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Careless errors in arithmetic


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My DD11 is intractably bad at arithmetic, because she makes what we used, in my day, to call careless errors: copying a problem with an addition sign instead of a minus sign, lining up decimal points incorrectly, adding in the problem number, etc. I was the exact same way! This seems to be slowing her down in math, to the point where I feel like we've been doing some of the same work over and over again for the past 18 months. My feeling is that this is just an EF issue and that there's not really much point in making her beat her head against the same issue when she'll either grow out of it ... or grow into a calculator. I'm tempted to make sure she's setting the problems up correctly and then just hand her a calculator. 

Math folks, what do you think?  

 

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Are they "homework" problems that she's doing on her own, that you catch later on when correcting or marking them?

One thought is that this list:

21 minutes ago, jrichstad said:

copying a problem with an addition sign instead of a minus sign, lining up decimal points incorrectly, adding in the problem number

might be shorter than you think. 10 items long instead of 10 thousand. It might be much harder to teach someone to "be more careful in general" than to "be careful about this issue in particular." You can't empty the ocean one teaspoon at a time but you can empty a teacup that way.

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9 minutes ago, UHP said:

Are they "homework" problems that she's doing on her own, that you catch later on when correcting or marking them?

One thought is that this list:

might be shorter than you think. 10 items long instead of 10 thousand. It might be much harder to teach someone to "be more careful in general" than to "be careful about this issue in particular." You can't empty the ocean one teaspoon at a time but you can empty a teacup that way.

They're mostly problems she does on her own, but I can also see her making the errors when I sit next to her while she works, too. 

I have given her explicit instruction about how to set up the problems and double-check, and I've modeled myself double-checking and correcting errors--everything that I can think of/ have read about to help a child past this. There's been SOME progress, I just don't know how much of our limited math budget (both in terms of time and also frustration) is worth spending on it. 

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I might separate math instruction from problems with documentation and careless errors.  

2 hours ago, jrichstad said:

slowing her down in math, to the point where I feel like we've been doing some of the same work over and over again for the past 18 months.

If she otherwise understands the math, I would continue to make forward progress, while still working on techniques to avoid careless errors.  I view these as very separate skills, plus I think it might be demoralizing to repeat material, and also make her more likely to make careless errors?  

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My kids are little so this is from personal experience. I finally addressed my careless error issue in math in college when homework was 5 problems and graded on correctness rather than the 20 problems I would have during K-12. So, if I were to address it with my kids I would assign essentially 1 question per "type" of problem, then just mark answers right or wrong. For wrong problems have them look it over and tell you what went wrong and assign additional 1 or 2 problems of the same type to check for ability to do it correctly. A college professor made me do that and then from then on no matter how homework was assigned in classes I would do it this way and it helped me tremendously with careless work.

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19 hours ago, jrichstad said:

My DD11 is intractably bad at arithmetic, because she makes what we used, in my day, to call careless errors: copying a problem with an addition sign instead of a minus sign, lining up decimal points incorrectly, adding in the problem number, etc. I was the exact same way! This seems to be slowing her down in math, to the point where I feel like we've been doing some of the same work over and over again for the past 18 months. My feeling is that this is just an EF issue and that there's not really much point in making her beat her head against the same issue when she'll either grow out of it ... or grow into a calculator. I'm tempted to make sure she's setting the problems up correctly and then just hand her a calculator. 

Math folks, what do you think?  

 

Please do not hand a calculator to a sloppy student. It's just a machine and Garbage In -> Garbage Out.

A calculator just gives her an electronic avenue to generate an incorrect answer.

1st) Are her answers correct? Meaning, did she get the correct answer to the problem that she wrote down even though it doesn't match what you'd expect based on the problem in the book?

2nd) What does a daily math lesson look like for her?

3rd) Does she produce similarly sloppy work in any other subject?

 

 

First and foremost, what math is she doing and what does a lesson look like?
 

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For my kid, this happens when she's bored, has too many problems of the same type, and just does not CARE about the answer. 

I tend to solve this by creating problems that she cares about and not giving her lots and lots of questions of the same type. 

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I have a child with ADHD,  predominantly inattentive. He makes a lot of what look like careless errors, not just in math but across the board. There's been a lot of conflict in our house about this. When we finally got the diagnosis (5th grade), it was incredibly helpful. He actually is trying, and often trying very hard. But math (and multistep arithmetic in particular) is extremely taxing for him. The psychologist actually told me to let him use a calculator. I held off for a year, but when he started Singapore 7, I started letting him use one. Not for every problem. I felt ok with this only because I knew he understood the concepts, but would "tire" easily if there were too many complex calculations.  

The other thing that helped tremendously is using graph paper for all math problems, and careful modeling of how to write out the problems neatly so he is less likely to overlook things.  I also transcribe more complex problems for him from the book onto his notebook, because looking back and forth between book and notebook often causes him to lose his place and end up doing the wrong problem (or mixing two problems).

