At the beginning, of course, there was no work to show. Simple addition, subtraction, and the like. It had to be done in your head, because it was more or less a single operation, without intermediate results.

But that didn't last long. Multiplication, division, longer and longer problems. They all had multiple steps, multiple things to do.

I understood math well at the time. I was flying through problems, having little trouble. One of those people that understood the principles behind it, when other people in the class were still struggling to figure out what was going on.

It wasn't long before I ran into that command, that requirement that so many math teachers lay down. Show your work. Never mind the fact that I was the first one done on a test, and with one of the top scores. Never mind the fact that I really didn't have a way to cheat. I still had to show my work.

Anyone who is able to do longer problems in their head knows that you can go a lot quicker, and develop shortcuts that don't really translate into how you work it on paper. You have to actually slow down the rate in which you work.

Sadly, I also suspect that by being required to put it all down on paper, I needed less mental effort. I didn't have to remember as much, couldn't work as fast. I suspect that it in fact harmed me.

I know eventually I would have had to start showing my work regardless. There comes a point where there's just too much that needs to be done. Too bad I didn't get to wait until this point, but had to lose abilities I once had instead...

I wonder if it had anything to do with the slow decrease in interest and performance in my math classes...

Primarily the reason math teachers ask you to show your work in high school is to prepare you for advanced algebra and calculus. Perhaps it does slow you down, but at the same time, if you can't prove your work, it will be thrown out. For all anyone else knows, you got the answer by magic. This is a basic tenet of science and mathematics: reproducability. If someone else can't do the same thing you did and get the same result, then you (or anyone, in the case of new research) don't understand what you're talking about, or you can't pass on that understanding to the next person, thus making your work pointless.

Also, it's worth noting that it's much easier to understand where you went wrong if your entire process is written down. This means that not only can you go back and fix your mistakes, other people can too if they find them. Think of it as mathematical open source.

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