Dumb arithmetic errors

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Feather
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Dumb arithmetic errors

Postby Feather » Sun Nov 28, 2010 5:21 am UTC

So. You guys are all good at math, and I've got an issue: I constantly make really dumb arithmetical mistakes. For example, saying [imath]3+3 = 3[/imath], or accidentally writing [imath]\frac{1}{2}[/imath] as 2. The problem is that I can never seem to catch them, no matter what I do -- I make the same errors if I work on problems quickly or slowly, and almost always make the same errors if I do the same problems again if I do the problem again. I've done this since I was a wee child.
Less commonly, I'll be going through a problem and just not see what I'm supposed to do -- it's always something really obvious, and I'll occasionally see it suddenly and think, "oh, duh, the [imath]h[/imath]'s cancel," or similar. More often I won't see it until I leave the problem alone for a while (not necessarily stop doing math for a while, just work on a different problem), which is obviously a problem when working under time constrains.
These are all really obnoxious, as I quite like math.
Anyone have tips/pointers/suggestions/things to try to stop doing these types of things?

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mdyrud
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Re: Dumb arithmatic errors

Postby mdyrud » Sun Nov 28, 2010 6:55 am UTC

Always go back and check your work. Make sure you can explain every number that you got. Also, check and make sure your numbers make sense at the end. Check the dimensions you got with the problem, and look for the size of your answer. Obviously, if you get the volume of a box for a maximization problem is several thousand cubic feet, something probably went wrong. The not noticing things when you first look at it, I can't really offer advice. The same thing happens to me. I've just gotten better at realizing when I need to move on to a new problem for a test, and then I come back to the other problem at the end.

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eSOANEM
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Re: Dumb arithmatic errors

Postby eSOANEM » Sun Nov 28, 2010 9:22 am UTC

Feather wrote:So. You guys are all good at math, and I've got an issue: I constantly make really dumb arithmetical mistakes. For example, saying [imath]3+3 = 3[/imath], or accidentally writing [imath]\frac{1}{2}[/imath] as 2. The problem is that I can never seem to catch them, no matter what I do -- I make the same errors if I work on problems quickly or slowly, and almost always make the same errors if I do the same problems again if I do the problem again. I've done this since I was a wee child.
Less commonly, I'll be going through a problem and just not see what I'm supposed to do -- it's always something really obvious, and I'll occasionally see it suddenly and think, "oh, duh, the [imath]h[/imath]'s cancel," or similar. More often I won't see it until I leave the problem alone for a while (not necessarily stop doing math for a while, just work on a different problem), which is obviously a problem when working under time constrains.
These are all really obnoxious, as I quite like math.
Anyone have tips/pointers/suggestions/things to try to stop doing these types of things?


Exactly the same thing happens to me all the time. Unfortunately I've yet to get over it completely, the only piece of advice I can give you is to check that your answer is reasonable (going back and checking my working doesn't normally work for me in exams, it too close to when I started the problem). Alternatively, if, like some of the exams I sat last year, you have about twice as much time as you need, do every question twice and compare answers, if the disagree do it a third time and go with whichever answer comes up twice (repeat last two steps until there is an agreement). Also, try doing questions by different methods if you can when redoing them, that way you're less likely to make the same mistake again.
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skullturf
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Re: Dumb arithmatic errors

Postby skullturf » Sun Nov 28, 2010 2:28 pm UTC

One piece of advice that I, and others, have told students: If you realize somehow that you must have made a mistake somewhere (because your final answer makes no sense, or because it disagrees with an authority), then work it out again, as opposed to reading your (now known to be faulty) work and looking for a mistake.

That may seem more tedious and time-consuming sometimes, but I believe it's good advice.

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agelessdrifter
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Re: Dumb arithmatic errors

Postby agelessdrifter » Sun Nov 28, 2010 2:30 pm UTC

I think everyone makes silly mistakes on math problems (sign errors seem to be the most common). I know you said they happen to you whether you work fast or slow, but surely they occur less frequently when you work slowly? Probably the best thing you can do is just check your work, as has been said. And be thorough about it. A common problem with work-checking is going back, looking at the problem, glancing at the work, thinking "yup, I remember how I got this answer and it makes sense" and moving on. Or, in the case of reworking the entire problem from scratch, remembering certain steps from the first go-through and just regurgitating them without working them through again. Obviously neither of these is helpful for catching mistakes.

As far as "not seeing what to do next", that'll come with more practice, eventually. You'll start to have more of a feeling for what, in general, to look for when you are stuck.

achan1058
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Re: Dumb arithmetic errors

Postby achan1058 » Sun Nov 28, 2010 6:15 pm UTC

First of all, recognize there is a difference between "good at math" and "good at arithmetic". People who are great at math aren't necessary great at arithmetic. In fact, even professors sometimes make such errors.

Having said that, the only real way to get better at basic arithmetic in my opinion is to drill. While on the whole I am very much against drilling, for basic arithmetics I will advocate it. If you don't know your addition and times tables well, you are going to make errors no matter how hard you try not to. If you think it's boring to do, then try playing some KenKen or something.

Now, once you get to the point where you are only occasionally making such errors, there are ways to help check your work. As you found out, repeating your work doesn't help much. Trying to read through it line by line helps even less. The way I find best to check work involving algebra is to sub in values. If you are asked to find a solution, then it better makes sense if you sub it into the original equation. If you are simplifying an expression, then you can try sub in "easy" values like 0 or 1, and both sides better be equal. Sanity checks are also useful. You wouldn't believe how many students hand in work that implies "The number of ways you can partition 3 objects into 2 sets is -1". If the only way you can check is to repeat your work, do not repeat immediately afterwards. Do some other problems, then come back to it. Also, don't do math when you are tired.

As for going through a problem and not seeing what to do, it happens, even to the best of us. (It happens significantly more often when you are in higher level mathematics.) First, make sure you do understand the material, as well as knowing the standard procedures and methods. If you don't actually understand the material, most likely you aren't going to be able to do the question. Then, it often comes down to playing around on pencil and paper. In fact, I sometimes take a walk when I am faced with a particularly tough problem.


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