How To Minimize Careless Errors:

by on October 24th, 2012

Remember those times when you were sure you got the answer right, only to find out that you got it wrong? For a moment, you even think that there must be a mistake in the answer key. Then, you take a look at the problem again, you check your work, and you say, “I can’t believe I did that!” You knew exactly how to do this problem and you should have gotten it right, but you made a careless mistake.

What’s a Careless Error?

By definition, a careless mistake occurs when we did actually know all of the necessary info and we did actually possess all of the necessary skills, but we made a mistake anyway. We all make careless mistakes (yes, even the experts!); over 3.5 hours, it’s not reasonable to assume that we can completely avoid making careless mistakes. Our goal is to learn how to minimize careless mistakes as much as possible.

How Can We Minimize Careless Errors?

Isn’t the whole point of a careless error that we don’t know when we’re going to make them? They just happen randomly and we can’t control that!

Actually, that’s a little bit true, but not entirely. It is the case that you should always expect to have a few careless errors here and there; as I said, we’re human and we’re never going to get rid of them completely. We can, though, learn to reduce the number of careless errors we make.

A lot of times, careless errors are due to one of two things: (1) some bad habit that actually increases the chances that we’ll make a mistake, or (2) our own natural weaknesses.

Here’s an example of the former: I’m working on a rate problem that talks about Car A and Car B; I go all the way through the problem and do everything perfectly… except I pick the answer corresponding to Car A’s time when they asked me for Car B’s time. Argh!

So, what’s my bad habit here? (By the way, I used to make this mistake myself!) I didn’t make sure that I knew what I was solving for. I would dive in, and do this long complicated problem, and by the time I got to the end, I’d forgotten what I was solving for, and I didn’t go back and check at the end. I also noticed that I was more likely to make this mistake when I set up the problem such that I was solving for the wrong thing first. You can solve for either Car A’s time first, and then use that to find Car B’s time, or vice versa. If they asked me about Car B and I solved for Car B’s time first, I rarely made that mistake, but if I solved for Car A’s time first… watch out.

So I developed several different good habits to put in the place of my various bad habits. First, I got into the habit of skipping several blank lines on my scrap paper and then writing “B time = ______?” and drawing a circle around it. Then, I’d go back up, do my work, and “run into” a reminder that I wanted to solve for B.

I also built the habit of solving directly for what I wanted. On any problem with multiple variables, I could solve for one of the other ones first, but if they want x, why should I solve for y first unless I absolutely have to? Now, while I’m setting up the problem, I always look first to see whether I can set up the problem to solve directly for x.

Finally, when I’m done with the problem and ready to pick my answer, I’ve built a habit to glance at the question stem on the screen – just to make sure that I really did solve for the right thing.

So, what did I do here? First, I figured out what specific mistake I was making and why I was making it. Then, I instituted three new habits that would minimize the chances of making the same mistake in future. Incidentally, one of those habits (solving directly for what is asked) also saves me time! (Note: you don’t necessarily need to set up 3 new habits; often, just one new habit will suffice.)

Figure Out Why

The key to minimizing careless errors: you must figure out why you made the mistake you made. Don’t just yell at yourself and then move on. There is some reason (or reasons!) why – and if you can figure them out, then you can also figure out what new habits will help you to minimize those same kinds of errors in future.

Here’s an example of the second type, a natural weakness; this is a common error that I see among my students all the time.

You’re solving this equation:

x – 1 = -20

      x = -21

And then you continue on through the problem. Except that x doesn’t equal -21… it equals -19. We have to add 1 to both sides of the equation, and adding 1 results in a larger number. -19 is larger than -20, but people go the other direction because negative numbers are weird and can cause us to make mistakes. If you notice that you make this same kind of mistake multiple times, you’ve got to do something about it.

So what do we do here? Remember when you first learned how to do algebra? We were taught to write “+1” under each side of the equation:

x - 1 = -20

   + 1    +1

      x = -19

Then, as we got better at algebra, we were able to stop writing that step out. If you find, however, that you’re prone to that particular error, make it a habit to write that step out every time.

