Standard, end-of-chapter textbook problems can generally be solved by rote
memorization of sets of formulas and so-called 'problem-solving
techniques.' Often, students solve problems by identifying quivalent problems
that they have solved before. Don't we want our students to be able to tackle
more challenging problems?

Enrico Fermi was well known for his
legendary ability to solve seemingly intractable problems in subjects entirely
unfamiliar to him (e.g., How many piano tuners in Chicago?). Such 'Fermi
problems' cannot be solved by deduction alone and require assumptions,
models, order-of-magnitude estimates, and a great deal of self-confidence.
We often use back-of-the-envelope estimates to familiarize ourselves with
new problems. So why do we keep testing our students with conventional
problems? Problems that contain the same number of unknowns and givens
and frequently require nothing but mathematical skills. What distinguishes
the successful scientist is not the ability to solve an integral, a differential
equation, or a set of coupled equations but rather the ability to develop
models, to make assumptions, to estimate magnitudes, the very skills
developed in Fermi problems.