Exorcizing the devil from the details
April 22, 2015 7:33 PM   Subscribe

I'm currently studying undergraduate math and though the concepts are clear, I lose a lot of marks through carelessness or small errors. Please help me pick up on/avoid these better.

I am sure I lack discipline. As a fairly bright sort I am accustomed to doing math in my head, which no longer cuts it at university level. Trying to hold it in my head for more involved problems results in small errors like losing a minus sign or slight number errors which throw the whole thing awry. I also have trouble mixing up capital and lower-case letters, which doesn't help.

The question is twofold: Faced with a similar detail-demanding discipline, what methods do you use to avoid errors? Similarly, how do you -find- errors after the fact?
posted by solarion to Education (15 answers total) 7 users marked this as a favorite
Best answer: I totally do this. Especially when I feel like I really get the material and feel like I can just speed through the work. The only way I have found to avoid it, is to re-work every problem, especially on tests. If I have two hours to take an exam, I use it all, checking and re-checking. I paid for the class, dammit! I'm getting my money's worth!

If I am tired or distracted, I know I will make more mistakes. When I reach this point, first I take a break. Stand up and walk around. Stretch. Get something to drink. (During a test, I just stop, relax my shoulders, roll my head around, rest my eyes for a moment.) Then I will take the time to write out all the steps - even simple arithmetic steps - one step on each line. (I actually kind of like seeing complicated math problems all written out line by line all tidily aligned on the equals sign. Dorky but true.)

I think there is a certain expectation at higher levels of doing things in your head and not writing out each simple step. But it's my grade and I'm the one who'll lose if I make dumb mistakes. So whoever thinks like that can just deal with it. It may take a little more time but I'll get the right answer in the end.

Good luck.
posted by Beti at 7:51 PM on April 22, 2015 [5 favorites]

Faced with a similar detail-demanding discipline, what methods do you use to avoid errors?

I generally couldn't, leading me to...

Similarly, how do you -find- errors after the fact?

I double and triple checked my work to catch errors I inevitably made.
posted by deanc at 7:56 PM on April 22, 2015 [5 favorites]

If there's a substitute for writing it all down, I haven't found it yet. (Even when it's no longer school-environment math and I can spreadsheet it up, I have to make sure I'm really clear on what each cell formula's doing.)

Get a nice mechanical pencil. It'll help make all the writing seem less tedious.
posted by asperity at 8:08 PM on April 22, 2015 [3 favorites]

Math is a muscle. You flex it by writing it down on paper.

Maybe you need a cheap german fountain pen and some nice french paper to motivate you to do this more?
posted by oceanjesse at 8:31 PM on April 22, 2015 [3 favorites]

Just to echo others, if you are making small mistakes when skipping steps, then don't skip steps. What Beti said above has a lot of truth to it: if you do things in an organized way it helps you see the flow of your ideas.

Also, like anything worth doing, math is hard and takes a lot of practice. You will get better at these problems the more of them you do.
posted by number9dream at 8:34 PM on April 22, 2015 [2 favorites]

I've always found that for all math problems I have to write carefully in tidy columns. If I scribble then I slip up. The column layout is essential for me to be accurate. And check answers, of course.
posted by anadem at 8:47 PM on April 22, 2015 [2 favorites]

Seconding the "triple check everything" recommendation. Try to do it different ways if possible, like simplifying the algebra in a different order, using a different technique. Honestly, if I find myself only able to solve a problem one way, it's usually a sign I need to learn more.

Also minus signs. Pay attention to them. They are probably more than half of all my algebra errors. Double check them as you're going from one line to the next in addition to normal double checking.
posted by Zalzidrax at 8:53 PM on April 22, 2015 [3 favorites]

I have Dyscalculia and while I also understand the concepts of math and science I also make very stupid errors with the simple arithmetic. I've found that it helps me doing math if I do it in different colors. I know that may not be possible with actual homework, but during study... that might help.

Also, saying the problems out loud while doing them helps a lot. I mean if you have the problem 2+4=x-2 say out loud "two plus four equals x minus two" and as you go through each step, say out loud what what operations you're doing. It makes you more aware of what you're doing and why. Mindful math. It helped me anyway. I still mess up, but not as much. Then again my brain doesn't like math so YMMV with that. You might not want to do that during finals... but yeah.
posted by patheral at 9:47 PM on April 22, 2015 [4 favorites]

it helps me doing math if I do it in different colors

That's an excellent idea. I was working on a long problem a couple of days ago and I could not keep track of all the sets of parentheses and brackets. I pulled out colored pencils and it helped quite a bit. I also use a red pen when I'm studying for negative signs that I tend to miss.
posted by Beti at 11:07 PM on April 22, 2015 [1 favorite]

I suffered from this throughout my degree. Check and double check then check again. Obviously you know how fast you work, and how much you can afford to spend time checking your work. Personally I tended to blaze through exams then go through and fix all my errors at the end, but that's just the way I work.
posted by Cannon Fodder at 1:28 AM on April 23, 2015

When doing math (stats -sorry) exams, my goal was to show the examiners, I'd learned everything they wanted me to, so my goal was not the correct answer as fast as I could (what I did in high school), it was to present the solution as if to an imbecile. So I did every step (even the stupidly easy ones), as neatly as possible (like I was teaching someone, because at speed, my writing is indecipherable, even to me), and then for fun, if the question didn't ask for it, but there was a further step I could do, I would because - ego.
posted by b33j at 5:06 AM on April 23, 2015 [1 favorite]

You mention that you tend to mess up upper and lower case letters. An approach I always took was to, at the top of the page, carefully rewrite the problem with friendly, hard to mess up variables.
I also did everything on what was called engineering paper, which had graph paper lines on one side that you could see on the other, which really helped me keep things neat without being constrained by regular lined paper. A really good pencil and eraser helped too.
posted by rockindata at 5:24 AM on April 23, 2015 [3 favorites]

1) Neatness counts. A lower case a could be mistaken for a 9. A tiny minus sign could be a smudge. Misreading one's own handwriting is deadly.
2) Make sure you copied the problem correctly. It's amazing how often this occurs.
3) Make sure you followed instructions. Solving for X may only be part of what you're supposed to do. You may have to substitute it back in various ways to find what they're asking.
4) Check that your answers work in the original problem. That is, if you solve an equation, make sure you check it with the original equation before you simplified it.
5) Do a sanity check. If a number is supposed to mean something, is it realistic? The height of a building shouldn't be 3 inches, a persons age shouldn't be an irrational or imaginary number, the speed of a car shouldn't be 500 miles an hour, a length shouldn't be negative, etc.
6) Redo stuff in different ways. Add from the top down and check by adding from the bottom up. After solving for x and using it to find y, solve for y and use it to get x.
7) Most textbook problems work out to be relatively simple numbers. If you find yourself getting answer like -237/394, it's probably wrong.
8) Give names to the types of mistakes you make so you can recognize them. Mistakes are often of a "type."
posted by Obscure Reference at 5:37 AM on April 23, 2015 [5 favorites]

I am a mathematician (and a math professor).

Write down all your steps, neatly.

Use words here and there to tell me what you're doing.

Don't do computations in your head.
posted by leahwrenn at 8:57 AM on April 23, 2015

Write down all your steps. If you have time, don't just check your work, do the problem again without looking at your original solution. If you're like me, recopying everything down to make it legible and neat after you solve it is also very worthwhile.
posted by Hactar at 10:21 AM on April 23, 2015 [1 favorite]

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