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.
Once all the sheep had passed, he got rid of the extra stones and was left with a pile of stones representing his flock.
Every time he needed to count the sheep, he removed the stones from his pile; one for each sheep.
This means students need a degree of mathematical maturity to process the shift from the concrete to the abstract.
Many high school kids, particularly from developing countries, come to university with an undeveloped level of intellectual maturity to handle abstraction.
If he had stones left over, it means some sheep had wandered away or perhaps been stolen.
This one-to-one correspondence helped the shepherd to keep track of his flock.
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.
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.