By Phillip Wankat and Frank Oreovicz

IT CAN TAKE YEARS IN THE CLASSROOM TO REALLY MASTER THE ART OF TEACHING.

How do experienced professors know the best way to explain difficult content or where to look for likely student errors? They rely on "pedagogical content knowledge," fancy jargon for what good engineering professors have always had: knowledge of how to teach specific content.

An important part of pedagogical content knowledge involves understanding students' preconceptions. The National Research Council's excellent book, How People Learn, by Bransford, Brown & Cocking (2000), says "People construct new knowledge and understanding based on what they already know and believe." Students' tendency is to extend existing knowledge structures, based on preconceptions, as new knowledge is learned. Preconceptions, which are always present, may be helpful, neutral, or harmful.

Incorrect preconceptions assume that the existing knowledge structure is faulty. Unless these incorrect preconceptions are corrected, the new knowledge structure will also be faulty. Students can correctly solve equations and still not understand what is happening. Their incorrect preconceptions survive beneath the surface as part of their knowledge structures.

On the other hand, correct preconceptions mean there is a correct, existing knowledge structure that can be tapped into with appropriate analogies. For example, most students have a reasonable idea about how to balance a budget. They can quickly see how to develop mass balances if they are first presented as analogous to balancing a personal budget.

Unfortunately, there is a hidden trap in the use of analogies and stories. The professor's idea of common knowledge may be different than that of the students'. For today's students the explosion of the Space Shuttle Challenger is history, dial telephones are antiques, and analog clocks are rapidly becoming obsolete. And "What's a typewriter?"

Although new engineering students always invent new errors, they also make classical mistakes such as using the wrong area in calculations. Pedagogical content knowledge can be used to quickly find student errors, to create plausible incorrect answers for multiple choice questions, or to design alternative instruction sequences that avoid or correct these errors.

Pedagogical content knowledge is also useful in teaching the design process. For instance, students tend to make predictable procedural errors when they first become involved in design. A very common error is to seize on the first feasible solution that is suggested instead of searching for alternatives. This tendency can be countered by requiring groups to brainstorm additional possible solutions and to turn in preliminary designs for several possible alternatives. Only after exploring alternatives are they allowed to complete their designs.

By labeling and dissecting it, we can more consciously use our knowledge of how to improve our teaching.

Phillip Wankat is head of interdisciplinary engineering and the Clifton L. Lovell Distinguished Professor of Chemical Engineering at Purdue University. Frank Oreovicz is an education communications specialist at Purdue's chemical engineering school. They can be reached by E-mail at purdue@asee.org.