8th Grade Math

Friday, I helped out with the advanced 8th grade math class. It brought me straight back to middle school. However, I also realized that my brain works differently from these students. Maybe a great portion of humanity. They did mental math. For example:

x+3=9

Of course, x=6. We also had

8+x=4

x=-4, obviously. But the math teacher asked about how they got the answer. Apparently, most people moved the constant to combine like terms. That is, they rewrote the problem mentally to read

x=9-3=6

x=4-8=-4

On the other hand, I did no math. I simply asked myself, "What do I need with 3 to make 9?" Or "with 8 to make 4?" A subtle difference, but I realized I was in no way doing mental math. It got more obvious with a more difficult problem:

12+x=2x+8-3

The class all matched up terms in their heads:

12+x=2x+5

12-5=2x-x

7=x

Easy as pie, but not what happened in my brain. I didn't combine like terms. I cancelled. Before even combining 8 and 3, I balanced out 12 and 8. Now my problem read

4+x=2x-3

Except, at the same time, I did the same thing for the x terms:

4 = x-3

And them you have x=7. The process happened quickly, so did not cost me time. It was simply completely different from what was happening in the brains of other people in the room. I'm curious to know if this is because they are 8th graders, because of the fact that they have all been taught the same way, or because my mind is a strange place to me.