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 firstname.lastname@example.org.