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Putting the Teacher’s Thinking at the Students’ Disposal
In Chapter 4, I said that one of my five jobs as the teacher of an inquiry-centered course was putting my own thinking at the students’ disposal. I do this job primarily through classroom exercises called “conceptual work- shops.” I alluded to these exercises in Chapter 3 when referring to “in-class study groups,” student groups that form for one class period to work on written problems given them by the teacher.
Writing focused, directed problems and getting students to work on them in small groups is another way to teach with your mouth shut. Yet it is a kind of teaching that differs distinctly from any we have examined so far. The teacher aims to make her students learn by designing an experience that will teach them. To understand how she can do this, we must return to the “perplexing problem” or “puzzle,” a learning scenario we passed over quickly in Chapter 2.
What Happens When the Canary Takes Off?
A canary is standing on the bottom of a very large sealed bottle that is placed on a scale. The bird takes off and flies around the inside of the bottle. What happens to the reading of the scale? Explain.
I presented this question as an example of a puzzle or perplexing problem after the discussion of parables in Chapter 2. At that time, I suggested that you take a moment to think about it. If you did not do so then, please stop reading now and think about how you would answer the question. What do you (86) think will happen to the reading of the scale when the canary takes flight in- side the bottle? Will it drop? Will it stay the same? Will it shift more than once? What will happen?
Designing an Experience that Teaches
Most people find this a challenging problem. They find that it engages their intuitions about weight, gravity, and other physical forces. At the same time, it destabilizes their thinking about these ideas, upsetting their mental balance. However they wish to answer the question initially, they are forced to question their own answer and think further. Precisely for these reasons, the puzzle stimulates their curiosity and energizes their thinking. In the language of Chapter 4, it creates a “present interest,” a need to know which originates in our automatic tendency to restore a disturbed equilibrium.
The canary problem can be a useful teaching device, a text that provoke curiosity in students and puts their minds in motion. But the canary problem, all by itself, is not likely to sustain inquiry for long. If a student becomes stumped, there is nothing in the problem to get him over his obstacle. And if he does not find the problem all that interesting, there is nothing in it to get him interested.
Let us therefore try to add some features to the canary problem, and by this means build up an organized set of activities around it to remedy these deficiencies. Starting with this puzzling problem, we will add one factor after another, and in this way gradually turn it into a sustained learning activity. Thus, instead of just hoping that students have the kind of instructive experience encountering the problem that we envisage, we will design an environment–with the puzzle at its center–that makes that experience much more likely.We can’t force the experience to come about, but we can increase its probability dramatically.
Other People to Talk To
The first thing someone puzzling about the canary needs is other people to talk to. So we will give him three companions and pose the canary problem to the group of four, asking them to agree on an answer. Making the problem a group problem has four important consequences.
1. Working with others requires each student to voice his own ideas aloud. This process of articulation does more than just translate what is inside his head to the outside world. It forces him to improve the (87) quality of what is inside his head: 1n giving words to his ideas, he must clarify them, distinguish them, give them shape. In addition, giving voice to his ideas allows him to know what he thinks. This may sound strange, but we often do not know what we think until we hear what we say.We are too close to the thoughts inside our our head to get any distance, and our unvoiced ideas are often too fuzzy and indistinct to be readily grasped. Putting our thoughts into words both forces them to take on a more distinct shape and allows us to become acquainted with them. So, even if his three companions never say a word, they help the student considerably by becoming an audience to his thinking.
2. But, of course, they-will say something. And so their second contribution is the obvious one of presenting new ideas and perspectives on the problem. Two heads are better than one, and four are usually better than two.
3. But even if their ideas are no better than.his own, hearing them is likely to provoke new ideas in our original student. Ideas are not static entities that collect in a room; they have a dynamic effect upon one another. They interact not like marbles, but like chemicals; their interaction can bring about the creation of something new. And that is the third contribution of making the problem a group one. Together, the group can develop new ideas that no single group member could have devised on his own.
4. Finally, the presence of the group creates motivation. Encountering the problem alone, unless constrained by external rewards s or punishments, a student will be moved to think about it to the extent that be finds his curiosity stimulated. But the minute he is part of a group that has been handed the task of solving the problem, he finds other people depending on his assistance. Most people respond to the unspoken pull of group norms. Thus, he is more likely to make a genuine effort to solve the problem as a group member than as a solitary individual.
A Sequence of Questions That Build
The next thing needed is a sequence of questions to follow up on the canary problem. The group working on the problem needs someplace to go. If they cannot solve the problem correctly, they need further activities to help them reorganize their thinking. And even if they do solve it correctly, they are not likely to be certain of their solution. They need a way to test their thinking and to stabilize the ideas that led to the correct solution. (88)
Moreover, we have no guarantee that the group will genuinely come to agree about the effect on the scale of the canary’s flight. We have asked them to agree, but they may not be able to. And even if a nominal agreement is reached, shyer or more polite participants may have suppressed their own convictions in the interest of group harmony. The group needs to work further in order to attain genuine understanding.
So we, who know the correct answer and understand the reasons behind it, must design a series of questions to follow up on the initial problem. These questions will provide guidance in solving the problem with.out providing an answer. They will give the students direction without taking over the job of thinking for them.
The following question makes a good follow-up to the canary problem:
A goldfish is lying on the bottom of a large goldfish bowl filled with water that is placed on a scale. The fish takes off and swims around the inside of the bowL What happens to the reading of the scale? Explain.
This problem is clearly related to the first one. It is similar in structure, yet different in some crucial details. We have swimming instead of flying, we have water instead of air, and we have a bowl open at the top to the surrounding environment. Do any of these changes affect the answer to the question? What is the effect of all of them in combination? That is what the group members will debate with each other.
This second question is helpful because it asks the same question about a situation that is similar to the first one yet transformed in certain crucial ways. Sustaining a train of thought across a transformation is the most useful way to test it, to sharpen it, and to stabilize it. That is why this question is useful regardless of whether the group answered the first question correctly or not.
