Humans are in a constant pursuit of order. We try to develop schemas to help us deal with frequently occurring situations. We constantly look for patterns. We try to make our lives somewhat predictable.
The brain doesn’t like to think. Thinking is hard. So the brain naturally gravitates towards pattern finding.
This is mathematics.
Mathematicians look around the world for patterns. Looking for truth. They take things they know to be true, and build on them. Constantly growing the body of patterns we know to be true.
The difference between me noticing that whenever it’s cloudy out I’m a bit gloomy and that the derivative of a parabolic function is linear, is that the latter is true always. It’s a fact that exists regardless belief, mood, perspective, or measurement.
I wrote the idea for this post down months ago, but it seemed relevant as this week I embarked on teaching my algebra II class how to factor polynomials. Something that nobody does, with the exception of math teachers and their students. (And I mean that quite literally. I went to the twittersphere and came up empty.) My advice to students was similar to other seemingly obscure content we learn in mathematics.
Treat these problems like puzzles and look for the patterns.
Because pattern finding, curiosity, and creativity in problem solving are all skills that are valuable and can be improved with practice.
Nobody does a puzzle and while they’re doing it says, “This is never going to help me in my life.” I don’t claim to be an expert on the motivation of puzzlers, but I did puzzles just to figure them out. I enjoyed the mental exercise.
This is how I want my students to approach math problems. I want them to enjoy and appreciate the pursuit of solving the problem. I know that’s abstract and might be difficult for teenagers to grab onto, but I’m not sure of any other justification for some of the concepts we teach.