the Art of Problem Solving, by Lucas W.

Take a geometry problem. Given congruent tangent circles O and P and a line segment tangent to O with length 15, one end on point P and the other on circle O, what is the radius of O? This problem is not solvable using the school's curriculum. MCPS skips over the one simple method needed to solve this in its 10th grade circle unit - the power of a point theorem. It is an easy geometry problem, with the theorem this is just a linear equation. The school teaches us too many formulas that we do not need, and not enough complex logic to solve problems. Worse, it even skips over some of the very useful methods. We do not want to learn math, at least with the school's way of memorizing useless formulas. We want to learn a skill which will help us in real life.

The power of a point theorem was first introduced to me by the Art of Problem Solving "AoPS", a book written to teach the art from which it gets its name. In under 200 pages, the book teaches everything from prealgebra to precalculus. Compare this to the several thousand textbook pages for the MCPS curriculum. Although AoPS notably likes to skip over points in its lessons, leaving gaps everywhere actually helps you learn. Struggling through a problem but making it in the end is an experience everyone should have. It helps teach resilience, the skill of not giving up. It teaches you amazing sets of theorems and formulas overlooked by the school. It will also teach you how to solve for complex values that the school gives you a calculator for.

AoPS is a much better tool to learn than the school's curriculum. It also saves money and resources by using less pages, does not baby you with every way you will need to solve the exercises, does not heavily rely on calculators for large numbers, and teaches you a skill for life. And one last problem to conclude this argument - if n=100, what is (n+1)!/(n-1)! ?