Careless math errors, and a prealgebra book question

[happypamama]

Help me think outside the box here. I know the standard is "80% or lower, slow down/back up." But what if the mistakes are mostly careless or otherwise not comprehension-related? DD, 7th grade, is at about lesson 60 of Saxon Algebra 1/2. There has been extremely little new information thus far. She works the practice problems with me and gets the right answers. Sometimes she forgets some of the steps for very new concepts -- that I expect and understand. That's not what bothers me. What concerns me is the seemingly careless errors. I don't really have a better word; sometimes she IS being careless and not giving it her all, and sometimes she's just unfocused. I don't think there a learning disability. But I'm seeing a lot of errors, like, she forgot to do a problem (out of 20 on have test sheet), or she added something wrong. If she does 20-25 problems on either a test or a lesson, she might get 4-6 of them wrong. Maybe one is something she is didn't know how to do or that she forgot how to do, and I'll go over that again with her. The others -- I hand the paper back to her and ask her to correct them and she can, no problem.

 

So what do I do about this? I don't really feel like putting her back a level is going to be productive, because I think she'll be bored, and I don't see what it'll accomplish. Her scores have been like this for the past several years, so it's not like it's something new. But sometimes if things are all really great, she'll get 90% right on the first try. I currently have her skipping 5 of the 30 problems each day (1-5 the first day, 6-10 the next day, and so on), because I thought 30 was maybe too tedious and fatiguing.

 

She and I have liked Saxon's no nonsense, not cutesy approach, as well as the spiral approach. But maybe a mastery approach would be better? I don't know. Is there a mastery prealgebra book that has a similar style approach to Saxon? (Like, not Singapore -- I don't think that would be a good fit at all. She does like Saxon pretty well.)

[Arcadia]

I don't really have a better word; sometimes she IS being careless and not giving it her all, and sometimes she's just unfocused.

... The others -- I hand the paper back to her and ask her to correct them and she can, no problem.

 

....Her scores have been like this for the past several years, so it's not like it's something new.

 

Before you check her work, get her to check her work and correct any careless mistakes. Then if there are any careless mistakes, give her back her work to check after the first careless mistake.

 

It has been a few years so it's time for her to do her own checking. If you already mark out those that are wrong, she won't see the need to check and be careful.

[Gil]

In my opinion, this is the age and stage where kids need to really take charge of correcting, analyzing and trying to learn from their math errors. I found this particular post to be very helpful. I can't say if switching books is a good idea or not, maybe you should try moving on to the next Saxon book, but start out slower--do half of a lesson, 7 days a week and aiming for 100% accuracy.

[happypamama]

Before you check her work, get her to check her work and correct any careless mistakes. Then if there are any careless mistakes, give her back her work to check after the first careless mistake.

 

It has been a few years so it's time for her to do her own checking. If you already mark out those that are wrong, she won't see the need to check and be careful.

Thank you. So when you say I should have her check her work, you mean that I should actually have her check the answers in the answer key and see if they match, not just that I should have her go over her problems and see if she sees any obvious careless errors before handing them to me to check? Just making sure I'm reading you correctly -- you're advocating that she be in charge of seeing how many she got right and wrong? I can definitely do that. That would be good for her.

 

She's come so far in organizational skills in the past couple of years; her math papers are much tidier than they used to be, and that's cut down on some of the errors. I'm just trying to help her find the additional organizational skills that she needs so that her abilities aren't hampered by attention issues. Thank you so much!

[happypamama]

In my opinion, this is the age and stage where kids need to really take charge of correcting, analyzing and trying to learn from their math errors. I found this particular post to be very helpful. I can't say if switching books is a good idea or not, maybe you should try moving on to the next Saxon book, but start out slower--do half of a lesson, 7 days a week and aiming for 100% accuracy.

Huh. This is food for thought. I'm keeping these ideas in mind.

 

That entire thread to which you linked to has a lot of very good suggestions, so thank you for posting it. I love the idea of keeping a chart of the types of errors, and I'm also glad to know that this doesn't seem uncommon for the age. It seems that attention, rather than ability, issues are common, and that moving her back a level isn't going to do anything.

 

I did sign her up for an alcumus account. She's good in math but not necessarily intuitive with it the way her younger brother is; she doesn't enjoy all the little tricks and patterns that he seems to have built in naturally. She's more of the "gets it easily when the steps are explained" sort of kid, which is why Saxon has worked well for her in understanding the concepts thus far, and she does well with the written explanations in Saxon (whereas younger brother wouldn't like all the wordiness but does well with Singapore's pictures and arrows). I had not thought that she would go for AOPS, but we will try out the alcumus account and see. I'm not at all opposed to switching to a different approach if need be. It could be that Saxon is too tedious, and fewer but harder problems might spark her brain more and get better results. I also need to go check out whatever Lial has for prealgebra also, since I think it's their algebra book (from a few years ago) that I have on my shelf. (I have that and the Saxon algebra 1 book, so my plan was to choose between them, but I'm open to other things.). Many thanks!

