Please help me figure this out about ds7 and Singapore

[HappyGrace]

DS7 is good at math-I never had to teach him any of it so far; he just knows it, even the basic facts-we never drilled them because they're just there for him. I posted before about ds being able to do things in his head with his own strategy. Sometimes he can explain what he did to me, and it is a Singapore type strategy that he just instinctively knows, but he usually gets the right answer. So we went with that because he doesn't like me showing him other strategies.

 

This was working in 1b with two numbers to 40 with regrouping (like 38-9). He can do any number you give him up to 100 and subtract or add a single digit with regrouping. (He can also add 2-two digit numbers in his head with regrouping and subtract 2-two digit numbers w/out regrouping.) I posted recently about should I 'make' him learn the Singapore strategies or not, if he is doing them anyway. He seems to be fine with the above topics-VERY easy for him-so we moved on.

 

But NOW we are hitting a weird wall with subtracting 2 two-digit numbers with regrouping (like 98-59). I tried showing him with the tens and ones columns, and also the base ten blocks (taking one ten apart so you have and 80 and 18 more units to subtract the 9 from.) It's not too hard for him; it's just that he doesn't like me to show him the strategies like this. He said you can't do that with the "actual numbers." It's like he is seeing it somehow in his head and can't mesh the manipulatives with that.

 

What should I do? Back up and "make" him go through learning the strategies somehow? That really frustrates him! It's almost crippling him now that he has always done it all in his head, because now that it's getting harder and he needs to be able to think of different strategies or be "taught" different strategies using manips, and it's not working for him. HELP! :tongue_smilie:

[Corraleno]

I had a similar problem with my son. He started school half-way through 1st grade, just before he turned 7. Even though we'd mostly unschooled before then, his teacher commented that his mental arithmetic was very good and actually more advanced than most of the other 1st graders. When the math got more complicated, though, he started floundering. He had his own strategies for mental arithmetic (largely visual), but they didn't work well when he was borrowing/carrying or using large numbers (large enough that they were hard to keep in his head through all the steps). And since he wasn't learning the why of math in school, just the steps, he didn't have anything to connect what he was learning to what he had already taught himself to do.

 

This is where Math Mammoth came in! If you read the instructions at the top of the page, you can't not get the conceptual part. It doesn't use manipulatives, but it illustrates them, and it shows the same problems with math and pictures side-by-side. I think you already have MM for your daughter, right? I'd try switching your son to MM as well. You wouldn't have to go back and start at the beginning, you can jump in at the level he's at. It will teach him the conceptual basis for borrowing & carrying, but in a sneaky way! Those few lines of instruction at the top of the page look deceptively brief and simple, but they will switch on the "lightbulb," even if your son doesn't want to acknowledge it. And he can't claim the way she teaches it "can't be done with real numbers" because she will show him right there on the page how it can be done!

 

Jackie

[HappyGrace]

You know, Jackie, I've been waffling back and forth about switching ds from Singapore to MM. MM is working so well for dd, but I just thought Singapore would somehow be more "meat" for him (I don't know why-MM is so good too!) We use and love CLE as our spiral "spine", and have been wondering HOW am I going to do both CLE and Singapore with him-quite time consuming. CLE and MM is a perfect fit for dd and not too time-consuming.

 

I'm so glad you posted this. I think he'd go right into MM2 because it is much more incremental that Singapore. I will sit down later and look ahead through the Singapore and MM, but I think you may be onto something! THANK you!

[Ali in OR]

I like to attack these problems from multiple ways of visualizing them. My youngest can be a bit strong-willed and at first she was resistant, but now she likes talking about the different ways to find the answer. Or if I do it one way, she'll tell me how she did it another way. It builds a facility with numbers to be able to visualize them differently. So a few concrete examples:

 

For 98-59:

"What would 99-59 be? Would 98-59 be one more or one less?"

"What would 98-58 be? Would 98-59 be one more or one less?"

My own personal favorite approach: 98-50 then 48-9.

Important add-on to that method: For a problem like 48-9 I like to ask dd what "decade" the answer will be in. Will we stay in the forties? Then I like to subtract enough to get down to the next 10 (subtract 8 to get to 40 in this case), then ask how many more I have to subtract (the leftover 1) and go down to 39. It helps to know simple number bonds really well here.

My dd's favorite approach for something like 48-9: 40-9 then add 8.

