Here it is. I’m gonna reveal it to all of you.
Every new piece of math uses old pieces of math. Math just builds on itself. Algebra uses arithmetic, calculus uses algebra, differential equations uses calculus, linear algebra uses lots of stuff…
This is true at any scale. Addition is just lots of counting, multiplication is just lots of addition, fractions are just another way to write and think about division.
So, say you don’t like a part of math. Let’s go with fractions, that is a popular topic to not like. So, when you have to do them, you muddle through as best you can and promptly tell yourself (and usually everyone else) that you are so glad it is over so you can forget about them. Sorry Charlie, ‘cuz you need fractions for decimals, and percents, and ratios, and proportions, and linear equations, and rational expression, and rational exponents, and calculus, and differential equations (seriously, if you don’t understand elementary school fractions by the time you hit differential equations, you are so screwed).
It annoys the hell out of me when a student comes up to me and just wants “the formula” so they can “do this problem.” Which is usually code for, “I don’t actually want to have to think at all to do this problem.” First, there usually isn’t “a formula” like the student wants. They want a magic code so they don’t have to think. Sorry, it doesn’t exist. Second, I will NEVER just tell a student how to do the problem. EVER. Because I understand that they need to understand all of the pieces in order to understand what they are doing now and what they are going to do next. I don’t really care if they don’t like fractions, they need to understand them in order to do almost everything else. I will go back to fractions (or whatever other fundamental principles they need) EVERY SINGLE TIME until they understand them. There are very often students who just get pissed off when I do this and stop listening.
To those students I really want to say: If you don’t want to understand; If you don’t want to learn; Seriously, get out of my class. I’m only interested in you learning the math, not in your gpa or your financial aid or you making your parents happy with a passing grade. I am here because I want to help people learn what they need to learn and understand what they need to understand. Not to hand out busy work and grades.
I don’t say that, but I REALLY want to.
I didn’t mean that to be a rant, but it turned into one.