Careless Mistakes in Math

[Aubrey]

This is kind-of a perennial problem, right? And it's easy to stay calm or even laugh about it when it's Someone Else's Kid, right? But if you'll humor me anyway...I'm at my wit's end, lol.

 

Ds has been getting slower & slower all year, & the lesson he's on now was just abysmal when he turned it in (lots of wrong answers). But when I looked at them, at least 2 were COPIED DOWN WRONG. We're about half way through Jacob's Algebra, & his algebra is fine. But BASIC SUBTRACTION? Careless mistakes.

 

I think what sent me over the edge was a subtraction error one one problem. I pointed it out, he corrected it--that is, put a different answer--and STILL got it wrong. He doesn't struggle with this; he's just in a hurry to move on.

 

The TM had select problems for him to complete, but by the time I'd graded it THREE TIMES, I made him start over & do ALL the problems.

 

a) It's taken him more than a week to do what should have been done in 1-2 days.

B) He made a lot of mistakes again--all basic math. (At least he's copying them down right, though.) :p

c) That one subtraction error I mentioned above? He did it AGAIN. Same wrong answer.

 

What's frustrating is...I don't know how to say it. If I look at his work, I'm really impressed with what he *can* do & how well he does it. He's got some lazy tendencies he's outgrowing, but overall, there's no way I could call him a "lazy kid."

 

I've started asking him before I grade stuff--did YOU check it first? Esp if he's having trouble, he gives me a desperate YES. And then he'll have his work right--all the way down to the answer, where he divided something like 270 by 15 & got 16.7 instead of 16. Probably because he's trying to do too much in his head--thank you, Singapore.

 

So maybe my answer is to just make him show MORE work? Make him write out the long division? I mean, he CAN do it in his head...I think he just gets to the end, & his brain checks out. If the problems (or parts of them) aren't hard enough, they're not worth his full attention.

 

And, yeah, we've talked about why those little things matter in real-life applications. (He wants to be an engineer.) If the slope of the bridge is 16.7 instead of 16, you could end up killing people.... He just giggles. :p

 

Slow down? Speed up? Grade harder? Give him push-ups? ;) Give him a cookie? Tell me what to do!

[Jane in NC]

Does he have access to solutions (not the steps but just the final answer)? I would let him check answers as he does the problems and let him find his own errors. This may prove to be painfully slow but this removes the aggravation from you to the responsible party.

 

When you say that it takes him a week to do work that should be performed in a day or two, what do you mean? Does he have an hour allocated for math daily and he does what he does? Or do you assign x amount of work for Tuesday--no outside time or computer play time until it is completed?

[regentrude]

Both my kids went through a phase when they made lots of careless mistakes; around the beginning of algebra, but the mistakes had nothing to do with the concepts - just sign mistakes, stupid arithmetic mistakes, etc. I tend to believe that this is a developmental issue.

We solved it by patience and perseverance. For visual clarity, use graph paper for math; one equation per line, equal signs aligned underneath each other. Use colors for signs. Write down ALL steps; a student who makes careless mistakes should not do anything in his head.

Limit math time to the amount the student can focus well and give concentrated, high quality work. It may be an hour - but it may also only be 30 minutes before mistakes start to happen - stop, and do another session later that day.

I never assign a certain amount of work for math, but rather a certain amount of time.

It will get better.

[Aubrey]

I haven't given him access to the answers--I guess...I'm afraid he'd use that as a short-cut. But maybe it's worth a try.

 

I usually assign x amt of work for Tues because he wouldn't get enough done otherwise. But no, I don't follow that up with no play time until it's done. I mean...sort-of? But after a certain point in the day, I just want them all to go play, you know? Or if it's a pretty day (lots of snow days here lately), I figure he needs the sunshine more than he needs more math, lol.

 

But that said, I've cut that amt of work in half and in half again, & he's still not getting it done in a reasonable amt of time. Partly--it's up to him to do it. He chooses other subjects to work on, staring out the window, helping the littles with something. Our schedule has been REALLY nuts this year--lots of moves--and now...we've got a new baby coming in about a month...just...lots of other things going on, you know? So while I understand...he also needs to be moving forward. At *some* pace.

[MommyThrice]

:grouphug: Same problem here, but I haven't found the answer. How old is he and how many problems is he working in a day? It did seem to get better as my son got older (but not until about age 17 AND as he started taking college courses.) He was willing to turn in work to me with mistakes, but not a college professor.

 

One thing that may have really helped him was studying for the PSAT. One careless mistake, and he lost credit for the WHOLE problem. He was in competition with some friends and was shooting for a perfect score every time. So, maybe give him some practice SAT or PSAT sections. Most are multiple choice, so they are either right or wrong. For some reason, my kids won't argue over multiple choice answers. Find some friends he can have a friendly competition with.

