Looks like the student is doing what they KNOW how to do, not what the problem is asking for. I would suggest trying to connect the skill they are using to the correct one to solve this problem.
I am guessing they think that somehow the division bar is a subtraction, since it looks like the same shape as a subtraction. They see numbers and they subtracted them from each other. With addition they just add the numbers that they see together.
Looks like they are thinking that subtraction ‘undoes’ division, but not in a consistent way. Perhaps by subtracting the number on the left from the one on the right. #15 looks like adding the left-hand and right-hand side numbers to combine them.
That was my initial thought too, James. They know that they are supposed to use the numbers involved, and probably with some arithmetic operation, but they have no idea what operation, or perhaps even what the symbols involved mean.
tieandjeans
There’s a directionality thing there that I can’t systematize. Subtraction seems to happen when items move from right to left, but #15 shows an additive operation when the term moves form left to right
Beverly
Great opportunity to teach them how to check their work!
What I see occuring is “combining like terms” and ignoring the equals sign. Although the subtracting in the last middle one is interesting.
suehellman
Ignoring operation signs and location, two smaller numbers add to make a third bigger one. I think he was exploring variations on an interesting theme.
This is what I was thinking for the first two– making the biggest number out of two numbers (since after all, aren’t addition facts what most students are most familiar with?). The last, however, feels to me like “I know I should move the 12 over to the other side” without really thinking about how to do the “moving” and just finding a combination of numbers that works (although maybe I would have expected to see a positive 10).
Peter Tompkins
Not a matter of “doing” the wrong operation. Ask the student what n/8 means and take it from there.
Here’s an observation: the student’s eye is moving from left to right. The eye goes from 19 to 8 and from 13 to 6 and from 12 to 2. As some people mentioned, this might be out of a need to simply avoid negative numbers, but I wonder if this is just how the student reads math, and whether the student has trouble seeing things out of the “left to right” sequence.