The goldfish problem not only poses a second question, but inevitably provokes a reconsideration of the first question. That is its first virtue. That is why we say it “follows up on” or “builds upon” the :first question. We are not really asking a sequence of isolated questions; we are using a sequence of questions to stimulate a single process of inquiry into a dynamic situation involving a number of physical concepts (mass, the force of gravity, air pressure).
The second virtue of the goldfish problem is that it engages a second set of intuitions about the interaction of weight, force, and motion in a physical medium. These intuitions are likely to lead many people to a different hunch about the answer than they had in response to the canary problem. This outcome indicates that their intuitions about the two different situations were not in contact with each other. By posing this particular question about a goldfish directly after that particular question about a canary, we forcibly bring the two (89) sets of intuitions into proximity. For many, this new contact will create a sense of self-contradiction. Both intuitions seem right in isolation, but taking them together leads to a third intuition: They both can’t be right. Or can they? The sense of a contradiction could be unfounded, but even if it is, it demands an explanation. Thus, the group may find itself discussing why the two situations, which seem similar, really are different. And so different answers may be justified. This is just the kind of discussion we want.
Thinking out loud together in this manner, the group is likely to progress. Even if they move away from a correct answer to the canary problem toward an incorrect one, they are making progress because they are thinking. They have located concepts in their minds, oiled them up, and gotten them moving by applying them to a particular concrete problem. They may be making new distinctions, new connections, or both. If their motion is in the right direction, we want them to move further in that direction. If their motion is in an incorrect direction, we want them to run up against further problems so that-through their own thinking–they will discover their mistake and change directions. In either case, their minds must become active. But also, in either case, more questions that continue building on the first two will be needed to advance the process we have begun with the canary and the goldfish.
By transforming the air in the canary’s bottle to the water in the goldfish’s bowl, we have forced attention on the medium in which each creature moves, and the mechanisms by which each counteracts the force of gravity when it leaves the floor of its container. Can we go further in this same direction by making these same aspects of the problem even more obvious? We can. We can do so with the following two questions (now numbered to make explicit their place in the sequence).
3. A man is standing on a scale. He then gets off the scale, places a large metal spiral spring (as large as he is) on the scale, and stands on top of the spring. What happens to the reading of the scale? Explain. (For simplicity’s sake, ignore the weight of the spring itself in answering this question.)
4. Suppose the man above replaces the spring on the scale by an “air spring.” This is a cylinder (as large as the man) with a piston that slides down into it. There is a column of air trapped in the cylinder, and the man stands on a platform mounted atop the piston. The cylinder is open at the bottom, but is connected to the scale by an air-tight seal. Compare the scale readings when the man is on the air-spring as opposed to when he is directly on the scale. Explain. (Once again, ignore the weight of the air-spring itself. (90)
With the addition of these questions we now have a somewhat complete and satisfying sequence of four questions that build upon each other in a consistent way. Notice, however, that they do not build in the manner of a mathematical proof or a logical argument. They build in a completely different manner. They build by carefully drawing together experiences familiar to the participants and ideas they already have for explaining those experiences. None of these ideas, taken individually, is new. What is new here is that they have never been brought together and never been made to reconcile with each other.
We all have unexamined “theories ” about what makes scales register , what makes fish swim, how birds fly, and how pistons push. These “theories ” range from vague intuitions to dear and well-articulated concepts-most tending to the former. Rarely in everyday life are they put to the test. Our sequence of questions not only puts them to the test one at a time, but, because it is a sequence, asks the students to come up with one consistent theory to explain all four situations. To succeed at this task, they have to re-construct their thinking-take their ideas apart and put them back together again differently. This is precisely the process that leads to understanding, and hence to knowledge.
Our sequence of questions also works by focusing attention on specific aspects of the problem. The original canary problem presents a perplexing question and leaves you alone to grapple with it as you will. But the minute we add the goldfish problem to it, we have asked you to focus on certain dimensions of the problem (those that the two problems have in common or those on which the two problems differ strikingly) and to ignore other aspects (those that fall into neither of these two categories). Thus, you are virtually forced to focus on the physical medium (air or water) and on the forces by means of which the two creatures propel themselves upward in their respective media. On the other hand, you are not likely to worry about the different shapes of the two animals, or their different colors, or the fact that one survives in air and the other dies in air.
Our sequence of questions, though coherent and satisfying, is not yet complete. The third and fourth questions construct.increasingly artificial situations in order to focus and direct the thinking of the group. But by the time we get to the stationary man standing on the air-spring, we have traveled quite a distance from the spontaneous canary in flight. Another question, or sub-sequence of questions, is needed both to make sure that the man and the canary remain connected and to deal with the problems created by the artificiality of the man on the air-spring and the counter -intuitive nature of the correct answer to the original canary problem (see below). Here is a sub-sequence that will help. (91)
5. (a) 1n the canary problem in 1, suppose the bottle is replaced by a cage that is mostly glass, but with very thin spaces between the glass bars. What happens?
(b) Suppose it is replaced by an ordinary wire cage?
(c) Suppose the bird is hovering over the scale and is not enclosed at all?
(d) What if the bird simply flies over the scale? Discuss.
We have assumed all along that our sequence of questions leads the students to think about the separate problems together. Question 5(a) makes sure they do. By returning to the caged canary, it gets the students to apply their current thinking about the man on the air-spring back to the original canary problem. In order to secure this connection, they will inevitably work their way backwards and forwards through the sequence: man-on-air-spring, man-on-metal-spring, goldfish-in-water, and canary-in-air. Question 5(a) thus deals with the problem of the distance traversed going from the canary to the air-spring and pushes the students to come up with one unified “theory” to account for all four cases.
