Simple memorization can go a long way in mathematics: Many students cheat their way through to the sixth grade without really being able to do math. But by then, at the latest, teachers expect their protégés to be able to abstract tasks and comprehend and calculate them in a different form. The grades of the rote learners then suddenly plummet.

A good way to protect yourself from this shock is to repeatedly calculate math problems backwards (or have them calculated for you). Only those who can explain their calculation in both directions to others have really understood it. In addition, calculating backwards offers many opportunities to identify and close gaps in knowledge.