[Laura Corin]

Does she know how to check her work?  I used to tell Calvin to check, but it turned out he had no idea what 'check' really meant.  I taped a list of steps to the table so that he could work through.  It started something like:

 

- Have I transcribed the numbers correctly?

- Have I chosen the correct operation?....

 

L

[threedogfarm]

Yes!  Definitely get her to check her work.  Also, how is she writing out her work? My 6th grader is doing AoPS after years of Singapore Math and I'm having him do all his work in a composition book with graph paper

 

In the early chapters I'm working side by side with him and not so much teaching the math but how to approach the math and how to organize his work.  Each problem has to be written out with the question (or equation) followed by his work in a neat, sequential fashion.  This way it is easy to see where he has gone wrong.  I have even pointed out, "Haven't we done a problem similar to this?" and have him go back and find it to see how he did it before, more so he can see that organizing his work and writing out each step has multiple purposes.  Each step of the problem is written out even if it's obvious.  I use the explanations in the book as an example.  I remind him that anyone should be able to pick up his comp book and be able to follow his reasoning.

 

By doing this he has found that sometimes it's his own handwriting that messes up the problem.  Sometimes it is indeed carelessness and best of all, by having to do each step he can easily find the point where he's confused.  And for him, he has found that doing each problem in an organized, thorough manner, he is able to find where he made the mistake(s) without having to redo the problem and possibly make other mistakes!

 

And I would not only have her check her answers but also have her correct each wrong answer step-by-step (not just say, "Oh, I understand where I made my mistake" and then move on).  With my children, this makes them more careful because they DON'T want to redo problems with careless mistakes because it takes longer in the end. . .

[happypamama]

And I would not only have her check her answers but also have her correct each wrong answer step-by-step (not just say, "Oh, I understand where I made my mistake" and then move on). With my children, this makes them more careful because they DON'T want to redo problems with careless mistakes because it takes longer in the end. . .

Oh, I definitely make her redo every single wrong problem, from the very beginning. I do think I will have her start checking her work in the answer key, though, and have her redo any that are wrong right away, rather than having me hand the paper back to her the following day. Immediate feedback might help her.

[Arcadia]

. So when you say I should have her check her work, you mean that I should actually have her check the answers in the answer key and see if they match, not just that I should have her go over her problems and see if she sees any obvious careless errors before handing them to me to check?

....

She's come so far in organizational skills in the past couple of years; her math papers are much tidier than they used to be, and that's cut down on some of the errors.

If she likes Saxon, stick with it. I have read the textbooks all the way to calculus and the text layout is clean and structured compare to some textbooks that maybe too distracting.

 

Since you are checking the following day, let her check the answers in the answer key once she is done checking her work for careless mistakes. Also get her into the habit of doing a quick check before moving to the next question. If she has to take a computerized test in the future, she won't have the time to go back and check her work.

[Cosmos]

Maybe it is tedious and she grows careless due to boredom. If that's the case, cut the problems in half. If they are correctly done, she is finished. If not, she needs to do the full set. That gives a student incentive to catch their own careless errors rather than waiting for a teacher or book to tell them which ones are wrong.

[happypamama]

If she likes Saxon, stick with it. I have read the textbooks all the way to calculus and the text layout is clean and structured compare to some textbooks that maybe too distracting.

 

Since you are checking the following day, let her check the answers in the answer key once she is done checking her work for careless mistakes. Also get her into the habit of doing a quick check before moving to the next question. If she has to take a computerized test in the future, she won't have the time to go back and check her work.

She has actually had to take computerized tests twice so far, due to our state's testing requirements. She did really well the first time and completely killed it the second time. I think the computerized thing is actually beneficial for her, because it only shows her one problem at a time, so it cuts down on the distraction. But also, those test questions were very easy, not a lot of writing, whereas there is much more writing needed for the prealgebra, and you're right, in the future, she won't have time to do more than a quick check.

 

We're going to try having her do a quick check, and then she will check the answers herself. She's an honest kid; I don't expect I'll have a problem with that. It just hadn't occurred to me that she should be checking them herself yet. I gave her a little more instruction about organization as well, because sometimes space issues cause errors, but also, I tend to see more wrong towards the end, so I'd like to see if I can get her to do half of the problems, work on something else, and then do the other half. She likes to work with music playing, which she and DH feel helps them concentrate better, but I have told her that if I don't see a decrease in those sorts of errors, I will be taking away the music for a bit so that we can tell for sure whether it's a problem or not.

[happypamama]

Maybe it is tedious and she grows careless due to boredom. If that's the case, cut the problems in half. If they are correctly done, she is finished. If not, she needs to do the full set. That gives a student incentive to catch their own careless errors rather than waiting for a teacher or book to tell them which ones are wrong.

