Like everyone, I started learning math in school. I wasn’t bad at it, but wasn’t a prodigy by any stretch of the imagination. I decided my path lay in biology and returned to math in 2016 (please refer to my previous post for a description of my mathematical journey). Today I’m writing about learning math: what worked, what didn’t work.
I think that there’s something called a mathematics gaze. It’s a style of thinking that some people can easily access and some not so much. Everything in learning math revolves around learning to access this gaze to do problems. Another word for this is intuition.
What is mathematical intuition? Does it have anything to do with the real world? For a while I was convinced that if I solved enough problems I would develop it automatically. The truth is a little more complicated. If you below average or average like me, it’s not enough to just solve problems. You need an instructor with intuition to teach you how to think like them. It’s the only way you can generalise past the equations you were solving.
Another thought I had while learning math is about making mathematical models. People who work in applied mathematics spend a lot of time making models of real world phenomena. They abstract out parts of the world they care about and put them into relationships with each other. Finding the correct representations and relationships is how they define success. To that end you need a strong handle on the various objects mathematics deals with and their relationships. Practice is the only way to get there. Another thought: Which seemingly distinct problems are actually the same? This is another handy trick I’ve found in learning math. Similar mappings can take one from “impossible” to “easy” in seconds.
I used to binge watch advanced math lectures on YouTube to “build intuition”. You might laugh but I actually think it works. I always went in expecting to understand less than 1% of what was said, but even that little from people with strong math intuition is enough to develop a little idea of how math is done: not just by solving problems in a specific pattern but how to branch out.
Overall what I’ve found is that for a determined low aptitude learner there is a way to learn math, intuition and all, with only two things: practice and a high intuition teacher.