 

One other suggestion... As you (or he) check his answers, have him write next to every wrong answer either:

1. "Concept" - Meaning he didn't understand or couldn't remember the concept. These are the things he should be studying on a regular basis.

2. "PAD" - Pay attention to detail.

You might show him both his actual score as well as the score he COULD have made without the "PAD" errors.

 

Well, as I am sharing my "wisdom" with you, I just noticed that my 17yo (the one that has overcome the distractions, remember?) has paused his Khan video and is playing Solitaire. :banghead:

[Aubrey]

One other suggestion... As you (or he) check his answers, have him write next to every wrong answer either:

1. "Concept" - Meaning he didn't understand or couldn't remember the concept. These are the things he should be studying on a regular basis.

2. "PAD" - Pay attention to detail.

You might show him both his actual score as well as the score he COULD have made without the "PAD" errors.

 

Although I've shown him the differences in his scores, I like the idea of marking them this way--I think that might help him to *see* what I'm telling him.

[Aubrey]

Oh, he's 12. I had him doing about 10 problems a day; I've adjusted that to 3-4, hoping he'd be inspired to pay more attention, but alas. I also ordered the Ask Dr. Callahan DVDs, & he likes those, but this lesson he's been stuck on? It's the first one he had the DVDs for, so there's no obvious help there, lol.

 

I wish there were a practical way to step away from it & give him a fresh start in a week or a month, but...the way this year has gone, I feel like that would just create more disruption. Fwiw--we started w/ NEM, then tried Saxon (because a friend had it to borrow for free), then Jacobs (thank goodness my ils' library had it, so I could SEE it!). With LoF pre-algebra 1 on the side back in Sept. So...only being half-way thr the book...isn't a reflection on him, if that makes sense.

[Kathy in Richmond]

Careless errors were a VERY common problem among the 10-12 year old age group that I taught in CTY math courses.

 

I agree that student access to the answer key to self-check as the homework progresses can help catch errors before they blossom, as can colored pencils, especially for those pesky negative signs that always seem to lose themselves.

 

Another thing that sometimes worked was to assign fewer, but more difficult problems. Engaging the mind helps; too much easy stuff is a recipe for day dreaming.

[Jane in NC]

It was best for my son to do some math in the morning when his brain was engaged, say 30 to 45 minutes. Then he would return to the subject later in the afternoon to finish things. Some extra processing time helped him--but this may be better with concepts as opposed to arithmetic errors.

 

To Regentrude--my son had some particularly dull witted days in which nothing would have been accomplished if I had not assigned x amount of work. He could have dilly-dallied away the time. A lot of hormonal activity can get in the way of academic accomplishments, you know?

[mumto2]

My ds has been having the same problems. Driving me nuts! The current method which is showing signs of working is doing the book work with complete access to a solution manual with complete every single step solutions. After he works through the assigned questions he takes the quiz and we move on. He is finally making an effort to write some work down and is trying to be neat. I think he has decided that I might be right because his scores are improving.

[TexasRachel]

Dd did this. I finally told her she couldn't practice piano (her love) until math was 100% correct. Her careless mistakes practically dried up overnight.

 

I did have to put my foot down and tell her to use *a lot* of paper to do math. That I needed to see the steps.

[Erin]

Does he have access to solutions (not the steps but just the final answer)? I would let him check answers as he does the problems and let him find his own errors. This may prove to be painfully slow but this removes the aggravation from you to the responsible party.

 

This is what I do. I give him a cheat-sheet with all of the answers on it, plus a few extra, just to be a pest. ;)

If he can't find his answer on the list, it must be wrong. Do it again.

[Kareni]

To encourage my daughter to be more careful (this sounds better than to say I was being cruel and heartless!), I had her correct all problems with errors and then do one additional problem for each error she had made.

 

Regards,

Kareni

[kiana]

To encourage my daughter to be more careful (this sounds better than to say I was being cruel and heartless!), I had her correct all problems with errors and then do one additional problem for each error she had made.

 

Regards,

Kareni

 

 

Quite honestly I think this is a great idea when the child CAN do better and just isn't because of rushing or carelessness.

[Jann in TX]

I agree with extra problems...

 

I'm willing to bet it is a maturity issue. Your son may be mentally 'mature' enough to understand the foundational concept--but NOT mature enough to follow through the basic arithmetic needed to solve the problem.

 

I've had fairly good luck assigning extra problems-- they have to fix their mistake then work out 1 additional problem for every missed problem. It is usually a quick turn around-- most students rather avoid the extra work!

 

I also agree with the previous poster who suggested showing your son his grade on the assignment. Students in public/private school do not get second chances (sometimes homeschoolers can develop lazy habits without that accountability).

 

Don't worry if it takes more time for him to complete a lesson accurately... eventually he will learn to pay attention to the details. At 12 he is pretty young for Algebra and has plenty of time to work on good study/homework skills.

[Julie in MN]

This is what I do. I give him a cheat-sheet with all of the answers on it, plus a few extra, just to be a pest. ;)

If he can't find his answer on the list, it must be wrong. Do it again.

