The shortcut taught without its limits can become a long way into trouble.

Shortcuts are rules with conditions attached, and the conditions are the part left out when they get passed on. Somebody learns the quick method without learning when it fails, uses it confidently in the case it was never meant for, and years of saved time disappear in one afternoon. The danger sits in the missing half rather than in the technique.

When you teach a quick way, say where it breaks in the same breath. When you learn one, ask what it assumes. A shortcut whose limits you cannot state is worth using cautiously.