If they succeed, they will have discovered that the scale reading in the sealed bottle with the bird flying around inside it.reads just the same as it does with the bird standing on the floor of the bottle. For the bird to stay aloft, the moving molecules of air that hold it up must push down on the scale with just the same force as the bird originally did (the force caused by the pull of gravity on the bird’s mass). This explanation works well to explain and harmonize the four cases (and is correct), but there may still be a nagging problem. The correct answer seems to suggest that if a bird in free flight flew over a bathroom scale, the reading on the stale would shoot up for a second (as the bird flew directly over the scale) and then drop back to zero-and we know that wouldn’t happen (Don’t we?)
So a secondary problem is created: How do we reconcile one “correct” answer we have figured out from a series of artificially constructed problems with a contradictory “correct” answer that we know from our everyday experience? The final sub-sequence is designed to stimulate a small process of thinking to reconcile the two “correct” answers. It turns out that the difference made by the sealed bottle in the original problem is crucial, and it is not hard to see why. The sub-sequence, in perhaps more detail than is necessary, will help almost anyone see why – and thus provides a satisfactory conclusion to the main sequence. Now our explanation of the canary problem fits not only with the other scenarios but also with common sense and everyday experience. We are ready to take a well-deserved break.
(For the reader’s convenience, I have assembled the five questions, which I will henceforth call “the Canary Problem.” in an Appendix to this chapter.) (92)
A Teacher to Call On
The problem s described in this chapter teach by their very structure. They don’t Tell directly. Rather they encourage the making of discoveries. They create an intellectual environment with a shape–an environment with constraints, demands, orientations, limits, opportunities, and invitations (see Chapter 7)–and they set the students free in it. They don’t do the necessary thinking for the students and announce the results. They require the students to think for themselves, to find their own results, and then to test them in new circumstances. In this way, they lead to learning that lasts.
By designing these questions and setting them before a group of students, we have served as their teacher. We have taught them something significant about matter and motion in a physical medium. A teacher who teaches by designing such questions is teaching with her mouth shut. Instead of telling her students what she wants them to know, she designs an experience for them–one that will engender, she hopes, the understanding she wishes her students to achieve.
A teacher cannot actually engineer an experience, however. The best she can do is to shape an environment for students so that, once students are set free in it, the experience she hopes for is likely to result.
The most crucial aspect of this environment is the sequence of the questions themselves. (I take for granted more obvious though necessary features of the environment: a well-lit, heated, quiet physical space conducive to intellectual work, chairs that can be arranged in small circles, enough space so the students can talk without being distracted by neighboring groups, and so forth.) We have already discussed a second feature of the intellectual environment–the presence of other students.
By supplying the written questions and the other students, the teacher has done the lion’s share of her teaching. But her work is not over. We are ready to add a third feature to our original scenario (the solitary canary problem): a teacher to call on.
The sequence of problems and the accompanying instructions must be written out and distributed to every student (for reasons we shall examine later). While necessary, this condition is not sufficient for generating the kind of experience we are after. Like the best-laid plans of mice, a teacher’s instructions do not always achieve their desired results, be they ever so clearly written out. So the teacher herself must be available in the room when the students are working.
Inevitably, questions will be misunderstood, instructions will be ignored or misconstrued, digressions will materialize. Beyond these obvious obstacles to learning lies a second set. All student groups will not run smoothly. Some will be dominated by one or two strong members. Some will suffer from an absence of any assertive members. Some will be led astray by misguided (93) “authorities.” And beyond this set of problems lies a third: the intellectual work itself may lead to tangles or dead ends. The questions are designed to point in a specific direction, but they cannot guarantee what direction any particular group will take. Like a computer program still in need of debugging, a group can land itself in a closed loop, energetically and endlessly dis- cussing something that leads nowhere.
In all these cases and more, the presence of a roving teacher, quietly monitoring the discussion groups, can make the crucial difference. The teacher will tell the groups at the start to feel free to call her over if they get stuck or need help. In addition, she will wander around, sitting in (not hovering over) one group at a time, listening to their discussion, intervening only if she thinks help is needed (and then briefly), and then departing to visit another group.
There is no recipe for the teacher to follow, but in most cases what is called for will be obvious. And in some cases, simple Telling may be what is called for. “The air serves the same purpose for the bird as the water does for the fish.” “The air in the air-spring won’t hold the man up unless it is pushing down on something.” But even in these cases, the Telling is brief, it occasions further inquiry, and it is tailored to the specific obstacles blocking four people discussing the problem. It doesn’t turn their minds off and transform them into passive listeners to a lecture. It removes a glitch that has blocked the for- ward motion of their minds and gets them moving again.
The teacher’s discreet but active physical presence in the environment is a crucial addition to our original scenario. She will find scores of different functions to perform, and each will be honed to the specific problem that has cropped up for four specific people. She is an important part of the environment she has created for her students but also a small part. She is more like a roving auto mechanic than an actor. Or, to stick with the theater, we may con- sider her a stage manager. She sets the stage and removes obstructions so that the play can proceed. (She is a stage manager during the play, but she has also written the script. She accomplished that work before she ever came to class- and in striking contrast to a lecturer, she is not the one who has to perform the script.)
An Ending to the Experience
In his definition of tragedy in the Poetics, Aristotle requires of that theatrical experience that it be (among other things) “whole.” “A whole,” says Aristotle, “is that which has a beginning, a middle, and an end.” An intellectual experience ought to be whole, too. If we aim to design a sustained learning experience for students, we will do well to give that experience some organic shape through time: We need to provide a beginning, a middle, and an end. (94)
In the experience we have been designing, the original canary problem constitutes the beginning. It presents a concrete, easily understood set of circumstances and poses a perplexing question about it. The initial question engages the student, creating “present interest” and a motivation to proceed further. When we get to the goldfish, we have entered the middle phase, and we stay in this phase through our encounter with the man on the air-spring. Question 5, with its sub-sequence of questions, provides an ending. The subsequence is designed to satisfy any lingering doubts, to integrate the conclusions produced from all preceding questions, and to provide a sense of intellectual closure.
