Fortunately my oldest child, who is now in 4th grade, has never had much trouble understanding math concepts and procedures. But, she does make a lot of careless errors, probably about the average number for her age.
I’ve asked a few math teachers what can be done to help her reduce the error rate and haven’t gotten too much useful information. They suggest: lots of practice, read the question three times, underline the numbers in the word problems, and underline the key words in the question part of the question, e.g. were they asking how many socks or how many pairs of socks. Pretty good ideas, but I’m betting that dopers have more and better to offer.
Check your work. All addition, subtraction, multiplication and division problems can easily be checked by going backwards and reversing the function. For instance:
4+7=11
check: 11-7=? It better equal 4
7-4=3
check: 3+4=? It better equal 7
4*7=28
check: 28/7=? It better equal 4
35/5=7
check: 7*5=? It better equal 35
There’s not a ton you can do for word problems. Those are testing not to see if you can properly add/subtract/multiply/divide, but to make sure you can recognize *when * you need to do those. Are you asking JUST about word problems?
These sorts of threads always remind me of a girl I knew in college. She was (and still is) incredibly smart, very gifted in math and science (she’s currently completing a graduate degree in computer science), but she could not do basic arithmetic to save her life. It wasn’t from not caring, or not trying. No matter what she tried, she couldn’t get the hang of it. Maybe your daughter’s like her.
What exactly is the problem? Is she saying things like 5*2=7 (adding instead of multiplying) or misunderstanding the problem itself?
If it’s misreading the word problem, then you should consider the fact that the problems usually make sense. So if your final result is “He was walking 900 mph” or “The dinosaur bone is 52 seconds old” or “The train gets to Chicago within 25 days” you probably used the wrong units or something. Ask yourself reasonable questions (“Should this be faster than that?” “Does it even make sense to have a negative answer?”) and you’ll know you made a mistake (though not where to find it).
But the key, I think, is identifying exactly what types of mistakes are happening.
If the problem is genuinely careless errors, I’d guess that it’s lack of motivation: she gains little satisfaction or praise from doing questions perfectly over understanding and doing them satisfactorarily, so doesn’t both to check answers assiduously.
If so, I’d suggest offering her a little treat for getting 100% on an otherwise easy assignment, etc, and see if she can do it when she wants to. (And offer the ‘do everything two ways’, etc, advice.)
(Probably won’t apply here, but I used to be careless - I think what I needed was to have more interesting problems that needed me to do the basic stuff right on the way.)
I think so. I hadn’t thought about it before reading the responses on the thread, but probably 90% of the mistakes I’m referring to are word problems. Her error rate on calculations is not zero, but pretty close.
No, what I was trying to say in the OP is that she gets it immediately almost all of the time. But after getting it, if Sally ends up with 12 PAIRS of socks or 24 socks, she’s likely to answer that Sally ended up with 24 PAIRS.
Thanks. If she’s anything like me she’d do it for pride for $1 Conversely, if she really can’t do it, might she really have some mild problem, slight dislexia or something? I don’t know any more, but just a thought.
What cured me was a teacher who slashed our grades for careless errors.
e.g. We’d have a 10 point problem. Accidentally changing a sign would drop 2 points. (His reasoning? “9/10 is an A. That error isn’t worth an A, it’s worth a B. -2 points.”), the second time in the same problem was another two points (“Well, the first one was worth two points, this is equally as bad, so you should lose an equal number of points.”). And so on.
After a test or two with that happening (perfect conceptual understanding, just some laziness in writing) students stopped making careless errors and started checking their work very carefully.
>> But after getting it, if Sally ends up with 12 PAIRS of socks or 24 socks, she’s likely to answer that Sally ended up with 24 PAIRS.
word problems involve 3 steps, the first and last of which are generally not treated as such by most teachers (and which is why they are probably as hated as they are):
convert the words to symbols
manipulate the symbols (arithmatic)
convert the symbols back to words.
it may help to perform them as distinct steps - write out what the numbers mean, including units for step one. it could also help to write out the form of the answer you’re looking for in step three before performing the calculations in step two.
this is going to be a little bit slower, but i think it will be more productive than simply exhorting her to be more careful…
These answers aren’t really suiting the question. All these things-- checking over problems, rereading, underlining-- is just saying “to make less careless errors, you should be more careful.”
From what I can tell, there are three basic causes of “careless” errors. One is that the person just doesn’t care enough to get it right. That can’t really be fixed without them starting to care. Another is some kind of learning disability (I’ve heard anecdotal evidence of “dysnumeria”, or a mathematical equivalent of dyslexia). This also can’t really be fixed other than by exhorting them to go slower and check their work. Finally, there’s the problem of complexity. While this probably isn’t coming in at the level of arithmetic, once you’re thinking on one level the lower ones often slip. I can attest that I still make at least two sign errors per paper I’m writing. Again, the only recourse is to go back and reread the work to make sure you’ve gotten it right.
Anyhow, there’s no magic bullet. Hopefully practice will make better (never perfect), but there’s really nothing else that’ll do it.
There is, of course, the possibility that the kid just might be a klutz.
Personal anecdote: Junior College (that’s, um, at the age of 19?) level exam, I lose marks because “-1 + 1 = 1” :smack:
I have to say, though, that there is also the kind of mentality that “Well, I know what the theory was, and I applied it correctly, it’s just that I screwed up on the execution. Oh well. :shrug:” because I’m soooo guilty of it. I never did excellently in math because of all my careless mistakes, but I managed to turn out well - I’d caution against focusing too much on those mistakes and demanding a “perfect grade”, because if she loses interest in the subject altogether, and starts to detest/fear math, careless mistakes will be the least of your worries. If she’s doing okay, and understands everything, the purpose of learning math is done. IMHO.