 

Even if my child wanted to whip through math on her own, I would still sit down and discuss it with her. I think that being able to manipulate numbers in many different ways is an advantage. The above methods are really pretty quick--these are not long ways to solve problems. My older dd went through this and does 2 digit addition and subtraction in her head very quickly and accurately and I think with a variety of strategies. I think your son's struggle is more on place value--the idea of tens becoming ones--and manipulating that image in his head. I would try some of the above strategies for a bit, but recognize that eventually he needs to be comfortable with place value renaming too. Just maybe not quite yet. At any rate, some conversation about the problems may help him talk through strategies and see different ways to get where he wants to go.

[HappyGrace]

I actually just remediated this topic with older dd (who didn't learn it conceptually earlier on) AND read it in Liping Ma's first chapter. So I have tons of strategies for it-just trying to figure out how to make it click with him. I think I will try my "friendlier number" strategy-similar to one you mentioned-where you make one of the numbers the next higher decade of 10 and then figure that out, and then at the end add or subtract the number you added or subtracted to do that. That might be better for his level, I'm thinking.

 

And meanwhile I'll try some other manipulative work to cement place value. We've never done much manip work, so I want to try a little more and see if maybe that just doesn't click with him, or maybe he just needs more of it (manips, that is.)

 

Thanks for the help, Ali!

[karensk]

....So we went with that because he doesn't like me showing him other strategies.

 

...

What should I do? Back up and "make" him go through learning the strategies somehow? That really frustrates him! It's almost crippling him now that he has always done it all in his head, because now that it's getting harder and he needs to be able to think of different strategies or be "taught" different strategies using manips, and it's not working for him. HELP! :tongue_smilie:

 

This reminds me of our experience when ds was in maybe 3rd through 5th grades (he's used SM PM-1 through 6). He was very reluctant and resistant to learning alternative strategies to solve a problem. If he was proficient with one strategy, he really did not want to learn a different one. Why take the time and energy to learn another strategy when you've already got one that works perfectly, right? And, as you said, the initial mental math strategy only works for so long, and then the student needs to learn another way to do the more difficult problems. And when ds had his mind made up against the seemingly useless alternative strategies, it was difficult to get him to engage and pay attention to me demonstrating any new strategy. Ds doesn't normally have a stubborn personality, but whenever we ran into these issues, he became very, very stubborn!

 

I think I just kept trying, little by little, to convince/persuade him that it worked and that he needed it because he would have to do more complicated problems that couldn't be solved the old way.

 

So we might've spent just a few minutes a day for several days on the new strategy, whatever he could tolerate. And then, after a few days, the steps wouldn't be quite so new and foreign to him. Once things felt a little familiar for him, it was smoother. And after he understood what I was demonstrating (maybe after a few sessions), I'd gradually have him do a part of the strategy with me, something like: I do the first step, he does the second, I do the rest. After awhile (or maybe on another day), we'll take turns with the steps, about half and half; then he'll do more of the steps than me. Finally, he'll do all the steps, still with me sitting there and talking through the process. This might be spread out over several days, maybe just 3-5 minutes of his discomfort per day; I never rushed it, but I never quit either. Eventually, ds would get to where he was comfortable doing the alternative strategies; it was just a much longer, gradual process...like a loooooong ramp.

 

Interestingly, I've had none of these kinds of issues with dd10, who has used SM PM-1 through 4A. Though she says that math is her least favorite subject, she quite willingly, quickly and successfully learns the alternative math strategies (more like a steep ramp, for her), which leads me to think that it might be a personality thing. And with dd, the difficult math issue we run into is dawdling...daydreaming when she should be working on her math exercises. Never had this problem with ds!

 

HTH!

[amsunshine]

Similar to other posters, I gently stick to teaching the various strategies, even when it seems like my dds don't want to learn them as they prefer others. I do think it is valuable to teach them to think about numbers in different ways. I tend to try to teach them with a lot of enthusiasm, in an effort to show how "neat" a particular strategy is, and how much faster and more accurate they can be using such and such a strategy. We use the base ten blocks and I finally purchased the number discs as well. There is something about the novelty of new malipulatives that makes my dds more interested in "playing" with the different strategies. :tongue_smilie: Oh, and I also have dd's "teach me" the strategy for various problems. They get a big kick out of that, and it really helps me see they "get it."

 

Also, I do the mental math drills faithfully -- these are where the strategies are used and cemented. Don't forget those!

 

Finally, your ds will be seeing these strategies again in level 2 and again in level 3. (I would imagine they are used in levels 4-6, too, but we haven't gotten there yet.) Think of 1b as giving him a taste of what's to come --and know the strategies are going to be consistently reinforced in the next levels. Resistance is futile. :)

Edited March 18, 2010 by amsunshine