Is he sometimes goofing off and not trying? yes. But not always, and it was devastating his self esteem when I would get on his case and he felt he had tried really hard. I've learned that it's pretty important that I try to hide any sense of  disappointment or frustration when he does make "careless" errors because it reinforces for him a sense that he's bad at math, when he's actually able to understand concepts very well.

All that to say, if you notice this "carelessness" in other areas of life, it may not be simple carelessness, and you may want to consider a learning difference or condition like ADHD.

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3 hours ago, WTM said:

All that to say, if you notice this "carelessness" in other areas of life, it may not be simple carelessness, and you may want to consider a learning difference or condition like ADHD.

Yes, this is my feeling--I have diagnosed ADHD, and I made (and still make!) careless errors in just about all my academic work no matter how hard I tried. That's why I don't like to use the words "sloppy" or "careless"--because I really did care and was trying as hard as I can, and I suspect the same is true for my daughter. Those words were hurtful when I was a child and it's taken me a long time to make peace with my brain (which is ... otherwise quite high-functioning!). 

We did a medication trial for her and decided it wasn't helping much, but it may be time to try again. I really appreciate your sharing your experience about being told to give your child a calculator.

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7 hours ago, Not_a_Number said:

For my kid, this happens when she's bored, has too many problems of the same type, and just does not CARE about the answer. 

I tend to solve this by creating problems that she cares about and not giving her lots and lots of questions of the same type. 

Based on what you've said about your kids, I suspect that we're looking at different issues 😄

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15 hours ago, mom2bee said:

Please do not hand a calculator to a sloppy student. It's just a machine and Garbage In -> Garbage Out.

A calculator just gives her an electronic avenue to generate an incorrect answer.

1st) Are her answers correct? Meaning, did she get the correct answer to the problem that she wrote down even though it doesn't match what you'd expect based on the problem in the book?

2nd) What does a daily math lesson look like for her?

3rd) Does she produce similarly sloppy work in any other subject?

 

 

First and foremost, what math is she doing and what does a lesson look like?
 

Over the past three years we've tried a few different math programs (and quite a while of not really doing math at all), because coming out of public school she'd developed some real math anxiety and I wanted to give her as much support as I could. In 4th grade, we worked through most of the elementary Life of Fred series, which was fairly successful. We then did RightStart for a good few months, and she HATED it. Too many manipulatives, too disjoined. Most of last year (5th grade), we worked through Mathematical Reasoning F. It was fairly successful because it's short and to the point, and she scored well on the standardized test that she had to take. 

I'm okay with continuing that this year, but I'm concerned it's not robust enough and so she's currently doing Saxon 7/6. She does the warmups, I work through the example problems on the whiteboard and teach the material (I'm very comfortable teaching through Algebra 1), and then I sit with her while she does the lesson practice and mixed practice.   

I mentioned below that I'm not comfortable calling her work sloppy, because I don't think it's intentional. She does sometimes goof off, like any kid. But mostly, she produces good work--her spelling is great, her sentences good, her responses thorough. 

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On 7/15/2021 at 12:58 PM, daijobu said:

I might separate math instruction from problems with documentation and careless errors.  

If she otherwise understands the math, I would continue to make forward progress, while still working on techniques to avoid careless errors.  I view these as very separate skills, plus I think it might be demoralizing to repeat material, and also make her more likely to make careless errors?  

This is what my gut tells me. I'm still not sure giving her a calculator is the best solution, but there might be a middle ground where she sets the problem up and then I only have her work out one or two arithmetic problems per set. 

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19 minutes ago, jrichstad said:

This is what my gut tells me. I'm still not sure giving her a calculator is the best solution, but there might be a middle ground where she sets the problem up and then I only have her work out one or two arithmetic problems per set. 

Sometimes I also used to split math into two shorter segments with a brain break in between. 

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31 minutes ago, jrichstad said:

We did a medication trial for her and decided it wasn't helping much, but it may be time to try again. I really appreciate your sharing your experience about being told to give your child a calculator.

How did you decide to try meds? Did the meds not help or did they  also have negative side effects? We have not tried meds. I go back and forth but I haven’t felt it is crucial yet because we homeschool and I can make accommodations for his learning style.  Like @daijobu said, I think of math instruction (understanding concepts) and being able to accurately complete the calculations as separate tasks. 
But it’s always a question in the back of my mind, especially as he gets older and I wonder how I can get him ready to function in non homeschool learning environments. 

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On 7/16/2021 at 7:58 AM, mom2bee said:

Please do not hand a calculator to a sloppy student. It's just a machine and Garbage In -> Garbage Out.

A calculator just gives her an electronic avenue to generate an incorrect answer.

 

 @jrichstad—My child does make mistakes even with a calculator. He has both fine and gross motor issues. It helps for him to have a calculator that has actual buttons (as opposed to one on an iPhone or screen based device that has no tactile feedback). I have to prompt him to place it flat on the table when he uses it. If he holds it in his hand, it’s sometimes not stable enough and he can push the wrong button without realizing it. If you end up deciding to try a calculator, perhaps this can help you.  Also, if it’s simple arithmetic, I make him do it by hand, unless he’s already done several of that type of problem that day.

