Wayne Bishop says: >Once the story has been expressed mathematically, algebraic manipulations should be carried out independent of the story with the final mathematical simplification or solution, as appropriate, reinterpreted in terms of the story.
That' sort of the point of algebra, heh? Even when those manipulations seem to travel through a fairy tale world of impossible quantities etc.
"When a disagreement arises between two philosophers, they will no more need to argue than if they were two [human] computers: it will suffice for them to take pen in hand, sit down at an abacus, and say to each other (inviting, if they like, a friend): let us calculate." --G.W. Leibniz
Some students will no doubt be comfortable with this idea, without it disturbing their spotless minds much. But what about those to whom this very notion of letting "mindless" calculation replace "understanding what's really gong on?"