Question 5 provides an ending to the intellectual side of the experience, but there is a social side to the experience as well, and a teacher neglects it at her peril. If you have been one of four students working on problems your teacher has prescribed to you in a room filled with many other groups of students working on the same problems, you are aware of yourself as part of a complex social arrangement. Before you are done, you would like to know what conclusions the other groups came to, how these compared with your group’s, what your teacher thinks of all these conclusions-and what, after all, are the right answers anyway.
To make the experience whole, we need to give it a more comprehensive and satisfying ending. That is the fourth and final feature we need to transform our original perplexing problem into a sustained learning experience.
There are many ways to create an ending, just as there are many ways to shape intellectual experiences as a whole. The simplest and most straight- forward is to allow some time at the end when each group can report the results of its investigations, these results can be compared, discussion can take place stimulated by divergent results, and the teacher can comment on what she has seen happening, as briefly or as fully, as directly or as indirectly, as she deems wise.
Providing an ending to the immediate experience that day in class, how- ever, in no way implies shutting off further exploration of the problem or the issues underlying it. If the Canary Problem were included in an inquiry-centered course (see Chapter 4), its teacher would certainly be committed to continuing the inquiry beyond the boundaries of one class day. The last thing she would desire would be to end it. But a commitment to on-going inquiry does not do away with the need to provide emotional closure and a sense of an ending to the immediate experience. If you put students to work on a challenging problem for a sustained period of time, if you force them to struggle and sweat, then you owe it to them to create an ending. An ending will not only give them a sense of intrinsic satisfaction (because the experience will feel, to some degree, completed), but it will give them a chance (95) to get some distance on their work, to reflect on it, and thus to take more away from it.
Conceptual Workshops
We started with an engaging puzzle, the canary problem, and in four steps we converted it into a sustained learning experience for students. We added (a) other people to talk to, (b) a sequence of questions that built on the original question, (c) a teacher to call on, and (d) an ending to the experience. By developing the canary problem in this way, we have provided ourselves with one image of an “experience that teaches.” At the same time, we have gotten a sense of what might be involved in a teacher’s designing such an experience. But a single example is always misleading. It will be helpful to look at another.
Before doing so, let us establish some terminology and examine the classroom context for these learning activities. The teaching approach exemplified by the Canary Problem was developed by a former colleague (Stephen Monk) and me in the early ’70s. It started as an attempt to promote more active learning for students in the large lecture courses we both taught at that time. We designated the approach as “the design of intellectual experience” and we characterized the teachers’ challenge as “turning the products of their academic disciplines back into the processes that led to them.” This language seems just as appropriate today as it did twenty-five years ago.
But we never came up with a suitable short name for the kinds of classes we were designing nor for the materials necessary to run them. We ended up relying on the vague but convenient terms workshops and worksheets. The latter were the written handouts containing the questions and instructions, and the former were the classes themselves: A workshop was a class in which a teacher distributed a worksheet and her students followed the instructions on it.
The problem is that for more than twenty-five years, and ever more increasingly, the term workshop has been used to designate every kind of activity imaginable–including sessions where experts are brought in to do nothing more than lecture to professionals on some special topic. The word has become virtually meaningless. Yet it is hard to give up: It retains its appeal through its connotations of active learning and its echoes of “the lab” and of John Dewey’s “lab schools.” But the term will not suffice without further specification.
Of late, I have come to call these classes “conceptual workshops.” This phrase emphasizes the conceptual nature of both the learning aimed for and the work required of the workshop’s designer. I shall continue using the term worksheets, hoping that my context indicates that these are the materials necessary to run “conceptual workshops.” (96)
The Classroom Context
A conceptual workshop typically runs for two to three hours (with breaks), but may range from fifty minutes to four hours. (Long ones may be broken up into segments and conducted on successive days, if necessary.) Students do most of the work in small groups, but some of the tasks may be undertaken individually and some by the class as a whole.
The size of the small group will depend on the teacher’s judgment of the optimal size for pursuing the work demanded by her worksheet. In the course of one conceptual workshop, students may participate in several different groups, small groups may join together to form larger groups, large groups may split up into smaller ones, or phases of individual and group work may follow each other repeatedly. However, the typical format is the simple one in which students divide into groups of about four, work for a fairly longtime on a sequence of questions, and then discuss the results of their work with the rest of the students in the class.
The teacher conducts the workshop simply by handing out a copy of the worksheet to every student and telling them to get started. She then roams from group to group, listening to the discussion s, and intervening when her words will advance (and not obstruct!) the activities the worksheet was writ- ten to promote. If there is a final discussion, she will conduct it, participating in it as she sees fit.
Teachers who intend to use conceptual workshops do well to use them regularly. As a one-time activity in a course where different styles of teaching and learning are the norm, a conceptual workshop is not apt to succeed. Students need to become accustomed to the different kinds of demands these classes make on them, to the different rhythm of work, and the different class- room atmosphere. They also need to get a taste of their distinct intellectual rewards. It does not take long for all these things to happen, but it does take some time. I typicalJy employ conceptual workshops once a week; others might opt for using them every second or third week (they take quite some time to prepare). But even if they occur as seldom as once every three weeks, students–adaptive creatures that they are–will have no trouble shifting gears appropriately on “workshop days,” once they have gotten some experience with them (and if they are convinced that the hard work demanded of them will pay off both in their learning and in their grades).
I never grade or evaluate the work students produce in the workshops themselves. I believe that students must be free to make mistakes without consequences while they are learning, and thus I hold off on evaluation until the end of a learning sequence. I also never ask students to submit what they write during conceptual workshops, though some teachers might wish to. I always feel that I have learned more than enough about their thinking–and (97) about what needs revising in my worksheet–by listening in on the group discussions during the workshop itself.
“Aporia“
In Search of Socrates, the inquiry-centered course described in Chapter 4, relies heavily on conceptual workshops. On a typical week, I conduct two of them, a long workshop on Monday and a shorter one on Friday. The following worksheet is from one of the Friday workshops. I designed it to illustrate one concept central to the understanding of Socrates’ manner of pursuing philosophy. By the time they get to this workshop, the students have already read and discussed the dialogues referred to in the first question, as well as Aristophanes’ satire of Socrates, the Clouds. As you read through the worksheet, envision yourself as one of six students in a discussion group. Try to imagine the kind of experience you would be likely to have with five classmates–all of you interested in Socrates–as you spend ninety minutes attempting to answer the questions.