I have considered this, and this might be a good solution. The problem is that with the spiral approach, this is a lot of work on me, because I have to pick out the problems myself to make sure she gets a good variety from day to day, that she both practices new stuff and reviews old stuff. What I think I'd really like is a Saxon approach but only based on 20 problems in a set, not 30, so that they've already done the work of setting up the variety for me. 30 problems is a lot of tedium. We have done things like "do the odds, but skip 13 and do 20 instead," but that was a huge pain for me. We also have done two lessons over three days, so that she'd do problems 1-20 one day, 21-30 and 1-10 of the next set the next day, and 11-30 the third day, but that's problematic because starting next year, I really need her finishing a course in a year, and math more often just isn't going to fit into our schedule. (We do math four days a week, due to being out one full day every week, and that works fine with the 140 or so lessons plus test days that Saxon has, because we school for more than 36 weeks, but it won't work if we need 50% more lesson days.). So I'm still thinking, but maybe the best solution is simply to do the odds of one lesson and the evens of the next and trust that overall, that will give us the variety needed.

 

Thank you!

[Cottonwood]

This was US last year!  I rambled on about it here somewhere. LOL  We started out w/ AOPS and quickly moved to Saxon.  She needed more practice and hated the whole to parts of AOPS.  She quickly loved SAxon, but OH my the mistakes.  I just couldn't figure out WHAT the problem was.  I was advised here not to keep jumping around in math curr.  Since she liked Saxon, I just stuck with it.  I started having her check her problems herself, mark the ones wrong, and fish out where it went wrong and circle it in red for me.  Then, she had to redo the ones she got wrong.  She was consistently getting too many wrong every lesson.  It was also suggested to me that maybe she is below her skill level.  I did consider moving her up to Alg 1 but she really wanted to finish the Alg 1/2 book.  So I let her.  This year I started her out with Alg 1 in SAxon and she hasn't missed more than ONE per day!!  I wonder now if she was bored and below the level she needed.  She also doesn't want to do ALL that extra work of figuring out what went wrong and redoing so I think she is much more careful now.  Oh and yes, messiness was a part of the problem so once we got that straightened out, that helped.  Add a little maturity and things are looking up. 

 

So yeah, have her check, figure out what went wrong, re-do, then turn in.  You might try a little Alg 1 with her in Khan.  See if she's actually ready to advance. If not, no biggie.

[Pronghorn]

I think it is partly maturity. My daughter makes fewer mistakes than when she was younger. I would build in some reward for careful work. Perhaps if she gets the first fifteen right she can skip the next five.

[kiwik]

Can you break them up and do 10 before each meal or something?

[Staceyshoe]

We used to have a big issue with careless errors in math.  Then I started assigned half the homework (either evens or odds).  Above a certain error threshold, and he would have to go back and do the other problems "because he needed more practice."  After a couple of days of doing double the work, he became much more diligent about doing them correctly the first time.

[happypamama]

Bumping this to update on what we are doing, because it's working well.

 

I go over the concepts from the lesson with her, doing practice problems as needed (but honestly, we are at about lesson 100, and little has been new; what is new is obvious and intuitive, just a little step).

 

I have her do twenty problems. It's 1-20 one day, 6-25 the next, 11-30 the next, 1-5 and 16-30 the next, and so on. She finds it pretty easy to keep track of, and that gives her a good variety every day. She checks it herself when she's done. If she gets 3 or fewer wrong (and ones she doesn't understand don't count; she doesn't check it until she's asked me about any she doesn't understand), she corrects those but is otherwise done. If she gets more than three wrong, she corrects those but also has to do the other ten problems in the set, correcting those until they are all right as well. Maybe twice she's had to do all of the problems. This approach is working really well, and we have seen careless errors drop a lot. So I am glad I asked for ideas!

[OneStepAtATime]

:hurray:  :hurray:  :hurray:

[redsquirrel]

so, so typical for the age.

 

My son was the KING of careless errors at that age. I thought I was going to go :willy_nilly: :cursing:

 

So, first of all, I defined a careless error for him. I was very clear that I did NOT mean plain old making a mistake or not understanding why he had to do something etc. But, getting something wrong because he couldn't read his own handwriting and just guessed?  Careless. Doing the wrong function called for? Careless. Not writing steps because he couldn't be bothered? Careless.

 

So, we did a couple things. I would have him check his work. But then he requested that when he thought he was done with one problem (answer checked and ready to hand in) I would check his answer before he moved on to the next question. That seemed to work a whole lot better for him. He needed that quick feedback to help keep him focused.

 

Plus, I would put out a line of chocolate chips, for every problem he got correct, he got a chip. For every question he got wrong due to carelessness, I got the chip.  For everything we did, I swear that had the biggest impact, lol. I stopped getting chips after about 3 days.

 

Another thing, and I don't know how much this comes into play with Saxon, but really, really make sure she knows how to write out her answers, legibly and in a way that you can tell what she did. That becomes SO important as you head into Algebra! My son was very good at math and could often just look at a question and determine the answer, or get halfway through and figure it out in his head.  I am not kidding that the most important work we did in pre-A was to create the habit of Writing Out His Work.

[ktgrok]

My son was like that. The cure was a year of Teaching Textbooks. The pre-algebra, actually. He would be careless, get the first problem wrong, then get annoyed with himself for getting it wrong, and be more careful on the rest of them. Having it graded instantly, so he got feedback right away, made all the difference. And that more cautious approach stuck even when we weren't using TT anymore.