How much grace do you give with math mistakes?

[matrips]

We've had a lot going on here recently, family stuff and other, but still trying to homeschool. Everything is not as scheduled and set in stone as it was. So math....

 

The kids are ahead in math, by at least a year I think. They are second graders finishing up MUS Gamma (currently on three digits times two digits) and CWP 3. They get the concepts but are making mistakes, sometimes really silly ones by adding instead of multiplying or just incorrect arithmetic. Some, not so silly. Misunderstanding twice as much and two times more are different in word problems. The CWP can be tough, so many steps to think through, and they do them the first time by themselves, unless they have a question. gamma, they shouldn't have so much.

 

Anyway, I've been looking at the mistakes as a benefit because it is showing them that neatness, writing down steps, really reading the problems carefully, etc is crucial. I've been checking their work and marking what's wrong. And then going through it with them (not doing it for them, but sitting with them). (the boys would like to do as much as possible in their head to avoid writing!). But they are showing me the work and the steps they do. When we were doing easier stuff, I would often just hand them back a book with the pages marked, and they had to go through and

find the mistake(s) themselves. I think I'd have a rebellion on my hands if I tried that with this

current work though. Am I setting myself up for trouble later, or is okay to give grace while they are learning hard stuff and really working on it? Thinking I would crack down next year again, once they should really be proficient at this stuff.

 

Thoughts? How do you usually handle mistakes? Are all mistakes equal? Does it depend on the type or the complexity of what they are doing? Or what else is going on in life/school? They've done a lot more 'here's your book, go do some math' in the past two months, than would be typical.

[MeghanL]

My philosophy is to repeat, repeat and then repeat as long as necessary. I am working on long-division with my oldest. For every.single.problem we go through all the steps. He still doesn't have it down pat. But, that's part of the learning process. My middle child has the same thing. Plus one, minus one. Doesn't matter. We get out the 100 number chart & pennies and we work it as many times as it takes until they "get it".

No, it's not as quick as I would like. However, I do believe that going through those steps over and over again will be beneficial. They will eventually get it. Just keep helping them as much as they need. (This is not to say do it for them. If they are simply trying to get out of doing the assignments, crack down on that!)

I haven't been homeschooling very long, but I have learned that you cannot rush the learning process. Concepts take as long as they take. Just keep presenting the information and steps and one day the lightbulb will come on!

[regentrude]

I am not sure I understand your question. Math mistakes happen. They happen many many times before the kid can do it without mistakes. Math practice is for learning. My kids have to correct all math mistakes they make and rework the problem until they get the correct answer - that's how they learn.

 

You can point out whereabouts on the page the mistake happened.

If it is a very complex involved problem, you can point to the line.

You can ask "how did you get from here to here?"

You can pick out a portion of the problem and ask them "explain to me how you multiplied these expressions" or "tell me how you set this up".

All these can guide them to the discovery of the mistake. Socratic, you know.

 

What I would not do is find every mistake FOR them. I might do this occasionally, at the end of a long, challenging problem, when the kid has done a great job with the hard parts :"Hey, you did it almost correctly, you just forgot a sign here".

[bolt.]

For me, a mistake is nothing more than information I (the teacher) need to know about my child's current level of proficiency, which then tells me their teaching needs. I teach to their needs. Your children's needs seem to be clear from their habitual mistakes, so that what they need to be taught about.

 

If mistakes are occasional, a fluke not a habit, I might point it out directly, like, "See, here, you made an error because you forgot that subtracting and adding are different. It's important to check the sign, or the answer isn't true."

 

If the error is systematic, occurring frequently, I wouldn't mention it as a correction -- I'd just say, "OK, next lesson I'll go over this with you again, and you can take another shot at these exercises."

 

Please consider different math strategies for different thinking styles: often it's a matter of something "clicking" when something else didn't quite do the trick. Repeating the same 'how to' lesson using the same strategy for solution often doesn't help very much.

[Hunter]

For my boys, all mistakes needed to be corrected. First they needed to see if they could fix the mistake themselves. If they got it wrong again, I went over it with them. Sometimes if I went over the problem with them, then I assigned a few more similar problems, or made them refigure the wrong problem several times.

 

With tutoring students it varies. They are pretty fragile, and are not spending as much time with butt-in-chair.

[Mandy in TN]

Mark it wrong. Let them fix it. Maybe they need graph paper to better line up their numbers? If they have the concept down, but are just little and lacking the focus or writing skills to be super precise I wouldn't worry. :)

Mandy

[matrips]

Maybe I wasn't too clear about marking their mistakes.. When an answer is wrong, I just mark the problem wrong. I don't find the mistake in the problem for them, or point out where they wrong. They review the whole problem, and generally find their mistakes quickly, and of course get frustrated with themselves for their careless mistakes. I encourage them to review the work they've already done though to see if they can see where they went wrong. I will lend guidance in cases where it's truly a conceptual problem. Or I may strongly suggest that they re-read a problem again or draw my favorite picture (a bar graph). I guess I thought I was pretty lenient already by telling them which problems were wrong, instead of having them redo the whole page to find it! :). Thanks for the perspectives. And I'll see about the graph paper for them, though it's usually easier for me to have all the work done in the books.