IN SEARCH OF SOCRATES
Spring 1995
FRIDAY WORKSHOP: “Aporia“
Part I (70 minutes): Divide into groups of six. Limit discussion of each question to about ten minutes.
Each group should try to agree on an answer to each question. Select one person ahead of time to write down the agreed-upon answer. If agreement cannot be reached in the allotted time, then the scribe should record the dissenting views as well. Select a second person at the start to keep an eye on the time and to make sure the group proceeds through the worksheet in a timely manner.
1. Consider six “moments” in a dialogue with Socrates, each drawn from a different dialogue:
a. From Laches ( l 94a-b), Laches says, “I am ready to go on, Socrates, and yet I am unused to investigations of this sort. But the spirit of controversy has been aroused in me by what has been said, and I am really grieved at being thus unable to express my meaning. For I fancy that I do know the nature of courage, but, somehow or other, she has slipped away from me, and I cannot get hold of her and tell her nature.”
b. From Euthyphro, (11b), Euthyphro says, “Now, Socrates, I simply don’t know how to tell you what I think. Somehow circle, and nothing will stay where we put it.”
c. From Republic I (334c), Polemarchus says, “No, by Zeus, I no longer know what I did mean. Yet this I still believe, that justice benefits the friends and harms the enemies.”
d. From Crito (S0a), Crito says, “I can’t answer your question, Socrates. I am not clear in my mind.”
e. From Xenophon, Recollections (IV.2.19), p. 111, Euthydemus says, “Socrates, I really don’t trust my own answers any longer. Everything that I said before now seems to be different from what I once thought.”
f. From Meno (80a-b), Meno says to Socrates, “At this moment I feel you are exercising magic and witchcraft upon me and positively laying me under your spell until I am just a mass of helplessness. If I may be flippant, I think that not only in outward appearance but in other respects as well you are exactly like the flat sting ray that one meets in the sea. Whenever anyone comes into contact with it, it numbs him, and that is the sort of thing that you seem to be doing to me now. My mind and my lips are literally numb, and I have nothing to reply to you.”
What is similar about these six moments? Formulate a paragraph describing what has happened at this point in the dialogue to the person conversing with Socrates.
2. There is a Greek word to describe this state. The word is aporia. Scholars of Plato use this word to describe moments such as these. Rather than defining it formally, it is best to define it inductively as you have just done, looking at the moments of aporia and trying to capture what they share in common.
In an article entitled, “Aristophanes and Socrates on learning practical wisdom” (Yale Classical Studies, Vol. XXVI, 1980, p. 75), Martha Nussbaum writes, “The paralyzing effect of the elenchos [refutation] . . . finds its comic expression in the Clouds in the scene in which Strepsiades, enjoined to look into himself and find a solution to his aporia, feels himself being bitten by bedbugs that drink his life’s blood and torture his genitals.” Taking into account Aristophanes’ penchant for extreme exaggeration and coarse caricature, do you think the scene where Strepsiades is tortured by bedbugs in his mattress reflects the state of aporia as you have conceived it above?
3. Go back to the texts and locate each of the six moments of aporia. For each one locate and describe what Socrates does in response (99) to each of these six moments. Just find out literally what happens next in the dialogue and describe it. (In two of the six cases, the answer will be: Socrates just goes on with the argument; the other four cases are more interesting.)
4. In each of the four “interesting ” cases, Socrates does something different, but is there any general characterization you can make that might account for Socrates’ way of responding to aporia when it occurs in a dialogue? Try to come up with one.
5. Xenophon wrote of Socrates, “He did not approach everybody in the same way” (p. 104). This statement may be interpreted to suggest that Socrates was psychologically astute, or could gauge people ‘s character with great sensitivity. Taking this interpretation as a hypothesis, see if you can understand the four cases where Socrates seems to offer a distinctive response to aporia as being responsive to the particular character of the person he is talking to and the particular context of the dialogue at that moment.
6. In the Symposium, as you have read, Alcibiades-after trying to seduce Socrates-wakes up after having slept the night naked under Socrates’ tunic to discover that “nothing happened.” Could we define this moment as a moment of aporia? In what way is it such a moment? In what way is it not such a moment?
7. Let us assume that the story Alcibiades tells at the end of the Symposium illustrates Xenophon’s sentence, “He did not approach everybody in the same way.” Exactly how did Socrates approach Alcibiades–and why?
Part II (20 minutes): Class discussion of the results ***
Like all conceptual workshops, “Aporia” attempts to create a genuine experience for students, one that is engaging, challenging, educational, and whole. How does it aim to produce this outcome? It does so in three ways: (1) It converts a product of knowledge into a process. (2) It provides a whole experience with a beginning, middle, and end. (3) It gets the teacher out of the middle of the classroom configuration.
Converting Products of Knowledge into Processes that Lead to Them
First, the conceptual workshop substitutes an intellectually structured environment for the direct Telling of the teacher. I thought it important for students to understand the concept of aporia and see its dynamic role in Socratic (100) dialogue. I wanted them not only to be able to identify moments of aporia in the texts, but to grasp how these moments functioned dramatically and psychologically in changing the ongoing conversation.
I could have easily given a lecture on this topic. In fact, I selected this worksheet as a specimen because, just from reading it, you can imagine what the lecture would have looked like. But I did not give a lecture; I converted my lecture into a blueprint for an experience. By means of sequenced, focused problems, I attempted to get students to discover for themselves the conclusions that would have been main tenets of my lecture. I converted my own knowledge back into the processes that led me (or others) to generate that knowledge, making my students generalize from six specific examples and then examine dramatic consequences in four of those cases.
