I'm not a teacher, but I'd say that "pile" and "heap" are nearer to being interchangeable than are "pile" and "stack" or "heap" and "stack". The key is the suggestion order, or disorder, that the words convey. I have a pile of medical journal articles lying in a heap on my floor, but I have a stack of folders on a shelf in my office. If I see or hear "stack" I think of an ordered arrangement, with heap and pile, I think more of a random accumulation of materials.
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