Edited by WTM
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Addressing your main question about whether to move ahead or keep your child at the same level until they can consistently answer accurately—

in the end I decided to keep my child moving ahead if he understood the concepts. Otherwise he was easily bored and thinking he was bad at math. In reality, some of the ways he approached problem solving were quite sophisticated- ways I had not thought of , but reflective of deep understanding

Sorry I’m finger typing on a phone now so apologies for the typos.

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49 minutes ago, jrichstad said:

'm okay with continuing that this year, but I'm concerned it's not robust enough and so she's currently doing Saxon 7/6. She does the warmups, I work through the example problems on the whiteboard and teach the material (I'm very comfortable teaching through Algebra 1), and then I sit with her while she does the lesson practice and mixed practice.   

If you did something short and to the point that worked well and didn't have the same issues, why not go back to that? Saxon is known to have a TON of problems, and I can easily see that being overwhelming to a kid. 

It's true that my kids are mathy, but I think making careless errors because there are so many problems in a row is pretty common. Do you think she wouldn't be able to learn if you moved to a program with fewer problems? 

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On 7/16/2021 at 9:39 PM, WTM said:

How did you decide to try meds? Did the meds not help or did they  also have negative side effects? We have not tried meds. I go back and forth but I haven’t felt it is crucial yet because we homeschool and I can make accommodations for his learning style.  Like @daijobu said, I think of math instruction (understanding concepts) and being able to accurately complete the calculations as separate tasks. 
But it’s always a question in the back of my mind, especially as he gets older and I wonder how I can get him ready to function in non homeschool learning environments. 

I decided to try meds because they were helping me so much, but they just didn't seem to have much effect--no side effects, either. We could have tried her on a different one, or a stronger dose, but I figured--like you say--that she's at home, where I can make accommodations. I don't think there's a rational reason to worry about it; I just felt like the fewer drugs on her developing brain, the better, I guess. 

I quit taking my meds a while ago because they were elevating my blood pressure and I chose to make some lifestyle changes instead. The lifestyle changes do help, but not as much as the Ritalin 🙂

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On 7/16/2021 at 10:05 PM, Not_a_Number said:

If you did something short and to the point that worked well and didn't have the same issues, why not go back to that? Saxon is known to have a TON of problems, and I can easily see that being overwhelming to a kid. 

It's true that my kids are mathy, but I think making careless errors because there are so many problems in a row is pretty common. Do you think she wouldn't be able to learn if you moved to a program with fewer problems? 

Mayyybe. That said, we did LoF for a long time, which may has fewer problems, but she made about the same # of errors. Mathematical Reasoning just doesn't feel complete to me--it's more of a supplement than a curriculum. I worry about her being ready for algebra in a couple of years without a strong teaching program.  

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25 minutes ago, jrichstad said:

I The lifestyle changes do help, but not as much as the Ritalin 🙂

Do you mind me asking, What kind of lifestyle changes? 

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36 minutes ago, jrichstad said:

Mayyybe. That said, we did LoF for a long time, which may has fewer problems, but she made about the same # of errors. Mathematical Reasoning just doesn't feel complete to me--it's more of a supplement than a curriculum. I worry about her being ready for algebra in a couple of years without a strong teaching program.  

Hmmm, you might have a point! Was she making the same kinds of errors in LoF? 

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1 hour ago, WTM said:

Do you mind me asking, What kind of lifestyle changes? 

Of course not! I gave up added sugar entirely (this has made a huge difference); go for a 20 minute walk every morning (I do other exercise later in the day, but getting out first thing makes a huge difference); scaled back on some of my out-of-the-house commitments; and do 10-20 minutes of yoga every night. 

I'm sure there are other things I could do that would help, but I only have so many hours per day to coddle my brain chemistry :D 

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54 minutes ago, Not_a_Number said:

Hmmm, you might have a point! Was she making the same kinds of errors in LoF? 

Yes, she was. She mostly understands the concepts just fine, and when I have her look at a problem again, she can fix it. (I have explained to her and modeled over and over how/ why to doublecheck answers, but she doesn't do it.)

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6 minutes ago, jrichstad said:

Yes, she was. She mostly understands the concepts just fine, and when I have her look at a problem again, she can fix it. (I have explained to her and modeled over and over how/ why to doublecheck answers, but she doesn't do it.)

Does this happen less if there are fewer problems or no?

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40 minutes ago, Not_a_Number said:

Does this happen less if there are fewer problems or no?

I haven't exactly run the the numbers or anything, but I would say proportionally no. If there are five problems, she'll get one wrong. If there are 10, she'll get two wrong.  

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16 minutes ago, jrichstad said:

I haven't exactly run the the numbers or anything, but I would say proportionally no. If there are five problems, she'll get one wrong. If there are 10, she'll get two wrong.  

Is that actually about the rate? Is that for one step problems or multi step ones?

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