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Teaching to Understand
On the Concept of the Exemplary in Teaching


Martin Wagenschein


If you can go to the source
don't go to the water jug

    Leonardo

The "Tübingen Resolution"1 suggested that the difficulty in covering large amounts of content could be overcome through the concept of the exemplary in teaching. In recent years this concept has found so much resonance that we must gain as much clarity as possible about it. For on the one hand we notice the concern that the ship, built with much hope but not yet ready, could perish when launched and loaded up too early. On the other hand we know that such a ship cannot be built on land. Its final construction plan must arise out of the experience of many explorations on the sea of educational practice.

The following remarks offer starting points for gaining conceptual clarity, but they are no more than that. My most immediate thoughts concern the field of physics, with which I am familiar. However, they also go beyond physics. I hold back as much as possible, but am also not overly concerned about my competency to go beyond my own field. After all, as educators we can't help going beyond the boundaries of the subject in which we feel at home. Otherwise we lose sight of the formative aspect of our tasks as educators. (The result of which can be seen from the hot or cold wars waged by the different professional scientific societies as they vie for time in the school schedule: nothing new comes out of these battles.) If we go too far beyond our subject, we run the risk of becoming dilettantes. But we as colleagues can correct and complement each other.

I will begin by trying to mark the boundary between the concept of the exemplary and other teaching methods. Then I will raise the question: In which sense can we as educators look upon a theme or problem within a subject as being "exemplary"2? Having determined that, the question is, being "exemplary" of what?


I

1. The System as a Course of Learning

Let us begin by looking at what we have to steer away from if the school is not to suffocate from the sheer mass of content and then perish as a kind of subject-matter processing plant. The older and more established a subject is, the stricter we tend to plan the learning steps. I'm thinking of mathematics - in contrast to a younger subject like social science - where we are likely to fall for the temptation to stick with prescribed steps, move from the simple to the complex, leaving out no step in a so-called systematic course of study. In mathematics we at first stay close to the axioms. In physics we begin with skills such as measuring, introduce basic concepts, and teach mechanics as the birthplace of physics. In biology we go through the world of the animals in linear fashion, starting with one-celled organisms and ending up with human beings (or the other way round), moving from the past to the present, step-by-step. In these approaches, the essential thing seems to be: Every single detail serves as a small stepping stone, leading the learner to something more complex and difficult, which he or she cannot yet grasp.

The reasons for working in this way are obvious. One thing builds on another, either logically or chronologically. There has to be order. If you leave something out, you will have to pay for it later. You don't know what you need the single detail for. These reasons are "logical," but that is all they are. They are not pedagogical. They only see the totality of the subject matter and overlook the child. The child is seen as a small adult, quantitatively limited in its ability to grasp things. But to be a teacher means: to have a feeling for the process of human development, for what the human being is growing towards, for the awakening spirit. And to be a subject teacher means to know both: the subject's being and its becoming within the learner.

The basic principle, "first the simple, then the complex," has some validity. But this principle should not stand alone. Its shortcoming is obvious: very often simple things are either not really simple at all, or they are trivial. The law of inertia becomes more and more astonishing, the more one thinks about it. To fully comprehend it would need several lives as a researcher, and it is a lamentable thing to see it dished up on page 3 of an introductory textbook with an explanation that leaves out far too much. Einstein writes that the law of inertia (1, page 12) is "usually the first thing we memorize in school physics, and one or the other person may even remember it." That certain angles are equal when a line cuts through parallel lines (congruent angles) may be believable, but the fact is too obvious. It is a boring observation that leads to nothing. It merely serves a purpose.

Such a systematic course of study doesn't give the learner long-lasting motivation. It only supports an concern for what is to come, for the weighty edifice still to be built (which also burdens the teacher, even though he is familiar with it). The student thinks: what does the teacher have in mind for today? The teacher begins: today we are going to do the following!

