From a 'not currently in front of the class' perspective, it's pretty clear what the student meant by 1/3 + 1/3 = 2/6. They were taking + to mean something like a general 'and' or combining action, not in the strict sense of standard fraction addition. It even has a name in mathematics, 'Farey addition'.
The kids clearly want to write it in shorthand, so maybe the thing to do is to come up with another symbol for this similar but distinct operation. For example, ⊕.
The kids clearly want to write it in shorthand, so maybe the thing to do is to come up with another symbol for this similar but distinct operation. For example, ⊕.