If I Ran a School... Part 1 Section 0

Introduction to Mathematic Education.

It's hard to know where to start when considering the problems I have with math education. So, let's start with the difficulties:

*Math is built upon math. The point of math is to start with something simple and abstract increasingly complex ideas from that. Because of this, falling behind in math means you will be behind in math for the rest of your education, unless either it stops, you work hard to get back on track, or a miracle occurs.

*Math works for certain people better than others. Certain people can just see math. Others need it put in their face and wiggled around for a while. The problem is, very few people can see it, grab it and wiggle it around in front of someone else. This leads to two types of math teachers (there are exceptions):
**The brilliant mathematician: This is the math teacher that clearly knows his math and teaches you useful tricks. The problem is, math just works for him, he doesn't need to think about, so he can't explain it very well.
**The formula teacher: This teacher can do math fairly well, but doesn't understand the churning of the gears well enough to teach how to think mathematically. Instead, they try to teach formulas to their students. Those who can see math understand why the formulas work, the rest are flipping the magic switch.

Most of the problems I have with math education stem from these 2 problems. There is one more large problem: Schools have a tendency to try and rush students through calculus. This is quite possibly the worst idea ever. Calculus is terribly easy so long as you have a thorough grasp of algebra. If you do not have a thorough grasp of algebra, calculus is impossible, absolutely impossible. There are other subjects in math that require a less thorough grasp of algebra, and help to expand your grasp of algebra. Further, because students only learn geometry, elementary algebra, and calculus, they have a very false impression of what math is. Mostly, what students learn is arithmetic.

This part will have multiple sections: first a brief explanation of how I would do math in our current school system, then a brief "lecture" on each subject, and finally a hierarchy for use in "my system"