When I say the word math, perhaps the first thing that comes up to your mind are a bunch of formulas or rules, that you even don’t know where they come from.

As a freshman in high school who is passionate about mathematics, it is frustrating to see this, and probably the main reason of it, it is that teachers only want us to mechanize every mathematical procedure and not to think beyond it, because they avoid logical thinking.

We only need to see the types of questions that are on a test or a worksheet, and we will realize, instantaneously, that most of them will be non-application exercises.

We can use as an example the Pythagorean Theorem, which indicate that the sum of all the legs of a right triangle, is equal to the hypotenuse (c² = a² + b²).

In school, the only thing that we do with this theorem is to replace the letter for numeric values and memorize it, but how we can prove this formula?

We can demonstrate it, using paper. We need a triangle with legs 3 and 4, and hypotenuse 5. On each of the sides, put a square with mosaic pieces. If we compare the pieces used for the legs and for the square of the hypotenuse, they are the same.

By demonstrating visually, the theorem, we are making mathematics familiar, understandable, and fun for students, and, also, we are approaching the main objective of math, which is to develop and encourage logical, critical and creative thinking. This is extremely useful, as it is crucial to understand abstract concepts and how to analyze things deeply.

Therefore, if we want to change the way we teach math to develop these abilities, it is essential that teachers prove every rule that they teach and apply them to the real world by using comprehensible examples for students, as I did with the Pythagorean theorem.

I know that this could be rather tedious and take considerable time, however, as William Thurston once said, “Mathematics is not about numbers, equations, computations or algorithms: it is about understanding.”