An inherent temptation is completeness, which leads to haste and a lack of thoroughness. And an impressive heap of gravel is thus built up. The very fact that the course of study is tied to the system buries that very system, and bars insight into it (Figure I). The system of the subject matter is mistaken for systematic thinking. I paint an exaggerated picture on purpose. A purely systematic course of study is hardly the goal any more, but it is still the dominant tendency, as curricula and plans show.

Education is not a process of just adding. Just as adding thread upon thread leads nowhere, so also does the selective removal of threads (Figure II). The fabric becomes threadbare and lacking in substance. The result will be a diluted systematic course of study. No one will think that knowing little is preferable to knowing much. But many a recommendation to give an "overview" and to offer the material in sweeping brush strokes seems to illustrate such a preference.

house in wilderness


2. Building Platforms

So what we need are selection criteria. We need to confine ourselves to the essential. We will consider later (in part II) how this could be done. Supposing we know the essential, a first worthwhile form for a course of study would be Figure III. We recommend the courage to leave gaps, which means the courage to be thorough and to dwell intensively on selected topics. So instead of evenly and superficially walking through the catalog of knowledge, step-by-step, we exert the right - or fulfill the duty - to really settle in somewhere, to dig in, to grow roots and take root. An expression some also use is "creating islands," but if we use that image we should simultaneously imagine an island-linking, underwater mountain range. We don't want dissolution and isolation, we want continuity, but concentrations and intensifications within that continuity, as Wilhelm Flitner (2, page 559) speaks of for history.

The supports of a well-anchored bridge can carry lighter arches. The more serious the concentrations, the smoother will be the connection between the nests of thoroughness. To do some gliding in the stretches is then not superficial, since it is based on the very supports. Other images offer themselves. We can think of plants that send out runners, which root and form new plants (as in strawberries). Or think of a bird's flight: we draw strength from the sense of the place we have gained at our previous nesting and resting place and from the certainty that we will soon set foot again on the ground. In the language of gliders: gain height in the upwind over one place, make rapid headway during the ensuing glide, then make the next quiet ascent.

In order to hold onto the character of stages, I choose the term "platform," conceived of as inside a tower, a place where one can stay a while. This should not be misunderstood as a desire to relax in order to avoid the strict guidance of a systematic course of learning. The picture is faulty insofar as platforms tend to be inhospitable and drafty. The kind of place we are talking about here, a place of intensification, has something homey about it.

The essential thing is this: Homing in on a specific topic still has the character of a step, but it also creates a platform. One still covers the whole subject but ascends from platform to platform, leaving a few carefully placed connecting steps.

This procedure can be referred to as example-based. I consider this to be a very useful procedure, but I would prefer to take the concept of the exemplary in a narrower and purer sense, as outlined below.

3. The Concept of the Exemplary in Teaching

To further characterize the exemplary in teaching, we need to go beyond the picture of a stage or platform. We can say right away: The particular aspect we delve into is not a stage in a process, but a mirror of the whole.

Why? Words we frequently hear in conversations about example-based teaching are: in place of, depict, representative, succinct, standing as a model, exemplify, paradigmatic. The relation the particular has to the whole, however, is not that of a part, step, or preamble; it is a center of gravity. It may be only one, but it carries the whole in it. This single aspect is not an element in a process of accumulation, rather, it carries and illuminates. It is not a stage in a progression, but it works like a spotlight. It affects things that are distant yet related through resonance. This is what the concept of the exemplary means. (See Figure IV)

This is also what Ernst Mach (3; page 344) means when he says that as a physicist he "would be satisfied, when every young man" (he forgets the girls) "has shared in the experience, so to speak, of a few selected discoveries of mathematics or physics and understood their consequences." Maybe Lichtenberg (4) points to the same thing when he says: "Something you have to discover for yourself leaves a trace in the mind that can also be used in other cases." Confucius, for one, is supposed to have said that he would send that student away who wouldn't understand how to apply in the three other corners what he had learned in the first one. The clearest formulation is in the "Tübingen Resolution" (5): Original phenomena of the spiritual world can become visible through the example of a single thing the student has truly grasped." I would like to add comments from two participants in the conversation at Tübingen: Hermann Heimpel says (6; page 7) that "the universal is contained in the particular and can be found: Mundus in gutta (the world in a drop)," and that it is possible "within the framework of a general survey to come face-to-face with history in particular places, and ... to apply this to other areas." Wilhelm Weischedel (7) speaks of the "presence of the whole in the parts" and says that "something of the essence of history only really lights up in a particular event. (Italics in this paragraph's quotes are added.)

