Teachers speak of a moment or short period when a student suddenly gains a massive understanding: the time when at last “the nickel drops.” But I have found that a class has a personality too, and that its nickel sometimes drops in a miracle of shared timing. (Of course every class has its outriders in both directions, but the advanced riders help their classmates find their way in the new terrain, and those in back gain in confidence and understanding from seeing their classmates familiarize themselves with ground that at first only The Teacher seemed to understand.) Since the ethos of a class can do much to help or hinder individual students, dropping nickels bring music to a teacher’s ear.
Unlike knowledge and skill, whose gains are usually slow and steady, understanding can come in a rush, as it did when Helen Keller figured out what “wah-wah” was, triggering the miracle that Annie Sullivan worked for as her teacher. Good teachers cannot and do not “deliver instruction” of this kind. Instead, they lay groundwork, do their planting, and then cultivate the budding grove. Like Japanese gardeners they take account of the specific features of the terrain and the planting to get the best out of a class.
This sometimes means adapting a plan to a particular class’s needs and sudden gains. I managed such an adaptation recently in my Theory of Knowledge class.
The International Baccalaureate program’s excellent but difficult course in ToK presents to its teachers a measure each of problems and opportunities. Unlike traditional subjects that have a coherence conferred by time and experience, ToK lacks this advantage. The order conferred by the “ToK Diagram” does not come with advice on such questions as “Where and how do we enter the Roundabout?” and “What do we do once we get there?” The entire curriculum consists of questions, and there is no Answer Key. Indeed, there is no official textbook, though enterprising authors have produced a few that are widely used in spite of the IBO’s recommendation against relying on them. The students who take it, usually juniors or first-term seniors, are just starting to develop their ability in “abstract operational thinking” as it is called, and some of them are late bloomers who have trouble with the concept work the course entails.
The opportunities are more than worth the difficulties. I have written elsewhere about the skill and understanding that accrue to students who take this course and take it seriously. It also has the potential for being a showroom of intellect and of classroom techniques, where the inventive teacher can try things on for size that might not have a place in something less experimental or flexible. When taught pass – fail, as I think it should be, ToK allows risk-taking by students: What they lose in not having their noses to the gradestone they gain in the chance to think in unaccustomed ways without serious penalties for the inevitable missteps. It also provides a great opportunity for conducting a colloquium, which students heading to college should experience.
We ToK teachers can do so much. During the unit on the arts my colleague the art teacher and I have asked students to do a criticism of a picture that comprises three steps: description, interpretation, and judgment. Classes have come up with critiques of Picasso’s Guernica, Magritte’s Le Retour, Whistler’s mother, and the Christ Pantocrator of Daphni. Applying the three-step critique to another art form, they criticize a favorite piece of music of theirs, which they may play in class if the thing to be played is under five minutes. I usually give a sample critique before they do theirs. In the past they have heard Louis Armstrong’s Dipper-Mouth Blues, Hank Williams’s Honky-Tonkin’, and the 8th Piece from Schumann’s Kreisleriana. They in turn have brought in everything from heavy metal to the Moonlight Sonata.
When we discuss how emotion can be a way of knowing, it is one thing to read about the need to know in Charles Sanders Peirce or José Ortega y Gasset, as they have done, and another to experience the need to know when they play “Petals around the Rose” with five dice and Teacher doesn’t tell them the solution or tell them the name of the game. They can contrast Western thinkers’ grounding of natural law in reason and Mencius’ grounding it in feeling with his thought-provoking example of a baby approaching an unfenced well.
When discussing logic and mathematics we can see how proof by contradiction depends on our taking as true an unproven axiom of Aristotle’s. We can ask why students accept a logical proof by contradiction in math when they don’t accept one in St. Anselm’s ontological proof of God’s existence, and they can read the proof to decide if, when, and why they part company with St. Anselm.
The physics teacher and I used to conduct the natural science unit together. She would apply her knowledge of physics, do Young’s Double Slit Experiment, and discuss peer-reviewed literature, while I would introduce Kuhn and paradigm shifts. We would supply each other’s shortcomings, play to each other’s strengths, and produce a good series of talks, demonstrations, and discussions.
The danger in a course with such various material is that it can become a disordered jumble of tricks and snippets. The opportunity, realized in a successful offering, is in giving students the chance to stand back from their studies, to examine them with a critical eye, and to see subjects not as endless strings of deliverables but as the husbandry of wisdom nurtured and pruned by people who know and love it.
In Modern Times Charlie Chaplin’s Little Tramp endures being fed by a feeding-machine, which can also stand as an image of a student being taught by a teacher who lacks the “endless discretion” teaching requires and views himself as “delivering instruction,” particularly in a mechanical way. The aim is rather to have the flexibility to meet the needs of a particular class.
And so we come back to my ToK class. Its personality had two salient traits. The first was, in general, to think of knowledge as something to memorize. Two corollaries: to teach is to tell what is to be memorized, and to learn is to memorize it. While this is of course sometimes true, as it ought to be, it doesn’t cover skill or understanding, which cannot be handled by telling and memorizing, not even in an on-line course. The class therefore had trouble taking seriously material that it didn’t have to get by heart. Its second trait was a tendency to silence during discussion time. Tendency is maybe too weak a word. Except two or three chattering standbys, the students in this class almost never spoke unless called on.
These traits make it difficult for a teacher to “establish the conditions in which understanding can take place,” and understanding is very much what ToK is about. Until the week before last, our discussions were short. Any attempt to sustain them ended up less like Plato’s Symposium than like Dr. Burney’s Evening Party.
Then last week something happened resembling in its suddenness a spring thaw on a frozen lake. Maggie, who had never said a word except when called on and then only “yes” or “no,” had questions every day. A number of students besides Grace took up a thread offered by Katie, who would start strands of conversation even though they never ended up tapestries in this classroom. Murty had some remarkable thoughts about sagacity, one of the twin powers of reasoning identified by William James. And Matt, whose papers showed extraordinary insight but who spoke in monosyllables, asked a question that led to our discussing how different thinkers seem to have an affinity for different subjects and intellectual pursuits.
Here was an opportunity. Given the tenor of the students’ remarks, I decided to change the order in which I would present my ToK units. We were finishing math, and I decided that we should read Pascal’s piece from the Pensées about the two kinds of mind and then move to history instead of the natural sciences as I had originally intended. The students’ comments and questions suggested that they would relish a contrast in type of thinking that considering history would provide, and that they were ripe for Pascal.
And so we began. This week has gone wonderfully. Finally I could see ahead of me the opportunities that good discussion brings to a class. Though leading a Socratic discussion has its challenges, there is nothing like it to develop and fix understanding. Not much of the academic year remains, but it should be a very fruitful time, and they will continue the course next year. I won’t say that I wish we could postpone summer vacation, but I can say with some confidence that when June finally arrives, the class will have turned out a success.
 British English says “the penny drops.” The expression comes from the moment when a jukebox or other coin-operated machine begins working as the user deposits a coin. I don’t mean by this metaphor to imply that teaching or learning is mechanistic.
 Google Mencius baby well to read it.
 Said by the ingenious education consultant Martin Skelton