I am going to add a bit of a different perspective as I am not an elementary math teacher but I work with high school and college age kids. It is definitely important to understand the concepts of addition and subtraction using manipulatives, pictures, the number line, etc. However at some point, depending on the grade of your child, memorizing the facts becomes a huge factor. I have seen students at the high school level that I can tell are picturing the number line in their heads and which way to move and using their fingers in a hopping motion. Once you get to more complicated math problems, you are asking to add, subtract and multiply many times. Too many times to be picturing the number line. This won't help on the ACT and SAT, they need speed and accuracy.
So once they understand the concept and when your school says it is OK, get them an app and have them practice repetitively until recall of the basics is easy for them.