The concept of the exemplary is the opposite of specialization (8). It doesn't want to get stuck in particulars, it looks for the whole in the particular. "Impossible!" will be the response of the person who only knows addition.

Since we are primarily focusing here on refining a concept, we could say that radically exemplary mathematics teaching could limit itself, for example, to considering the one classical proof for the fact that there is no end to the series of prime numbers (9). In doing so it would make visible quite a bit (but not everything) that is characteristic for mathematics. The example is exaggerated on purpose and should not be taken as a proposal. Yet I'm convinced that a single such excursion, granted only that it is deep enough, could reveal more about mathematics than many a person has gotten out of mathematics who passed their finals unscathed. (For further examples in physics and mathematics, see references 11 and 12). Richard Goldschmidt (14) demonstrated 30 years ago how one can illuminate essential biology simply by looking at a roundworm. Kerschensteiner writes (13): "Forty years ago Prof. Götte of Strasburg wrote an excellent booklet in which all essential manifestations, concepts, and laws of the field of zoology were studied and put into context by looking at five to ten animals."

4. Spontaneity

So far I have purposely taken a somewhat one-sided approach by starting from the subject matter. Even teachers who work in authoritarian ways or only lecture could consent to this approach. They would be, however, preparing the platforms themselves and also the mirrors for the whole. But we also need to understand that the other half, the whole and spontaneous child, warrants just as careful consideration. Therefore the Tübingen Resolution says that a topic needs to "genuinely understood" and also Heimpel (6) speaks of "a true encounter." Hence the wish for intensification.

So we must consider both child and subject matter in equal measure, that is to say: the areas of intensification - the platforms - should also entail intensification of the activity of the child. They must be vivid and lead into the subject matter and into the soul of the learner. The process of mirroring must not only reflect the whole of the subject matter - ideally the whole of scientific pursuit - but should also bring light into the whole being of the learner (not only appealing, for example, to his or her intelligence).

5. Approaching and Getting in

Even when we progress from platform to platform in a course of study, we need not enter the tower of a subject at ground level, beginning with the most elementary and working upward from platform to platform. Getting into a subject means plunging in - finding a relatively complex problem about which the students have no previous knowledge, a problem that will challenge them and elicit their spontaneous engagement. (Figure III')

Take optics for example. Instead of going through the customary sequence (luminous and illuminated bodies, shadows, rectilinear dispersion, darkness, etc.), we could start with a problem that Kepler (15) poses in his Optics (1604). He starts with the question where "sundollars" come from: "That a sunray, which penetrates through a slit, appears in the form of a circle on the surface beneath, is a fact everyone is familiar with. One sees this under dilapidated roofs, in churches with holes in the windows and likewise under every tree. Attracted by this wonderful phenomenon, people in antiquity have tried hard to find the causes for it. But up to now I have not found anyone who has found a right explanation" (15; page 13).

Figure III' tries to indicate that we enter from the outside and that energetic thinking leads to the basic concepts (to rectilinear dispersion in this case) and to more complicated questions. A second immersion repeats this procedure on a somewhat "higher" level, for example, in the phenomenon that Goethe describes (20; pages 58-62): A white pebble in clear water against a dark background seems not only elevated, but also appears to have colored edges, the more so the deeper it sinks. Starting from this experience we can explain all that is involved with refraction and dispersion, lead into the related topic of reflection, and move up from there to the spectrum.