[Down_the_Rabbit_Hole]

For K and 1st I do not mark anything wrong, but will tell them what is wrong and rework the problem with them. I find it is upsetting for a very young learner to see those X's or circles instead of all checks. 2nd through high school I mark the answers wrong and they need to correct the problem. From 2nd to 8th if I see a writing mistake I might point that out asking if this was the answer they wanted and then tell them to be careful next time. If it is a actual math error and they have trouble seeing what is wrong then I help. Most of the time they see the error and fix it. High school I will add an arrow where the error occurred in the problem if they worked the problem right but made a simple error. If the problem was worked wrong I circle it.

[Mommy22alyns]

I also circle and they go back to correct. If it's something small like a sloppy number (Sylvia) or missed label on a word problem, I draw a small arrow. All of this is in pencil, because they go back and erase my circles.

[songsparrow]

I've been checking their work and marking what's wrong. And then going through it with them (not doing it for them, but sitting with them). (the boys would like to do as much as possible in their head to avoid writing!). But they are showing me the work and the steps they do. When we were doing easier stuff, I would often just hand them back a book with the pages marked, and they had to go through and Find the mistake(s) themselves. I think I'd have a rebellion on my hands if I tried that wi th this current work though. Am I setting myself up for trouble later, or is okay to give grace while they are learning hard stuff and really working on it? Thinking I would crack down next year again, once they should really be proficient at this stuff.

 

Thoughts? How do you usually handle mistakes? Are all mistakes equal? Does it depend on the type or the complexity of what they are doing? Or what else is going on in life/school? They've done a lot more 'here's your book, go do some math' in the past two months, than would be typical.

 

What you're doing sounds fine to me. It never occurred to me to tell my kids that they got 2 out of 20 problems wrong, but not tell them which two and make them find them. Usually my girls hand me their sheet as soon as they're done and I check it on the spot. I'll say things like "1 is correct - good, 2 good, 3 nice, oops 4 isn't correct, take another look at that one." Usually they see right away what mistake they made and correct it. If they don't, we discuss it. If there are any other problems using the same concept that they may have gotten wrong because of the same misunderstanding, I'll say "You might want to check #6, too" although they often realize that before I even say anything. I never thought of this as being lenient.

 

As far as the types of mistakes, if I'm seeing mistakes with the concept, we continue to work on it. If they understand the concept and are just making computational errors, we move on. They can work on their computation skills with other concepts.

[Momling]

I just have the girls fix the mistakes I circled. If they still get it wrong, we do it together and then the next day, we'll repeat the missed problem.

[FriedClams]

Anything wrong - for any reason (including writing sloppy) - gets corrected. I also usually add one problem for practice - especially for silly not thinking mistakes. Math is all about accuracy. Teaching focus and accuracy early will make later

math a LOT easier.

[kiwik]

I can't imagine why you would tell them they made a mistake but not where. I can't imagine even thinking that might be helpful.

[FriedClams]

I can't imagine why you would tell them they made a mistake but not where. I can't imagine even thinking that might be helpful.

 

 

I do it often. Sometimes they need to just walk through the thinking of the problem to find their mistake - and other times they need direction. If I point out an error - they fix the problem, but it they figure it out by correcting it themselves - I usually don't see that type of error again. "OH!!! I forgot to..." is an awesome thing to hear.

[jennynd]

I am mean. when DS made a mistake on one page, especially careless mistake. I tell him there is one mistake on that page. and he has to go through each question to find out which question he get it wrong on that page and correct it.

[boscopup]

I just mark wrong answers with a red X (my son has no problem with that), and he goes back and figures out what he did wrong and corrects it. I do tell him which problems are wrong, but I don't usually tell him where he went wrong in the problem.

[TXBeth]

I don't call what you described "giving grace." I call it "teaching math."

[Dana]

I do it often. Sometimes they need to just walk through the thinking of the problem to find their mistake - and other times they need direction. If I point out an error - they fix the problem, but it they figure it out by correcting it themselves - I usually don't see that type of error again. "OH!!! I forgot to..." is an awesome thing to hear.

 

Yup.

 

It depends on what the error is. If it's a mistake made as he's learning new material, I'll generally say which problem it is on a page, but I won't say where in the problem. In fact, I don't think I ever say where it is in the problem... sometimes it's a misspelling :)

 

Just as proofreading your English work is important, it's important to be able to catch your math errors.

The age of your child matters too. I don't think I started saying, "You've got two problems wrong on this page," until my son was in 3rd grade or higher... and again, this is on material that is review.

[kiana]

 

Yup.

 

It depends on what the error is. If it's a mistake made as he's learning new material, I'll generally say which problem it is on a page, but I won't say where in the problem. In fact, I don't think I ever say where it is in the problem... sometimes it's a misspelling :)

 

Just as proofreading your English work is important, it's important to be able to catch your math errors.

The age of your child matters too. I don't think I started saying, "You've got two problems wrong on this page," until my son was in 3rd grade or higher... and again, this is on material that is review.

 

 

Yes. Also I think it is important that the work be relatively low in errors in the first place. If the child is making multiple small errors that result in half the problems being wrong, I don't think that telling them 'You have 11 incorrect problems out of twenty. Find them and fix them' is a good idea.