Careless Mistakes

Date: 02/04/2002 at 16:45:23
From: Dannie
Subject: Tests in Algebra

Hi,

It isn't really a math problem but it is a problem. Last Thursday I 
spent 2 hours studying for a math test (I'm in 8th grade). I had no 
distractions, a lot of light, no TV or music on, and I really 
concentrated on my work. I took a test Friday and got it back today.  
It was an 86 and my homework was a 50! 

No matter how hard I try it's not good enough. I understand the 
material - it's the other stuff, like when it asked me for the range, 
domain, and inverse of ordered pairs, I just put the inverse because I 
misread the question. Or like when I had the right answer on scrap 
paper but I left off part of the answer when I wrote it on the answer 
sheet. It makes me feel really stupid. 

I've had this problem with careless mistakes since 6th grade, but it's 
getting worse. Proofreading my work helps very little and sometimes I 
don't have time when I'm done with the test.  What do I do?

- Frustrated

Date: 02/04/2002 at 19:23:14
From: Doctor Rick
Subject: Re: Tests in Algebra

Hi, Dannie.

You sound like a diligent student with good study habits. I hope you 
can see all the things you do well, and not dwell too much on this one 
stumbling block. I can understand how frustrating it is when something 
like this keeps you from showing the ability that you really have.

You have observed some specific kinds of mistakes you make, and that's 
a great way to start. One step in problem solving that many people 
forget about - even after checking your work, which is easy enough to 
forget - is to look back on what you've done and see what you can 
learn from it. Sometimes you see something positive that you'll be 
able to use again - a trick that worked, or a pattern you saw ("when I 
see this, I can try that"). Other times, as in your case, you see 
something to avoid next time. The question is, how can you avoid these 
sorts of mistakes?

You say that you misread a question, so you didn't give all the 
answers that you should have. This is a reminder that another 
important step in problem solving - the first, and sometimes the most 
important - is to ask, "What am I supposed to find?" Try making a 
ritual of starting a problem by listing exactly what you are supposed 
to find. Then when you finish your work, write each answer next to the 
list, or at least check off your list as you copy the answers. This 
will also solve your other observation: that you forgot to copy all 
the answer from your scratch paper.

You have shown great observation and self-examination skills as you 
looked at the papers you got back. Keep that up. As you notice other 
sorts of things that mess you up, think of this as just another 
problem to solve: what can I do next time that will make it harder to 
make the same mistake, or easier to catch it?

I hope this will help. I'm impressed with your observation and 
perseverance, so I think you can make this work!

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/