So after plunging into a problem we dive down into what is fundamental and search for what is required to explain it. In this process we no longer amass and store data, but search for what we need, going to work in the same way original research occurs. An uncommon phenomenon demands our attention, and we in turn find the simple within it.

A tried and true entryway into mechanics is the seemingly harmless question, "Where does a stone land that is held out of a tower window and dropped?" Such a question seems trivial at first, but becomes confusing as soon as we think of the curvature and rotation of the earth. The complications are resolved by further thinking that lays bare the law of inertia, a proof for the earth's rotation, and above all: it opens up the way physicists think.

The challenge is choosing the problem one starts from. It should neither be too simple nor too complex, and we should not get too fanatical about the whole procedure. Keep in mind that the principle of going "from the simple to the complex" remains - in a limited way - valid alongside this approach.

6. The Exemplary as a Way of Experiencing

I want to return once more to section 4. For the initial entry into the subject matter it may suffice that a problem is "interesting." But for an exemplary topic that should - all by itself - mirror the whole, we will need to aim for a stronger spontaneity, a deeper "engaged grasping" on the part of the learner. This would be the total opposite of the kind of "processing machine" that present-day schools are threatening to become. We need to reflect anew on the concept of "awareness" (66).

I quote Max Picard (16): "What characterizes the human being of our time is this: there is no longer an encounter between the human being and the object, it is no longer an event to have an object in front of us. We already have it before we have reached for it, and it leaves us before we let it go. We only get at the objects in a roundabout way, indirectly, provisionally, approximately, noncommittally, that is to say we do not get at the objects at all. Rather, they are delivered. It is as if everything has happened before ... All objects seem to belong to an enormous processing machine, which we human beings are part of: we are the place where all that has been processed is delivered. The meaning of an encounter, however, is to give an object we face time, and that means love." All this seems applicable to school situations, word for word.

In this context people in education like to speak of "encounter" (17). O. F. Bollnow (18) has given good grounds to reserve this concept for characterizing transformations of a high level (Saul to Paul) that are very rare in teaching. So we would do better to speak of an "event," or "experience." In natural science, the word "occurrence" might express the hard nature of science.

This all has direct consequences for the schedule. Exemplary teaching doesn't fit in a chopped-up schedule with forty-five minute periods. It needs bloc scheduling so that we can work on the same theme for two hours every day. That way teaching and learning find a way into the hearts of both students and teachers - and will be working there day and night.

7. Getting into the Concept of the Exemplary in Teaching

Conventionally, the entryway into a subject presupposes a lesson plan with steps, going from platform for platform. The concept of the exemplary in teaching - in its pure form - does not have this structure. It can limit itself to a single, outward-radiating problem. It doesn't have step character but jumps into the problem without preparation. (Rendering a Figure IV' superfluous.) However, plunging in to the entryway of a problem (even though we can keep a stepwise progression in mind), can itself be exemplary. Similarly, an oven works not only through convection but also through radiation.

8. The Concept of the Exemplary in Teaching and the Idea of a Recognized Body of Knowledge

[In relation to the recognized body of knowledge] Heimpel (6) spoke of working "within the framework of a general survey," and Wilhelm Flitner (2) stressed that before all else history needs narrative. One could say that similar things apply to the natural sciences, but in science it would not be good talk about the content; rather, science should be done. There are, however, certain things people really need to know nowadays. Not the details about how a radio works or the world's age according to modern cosmogony, but rather, to mention a few examples: what freezing does to your pipes, or that you shouldn't use an electric switch when you smell gas, plus a few more things like that, not all that many. And not only useful things. For example: the reason why the inclined stem of a plant coming out of the water looks like it is broken, but is not in reality. We should know how such things relate to each other. Not only because they are easier to remember that way. A certain understanding provides an experience that engenders faith in the world and is therefore of lasting educational value, namely understanding that things "in the physical and in the moral sphere are never isolated," as the physicist Tyndall (19; page 114) puts it. Such a recognized body of knowledge provides the basic landscape for the deep-boring activity of exemplary learning in the middle and high school.

