Carrying in your head or on the page? Teaching philosophies, please.

[violamama]

My oldest has been doing a bunch of carrying in addition now (Singapore 2A but I'm a slouch about consulting the teaching book and we often just do the assignments directly together). It's new to me in terms of teaching. My husband always writes the carried number, and even tends to sort of gesture them in the air with his hand when he does it "mentally". I tend to prefer not to write them, and just put the combined sum at the bottom of the next column.

 

My son does it without writing the carried numbers. Should I encourage him to keep going that way, or are there good teaching philosophy reasons to have him write the carried number also? Will this change when he's doing larger numbers? (We're at the three digits + three digits stage now.) What about later when he's multiplying or doing subtraction with borrowing?

 

I'd love especially to be pointed to some articles or blog posts on the difference between teaching to show every step on the page or keeping some of it mental.

[Hwin]

I would prefer that my son write the carried number so that I know he understands both the process and arithmetic, but I wouldn't push it if the answers are correct and if I felt confident that he understood the why and how. I don't know if Singapore is like Math Mammoth, but they really spent a lot of time on carrying/borrowing, and I think it was a little too much review by the end for my son - to where he wasn't sitting there like a good little boy doing it by the book and just wanted to rush to the end and be done. He actually got better at adding/subtracting once we stopped doing it every day.

 

I sometimes write with my finger on a surface if I'm carrying numbers ^_^

[misty.warden]

Writing carried numbers was explained to me as a step to help make less mistakes than just tying to remember what to add. Then again, seeing a jumble of written and crossed out numbers above the original numbers can be just as confusing, IMO. I'd let him stick with whichever way he makes less mistakes.

[christielee7278]

I ask that my boys write it out so we can see what went wrong if a mistake is made.

[blondeviolin]

It depends on of you're working on the traditional algorithm or mental math. I'd strongly advise you to get the HIG so you know what Singapore itself emphasizes.

[sueh16]

IMO if he is doing the math accurately and he understands why he's carrying, I see no need to write the carried #. If he starts making careless errors then he should start writing the #.

 

Sue

[Kuovonne]

I have my kids carry in their heads when the problem is presented horizontally,

and carry on paper when the problem is written vertically.

 

Writing the carried number is important when adding a long column numbers and

when doing the standard algorithm for multi-digit multiplication. When adding a column

the carried number isn't always one, and there are more numbers to keep track of, so

it is important to write the carry. In multi-digit multiplication, a common beginner mistake

is forgetting to add the carry, so it helps if at least writing the carry is automatic.

 

Writing the carry also makes identifying and correcting mistakes easier.

[Elfknitter.#]

We're still working on it, so I ask to see them. If the problems were done consistently well with and slowly without them, then I wouldn't require it.

[dbmamaz]

My son does a ton of math in his head. Often I will ask him to write it down once in a while, just so he knows the method, but if he's getting them correct . . .id make him write it down once or twice a month. Well, except he's so stubborn he'll scream and cry . . .so I can only get him to do it if he's made a few mistakes in one day lol

[Walking-Iris]

Both. When working on mental math, just do it...mentally. But when my ds is writing down the problem with pencil and paper, he writes the number. It does help see where a mistake was made. I don't know how many times I've said, "you forgot to add the 1." I think getting in the habit of writing it will help with subtraction.

 

I also have my ds write it different ways at times to reinforce the concept. We've had lessons where we write the complete sum (without regrouping) and then write it again under (on graph paper) to visually reinforce the place value/regrouping concept. We've done them mentally, we've done it written out. As long as they understand the "why" of the regrouping then it's good whatever you do. I think you'll find that writing it down will make other operations a bit easier to learn at first.

[dbmamaz]

my son, tho, still refuses to do multi-digit multiplication the ordinary way . . . he does it in his head in stages, writing down the numbers he comes up with . . . like 231 x 42 . . . idk, for that he might do 2 x 231 and 40 x 231 but sometimes he'll do 2x1 + 2x30 + 2x200 + 40 x 1 + 40 x 30 + 40 x 200 . . .he doesnt write down the 40 x 200 part, he writes down each answer along the way, and then sums them in his head after he's written them down. i know its slower, but he gets the right answer. some time before he returns to school, he needs to learn to do it the faster way . . . but for now i figure he's giving himself practice with other things?

[Dana]

but sometimes he'll do 2x1 + 2x30 + 2x200 + 40 x 1 + 40 x 30 + 40 x 200 . . .

 

This is exactly how you'd multiply two polynomials (x-3)(x^2 + 5x -8) ... distribution! :)

You might show when one approach is "better" than another, but as long as he can get the correct answer without it taking "too long", cool! :)

 

(As to the original question... both have benefits & I agree most with the pp who said write carried digits when doing vertical arithmetic & hold it mentally with horizontal.)

[dbmamaz]

This is exactly how you'd multiply two polynomials (x-3)(x^2 + 5x -8) ... distribution! :)

You might show when one approach is "better" than another, but as long as he can get the correct answer without it taking "too long", cool! :)

yes, this one's father is a genius mathematician, and math was my fave subject as well. his intuitive grasp of math is often breathtaking.