There is no shortcut to grasp any abstraction.
Each of us need to cover our journey to reach any abstract concept.
If I talk about any abstract concept in mathematical context – I will suggest 3 following steps
- Take concrete examples
- Make your own stories/drawings based on that abstract concept
- Keep on repeating point 1 & 2 until you feel that abstract concept
X + Y = Y + X
It is an abstract concept.
If we tell our kids that 2 + 3 = 3 + 2
A young child can understand it easily but he can not digest x + y = y + x.
The first one (2 + 3 = 3 + 2) is a concrete example while the second (x + y = y + x )is Abstract.
The aim of learning should be to go through so many concrete examples that Abstract concept becomes absolutely simple and intuitive.
Lot of kids say that they hate algebra. I tell them that you are too young to decide it 🙂 You need to play with it bit longer to decide whether you love / hate algebra.
Why do we need abstractions?
Why cant I start from a guess and keep narrowing my range as per the observation.
Example – The sum of 2 numbers is 26 and the difference is 2. What are the numbers?
I told him, between 1 and 2 there are infinite numbers, how long he will keep on trying. Guess and check is introduced at younger age so that you guys develop a better feel for the numbers.
But, when the question contains real numbers, things are not that discrete. It is continuous now.
So, we assume x, y, z for the numbers and then form the equation to find out the answers.
English language gives us sentences, Maths gives us equations.
Do we always have to use x, y, z?
I saw an opportunity to have a meaningful discussion to open up the spectrum of understanding a bit more.
I told him that you can use anything. We just need a placeholder kinda. You can even use drawings for every number. But, it will take more time when you complete your drawings at every step of calculation. But, eventually the answer will be same and you are free to use drawings.
When we need placeholders, we will pick something that we already know. You guys know english alphabet very well so, you pick letters from there.
If somebody is studying in hindi medium, they will pick characters from there and the beauty of maths lies in the fact that mathematics logics are same for both students.
Mathematics is genuinely the most universal language.
