The problems we pose to our students are the ultimate measure of what we hope to teach. This article describes some design principles for constructing ranges of such exercises. The last section states the design principles upon which those strategies are based. The use of interesting problems benefits everyone. Instructors can break away from a dull routine.
Students rise to the challenge of problems that require thinking.
And interesting problems let mathematics present a better face, showing itself much more than a dull concoction of recipes and rules.