Well, there's definitely something wrong with her method if the result is 106 whereas your method produces 105.
I was taught the same way you were. There are many different ways to do addition. Whatever works best for the individual is fine as far as I'm concerned. However, it seems a lot of get easily confused if taught a lot of different methods. In that case, sticking with a single simple method seems superior. I know that when I was introduced to 'New Math' in the 9th grade and was taught set theory and a variety of different bases, I was overjoyed at entering into a new and wonderful universe. I never pursued this joy in college however. I regret that.