 

Clever!

 

 

I was just talking about this very topic to my 28yo son regarding my 17yo son this evening (mostly in regard to chemistry, since he does math through dual enrollment). We both agreed it's a maturity thing with boys. And since we don't have the peer pressure or teacher-pleasing going on in our home, we lose some of that initiative. My oldest ds is an engineer and said he matured a lot in college, in terms of realizing the value of going through the steps even if they are dull :) and seem unnecessary a lot of the time.

 

I didn't mention this to my son, but my personal opinion is that the majority of boys just aren't detail-oriented people. Of course the engineer in my oldest might disagree, but really I think he tends towards big-picture thinking and detail work has slowly developed from torture to useful as he matured?

 

As for writing out long division and other simple calculations, I can't imagine that would create fewer errors, at least with my son. He was trained in Singapore mental math, and did math facts for many years, so he just does most of that in his head, and writing it out would only cause more errors. Besides which, calculators are allowed on tests and in college courses.

 

Not a lot of help, but just to say that at age 12, in a home setting, you may need to compromise, in my experience. I tend to require writing every step if he has to make corrections. Or, you could require written steps for at least one example, etc.? I'm sure a few have won the battle by using strict rules, especially with a rule-following oldest child, but I think many more probably crashed and burned in that battle in a homeschool setting?

 

Julie

[jenn-]

My DD is the same way (also 12). One thing that has helped is the threat and follow through of a 100 problem timed test on whichever function she messed up on. That said she still managed to reduce 5/12 to 1/3 on her most recent test because everyone knows that 12 is divisible by 5, right?

[Katy]

I'd tell him he's making a lot of careless mistakes so at this point he's in charge of correcting his own work in red ink, (show him the answers not the solutions), have him rework the problems himself, and explain to you what he did wrong - His new "assignment" will be explaining what he did wrong, essentially requiring 100%.

 

Also, I'd have him work through Khan Academy one or two days per week. If you make one careless mistake you must do the whole problem set again, which first frustrates and then requires focus.

[Kareni]

That said she still managed to reduce 5/12 to 1/3 on her most recent test because everyone knows that 12 is divisible by 5, right?

 

Definitely! And, as the t-shirt says, 5 out of 4 people don't understand fractions.

 

Regards,

Kareni

[JanetC]

The things that helped us:

 

1. Immediate feedback -- reduce math to 2 to 4 assignments of 1 to 3 problems each. Grade them IMMEDIATELY after they are done, and point out the careless mistakes. Discuss why they might have happened (you didn't write the decimal place dark enough and lost track of it, etc.). Don't accept "I'll try harder" as a plan for improvement. Talk very specifically about what happened. "I'll use better handwriting so my sixes and zeroes don't get confused," is a plan.

 

2. Reviewing strategies for estimating and checking answers -- At our house, there is a difference between a math problem you "got wrong" and an answer so bad it "stinks" (for example, a negative result when a quick inspection shows the answer should be positive). While going over mistakes, discuss which answers "stink" and why. Again, immediate feedback is key. No partial credit for stinkers.

 

3. Grading -- I tended to just mark things right or wrong earlier in grade school, but not total up percentages or letter grades. When accuracy became more important, I introduced grades. Especially on an assignment with 2 or 3 problems, the careless mistakes make a drastic difference in percentages and letter grades (even with partial credit). They can see that paying attention to detail makes a big difference.

[Erin]

And the above three are precisely why I give him the list of answers. That way it's ALL on him.

 

Immediate feedback, he can hunt through his own work for errors in his steps, and when he tracks down his answer, he's fairly sure he's right.

[happypamama]

Two things really helped with careless mistakes in math for my DD.

 

One, letting her do the work on the iPad instead of paper. It's more fun that way, and it's an incentive to do good work the first time.

 

Two, we use Saxon, so there are 30 problems every day. It is very rare that she makes a mistake because she didn't understand something; it's almost always careless mistakes. So if she gets 90% right the first time around (I make her correct anything that's wrong) on the tests, she only has to do 15 problems on the next several sets (there are five sets between tests). This incentive really helped, and her test scores didn't go down as a result of only doing 15 problems. (I hand-pick them each day, so that she gets a variety of problems.) With only 15 problems a day, she gets a higher percentage correct.

[Starr]

I found with ds it helped a lot to go back and do a year of basic math. We used Lials Basic math. It says *college* on the front. It gives another year to work on computations and get faster with fewer errors. We've had a lot of bridges fall over the years. You know, "what are you doing?" "Thinking thoughts."

[letsplaymath]

We do our work together, orally (buddy-math style), so when dd makes one of those mental-glitchy mistakes, I just give her "the look", and she knows she needs to double-check it. And sometimes she catches me in similar mistakes. Mental glitches may be more common in the early teens (puberty-related?), but none of us are immune.