Although the worksheet is organized as a sequence of questions, beneath the separate questions lies one overall problem-to-be-solved. This underlying problem provides the focus for the intellectual work and the unity for the intellectual experience the students will undergo in pursuing their work. In “Aporia” the problem-to-be-solved might be formulated as follows:
In reading many Socratic dialogues, we find that Socrates’ questions invariably lead each person he is conversing with to a similar state of psychological confusion, a state of mind that seems to prevent their proceeding further and threatens to abort the inquiry. What are the implications of this repeated pattern for Socrates’ manner of pursuing philosophy?
Of course, the worksheet doesn’t pose the problem so baldly and pedantically. Rather it leads the student to it by concrete and gradual means. Nevertheless, any reader of the worksheet can see that this problem is guiding its author every step of the way.
In the Canary Problem we can similarly locate a single problem-to-be-solved that serves as its organizing principle:
What force overcomes the force of gravity when a bird takes flight, allowing the bird to fly in an upward direction , and what evidence is there of that force in a closed physical system?
I decided to teach my students the concept of aporia by presenting them a problem-to-be-solved rather than directly explaining the concept to them. But I didn’t just give them one problem and let them flounder. I charted a journey for them, and gave them guideposts at each stage. There is an art to finding the right amount of guidance for an intellectual journey. Too much, and the teacher ends up with a lecture posing as “active learning.” Too little, and students get lost, become frustrated, and make no discoveries at all. To find the right balance, a teacher has to know her students well, and also her subject matter. (101)
Additionally, there is an art to writing conceptual worksheets that allow students of diverse capacity (and preparation) to engage the questions and get somewhere. The same problem, if well selected and posed appropriately, can provoke different levels of response in different students. Within limits, therefore, different students will have different kinds of learning experiences in response to the same worksheet.
Making the Experience Whole
Second, the conceptual workshop not onJy converts a product of knowledge into an intellectual experience, it also aims to make that experience “whole.” The workshop needs a beginning, a middle, and an end. The first question of “Aporia” constitutes the beginning. The beginning of an intellectual experience must provide a ready way for students to engage their minds, using the ideas and knowledge they already bring to it. A concrete problem is usually the best place to begin. In this case, the six quotations provide the concrete starting point. These passages are all taken from dialogues they have read. The material is familia , but the selections, juxtaposed as they are, also provide something new. For when originally read, the moments quoted sped by quickly; there was no particular reason (except in the vivid Meno passage) for them to stand out. The first question posed, while not overly difficult, is an interesting one; it leads students to see something new in already familiar material.
The beginning will either introduce the problem-to-be-solved that motivates the entire conceptual workshop or it will set the stage for its later presentation. In “Aporia” the first question introduces the problem-to-be-solved in a direct and straightforward way. But it doesn’t develop the problem fully. That will not happen until the third question .
The second question begins the middle phase of the experience. This is, of course, the most extended phase, and also the most differentiated. It is likely to have several sub-phases, since it provides the “meat” of the experience: the part most responsible for the change in thinking the teacher is hoping for.
In this worksheet, questions 2-5 constitute the middle phase. Question 2 allows the students to refine and clarify their answer to Question 1 by asking how well their explanation of aporia fits when applied to an extreme caricature (the paralyzing effects of bedbugs). Question 3 (“Describe what Socrates does in response to each moment of aporia”) advances the understanding of the concept itself by moving from its meaning to its function. It sends the students back to their texts and makes them examine the role played by the state of aporia in the dramatic forward motion of the Socratic conversations. But to begin with, only specific answers are asked for, a different one (102) for each dialogue. Question 4 then asks for a generalization from the specifics: What is common to all four cases? This turns out to be a difficult question.
Question 5 (“Try to see Socrates’ responses as specific to the character of the interlocutor”) is useful regardless of whether students have answered question 4 successfully or not. It provides some clues and prompts either a refinement or a revision of the answer to question 4 (the central question of the worksheet). By the time they have finished question 5, students should have a pretty good initial understanding of the concept of aporia. This understanding will not have been given to them; they will have built it on their own as a group.
An intellectual ending to the experience is provided by questions 6 and 7. In a way analogous to question 5 of the Canary Problem, questions 6 and 7 together ask students to apply their new understanding to a situation both similar to and different from the cases from which they have developed that understanding (here, a rather bizarre case–Alcibiades’ failed seduction of Socrates). This demand forces them to test their new ideas, to sharpen the edges of their conception of aporia, to convert what may still be a rough and rigid framework to one that is more dynamic and flexible. It provokes crystallization of the concept as well, so that when the experience is over they have something to take away from it. (New ideas, even when clear for a moment, have a way of falling apart when one turns attention elsewhere.)
But, as discussed above, an intellectual ending is not sufficient; an ending that provides social, emotional, and intellectual satisfaction is best. So, for the reasons specified in our discussion of the Canary Problem, the worksheet offers a Part II in which the whole class comes together and, under the teacher’s guidance, discusses both their answers to the worksheet questions and their experiences struggling to come up with those answers.
Reconfiguring the Classroom: Getting the Teacher Out of the Middle
Third, after the teacher has created an intellectual experience for her students and made it whole, she restructures the physical and emotional configuration of the classroom. The typical classroom is organized around a teacher. Physically, she is usually at the front of the class, facing a group of students, all of whom are facing her (and ignoring each other). Emotionally, she occupies the center of the class, the chief object of each student’s concern. She is like the hub of a wheel, and each student is like a small segment of the wheel’s rim. The spokes of the wheel vividly designate the axes of attention and concern in the traditional classroom.
But in a conceptual workshop, the teacher steps out of the middle. Instead of mediating between the students and the material, she places the (103) students in direct contact with the material, stepping to one side to permit a direct encounter. The class now looks like a series of small wheels: Students still constitute the rims, but now the intellectual material is at the hub. The teacher is reduced to acting as a mechanic who roves around making sure the wheels turn smoothly.
