[Izkata]

> Ok kids, today we're going to learn this new formula. You put a number in, do some arithmetic, and you get an answer out. I am not going to bother explaining the importance of this formula, how it came into existence

Short story time: I never could memorize various geometry equations, like surface area or volume of basic shapes. Then one day while bored at my part time job, I found a paper and pencil and decided to use what I'd just learned in calculus to see if I could derive one of those equations, by leaving variables in instead of using concrete numbers.

It totally worked, I reinvented the volume of a sphere equation and ever since that day I've never forgotten it because now every part of the equation has meaning. I know why it is the way it is, and it makes sense.

[foofoo4u]

This gets to the heart of what math class needs. Which is a process of learning how to re-invent formulas, constants, and other concepts. Through this, students will come to appreciate why such things exist. And they will appreciate it further if students are first challenged to solve such problems in the absence of it.