Math concepts for the non-mathy

[SKL]

So I'm trying to remediate / solidify math concepts with my Miss A by the end of the summer. I've started asking her to verbalize what she's doing as she works out multi-step problems. I'm hoping this will help her to better recall the steps etc. But she finds this very difficult. The other day she said, "I'm thinking. I can't talk and think at the same time." She'll work the problem mentally, even whispering to herself, but won't say aloud what she's thinking. Is this something normal that will be resolved with repetitive practice, or do I need a new approach? What are some concrete suggestions that worked for you at this stage?

[Penguin]

I am not sure about the age of your daughter, but I had a similar need & I found sections (Problems without Numbers, Are You a Good Thinker) of Practical Arithmetic to be great.

 

I don't have the books at hand, so I will just make up two typical problems to give you the idea. There are three volumes so they get incrementally harder.

 

If you know how many apples you want to buy and you know the cost of one apple, how do you know how much money you will need?

 

Lisa needs some fabric to make a dress. What does she need to know to figure out how much the fabric will cost?

 

At first, he found this very difficult to do. But keeping at it really paid off and taught him how to verbalize what he was doing. There are NO numbers, so you CAN'T just write down the answer.

[Spy Car]

Asking your daughter to explain her math reasoning is the best thing you can do.

 

Will it perhaps exasperate her and test your patience as well? Absolutely!

 

It it's own way it is like the torture of early-reading and "sounding it out." But like working on the phonics pays huge dividends, spending the time to work thought this process will be rewarded.

 

Bill

[EKS]

Asking her to explain what she is doing might be different from explaining why she is doing it and from your post I can't tell which thing you're wanting her to do. If you want to solidify her conceptual understanding, engage her in a conversation (using manipulatives as appropriate) about her reasoning (the whys rather than the whats). I wouldn't make her do this for every single problem, but have her do it regularly. When I say "conversation" I mean that it should grow out of a natural interaction with you rather than be some sort of oral exam she has to pass.

[regentrude]

Can you ask her after she did a problem and have her explain to you what she did? That may be easier than narrating while she thinks.

I do not think there is any better approach thyan talking about math; the best solidification of concepts comes from teaching somebody else. So, let her teach you - of even her dolls.

[SKL]

I've tried the "why" questions and she is so far from being able to articulate that, I felt the "what" would at least be a step in that direction.

[mom2lydia]

For my daughter in 2nd grade she is not able to explain it to you why or what she did just that she did it. She can show you the problem and give you the answer but the ability to explain it either during or after is just usually not there. Sometimes she can tell me that she figured out 92-13 because 92-10 is 82 and 82-3 is 79 but that's only sometimes and it's how she does it even though her teacher considers that method "wrong" She developed doing it this way on her own because it worked for her and she gets the right answer but she will rarely show or tell how she did it because she is afraid of her way being wrong in those few instances she is even able to explain it.

[SKL]

Thanks for all the comments. Seems they are diverse, but I am glad to see most of you agreeing that this is really hard. I like the idea of having her explain one problem that she just completed each day, for now. One thing I have done sometimes is to have her use manipulatives (c-rods or base 10 pieces) to "show me" the solution to a problem she has done on paper. This requires few words, but still checks comprehension. ... Just a wee update - yesterday Miss A was flying through the double-digit subtraction (without regrouping) and I was thrilled! Then subtraction with regrouping started . . . ahem . . . but hey, I see light at the end of the tunnel.

[Arcadia]

My kids B&M school does not have manipulatives other than for kindergarten. Besides manipulatives, see if your daughter is willing to draw out the steps/working for the math problems. She can always draw even in a class math test.

My boys can't explain while they are working out their math problems. It breaks their train of thought. They can explain after they are done. My older gives a very concise explanation while my younger explains in an elaborate fashion, so very different styles.

[Spy Car]

Thanks for all the comments. Seems they are diverse, but I am glad to see most of you agreeing that this is really hard. I like the idea of having her explain one problem that she just completed each day, for now. One thing I have done sometimes is to have her use manipulatives (c-rods or base 10 pieces) to "show me" the solution to a problem she has done on paper. This requires few words, but still checks comprehension. ... Just a wee update - yesterday Miss A was flying through the double-digit subtraction (without regrouping) and I was thrilled! Then subtraction with regrouping started . . . ahem . . . but hey, I see light at the end of the tunnel.

