Teachers and lecturers can improve this abstract thinking by being aware of abstractions in their subject and learning to demonstrate abstract concepts through concrete examples.
Experiments are also helpful to familiarise and assure students of an abstract concept’s solidity.
The earliest example of abstraction was when humans counted before symbols existed.
A sheep herder, for instance, needed to keep track of his flock of sheep without having any sort of symbolic system akin to numbers.
There is real strength in this: we’ve created a space where the rules are minimalistic, yet the games that can be played are endless.
Another advantage of abstraction is that it reveals a deeper connection between different fields of mathematics.
This is because of the way mathematics was taught at high school.
I have seen many students struggling, giving up or not even attempting to study mathematics because they weren’t given the right tools at school level and they think that they just “can’t do maths”.
Today, we use the Arabic numbers (also known as the Hindu-Arabic numerals): 0,1,2,3,4,5,6,7,8,9 to represent any integer, that is any whole number.
This is another example of abstraction, and it’s powerful.