The Question Concerning Technology (in the Statistics classroom)

In the past thirty years, cheap, ubiquitous computing power has allowed the field of statistics to address a wide variety of questions that previously would have been impractical. Any situation in which a closed-form expression for a particular quantity does not exist would have been virtually impossible to calculate by hand, and problems involving a large number of coefficients would have been unthinkable to solve. But computing has also made it easier than ever for anyone with little statistical understanding to use a statistical package, treat a procedure like a black box, and obtain a p-value without understanding the assumptions inherent in that procedure. How should the field of statistics teach technology to address both the increasing importance of computers and the dangers inherent in using them blindly?