Stupid Mistakes
Dr. Kim Johnson, Logic (Lively Logician) and Counting to Computers with The Lukeion Project
Celebrating your wins on tests or essays is crucial. But don’t dismiss the stupid mistakes out of hand---sometimes there is more to them than just carelessness.
Correcting “Think-Os”
A stupid mistake can also be called a thoughtless error. Sometimes I call them “think-os”. Like a typo, a think-o is something that you knew or understood well but wrote or typed incorrectly. Most often they stem from a momentary lapse in concentration.
Given that they are so fleeting, why should we not dismiss them and move onto something that is more important? The truth is, sometimes thoughtless errors turn out to be very important.
In 1999, scientists launched the Mars Orbiter with hopes that it would expand knowledge of the climate on Mars. Their hopes were dashed when, instead of exploring Mars, the orbiter crashed into the surface. The European scientists on the project used the metric system, the Americans used the English system, and so their calculations didn’t’ match up. This was truly a thoughtless mistake because every scientist in that group understood the difference between metric and English measurements. This thoughtless error cost millions of dollars.
“Fine,” you might say “…but I am not in charge of million-dollar projects, I’m just taking my Latin exam, doing some math homework, writing an essay, or taking a history quiz. A stupid mistake in these situations does not have any dire consequences. So why should you care?”
You should care because sometimes a seemingly innocent mistake hides a deeper misunderstanding. For example, if the instructor asks for one form of a verb and you give another, or if you are expected to give a number and you give a function, perhaps you never fully understood the difference and need to clear something up. It’s just a simple mistake---but it indicates that there is something you need to understand more fully before moving on.
Another type of worrying mistake is one that you make over and over. In working with students, I’ve noticed that each student has their own personal set of repeated mistakes. My personal set of mistakes is to lose negative signs and copy down digits in the wrong order. One friend misspelled the word “their” nearly every time he wrote it. Some students have particular facts that they always get backwards.
The best part about these mistakes is that you are not doomed to make them forever.
How To Avoid Careless Errors
Obviously, if you have a gap in your understanding of some part of the topic, work to figure it out! Honestly appraising your work is crucial in clearing up misunderstandings. Without evaluating the mistake, you might think there is nothing left to think about and move on. The great thing about fixing mistakes which come from misunderstandings is that by fixing them early, you eliminate a whole raft of mistakes later. It’s kind of like killing a mosquito in the spring will eliminate thousands of mosquitos later in the summer.
Fixing mistakes that you make again and again can be slightly more difficult. The problem with trying to fix repeated mistakes is that they indicate a type of momentary blindness and inability to notice errors.
The first and obvious thing to do is to check your work. This involves a few things. First you must write something down to check. Have you ever heard your teacher tell you to “show your work?” This is why! Although an abacus or a counting table is a powerful tool, written work wins, hands down, when you are trying to catch errors.
Second, coming back to your work after a day or at the end of the test is another good habit. Even a few minutes can give enough distance so that mistakes become visible instead of seeming to be correct. When checking my work, I think of it like a “hidden picture” puzzle, or a “spot the difference” puzzle---each difference should be deliberate, not an oversight.
You can develop a habit of going over your work looking for your most common mistakes. For example, my friend would search his papers for all instances of “their” spelled in his particular way, and I watch for lost negative signs. You can learn what errors you tend to make and look specifically for those mistakes. By focusing on and analyzing what you first dismissed as “stupid mistakes” you can find them and even get better at avoiding them.
Another strategy for catching foolish errors is to check with someone else. When mathematicians are working, they often work together. This is in part to generate more ideas, but it also allows them to catch each other’s momentary lapses in thinking. Even the most accomplished writers have editors. Software engineers review each others’ code to catch bugs. We can help each other reveal thoughtless errors.
Sometimes this is not allowed because of an honor policy, but even then getting another person involved can help. One of the best ways to catch errors is to explain the work to someone else. By going over your work out loud you introduce another sense---your ears can catch what your eyes do not. Pets are some of the most patient listeners. Even though your dog will never have to factor quadratic equations of conjugate Latin verbs, they will listen patiently and never judge when you find a mistake.
Get Over It
Finally, not all mistakes are signs of misunderstanding or part of a pattern. Sometimes a stupid mistake is just that. If that’s the case, your most potent tool is to just leave it behind and move on. Dwelling on mistakes takes mental energy that would be better put to use in learning new material and analyzing new ideas. Try pretending that you are looking at someone else’s work as a teacher or a scientist. Then you can judge more accurately whether the mistakes require further action or if they are not matters of concern.
Mistakes will definitely come, that is certain. Making mistakes is part of being human. Learning to deal with them appropriately---with honesty, attention, and grace---makes us better humans