This reconfiguration of the classroom depends importantly on one simple fact: The questions and instructions have been written out ahead of time, reproduced, and distributed to each student. If the teacher transmits her questions orally or at the board, then she is back to having all eyes and ears on her. And the moment confusion arises, the students are forced to deal with her personally. With a written worksheet, the teacher’s instructions are still present, but depersonalized. The students don’t have to turn away from their classmates toward the teacher to recall the instructions; they can simply scrutinize the worksheet they have at hand and no disruption of the small group becomes necessary.
The new classroom configuration of the conceptual workshop yields three distinctive virtues. The first is that it takes the students’ attention off the teacher and places it directly on the material. The second is that it allows the teacher to exploit the learning potential of the group. Most teachers abstractly recognize the value of class discussion in promoting learning. But in traditional classrooms, discussions aren’t usually spontaneous or genuine, and they don’t get very far. Typically, interchanges between the teacher and individual students pass for “class discussion,” and if spontaneous debate or thoughtful inquiry does break out among students, it is usually short-lived. Or, a teacher may throw out a “discussion question” to her class, and suffer painfully along with her students while everyone waits for “discussion” to en- sue. If it does at all, the discussion take place among the two or three students who everyone knows can be counted on to carry the ball and satisfy the teacher. Neither of these familiar situations produces the kind of discussions teachers hope for when they decide to take a step away from Telling and to- ward generating a more electric classroom environment.
But the conceptual workshop avoids these pitfalls. If, at the worst, only two students carry the ball in a discussion group of four, then you’ve got half the class talking right there. And students can’t direct their responses to the teacher in the course of the workshop, because she is not there; she is off somewhere else listening in on another group. And so, if the questions are well written–if they are clearly focused, build on each other, and allow the students to make intellectual progress–students find they can learn a lot through discussion. Almost all the benefits of “letting the students do the talking” discussed in Chapter 3 come into play during conceptual workshops, but in an environment where the shape and direction of the conversation have been dictated by the teacher. The group nature of the work contributes a social texture to the experience that makes a big emotional difference. Students leave successful conceptual workshops feeling they have really accomplished something, and the emphasis is not only on “accomplished” but also on “they.”
The third virtue of the reconfigured classroom is the unparalleled opportunity it offers the teacher for witnessing the level of understanding that her students bring to the subject matter she is teaching. During all the time she is sitting in on the small discussion groups, she is hearing her students’ responses to her specific, pointed questions about the material. When a small number of students discuss specific concepts and concrete examples in detail, their level of understanding is dramatically revealed to an educated listener. Their implicit assumptions, the gaps in their knowledge, the way they connect ideas together, what they distinguish and what they fail to distinguish–all this and more becomes evident to an attentive teacher.
Listening to these discussions is inevitably a humbling experience. It al- most always shows that students are less far along than the teacher has assumed. It usually reveals a need to back up a few steps and go over (by what- ever means) material that the teacher assumed the students had mastered. For obvious reasons, many teachers would prefer to be spared exposure to this evidence. But if they take their intellectual goals seriously, and if their goals pertain to what the students are learning, and not simply to what they them- selves are teaching, then they will be grateful for this insider’s view of their students’ understanding. It will show them, better than any classroom discussion or exam, what they need to do next to make progress toward the understanding they are after.
Putting the Students to Work
Imagine for a moment that you are the teacher of a college course on Shakespeare. You have forty students in your class and you meet them for two-hour sessions. The next play on the syllabus is Troilus and Cressida, one of the most perplexing and problematic of Shakespeare’s plays. It presents a nasty world peopled with petty characters; critics have never even agreed whether to call it a comedy or a tragedy–clearly it is neither. It has puzzled readers and audiences ever since it was written.
But you have a bright idea about how to approach it. Your idea is to consider the play as part of a sequence of plays: Henry V, Julius Caesar, Hamlet, and Troilus and Cressida (and they were almost certainly written in this order, (105) although with other plays intervening). Once these four plays are viewed as a series, certain themes emerge, and Troilus, extreme as it is, begins to make sense, since it presents the end point of a progression (or regression).
Your first thought is to write a brilliant lecture developing your ideas. But then you ask yourself: “Why not make the students do the intellectual work they would normally watch me perform in a lecture?” It would be easy enough, in this case, to design a conceptual workshop to this end. All you have to do is to present them with your central hypothesis and ask them to investigate each of the themes that you think are germane. The worksheet couldn’t be simpler.
First you present your hypothesis: “Consider Troilus and Cressida to be the final play in a sequence of four,” going on to name the other three in the appropriate order. Then, in Part I, you present six themes (e.g., “the balance struck between honor and self-interest”; “the kind of world the characters in- habit”; “the nature of the father (or father figures)”; “the shape and function of anger”). You ask your students to trace each theme, one at a time, through each of the four plays in order, instructing them to spend ten minutes dis- cussing each theme and to take notes on their discussions. In Part II, you ask them to synthesize the results of their six small discussions by answering in writing one general question about the major theme you think connects all four plays (“the challenge to a young man of achieving a viable adult male identity”). Part III is devoted to hearing and discussing each group’s answer to that question. (The worksheet is included in the Appendix to this chapter.)
It is the evening before the class and you have written your worksheet. You suddenly realize that nothing prevents you from still giving your brilliant lecture–after your students have done the conceptual workshop! What could better prepare them to learn from your lecture than the experience of having done this workshop? And what could interest them more in your lecture? Not only will they listen with fascination, but they will now be in a position to critically appraise your ideas, since they will have “researched” the same topics and developed their own point of view on the material.
If you have never designed and conducted a conceptual workshop before, there is a further aspect of the experience you will not appreciate until the next day when the workshop actually takes place: what it feels like to be a teacher in the midst of a class run as a conceptual workshop. Let us assume for simplicity’s sake that your students are familiar with conceptual work- shops and have participated in them many times before, but this is your first experience “running” one.
