उतादकम्यत्पवद नि बुदेर धि षि तम्सतुरषेण संखाः |
वकस कृ तस तदेकबीजमवकमीशम्ग णि तम्च वने ||
This is the first shloka from Bhaskaracharya’s 2nd part of Siddhanta Shiromani known as “Bija Ganita“, wherein Bhaskaracharya is praying to Ganit.
In traditional India it was our acharyas like Aryabhatta, Bhaskaracharya, Varahamihira, Madhava etc who studied ganit and its scientific application, because they did not perceive ganit and vigyan separate from their own spiritual practice. Rather, they saw these subjects as an opportunity to study the creation of the creator. This drishti of seeing parmarth (parmatama) and vyavhara (interaction) together is integral to Bhartiyata drishti. It is this drishti that we need to present to our children as parents and acharyas.
Apart from shraddha that the child builds towards elements of Bhartiyata, towards Parmatma, Guru and even Ganit itself, Ganit is a subject which is integral to the holistic development of a child. It helps build logical, analytical, quantitative and numerical abilities in the child. If we deal with Ganit only at the numerical level, we shortchange the whole possibility of seeing ganit integrated with Vyashti (Person/Family), Srishti (Nature), Samashti (Society), Parmeshti (Paramatma). Then, we will tend to see ganit only as a tool to count and to calculate. A drishti devoid of such connection slowly forms a habit of seeing things, resources, people as objects of exploitation and consumption. This is the very disease that is prevalent in the world today. More on this in my later letters.
At Vidyakshetra, it is our endeavour to give our students this crucial inter- connection between vyavahara and parmarth not only through Ganit & other subjects, but also through our environment and our daily interactions.
For eg: When I ask why multiplication happens from left to right and
For eg: When I ask why multiplication happens from left to right and division from right to left, most people can’t answer. The reason is, their teachers like most of ours, didn’t give them the connection between the place value system and four processes. Else, they would have learnt that multiplication is multiple addition and hence it goes from the smaller unit to larger one i.e from left to right. Whereas division is multiple subtraction which means going from larger unit to smaller i.e from right to left (thousands to hundreds to units).
An unsettling point is to see children learn fractions/decimals and percentages without knowing its usage and how fraction is different from division; why decimal is needed when we have fraction and what do we mean by percent and why only percent (per/100) and not per/50 (perfifty) or per/1000 (perthousand)?
Near to far is a very well known pedagogical principle. When we introduce any new concept in ganit to children, we introduce it using objects which they can hold, touch, smell, count, give away, collect more of or distribute, divide etc. After which we do the above processes using images, because the image is closer to us than numbers. If I say “banana”, most of us will see a yellow banana or a bunch of bananas baring few, maybe one in a hundred would see the word “banana”. Objects and images connect with our feeling realm and hence all the children are able to learn the concept comfortably and enjoy this process of learning. More practice is provided later when the numerical form is introduced and only then sums are done. Thus, in effect we learn the concept by utilizing and nourishing all three shaktis: kriya, iccha and gyana also known as hand, heart and head.
One of the most important stages in the life of a student of ganit is when the child is introduced to money and business ganit. This is the first subject in modern mathematics which is directly taught in its form of application, but the siddhantic (principle) aspect of this important topic is absent in almost all curriculum. It is very crucial to teach children the difference between cost and value, need and greed, tangible and intangible profit, richness and prosperity, history of money and only then move to commerce and economics as we know today.
Around 13 years age, when the child is introduced to beeja ganita (algebra) it is pertinent to introduce to the child the Karma siddhanta where we experience the good (positive action), the bad(negative action) and the neutral (inaction). Also the dualities of the world as in good/bad, truth/lie, beautiful/ugly, high/low etc. While the bulk of mathematical learning happens around numbers, equations, figures, formulas and graphs, it is to our own peril if we introduce ganit in just numerical form and not in living form with its connections with life.
In senior classes, where ganit/science/ geometry come together, projects and applications take the center and through those projects and applications we connect the subjects. For example designing and constructing houses, wherein children of Vidyakshetra have constructed different types of houses over the last 5 years (more about this in later letters). Seeing ganit in plants and the sequence of leaves and design of petals, in conch shell, perfect proportions in humans, mathematical patterns in ice cube, water and sand particles etc. Learning ganit in this manner opens a whole new world in front of our children and ganit is no more a subject to fear, rather a subject which children look forward to and thoroughly enjoy.
PS: Another important question that comes to the mind of the readers is, if Vidyakshetra does Vedic Ganit with children. While we continue to research and develop our expertise in the space of Vedic Ganit, at present we do modern mathematics using methods shared above. Vedic mathematics is not just a collection of few sutras for doing quick calculations. Vedic mathematics today is an area of research in the works of Aryabhatta, Bhaskaracharya, Varahameer, Madhva, Ganitachrya, Ramanujan and more. It’s a vast ocean and at Vidyakshetra we have started exploring it. Wherever possible we have started introducing some concepts from the above listed works of acharyas. While it is our deep desire to teach Vedic Ganit, it will take us some more years to be ready to bring it in our classes.