Design principles

Principle I

Be ambiguous.

Use poorly posed problems. Provide too much or too little data in otherwise standard problems.

Formulate questions with many solutions or no solution.

Replace numbers with parameters.

Admit multiple solution strategies.

Principle II

Ask about, not for.

Ask about the results of a process or method, not for its application.

Ask students to match problems and methods with outcomes.

Principle III

Explore vocabulary.

Ask students to provide examples of concepts, properties, and terms.

Inquire about the interdependence of concepts, properties, and terms.

Principle IV

Shift context and perspective.

Employ the rule of three: pose questions from the graphical and numerical perspectives, not just the algebraic.

Use mathematical modeling to set questions in a physical context.

These principles are neither foolproof nor exhaustive. But they lead to exercises that make teaching more rewarding and learning more complete.