You pass out the worksheets and tell the students to get started. There is a brief pause as they read the initial instructions telling them what size groups to form, then some scuffling and shuffling, and before you know it, small (106) groups have appeared all over the room, and students are busy at work. All eyes face inward, and the groups begin to talk quietly. The sounds of the many groups blend together, creating a busy and surprisingly soothing hum. No one is looking at you. In fact, there appears to be nothing for you to do! You feel strangely uncomfortable, the odd man out. What kind of a class is this, you find yourself wondering, where there is no comfortable position for a teacher to occupy?
So you leave to get a cup of coffee. Five minutes later, coffee in hand, you quietly open the door to the classroom, half-convinced it will be empty. But lo, the students are all there working away; no one seems to have noticed either your exit or your subsequent entrance. And now your mood shifts. Forty students are working hard, and you don’t have to do anything but sip coffee! “What a great job,” you think, forgetting the many hours you spent, first studying the plays and then designing the worksheet. You feel a great load lift from your shoulders. The class is running itself, and you are free to watch, listen, put in your two cents where you think it might help, and simply oil the gears of this industrious “workshop” of busy workers. (You feel the full impact of the term for the first time.) And so you go over to one group of students, pull up a chair, and begin to listen. And then things begin to get really interesting.
Creating Blueprints for Learning
In a way, designing experiences that teach (via conceptual workshops) is one instance of “teaching through writing” (discussed in Chapter 5). The teacher writes a document and gives it to her students. The document is a blueprint for an experience. By following the instructions on the document, by working together to solve the problems she has set for them, the students will have an intellectual experience. From the experience, if things go well, they will learn. (For another example of a conceptual workshop, see the Appendix Follow-Up to Chapter 9.)
Writing is thus the primary medium through which the teacher does her teaching. The main differences between this approach to teaching through writing and those discussed in the previous chapter are (1) the teacher’s presence is still required-some talking will be needed to supplement the writing, and (2) the teacher’s writing doesn’t tell or explain; it poses problems and sets forth activities. The conceptual workshop is thus an instance of teaching even further removed from Telling than the cases of teaching through writing discussed in Chapter 5.
Though the teacher refuses to directly Tell her students what she thinks about the subject matter, she is not withholding her knowledge from them. A (107) glance at any decent conceptual worksheet will show just how much she is giving them. Designing a specific intellectual experience rests on a foundation of knowledge. A teacher needs three kinds of knowledge to succeed: (1) knowledge of the subject matter, (2) knowledge of how a grasp of that subject matter is best put together (i.e., of how the subject matter is best learned), and (3) an overall knowledge of the strengths and weaknesses of her students.
The teacher, then, attempts to create a blueprint for learning by keeping her mouth shut and instead designing an environment for her students with the following three features: (1) The teacher presents an overall problem-to-be-solved, which is broken down into smaller problems that build on each other and which requires an advance in thinking to solve. The teacher thus converts her own knowledge back into intellectual activities and induces her students to go through these activities for themselves. (2) The teacher creates a blueprint for a “whole” experience; she provides a beginning, a middle, and an end. (3) She reconfigures the classroom so that she is “out of the middle” so the students can focus their attention on: (a) the subject matter, (b) each other, and (c) the written questions and instructions she has distributed to each of them. By creating such an environment, she is giving her students a great deal. She is Teaching them. Yet her mouth remains closed. (108)
Appendix to Chapter 6
The Canary Problem
- A canary is standing on the bottom of a very large sealed bottle that is placed on a scale. The bird takes off and flies around the inside of the bottle. What happens to the reading of the scale? Explain.
- A goldfish is lying on the bottom of a large goldfish bowl filled with water that is placed on a scale. The fish takes off and swims around the inside of the bowl. What happens to the reading of the scale? Explain.
- A man is standing on a scale. He then gets off the scale, places a large metal spiral spring (as large as he is) on the scale, and stands on top of the spring. What happens to the reading of the scale? Explain. (For simplicity’s sake, ignore the weight of the spring itself in answering this question.)
- Suppose the man above replaces the spring on the scale by an “air-spring.” This is a cylinder (as large as the man) with a piston that slides down into it. There is a column of air trapped in the cylinder, and the man stands on a platform mounted atop the piston. The cylinder is open at the bottom, but is connected to the scale by an air-tight seal. Compare the scale readings when the man is on the air-spring as op- posed to when he is directly on the scale. Explain. (Once again, ignore the weight of the air-spring itself.)
- (a) In the canary problem in 1, suppose the bottle is replaced by a cage that is mostly glass, but with very thin spaces between the glass bars. What happens? (b) Suppose it is replaced by an ordinary wire cage? (c) Suppose the bird is hovering over the scale and is not enclosed at all? (d) What if the bird simply flies over the scale? Discuss.
(109)
Shakespeare’s Truth
Spring 1999
WORKSHOP: From Henry V to Troilus and Cressida
Divide into groups of four.
Introduction: The purpose of this workshop is to situate Troilus and Cressida at the end of a sequence of four plays (Henry V, Julius Caesar, Hamlet, Troilus and Cressida-written in that order) to trace Shakespeare’s developing treatment of a number of interrelated issues. This kind of analysis provides excellent preparation for formulating an interpretation of the play. I will include in the Program Notebook in the library a paper that presents the interpretation I arrived at after doing work of a kind similar to that required by this workshop.
Part I (60 minutes):
For each of the subjects below, trace through the sequence of four plays and discuss how each play treats or presents the subject in question. Take notes on the highlights of your discussions. Spend about ten minutes on each.
1. the balance struck between honor and self-interest;
2. the kind of world the characters inhabit;
3. the image of women (as “love objects”);
4. the nature of the father (or “father figures”);
5. the image of brotherhood;
6. the shape and function of anger.
Part II (30 minutes):
Synthesize the results of your analyses from Part I by first discussing, and then writing an answer to, the following questions: How does each play envisage and treat the challenge of growing from boyhood to manhood and of achieving a viable identity as man/king/husband/future-father? In addition, what shape is there to the progression of Shakespeare’s treatments of these themes over the four plays?
Part III (30 minutes)
Meet together as a whole class to discuss your responses to Part II.