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.

The Advanced Placement Program (AP) is big business for College Board and its contracting partner, Education Testing Service (ETS). The College Board contracts with ETS to help develop and administer the AP exams, so I think it is fair to treat them as one entity that, in this article, I'll call the College Board. Last year, College Board administered 1.8 million exams. It costs a student $82 to take an AP Exam. If you are doing the numbers with me, that's $147.6 million in income for College Board.

According to the College Board:

• Nearly 15,000 schools participate in the AP Program. This represents 60% of U.S. high schools.
• Last year, 1.1 million kids took AP exams.
• More then 60,000 teachers attend AP workshops and institutes for professional development.

College Board has a big investment in AP, and there is a lot of "sounds too good to be true" information coming from College Board about the influence of AP on students and their eventual success in college. You can download a PDF from College Board that contains pretty glowing "facts" (see AP Fact Sheet). However, there are some significant problems with AP classes and the quality of those classes.

Back in January, the Washington Post ran an article about the lack on any relationship between student involvement with AP courses and college performance. This information was drawn from a study done at UC Berkley by researchers Saul Geiser and Veronica Santelices. The study, titled "The Role of Advanced Placement and Honors Courses in College Admissions," offers some sobering conclusions about the impact of AP courses on college bound students.

Taking AP Classes May Not Improve College Performance

The big shocker from this study (based on a sample of 81,445 students) was that there is no relationship between college performance and completion of AP courses. According to the researchers, "the number of AP/honors courses that students take in high school bears almost no relationship to their college grades."

AP Exams Do Predict College Performance

I suppose the next question you might ask is, "Is there a relationship between performance on the AP exam and performance in college?" The answer seems to be, yes. There is research to suggest that performance on the AP exams may be a good indicator of student performance in college. ETS has issued two unpublished studies that support this conclusion: "Advanced Placement Students in College: An Investigation of Course Grades at 21 Colleges" and "AP Students in College: An Investigation of Their Course-taking Patterns and College Majors."

AP Classes May Not Prepare Students for AP Exams

The conclusion you would have to draw from all of this is that AP courses do little to prepare students for AP exams or college.

So how did we get into this mess? CNN recently reported that high schools are faced with increasing pressures from communities, parents, and even students to offer more rigorous college preparation courses. Might schools, faced such pressures, have resorted to slapping the "AP" label in front of just about any course that seemed remotely related to college preparation? Why not? Until the Geiser study, no one was asking whether these courses actually prepared kids for the AP exams or college.

My friend, Todd Kettler, an advanced academics administrator in Coppell ISD near Dallas, TX, commented to me this morning, "This stuff has gotten goofy. I've seen schools in other districts offering AP photography classes. There isn't even an AP photography exam!"

Even students realize that these courses do little to prepare them for the AP exam. Increasingly, it is clear that the majority of students are not taking AP classes to prepare for AP exams or college. They are taking the classes for the "bonus" points such classes add to their GPA (AP classes often weigh more heavily when calculating GPA). In fact, according to the The Detroit News only about 40% of students taking AP classes eventually take the AP exams. Essentially, 60% of students taking AP classes are doing so to inflate their GPA and their chances of being accepted to college.

The College Board Will Begin Certifying AP Classes Beginning in 2007

Even College Board recognizes that there is a serious problem with AP class quality. This year, College Board has announced that it will begin auditing AP course offerings beginning in 2007. Only students who complete a College Board certified AP class will be able to have the "AP" designation (and weighted grade) next to a class title on their transcript. To determine if a class qualifies for the AP designation, the College Board will audit a prospective class' curriculum, sample assignments, and sample examinations. Later, it is expected that the level of a teacher's training in AP will influence the audit results.

While I believe College Board should have become involved in certifying AP class much sooner, the organization's efforts to ensure that AP classes align with and prepare students for the AP exam and college success ought to be supported.