Can you Learn Precision?

I'm studying for my first quiz. It will be tomorrow at 4 p.m.

The material is easy, stuff I could do in junior high school and certainly 9th grade. What's missing on my part though is precision.

I preach to students about finding just the right word or just the right light or framing for a photograph. But the fact is (I think) that there isn't any just right word or just right structure or just right light or just right framing or just right point of view. It's what you pick, and if it works, it works.

The numbers have to be right. One tiny mistake and the whole thing's wrong and gets wronger by the minute. And I'm making lots of tiny mistakes. It's being just like earlier in the month when I was doing those addition problems when I could add the same list of numbers three times and get three different answers. When I became very, very careful and slowed down a lot, I'd more often get it right.

This seems to be a whole different way of thinking or at least proceeding going on here.

I wonder, can you be imaginative and deliberate and careful and precise all at the same time? It has always seemed to me that deliberate and careful and precise usually kill imaginative, creative, and resourceful.

One of the reasons I decided to pursue math was to give myself the chance to explore new ways of thinking, new ways of approaching problems and solving them, and to learn how other people approach the world. Well, I'm getting my first taste already. I'm not frustrated, just curious. Can you learn to be careful enough to be accurate? What are the costs of being that careful? Is it simply laziness or is being precise its own skill and you can acquire? And if you can acquire that skill it probably doesn't happen by typing words into a computer.

I'm off to work on solving an equation that I've already done twice. The quiz should be fine.