This is not to say that in establishing the landscape we should hold to the one-step-at-a-time approach, which brings with it the danger of subject matter overload. There are two reasons for this.

First, the recognized body of knowledge need not be as over-filled as we might initially assume. For example, in physics and in biology it brings considerable relief to confine ourselves to the appearances (the phenomena) (20; page 19) and to give up accelerated introduction of mathematics and theory, as is done again and again (21, page 170). The only thing needed is that high school science teachers, who tend to be better educated in their subject field than in cultural history or pedagogy, learn to trust and see that concentrating on the phenomena also constitutes physics and biology. It is equally possible to simplify the approach to basic astronomy without sacrificing rigor and insight (22).

Second, in acquiring this basic knowledge there can already be a certain amount of "diving right in" and the principle of the exemplary is at work. In elementary and middle school we can already build platforms, and thereby illuminate the subject matter by looking at specific examples. Of course, to convince people that this can be done would require extensive demonstration from actual educational experience.


II

1. After this attempt to contrast the teaching according to the principle of exemplary with other teaching methods, I now turn directly to this approach with the following question. What is the nature of topics that can serve as examples - exemplars - for a specific subject, and what makes them so? What does "illuminating the whole," which I alluded to above, mean?

Posing this question immediately brings up what the answer should not be. Teaching should not result in a generally applicable "catalog of example materials." That would be the death of the actual procedure. From the point of view of the subject matter, it does of course matter what topic one chooses. But the teacher also needs to be personally captivated, which is always an individual matter. The risk and the uncertainty is an essential part of the process, something that K. Barthel has drawn specific attention to (23; page 36). Both teachers and students must be challenged by a problem, if it is going to be truly exemplary. And not only that, it should also challenge their assumptions. There is no need to have a narrow catalog of topics that can serve as examples, but a wide range of individual reports on what has been done in practice, not for imitation, but for stimulation. We teachers must listen to each other as individuals, not obey a preset course like functionaries. Also, we might not succeed at all in finding topics that are either strictly good examples (radiating), or only platforms (intensifying). But it is not superfluous to know what we actually value in a specific topic.

2. Once again I will start with physics. Spranger speaks of the "Fruitfulness of Working with the Elementary" (24). The word "fruitful" is right in line with what we're looking for. It speaks about the "pure case," that is to say "a case that is immediately understandable in the way it is built up .... that gives the basic pattern for the fullness of what you'll meet in actuality." For physics he mentions: the fact that rectilinear motion is the most simple, and also the parallelogram of forces. I add: the Newtonian axioms of mechanics per se, especially "force equals mass times acceleration," the law of conservation of energy, perhaps the principle of relativity, and so forth. This is what Kepler means in his preface dedicated to Emperor Rudolph the Second, when he reports that he "has been able to tackle a few optical theorems that may seem unimportant, but contain the seeds for the highest things" (15; page 7).

Elementary topics in this sense are always to be found in objects that have already been researched. They are no longer found within nature, but in a nature isolated by the lens of physics. We are dealing with a result that has been reduced by physics, and something general has been selected that contains the multiplicity of individual cases. When you have mastered "force equals mass times acceleration," you can, by integrating that knowledge, basically handle any mechanical situation.

Dealing with a basic, elementary topic of this kind is therefore the most important aim of physics instruction. These are the simple things that are "not so simple," and therefore not what you can start with in school. For a person new to the subject it is the last thing to discover, the result of an immersion in a multiplicity of strange phenomena. "A so-called pure case can only be grasped after careful analysis of experiential data and by means of subsequent thought construction. In studying a subject, such an achievement comes by no means at the beginning, but is the result that comes after the facts have been mastered. It is the ripe fruit of mature thought" (Spranger, 25). Teaching cannot start with the fundamental laws, but must steer towards them. After plunging in, the teacher has to get down to what is basic and open it up. If after that process students grasp the laws, these laws will provide the keys for further mastery of the subject.

