This morning I was trying to come up with some good problems for students to use to find local maxima and minima. It's an awesome feeling to be able to combine everything I know about graphs and polynomials and end behavior to create polynomials within the window that I want that do what I want. It's cool to think that I don't have to just guess random things. So the graph is too long and skinny? I can do a vertical compression or a horizontal stretch. I want two local maxes and one local minimum, so I know I need to give it a negative leading coefficient and an even degree. It might be neat to come up with some sort of guidelines and have the students come up with their own polynomials. I wouldn't want them to just guess and check though. I might have them write something that says what they would have to do to a graph to get the desired results. It really forces you to use everything you know about polynomials and graph behavior and actually apply it.
Tonight I'm thinking about the unique way that God has created me. I have been a math teacher. That has been my only career until being a coach these last 3 years. I've continued to be a math teacher while coaching. God created me with a deep love of learning. Mathematics is a bunch of well defined rules that give us an incredible playground of puzzles. I became a teacher because I wanted to do mathematics and work with people. I would never have become a teacher of any other subject. I get that you can learn in Science and Social Studies and English, so why do I love math so much? I love the definitions. Something is how we define it. I think of the stupid Neature Walk videos from high school... "It's called an aspen because that's what it is..." But really, the world operates a certain way, but in mathematics, the world exists in perfection in our minds. When we say something is a circle, we mean it is the set of all points equidistant from a center. Where...
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