 

 

I would do it the other way around, have her "show you" the solution (as she explains it) with the manipulatives (as necessary), then have her do it on paper.

 

I'd also push though and do a lot more than one problem a day. If she can explain her reasoning, she will develop strong skills, and dramatic progress will follow.

 

Bill

[SKL]

I would do it the other way around, have her "show you" the solution (as she explains it) with the manipulatives (as necessary), then have her do it on paper.

 

I'd also push though and do a lot more than one problem a day. If she can explain her reasoning, she will develop strong skills, and dramatic progress will follow.

 

Bill

But if she finds this terribly frustrating, it's just going to end in tears, not progress. I've tried this and she just gets stuck time and again. Maybe I can try this approach as I start back at the beginning in the summer, with stuff she already finds very simple. It could be the confidence thing too. ... I must say I will not have time for her to explain every problem every day, not at the rate she goes currently. My goal is to have her in bed before 10pm every night, which currently is not happening.

[mathnerd]

You have the right ideas - making the child walk through the solution with a teacher/coach helps solidify the knowledge as well as reinforces the concepts already learned.

What works for me is to make it a game for my DS. We pick 3 problems at a time and I become the student who lacks understanding of concepts and my child becomes the teacher. The child then "teaches" me how to solve those 3 problems. I throw in a mix of thoughtful, funny, weird questions to the "teacher" to keep it interesting and let him explain his thought process and also make him think about several "what ifs". One thing I noticed is that though my child is happy to teach me, his vocabulary and ability to explain clearly and logically is highly lacking - we were doing "consecutive odd numbers" yesterday and he got really frustrated because the words and thoughts were not flowing freely. I had to supply all the vocabulary and then aid in the explanation. Until then he refused to explain the solution to me.

So, what you are facing could well be a lack of fluency of words and thoughts, in which case, you could prompt frequently and supply the sentences needed to complete each thought.

[Spy Car]

 

But if she finds this terribly frustrating, it's just going to end in tears, not progress. I've tried this and she just gets stuck time and again. Maybe I can try this approach as I start back at the beginning in the summer, with stuff she already finds very simple. It could be the confidence thing too. ... I must say I will not have time for her to explain every problem every day, not at the rate she goes currently. My goal is to have her in bed before 10pm every night, which currently is not happening.

 

 

If it is absolutely necessary, you could start out supplying some of the structuring "narrative" and allowing her to supply the details. Then, as you progress, you could drop back and just ask

leading questions, etc.

 

This really is an approach that's worth cultivating. I won't claim it won't be work. It will be work.

 

Bill

 

 

[Spy Car]

 

But if she finds this terribly frustrating, it's just going to end in tears, not progress. I've tried this and she just gets stuck time and again. Maybe I can try this approach as I start back at the beginning in the summer, with stuff she already finds very simple. It could be the confidence thing too. ... I must say I will not have time for her to explain every problem every day, not at the rate she goes currently. My goal is to have her in bed before 10pm every night, which currently is not happening.

 

 

If it is absolutely necessary, you could start out supplying some of the structuring "narrative" and allowing her to supply the details. Then, as you progress, you could drop back and just ask

leading questions, etc.

 

This really is an approach that's worth cultivating. I won't claim it won't be work. It will be work.

 

Bill

 

 

[kiwik]

Like many others I have been following your threads and have huge sympathy for your daughter's problems and your efforts to help. I do know however that my son would not cope with school at all if he was up to any where ten even once a week. I know you work full time and your time to remediate is limited but I'm wondering whether more sleep may help with some of the problems.

[SKL]

Like many others I have been following your threads and have huge sympathy for your daughter's problems and your efforts to help. I do know however that my son would not cope with school at all if he was up to any where ten even once a week. I know you work full time and your time to remediate is limited but I'm wondering whether more sleep may help with some of the problems.

My goal is to cut it back to 9:30 by the end of summer. That said, I have seen her perform with varying levels of sleep, and it doesn't make a measurable difference as long as she's in bed by 10-10:30. I mean, assuming she's doing something productive with the time. She doesn't have to get up until about 7:30am and she's a very good/sound sleeper. I would love for her to have more sleep, but the price would be never being remotely close to ready for the day's math lesson, missing homework, bombing tests, etc. It's a tough balance to figure out, that's for sure, and I do doubt myself on this at times.