The definition of the algorithm given to the student may involve language like "take the first number and..."
The steps are the steps.
Secondly, a student that knows the difference between different techniques and can call them up at will (such as the difference between 5 sets of 3 and 3 sets of 5) is better off than a student that only knows how to produce a particular answer for a particular question.
Teaching and requiring that a commutative operation be ordered doesn't seem like it is going to contribute to that.