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Addition Error Pattern   
by Gail Englert

A response to the question:

What strategies can you suggest to help remediate this addition error pattern?

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As part of a masters in elementary program, I have been assigned the task of remediating the following addition error pattern: Whenever a column of addition contains a zero, the student writes a zero in the answer for that column -

                   569
                   350
                  +323
                  ____
                  1230

The tens column was missing the regrouped digit because of the error and the hundreds column was added correctly.

What strategies can you suggest to help remediate this error pattern?

Thank you,

Shirley

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Dear Shirley,

Have you tried letting the student model the problem using place value materials? The sums for the place values can be recorded in a chart that has the places named, like this:

      Hundreds     Tens        Ones
        5           6           9
        3           5           0
      + 3           2           3
       ___        ___          ____
        16         13           12 (all of which need to be regrouped...)
If the problem is modeled, the student can see that there is a place for each digit in the sum. Of course, just doing one problem won't fix the misconception. If you let the student make the "discovery" about what happens by providing guided practice that involves discussing what the student notices, s/he will draw the appropriate conclusions eventually. You can also reverse this activity, by having the student compute the sum, and then checking it with place value blocks to see if it is a sensible answer.

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Dear Gail,

Thank you, but that does not address the problem of not understanding the concept of zero.

Shirley

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Dear Shirley,

I guess I was thinking more about the idea that the student didn't realize there were amounts in the ones column that weren't being added. I do think that is part of the problem.

As for the zero... does the student do this (I understand that it is a hypothetical student) for a zero no matter where it is placed? Or is it only happening in the ones column. I guess I would start by having the student orally explain to me what s/he was doing as s/he added a set of numbers. Then, when s/he put down the zero, incorrectly,I would have an idea of why that was happening.

Perhaps the student saw the teacher add a set of numbers that just happened to add up to a multiple of ten, and thinks that you always get a multiple of ten. That is the reason it is important to choose sets of numbers to use as examples carefully, since you never know the conclusions children will draw from examples. Not only that, but you must be sure to listen to their reasoning, because they might be getting the wrong answer for the right reason.

So, to say simply, I think that your first step should be to listen to the student's explanation, since the problem is one of misunderstanding. Then you can use place value blocks to prove to the student that a zero doesn't always belong in the ones place. You can check for understanding by having the student generate two sets of numbers, one that will have a sum with a zero in the ones place, and the other which won't. Let the student explain why.

-Gail, for the T2T service

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