Some memorable comments from student course questionnaires:
He is more interested in how much we learn than the letter grade we get. He teaches discipline which can be applied to all courses.
He encourages the students to grasp concepts on their own, rather than babying their way through lessons. He challenges the student to learn.
Graded work unfairly, based on what he thought was right.
In our day the operative paradigm among many of our institutional decision makers is the business model. This view sees our students (and society at large) as consumers of a product called education, and it evaluates success in terms of externally quantifiable outcomes, balancing measurable benefits against monetary cost. On this view, the faculty member in his or her role as an educator is simply the talent, a specialist contracted to deliver the product.
Not me. I am a constituent of the academy, a practitioner of an ancient profession that posits the quest for knowledge as the highest calling of humanity, and I view aspiration to truth, beauty, and wisdom as the only essential obligation of the student. I believe that knowledge is made, not found; shared, not given. My mission is to open for students the door to my particular discipline, to guide them in their study, and to instruct them in the art of learning. My mission is also to build and to preserve the academy as a living institution, for my students, for my colleagues, and for them that come after.
The Myth of Intelligence
What people commonly think about intelligence is wrong, and this matters. In particular, an unexamined belief in the “intelligence quotient” is widespread among our students, and this has pernicious effects on their individual learning and on the dynamics of our classrooms. Intelligence, whatever it is, is not something of which you can have an amount. Rather, intelligence is best understood as an activity in which one may participate, or not, or participate in to a greater or lesser degree. But it is not something one can possess, like a substance in quantity, any more than one can possess the light by which one sees. My experience teaching mathematics to hundreds of undergraduates at diverse levels over many years has confirmed this theorem so often that it is now the foundation of my attitude as a teacher, and the touchstone of my methods.
My thesis that the intelligence quotient (IQ) doesn’t quantify intelligence is shocking to many. That IQ is a measure of intelligence is generally accepted, despite its disreputable roots in 100-year old eugenicist theories of racial superiority and its controversial status among current psychologists and cognitive scientists. However, it is not my purpose here to engage the debate over the existence of g (that thing in our make-up which, if it exists, IQ is presumed to measure), nor even to remind the reader of the perils of reifying a theoretical construct. My concern is not theoretical, but practical. My concern is pedagogy.
So stipulate for a moment that intelligence isn’t stuff, like muscle, but an activity, like running. This in no way precludes what is confirmed in our experience, that there roam among us those exceptionally gifted and those sadly challenged—with the rest of us occupying the great middle. But if intelligence is something one does instead of something one has, there follow three consequences of urgent concern to the teacher.
The first consequence is that students, among their other differences, may be brighter or less bright, quick or slow, but—real disabilities aside—there are no dumb ones. Every student, given the inclination and good pedagogical support, can master any or all parts of the undergraduate mathematics curriculum.
The second consequence is that there can be no abdication of responsibility by either the student or the instructor on the basis of the student’s supposed ability. No student wins a nod from me with the tired assertion that he or she is “right-brained,” or “artistic,” or a “visual learner.” Similarly, no student will hear from me the devastating betrayal, “maybe you’re just not cut out for this,” as I saw friends of mine betrayed when I was an undergraduate. Instead, my responsibility as an instructor is to meet the learning styles and needs of diverse minds, leading but also adapting, striving with my students to achieve their goals while upholding for them the spirit and standards of the discipline I teach. The student, on the other hand, must take responsibility for his or her own learning. Students often suppose that in coming to college they have purchased a degree, but this is false; students have purchased only an opportunity. It is up to them to seize that opportunity, to determine what that opportunity means to them individually, and to convert it into achievements.
Thirdly and finally, understanding intelligence as an activity to be engaged in, rather than a capacity to be exploited, confirms Plutarch’s ancient dictum that “The mind is not a vessel to be filled, but a fire to be kindled.” When I am in the classroom I am not there only to impart, nor are my students there only to receive. Rather, we are engaged in a cooperative effort—we are doing mathematics together. Although I always maintain good order, my classes invariably resemble conversations much more than they do traditional lectures. No student in my classroom is allowed to remain merely passive, and every student has the right and the obligation to contribute to our common activity—learning math.
Instructors often obsess over behaviors. How is attendance? Are they doing their homework? Do they study enough hours out of class? Did they read the textbook? But behaviors are effects, not causes. They are but leaves and flowers; the roots are engagement, a clear understanding of goals, self-confidence and confidence in the support of the instructor, the ability to self-assess, and prior achievements upon which to build. It is difficult to put students in touch with their inner adult, and some resent an instructor for trying. It will win the instructor a few flamings on their student evaluations. But the rewards for students who awaken intellectually are priceless, and they write evaluations too.
We all remember the special teachers, the ones who reached us when we were ready, who helped us to the next stage in our pattern of personal growth. I had two: Mr. Richardson in 6th grade, a humorous, frank, and forceful personality, and Mr. Ayyoub in my first year of college, a quiet and methodical man often exasperated by the apathy of some of his students, whose love of ordinary mathematics seduced me into my career. I reflect on them, not often but often enough, and puzzle over our shared vocation.
There is alchemy in what we do. When a lecture really works my students and I have more energy at the end of the hour than we had at the beginning, and there is a bright fire kindled in our heads and chests. It can sustain me the whole day. That is all the purpose one could wish for. The wind is not always at our backs in the classroom, and our course may sometimes be doubtful, but the reason for the journey is perfectly clear.
