How do You Subtract?

Subtraction on one of the basic things that you learn in Math. Same as adding, dividing, and multiplying. Those are the first things that come to mind, right? Well, as simple as these things seem, they're not. I know you're going,"They're not?" 

Hmm. Well, maybe for you, but not for me. All of you know--or at least I believe you do--that I'm home-schooled, so it's my lovely Mother who grades my work. So, today my Mom was grading my work(still is. She's in the chair next to me as I'm writing this, actually. ;])and she looked at me. Being completely serious, she stated,"You're missing half your problems, Abbi."

I gave at her with a look that said, "Nuh-uhh." Well, turns out I am. And most of them are subtracting. Now, I know that I know how to subtract;but, according to my Mom, I don't. She says I do it SDRAWKCAB. Hah. How do you subtract backwards?! Well, since I'm obviously an expert at it, let me show you with a normal problem:

12345

11456

-           

The way I would do it:

Now, you take 2 and make it 1. You cross out 3, make it 12. Then make 4, 13, make 5, 15. After, you subtract.

1 12 123 134 155

1  1          4 5 6

-                         

00889

(Those smaller numbers were the previous numbers)

So, apparently you're not allowed to subtract from the right to the left, but you're supposed to do it from the left to the right. Am I making any sense? I am absolutely positive that when I was in 1st grade(when I learned math like this), I learned it right to left. Maybe it's because I'm getting into the harder subtraction, to where I'm going to be needing to do it the other way, or something. I just don't know.

Or, maybe, I just don't know how to subtract! xD