cheenta are themselves deeply involved in non-routine problem-solving, research, and business collaborations. They bring the experience and energy derived from their own ongoing journeys into the classroom.

Each session lasts three hours.

Hour 1 — Patterns Lab

During the first hour, students work on carefully designed mathematical problems and hands-on laboratory activities. These activities are crafted to stimulate analytical thinking, reasoning, experimentation, and curiosity.

Example 1: Start with a dot diagram and draw a sequence of shapes on it, with each shape formed using straight line segments. Can you create a meaningful sequence in which every element is visually different from the others, while the number of dots touched increases by exactly 2 at each step?

Example 2: Cut a horizontal strip of paper. Twist one end and paste it on top of the other end, joining the two ends together. What happens if you cut through the middle of this object? What happens if you cut along a line closer to one of its edges?

Hour 2 — Nature & Community Lab

During the second hour, students step outside the classroom and explore nearby natural and community spaces. They collect data, observe patterns, and interact with the community to develop a deeper understanding of the world around them. The observations and data they collect are subsequently brought back to the classroom and analysed using mathematical tools.

Example: Visit trees in your neighbourhood and collect 40 fallen leaves, taking no more than four leaves from any one tree. Do not pluck the leaves; collect only those that have already fallen to the ground. Count the number of veins on each leaf and organise your observations in a table. Plot the data on graph paper. Based on your observations, predict how many leaves with 10 veins your friend might find if they collected 100 leaves in a similar manner.

Hour 3 — Creative Lab

The third hour is devoted to artistic expressions inspired by discoveries made in the Patterns Lab and the Nature & Community Lab. These may involve painting, music, literature, theatre, or other forms of creative expression.

Example: Use the collected leaves to create eco-prints on small pieces of cloth. How does the pattern in your eco-print relate to the first problem from the Patterns Lab?

Review and Evaluation

Each student maintains a reflection journal and writes in it after every session. Teachers read and comment on these journals. At the end of every 16-week period, students share key ideas, discoveries, and reflections from their journals with parents and teachers.

The journal, teachers’ comments, and student presentations together form the basis for reviewing and evaluating each student’s progress.

Vision

Cheenta aims to nurture a happy, curious, and creative childhood for children in elementary school. The programme is designed to build skills in non-routine problem-solving, experimentation, observation, and imaginative pursuits.

As they progress, students are expected to develop the intellectual independence and creative confidence needed to engage meaningfully with mathematical olympiads, science fairs, and research projects.

Mathematics in Non Routine Spaces for Elementary School

Mathematics lets us enjoy deep insights about the world around us. These insights may otherwise remain hidden from the eyes of a casual observer. The joy of this deeper understanding is comparable to literature or music. One may also build practical things using these insights. That engages the creative side of human nature.

Kids in elementary school can also enjoy this process of discovery and creation through mathematics. Designing lessons around this impetus can transform a child into a thinker and doer at a very early age. At this stage, the math should deliberately be easy. In particular, it should rarely involve complex formulae. Instead, math should be a vehicle of pattern discovery and elementary abstraction.

In this note we share a few open-ended questions that can be transformed into lesson plans in a non-routine mathematics program at the elementary school level (grades 1 to 6). These are not stand-alone lessons. In Cheenta, we combine non-routine problem solving sessions with math in non-routine spaces to produce a holistic experience for the children. Let us clarify this point before proceeding to the questions.

Non-routine problems in mathematics are found in books like Mathematics Can Be Fun by Yakov Perelman or Math Circles for Elementary School Students by Natasha Rozhkovskaya. There are several other books of this flavor. They contain problems that are deliberately non-repetitive. The motive is to help the child think rather than remember.

Mathematics in non-routine spaces, on the other hand, involves external objects such as gardens, road traffic, paintings, and the sky. These begin in spaces that are apparently non-mathematical in nature. A student and a mentor use elementary skills such as counting and pattern recognition to gain deeper insight about the space. That is part of the exercise. Additionally, they may want to create something with that insight. This layer may need more mathematical tools. The motive is to lead the child to think about mathematics in the context of the world around them, and to derive happiness and creativity in the process.

A word on method. Every problem below generates data: growth logs, sky maps, thread counts. The child maintains an observation journal throughout. The journal is the central tool of these activities. It gives the open-endedness a structure. It also shows parents what the child is actually doing, and over months it becomes a record of how the child's thinking matures.

