StemHacks: Why I Love Sign Errors

StemHacks: Why I Love Sign Errors (and other things most people hate)

Sign errors, and other tiny errors that are very easy to make, can totally mess up calculations and derivations. There are so many opportunities to make these sorts of mistakes that in even a moderately simple derivation there's a significant possibility of making at least one such mistake. This is why checking your results is so important. For example, after figuring out the roots of a quadratic, try putting them in and making sure that $y$ actually does $=0$! Now, most people hate sign errors, and this makes sense: It wastes time and reminds you that no matter how hard you try, Wolfram Alpha will always be better at math that you are, and you'll wonder why you're being put through this pain when you could just let a computer that doesn't make simple errors do the work for you!? (Answer: If you actually want to understand math, which is more and more important as you get into the advanced math used in science and engineering, you need to know what's going on under the hood, even if you can't do it as well as the computer can.)

But,strange as it may sound, I actually love these little errors -- in moderation anyhow. I too can become frustrated if I'm trying to a bunch of results and I am tired and so keep making mistakes. But if I'm just doing math for fun, which I often do, I find getting the wrong answer to actually be both fun and educational.

One reason that I like making mistakes is that I don't feel like checking my results was wasted effort. But the main reason I like making mistakes is that I like the detective work of figuring out what went wrong.

Math has many different kinds of pleasures. There is the "Tada!" pleasure of figuring out a new technique and seeing it work. Then there is the "Cool!" pleasure of understanding how a new proof works, and the very rarified "Bam!" pleasure of discovering a proof or derivation for yourself that you've worked really hard on. (This can be so even if the proof you've discovered is not a new one to the whole world; rarely do you get to prove something that hasn't been proved before, but it's still very satisfying to discover a proof that's new to you even if it's not new to the world.)

Finding and fixing tiny errors, such as sign errors that led you down the garden path to an incorrect result is a different kind of pleasure -- something like Aha!, and then you get the "Bam!" when the derivation concludes correctly. Another kind of pleasure that error correction provides is the pleasure of telling self-deprecating "I was such an idiot!" war stories, which are good in classrooms to show your students that you're human too, and that their mistakes aren't to be taken as a demonstration of their failure, but rather as a demonstration of the success of checking their results, and of their prowess as a mathematical detective.

As they say: To Err is Human. To able to fix your errs is one of those small satisfactions that comes with being human.