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 students that study in traditional lecture style lessons learned 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 learned using more conventional methods, were able to solve the question by attempting to apply the mathematic formulas they learn in the more complicated manor that this question required.
The second group, who had learned in a more unconventional ways 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’s untraditional learning environments.
In the second group of students that used practical yet unconventional methods to solve these questions, only 20% failed. However, the failure rate in the first group was 80%.
This example demonstrates that complex integrals and calculations have no meaning when used incorrectly or in irrelevant cases. Learning to think “outside of the box” of traditional learning methods put student in a position to succeed in life by proving to children there are many correct ways to solve a problem.