## Why GanitCharcha ?

Mathematics curriculum are usually defined in a way that does not provide adequate scopes for students to learn how to ask mathematics questions. Students are rarely introduced with the mathematical ideas behind the formulas, procedures and theorems and that is what is important to help them fall in Mathematics. Let us recall in this context two famous quotes which are very relevant.

" In mathematics the art of proposing a question must be held of higher value than solving it. "
- by George Cantor
" Millions saw the apple fall, but Newton asked why. " - by Bernard Baruch

GanitCharcha does not teach Mathematics, it ensures growth of mathematical mind so that we learn to enjoy Mathematics. The best way to help students enjoy Mathematics is to allow them to engage with Mathematics. Encourage them to make productive failures - that will enable in them a sense of accomplishments, thereby enhancing their confidence and love towards Mathematics. Needless to say, that it is a continuous process.

There is a need to look into the subject from a totally different angle of what prompted Mathematical discoveries and Inventions. And being able to relate a problem with the associated solution or discoveries, will help students in many ways like the following.

They will learn to ask relevant mathematics questions.
It will make the subject interesting to them and they will begin to love the subject.
Students will also learn to relate mathematics with its applications or vice versa. And last but not the least,
It will help to build problem solving attitude in students.

Having said all these, let us consider a few small examples. Suppose a child knows the technique of how to add. Then one fine morning he/she is introduced with multiplication table for $2$. The teacher says it is simple and you can very easily memorize it. You need to start with $0$ and then go on skipping by one digit and you get $2, 4, 8 , 10, \ldots$ in succession. And that is your multiplication table for $2$.

But in this process, the teacher has forgotten to help the student understand the need, the motivation behind the multiplication table. Ask the student to compute $2 + 2$, $2 + 2 + 2$, $2 + 2 + 2 + 2$ and so on. Help him/her to find the pattern and that will engage the student in a much positive way rather than just to memorize tables. Repeat this procedure when teaching multiplication tables for $3$, $4$, etc.

Then challenge the students with additions $2 + 2 + 2$ and $3 + 3$ or $2 + 2 + 2 + 2$ and $4 + 4$ in pairs. And allow him to discover one such pair for which the sum matches. Furthermore show them in the multiplication table that they are required to remember only half of the multiplication table, not the full. Believe me, you will be amazed to see that your little student is enjoying too.

This seems very trivial, so why not take another example. Any number multiplied by itself will always yield a positive number and the first number is called the square root of the later. Square root of a number then seems applicable for only positive numbers. Natural question is therefore, what is the square root of a negative number. It can not be answered from our knowledge of numbers so far, so came the definition of Imaginary Numbers. The square root of $-1$ is defined as the number $i$, assuming it exists, such that $i*i = -1$. Therefore, $\sqrt{-2}$ is defined as $\sqrt{2}.i$ and so on.
The symbol $i$ was introduced by L. Euler in 1777.
The fact that the algebraic identity $\sqrt{a}. \sqrt{b} = \sqrt{a.b}$ does not hold when $a$ and $b$ are negative and it lead to inconsistencies since $-1 = \sqrt{-1}.\sqrt{-1} = \sqrt{(-1).(-1)} = \sqrt{1} = 1$. This inconsistency led to the use of the symbol $i$ for $\sqrt{-1}$.

German mathematician Leopold Kronecker once told - "God made the integers, all the rest is the work of man". Given this, do we really ask ourselves the question how different numbers like rational, irrational, imaginary, real came when we study this or when we teach this. The evolution of numbers are itself very interesting and has a long past from ancient history to the modern times.

"We are also interested to know from you - your experiences, your thoughts on this. That would enable GanitCharcha to accomplish it’s mission in a much more efficient and meaningful way. Ganit Charcha is working towards the following mission."

1. GanitCharcha’s mission is to help students fall in love with Mathematics.
2. GanitCharcha aspires to be a virtual Mathematics Incubator that aims to actively engage students with mathematical concepts and techniques while helping them to find their path to success in life.