Horizontal/Vertical math?

[bbrandonsmom]

So we just finished up Singapore 1a, and the only problem we ran into (other than not having a scale), was addition/subtraction over 10. Ex 12 + 5. The problem comes from the problem being horizontal. If I put the problem like this

12

+5

___

 

He would get it. Horizontally, he circles the ten, then adds the remaining ones, but tends to forget to add the remaining one, back to the ten. Vertically, to the eye, it looks easier I think, to separate the 10, and if he understands that the ten is not a one, then him adding this way shouldn't hurt right? I am thinking it might help if he does some of the vertical problems, and then show them side by side on a dry erase board, so he can see they are the same problem, visually. The same applying to subtraction. I think if he didn't understand what the 1 stood for, it might cause problems.

 

He's also going to be taking a math class in co op, and while I'm going to let the teacher know what we have been doing, I know he's going to be exposed to different methods to solving problems. I don't have a problem with that, as long as it doesn't cause confusion, because for math, isn't it that the kids have an understanding of math, not just the surface? I know in Liping Ma's book, on the subtraction chapter, she spoke of how students fared better when they had a teacher who showed them multiple ways to solve a problem.

 

For those of you using horizontal math, did you run into this problem, and did you try vertical math, to help with understanding that it was still the same problem? The only problem I can see with this, is doing the whole separating the ten, therefore creating a different problem, so the first problem, becomes 3, really. Ex:

12 + 6=

2+6=8

10+8=18=12+6=18

Those steps are subtracted doing vertical, from what I can tell. Unless visually, you broke it down like

12

> 8

+6

____

10+8=18=12+6=18

 

I'm sure I'd confuse myself if I did this with subtraction. The point is, he knows that problems are not stone, and are made of different problems, so back to my question about using both horizontal and vertical to help with understanding? Thanks :)