Each of these problems is open-ended in nature. Kids may have different answers. Each problem has two key levers: discovery and creation. Discovery asks the child to observe, measure, and find patterns. Creation asks the child to build something with what was found. Both levers require some element of mathematical science. Each problem ends with an invitation to invent a definition, because definition-making is the deepest mathematical habit a young child can form.

Problem 1

Space: In-house or terrace garden.

Find a few saplings in a nearby nursery. Plant them in your home garden (this can be just one plant at the corner of a table). A plant may need soil, water, fertilizer, pesticide, and sunlight. Not every plant needs everything.

Discover.

Measure the growth of the plant over time and its relation to the inputs that you provide. Record both in your journal. Do you see any relation between the input and the growth? Observe the measurable aspects of the leaves of the plant (for example, the number of veins). Do you see any pattern? Is there a number such that most leaves have that many veins?

Create.

Can you design a more efficient input system next time to improve the growth of your plants? Can you draw a chart that predicts how tall your plant will be next week?

Invent a definition.

What does it mean for a plant to be "growing well"? Height alone? Number of leaves? Something else? Write down your own definition and test it against your plant.

Note for mentors and parents: the mathematical undercurrent here is data collection, tabulation, and elementary correlation. At higher levels the same problem supports rate of change and prediction.

Problem 2

Space: Sky

Look up. Do you see any bright objects in the night sky? Use a compass to understand directions and create a sky map in your journal.

Discover.

Observe the motion of your marked objects over a period of time. Is there a pattern? Is the moon close to certain other objects in the sky? Does it stay close over time?

Create.

Leave the compass at home. Just by looking at the night sky, can you identify north, south, east, and west? Are you able to make a map of your locality using that?

Invent a definition.

Can you find a way to define how far apart two celestial objects in your map are? You cannot use a measuring tape on the sky. What will you use instead?

Note for mentors and parents: the mathematical undercurrent here is coordinate systems, direction, and angular measure. The distance question quietly introduces the idea that a metric must be chosen, not assumed.

Problem 3

Space: Embroidery

Pick up a few embroidered clothes at your home. How many colors does a typical piece use?

Discover.

How many times does one color go beneath another color? Do you see any pattern? Do the patterns repeat? Does the design look the same if you turn the cloth around or view it in a mirror?

Create.

Can you design an embroidery style of your own that others find beautiful? Use graph paper to plan it before touching thread.

Invent a definition.

What makes two embroidery styles "different"? The colors? The repeating unit? The symmetry? Write down your own rule for telling styles apart, and test it on the pieces at home.

Note for mentors and parents: the mathematical undercurrent here is counting, repetition, and symmetry. At higher levels the same problem supports tessellations and transformation.

Thousand Flowers - a ‘new’ approach to learn mathematics (for children)

Understand


The Thousand Flowers Program is designed to provoke interest and curiosity in mathematics. It is particularly useful for children of age group 6 to 10 years, when they are starting out with the subject.

The program wants to inspire interest and disregard intimidation. It uses a hands-on approach that freely draws from modern computational tools like GeoGebra and methods from antiquity such that compass, papers, straightedge. Over the last 10 years, we have implemented this program at Cheenta with varying degree of success. We continue to run this program with the hope of creating the next generation of innovators and mathematicians.

In this document we will describe the curriculum, lesson plans and tools of this program. We hope that these tools will be useful for learners of all age.

Historical Remark


Thousand Flowers program draws inspiration from Rabindranath Tagore’s Sikkhasotro experiment, Vasili Sukhamlinsky’s experiements in Soviet Union, Cedric Villani’s 21 points suggestions, Singapore method and Math Circles in Eastern Europe. It has been developed over a decade of experiments with thousands of learners from several countries. To understand the pedagogical principles of Thousand Flowers program, pleaser refer this article.

Curriculum


Presently, the curriculum is spread over 4 modules. It can be delivered over 52 weeks. There are two variants of the curriculum: Level 1 (age 6, 7) and Level 2 (age 8, 9 and 10). Apart from the ‘topics’ in the curriculum, there is a critical ‘math-circle’ component of this program. We will explain more of that later.

Each module is expected to have 12 weeks duration. At Cheenta, we recommend the following study-hours:

  1. 75 minutes of group class discussion
  2. 45 minutes of 1-on-1 discussion (with a faculty)
  3. Three hours of at-home activities

Spatial Patterns

Numerical Patterns

Mathematical Imagination

Arith-metry

We will add the lesson plans and problem sets on each topic from each module to this document.

Dr. Ashani Dasgupta
Cheenta
Passion for Mathematics