“Complex integrals and calculations have no meaning when used incorrectly or in irrelevant cases. In fact, certain calculations have no meaning if they are not effective in real time.“
– e² Young Engineers –
There is great significance in the way children succeed in thinking by themselves and from their own experience.
The following is a question from the PISA test, an OECD test which is conducted as part of their international research into education, and which has taken place every three years since 2000. The children are expected to translate theory into practice with the tools they’ve acquired at school.
Question: You have bought a new house and decided to build a fence around the perimeter. How would you measure the length of the fence?
Most of the children had studied the exact formula to calculate the perimeter, and remembered that the number Pi=π=3.14.
From that point, arriving at the rest of the solution was easy.
However, some children who had studied in a more unconventional way used a rope and measured the perimeter length to prove to themselves the formula and the number Pi=π=3.14.
The question became more complicated when the perimeter was asymmetric.
The kids in the first group, who had studied more conventional methods, were able to solve the question using complicated formulae and integrals.
The second group, who had studied in a more unconventional way used the same rope to calculate the right measurement and solved the problem using an experimental approach.
This is an efficient implementation of the tools acquired by the second group in their schools.
In the second group, which used the practical, unconventional method, only 20% failed this question, while the failure rate in the first group was 80%.
We have shown you this example to demonstrate that complex integrals and calculations have no meaning when used incorrectly or in irrelevant cases. In fact, certain calculations have no meaning if they are not effective in real time.