"Adding by Place"

Traditionally we were taught to line up our numbers and add. If it equaled more than ten, you carried the one and then added up that row. This method is definitely a way to solve a problem, especially if you have a sound understanding of place value. A lot of us would just do it because if we didn't do it that way it was wrong. It was also the only way we were taught which goes back to the old saying of "you do the best with what you know how to do". Research has shown that students come to us with their own understanding of math and it is our job to tap into their little brains and find out what works best for them.
Investigations teaches multiple ways for students to solve problems. It is also important for the teacher to understand various ways, so when a child is trying to explain how they are thinking of a problem we can accurately model and help the child communicate and visualize their thinking.

So a strategy that is helping students understand place value when adding numbers, is "Adding by place".
Example:
36+23=
Tens place 1st: 30+20=50
Once place 2nd: 6+3=9
Combine the two: 50+9=59

Now, of course this takes a little more time and there is always the "quick" way which is never discouraged. Educators have noticed it is sometimes too quickly introduced though before the student has a strong understanding of why they are "carrying that one". So this is just foundation work so when students get to numbers in the hundreds of thousands there is a stronger foundation in place value.
Hope this helps...