In addition to Douglas Julien, I read that ia (with the line over the a that my keyboard won't do) is closer to the definite article "the" and carries the meaning of "that you and I both know about." So roughly "the homework (that you and I know is yours) you." It's not the same as kou "yours." It helped me to get the feel for the thought behind the construction to know that "ia" carries that more specific article and referent meaning combined.
I thought aʻo was learning/teaching, while haʻawina is lesson or assignment. Obviously there is some overlap between those two, and it makes sense for there to be contexts where either could be used, or where aʻo can mean lesson, but Iʻm pretty sure haʻawina is "lesson" just as much as it is "homework" or "assignment", and aʻo is a bit further away from the English word "lesson" than haʻawina is.
Am I approximately right about this? Can someone clarify?