Guest post by: David White, Ph.D.

I spent part of this summer (my twelfth to do so) teaching philosophy to gifted seventh to ninth graders at Northwestern University's Center for Talent Development. One course I taught concerned logic and critical thinking.

The system we studied consists mainly of symbolic logic, and involves applying a series of axioms to arguments to determine their validity. For a philosophy teacher, this is a refreshing change of pace because the content of the course is cut and dried. Here, no one disputes "modus ponens"—the Latin term for one of the most basic axioms in logic that presents a mode of affirming a variable and its consequent (i.e. “if p then q, p, therefore q,” or, in other words, “If it is raining [p], the streets are wet [q]. It is raining [p], therefore the streets are wet [q].”)—an axiomatic rule of inference beautiful in its simplicity. Unlike virtually everything else in philosophy, which can be and usually is disputed, introductory symbolic logic stands on its own mountaintop of certitude, impervious to questions and critical attacks.

As it happened, however, I had a creative group of students this summer, and several young logicians began playing around with—or, more elegantly stated, thoughtfully analyzing—the axioms. They inferred propositions from axioms, then wondered out loud whether these derivations were equivalent to the rules of inference listed in our college textbook as "givens." Two of these creative student-produced axioms were subtle and elegant; furthermore, when I looked at them on the board, I, the logic teacher, did not know how to respond to the students' queries.

Grappling with Insecurities when Teaching Gifted Students

Consider then the "I don't know the answer" phenomenon all-too-familiar to teachers. By training, I am a university instructor, so when I started philosophizing with younger students, I observed a number of teachers working with gifted students from grades 6 on. I often witnessed excellent teaching, but I also noticed now and then a pattern of reluctance to engage students in discussions on points that, accustomed as I am to theoretical disputes, were of considerable interest and well worth developing. There may be various explanations for such pedagogical reserve, but I have always wondered if such reluctance was due to a sense of residual uneasiness, perhaps even fear, that the teacher may appear less than competently knowledgeable as “The Teacher of the Class,” especially during the vigorous discussions that often occur among gifted students.

I believe that no teacher, regardless of subject matter and level of instruction, should ever be concerned about admitting that they "don't know” the answer to a student’s question. My discipline, philosophy, deals with fundamental questions of such complexity that I learned decades ago not to be bothered by admitting that I didn't know the answer to a question posed by some thoughtful undergraduate. But it took a few years to learn this lesson—perhaps because graduate students in philosophy tend over time to adopt an air of omniscience, lest they reveal themselves as less learned and less thoughtful than their peers, an attitude which often becomes ingrained as a shield for a professor's frequently fragile ego.

Secure Enough to Tell a Gifted Student, "I Don't Know"

There are, of course, obvious classroom junctures where a teacher's "I don't know," would not be an appropriate response. The geometry teacher who has not fully mastered the intricacies of the Pythagorean Theorem needs to brush up; basic competence in a subject is presupposed by students and fellow educators (although an inquisitive student might apply the Pythagorean Theorem, produce an irrational number, then ask why it was called "irrational"—a question not easily answered!). But what holds for philosophy will surely hold for virtually every other subject. Saying "I don't know," when, in fact, the teacher doesn't know is not just simply being honest. This admission publicly registers the undeniable fact that no one, regardless of the extent of their formal education and personal intellectual energy and brainpower, has all the answers on a given subject.

Furthermore, I suspect that students, especially gifted students, respect their teachers more for admitting they don't know some answers than trying to camouflage their lack of knowledge with a response that is both ad hoc and less than compelling. The practice of classroom humility should surely be standard operating procedure for any teacher. It is interesting that in a recent article about some of McGill University's favorite professors, the one quality each professor cited as important was "humility." Everyone in the room benefits from this seemingly small but, nonetheless, significant display of virtue.

A footnote: After some struggle, I produced a satisfactory answer to my summer logic students—their derivations were indeed equivalent to the given axioms, although we had to prove this using truth tables in order to be sure!

About this Blog Entry's Guest Author
David White, Ph.D., has written eight books and over 50 articles in philosophy, literary criticism and educational theory. Since 1993, he has taught programs in philosophy for the gifted centers and various magnet schools of the Chicago Public School system, the International Baccalaureate program at Lincoln Park High School in Chicago and Northwestern University’s Center for Talent Development, grades 4-9. Dr. White is an adjunct associate professor in the philosophy department of DePaul University and also teaches for DePaul’s American Studies program. He is the author of Prufrock Press' popular Philosophy for Kids: 40 Fun Questions That Help You Wonder About Everything!. Dr. White's newest book, The Examined Life: Advanced Philosophy for Kid is scheduled for release in late October of 2005.