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.