Note that I said “if you’re prone to that particular error.” If you make that error once in 6 months, then you don’t need to start writing out +1 (or whatever it is) every time – you can consider that a “random” error. But if you make that error a few times over the course of a month, then start writing out this kind of work because you know that you’re at risk of making this kind of error.

What About Verbal?

I gave math examples above, but this whole process works just as well for verbal — and, again, the key is figuring out why you made a particular error. If you realize that you tend to make mistakes on harder sentence correction questions because you pick what “sounds good,” then you’re going to have to train yourself NOT to pick based just on what sounds good. It’s okay to think, “Hmm, B doesn’t sound as good as A.” But then ask yourself why. If you can point to one specific reason why B actually is bad, then you can cross it off confidently. (Note that this is different from “Oh, B is definitely wrong.” If you think that, then you’ve likely noticed at least one specific reason why B is actually wrong even if you haven’t articulated that reason clearly, so go ahead and cross off B. If, on the other hand, your thought is more along the lines of “Hmm, I don’t like B so much,” then take the extra step to ask yourself why.)

Keep Track of Careless Errors

Start a file on your computer, or keep a notebook handy when you’re studying, and jot down the careless errors that you make. Periodically, go back over the list and look for patterns: the same or similar types of errors. If something just happens once, that’s okay. But if there’s any kind of pattern, then start asking yourself why and what you can do to minimize the chances of repeating that pattern in future.

If you haven’t been doing this in the past, take an hour sometime in this next week to run back through the problems you’ve studied over the past week (or however far back you can go while still remembering what errors you made and why you made them). Jump-start your log using these recent problems and then make a habit of continuing to pay attention to such errors in future!

Last But Not Least…

Sure, we all get a little upset when we make any kind of error. But after that first moment of irritation, realize something: you just found an opportunity to get better. You want to find these careless mistakes (and any other kinds of mistakes) while you’re still studying so that you can prevent them from happening during the real test! If you aren’t finding careless errors while you study, then something’s wrong – because I guarantee you that you’re making them. And, if you’re finding them but not doing anything about them, then you’re losing opportunities to improve. So be a little bit glad when you make a careless mistake, because you know that you’re now going to take steps to avoid losing points in that way in future!

3 comments

  • Great article Stacey, and yes, nothing hurts more than loosing score in the questions to which we know the answers.

  • Hello Stacy, I am always a big fan of your essays. You articulate things better and provide a suggestion that is actually implementable rather saying “be careful.” I have issues of question read errors. When the question says “positive integers x and y are…”, I most of the time miss that “positive” part. I have issues with qualifying words. Even if I write "+ive i" at the top, as I move along on my calculations, I unknowingly make the assumption that x and y can be either positive or negative. Do you have strategies around these kinds of errors?

    • Thanks. :)

      You wrote "even if I write +ive i" - does that mean that you don't always write it down? If not, that's part of the problem. One habit to build for EVERY math question is: what are the constraints? There's almost always at least one. If you build the habit to look for / think about / write down the constraints *every single time* that will help. And if you ever get to the point where constraints matter (eg, "I have to test some numbers...") then one default habit to build is the thought: "What am I allowed to pick?" Every. Single. Time.

      Next, since you know that you're having issues with constraints, make yourself start to write them out more completely. Positive Integer. Capital letters. Put a circle around it. Later, you might build the habit will enough to be able to write +ive i or + int or whatever. But, for now, because you know this is a weakness of yours, exaggerate the importance of the information. Just the annoying-ness of having to take the time to write it out will help you to start building the habit of making yourself think about the constraints all the way through. :)

      If this always tends to happen with pos / neg, you might also try jotting down a number line. Circle or otherwise indicate on the number line what you're allowed to use for this problem and keep the index finger of your non-writing hand pointed at that number line. (Again, you won't necessarily need to do this always - once you build the habit of checking these things, you won't have to go through such drastic measures!)

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