They do not have a true understanding of reverse operations.

I like this theory…

I wonder if they would add if n were in the denominator?

Students always try addition or subtraction first. It’s a little odd that the stu added in the last one – although there is a +.

I think they generally have an aversion of negative numbers. In this case they are always subtracting the smaller from the larger.

Nice consistency on the part of the student. Additive relationships throughout, and complete avoidance of negative solutions.

Yes. Indeed.

Oh snap! Looks like kiddo was treating division as some sort of subtraction.

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.

In every case they’re adding, but the numbers that they’re adding aren’t always coming from the same place in the equation.

There isn’t even a consistent error. 19-8 = 11, but 6-13 = -7. And the last one is even weirder.

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.

Equals sign means nothing to this student.

Wonder what would happen if 19/1 = n/8?

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.

This seems like a situation where a student throws operations at a situation and tries to see what sticks, because they have no idea what to do.

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.

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

Great opportunity to teach them how to check their work!

Justin — I think Christopher said it well: The kid was completely avoiding negative solutions.

Yeah, that’s possible. Is that because they don’t want to deal with negative numbers of because they don’t know that they exist?

I wonder what would happen if the teacher required substitution to check the answer.

What I see occuring is “combining like terms” and ignoring the equals sign. Although the subtracting in the last middle one is interesting.

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).

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.

## 27 replies on “Solving Simple Equations”

They get subtraction and division confused!

They do not have a true understanding of reverse operations.

I like this theory…

I wonder if they would add if n were in the denominator?

Students always try addition or subtraction first. It’s a little odd that the stu added in the last one – although there is a +.

I think they generally have an aversion of negative numbers. In this case they are always subtracting the smaller from the larger.

Nice consistency on the part of the student. Additive relationships throughout, and complete avoidance of negative solutions.

Yes. Indeed.

Oh snap! Looks like kiddo was treating division as some sort of subtraction.

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.

In every case they’re adding, but the numbers that they’re adding aren’t always coming from the same place in the equation.

There isn’t even a consistent error. 19-8 = 11, but 6-13 = -7. And the last one is even weirder.

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.

Equals sign means nothing to this student.

Wonder what would happen if 19/1 = n/8?

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.

This seems like a situation where a student throws operations at a situation and tries to see what sticks, because they have no idea what to do.

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.

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

Great opportunity to teach them how to check their work!

Justin — I think Christopher said it well: The kid was completely avoiding negative solutions.

Yeah, that’s possible. Is that because they don’t want to deal with negative numbers of because they don’t know that they exist?

I wonder what would happen if the teacher required substitution to check the answer.

What I see occuring is “combining like terms” and ignoring the equals sign. Although the subtracting in the last middle one is interesting.

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).

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.