Wednesday, June 20, 2012

Intellectual Toughness

As the author of a widely used thermal physics textbook, I get a steady stream of email from students around the world who are using the book. By far the most common type of inquiry is requests for answers to the end-of-chapter problems. Some students ask for the answer to a particular problem; others want copies of the entire solution manual.

To most of these students, my standard response is “Ask your instructor.” However, not all of them are using the book in a traditional classroom setting. Some have moved on to advanced studies or workplace settings where for various reasons they need to go back and brush up on their undergraduate thermal physics.

Of course I’m delighted that people are using the book in such diverse ways. But I’m also dismayed that, even after earning an undergraduate degree, so many scientists and engineers still believe that answers come from textbook authors.

The whole point of science is that you can figure out answers for yourself, without relying on any authority. For physics textbook problems, that usually means you have to do some sort of calculation. And how do you know if the calculation is correct? Not by consulting a teacher or solution manual or some other authority! Mathematics has its own internal logic that tells you whether it’s correct, without reference to anything external.

But what about careless errors, which everyone makes from time to time? There are endless ways to catch them without any appeal to authority. Do the calculation a different way. Compare the answer to other known facts. Ask one of your peers to check your work.

Our educational system does a lousy job teaching these skills. In our fervent desire to “cover” as much material as possible in our courses, we don’t give students time to ponder their results and root out their own mistakes. Instead, we authoritatively mark their answers right or wrong, then hurry on to the next problem.

Nor is this situation unique to the mathematical sciences. Students of biology, economics, sociology, and history must all learn to distinguish truth from falsehood without an instructor’s help. Critically examining one’s methods, and thus developing confidence in one’s answers, is fundamental to every discipline that deals in hard facts.

It’s not enough to teach facts, or even to teach specific technical skills. We somehow need to help our graduates develop the intellectual toughness to know when they’re right, so they can become leaders in their chosen fields.