I think that math teachers know a lot more than they think they do. Coming from a physics major that might not seem incredible but hear me out. Math is very much related to life, and not just because of its application. I promise not to confuse anyone with math terminology, or at least I'll try my best.
My friend Peter Hill is a math teacher at the high school I graduated from. In one of his online devotionals he talked about watching his students do algebraic equations. At the end of the problem they would simply put a number. He talked about how the number doesn't mean anything under two circumstances. 1, if they don't say what the number represents, ex:5 isn't an answer but x=5 is. Without context a perfectly good answer isn't worth anything. And 2, if you don't know how you got the answer. Any debater knows you can't just throw out facts without knowing where the facts come from and how to defend them. You need to be able to defend you position and your answer.
In our lives this translates to the never ending battle with society to defend your ideas, opinions and beliefs (or culture). If we have ideas without context (x=5) you can't begin to share them with others. They're just ideas and they only mean something to the person who thought them up. When we add context they begin to mean something to the people around us. Context is great, but if you can't prove it, or at least back it up with testimony or reference, you've hit a different wall. That's because you can know the truth, the whole truth and nothing but the truth but if you can't defend it people won't take you seriously.
Now let's do some more advanced math and quote my math 221 prof: "don't make mistakes".
Now that sounds really ridiculously simple, but who amount us can claim to have managed this. I can't. What Dr. Broughton is talking about is a really complicated theory call Matracies, where you try to solve several algebraic equations at one time. Mistakes are like a cancer, they take over all the good work you do and make it wrong too. If you slip a negative sign into the matrix where there isn't a negative number then all your proceeding calculations will be wrong. Heaven forbid you make a second mistake.
But what I take from that isn't simply don't make mistakes. Its a bit deeper in that if you don't know you're wrong, or going about something wrong, you can do a lots of things with good intentions that are completely worthless. We need to continuously check ourselves to see if we're on the right track and haven't slipped a negative in where it doesn't belong. We also need to occasionally admit that we've made a mistake, that we might be wrong, and that we need to reevaluate or even start over.
From math we take these little lessons and if we care enough to learn them and then apply them, we might just get somewhere.
What can I say? Math teachers are a little smarter than we thought.