Even though in choosing a problem it is necessary to make sure that the solution will reveal something fundamental, we're not there yet. If a truly formative education is what we are after, there must be more. For we can imagine a physicist with an excellent education or a student preparing for college. Each may be capable of applying "force equals mass times acceleration," and still lack education in a deeper sense.

A subject-method-object triad lies at the heart of education (28). It involves, first, understanding that the true process of education is one in which we are gripped by what we apprehend and thereby are as a whole person engaged in the whole of the subject matter. Second, it involves the recognition that we can no longer understand physics as teaching us how "nature really is" (see 26 and 27), but as one way to understand nature that is based on a specific set of rules for questioning, a method that enables us to ask nature questions. Thirdly, it involves knowing - with Litt (28; page 55 ff.) - that this method starts off by first producing subject and object, through limiting the human being to the "onlooker" who is strictly confined to using logic (29), and through limiting nature to that which can be measured.

We can only consider an education truly formative that constantly works with this triad (28) of subject-method-object (or even goes as far as making it the subject of the education). At that point we are not merely teaching physics. A teacher who is confined to his or her subject and untouched by larger philosophical implications will not be able to teach physics in such a way that supports a broader process of education.

3. In Heisenberg (26; page 39) we find a biographical remark about his experiences in school that shows exactly what I mean. He says that "I found it extraordinarily remarkable and stimulating that mathematics somehow fits with our experience. Ordinarily the various landscapes of learning that pass by us in school do not make us feel at home in the world. The teachers illuminate them according to their capacities, sometimes brightly, sometimes less brightly, and we may retain some memories for longer or shorter periods of time. But in some rare cases something that has entered our field of view will all of a sudden become radiant … and finally the light it emits will begin to fill an ever greater space in our thinking, will begin to touch other subjects, and at last will become an important part of our own lives. That's how it was with me when I realized that mathematics fits with things of our experience ..."

In these sentences one clearly recognizes all the characteristics of the exemplary in teaching. That certain material, which he doesn't mention by name, became such a telling example was not because it happened to be intrinsically elementary (like, for example, force equals mass times acceleration). Rather, he saw that certain natural sequences can be conceived in terms of mathematics. Maybe we can call something like this fundamental (30; 59), to distinguish it from "elementary" or "basic."

We're not dealing with the "basics" of physics that allow the observer to solve many individual problems, but with something that lies at a deeper level, something that deeply stirs what is inseparable: the foundations of being human and the foundations of the subject matter. We see the human being in a new light and we feel how - under certain conditions - we are able to find mathematical natural laws. And we see nature in a new light. Nature gives itself over - under particular conditions and through the ceremony of experiment - to these laws. It remains, however, also beyond them, smiling enigmatically. Pythagoras and Kepler had this kind of stirring experience.

Such a stirring experience is not only interesting. And yet not everybody who can apply the axioms of Newton will notice that. You have to become at home in something before it will reveal itself in this way. This experience will then become radiant as opposed to being illuminated by a teacher who goes over it with you. It lights up, all of a sudden, provided patience preceded it. All these hallmarks are in complete accordance with what Plato said in his letters: "in the pursuit of knowledge, maintained over a long time, in dedication to the object of study ... [insight] appears all of a sudden in the soul as a light, kindled by a spark, which will continue to feed itself through itself." [translation from German translation of Plato's Letters by O. Apelt Leipzig, 1918, page 72]. Insight fills a large space, not in the subject matter, but in our thinking, yes, in the space of our own lives.

We have here a rare, high-order occurrence in which a person is completely gripped, body and soul, by a fundamental experience. Such a formative experience stimulates true education. From this example we can draw the following general conclusion.

Certain topics, or more to the point, a certain problem, can stand as an example or exemplar of a fundamental experience. Galileo's question of how a ball rolls down an inclined board can be the exemplar for the fundamental experience that a sequence of events can be framed in terms of mathematics. Such a fundamental experience moves us and shakes up our relation to things and can therefore be called a truly formative experience. Insights into basic laws - such as the law of inertia in the case of Galileo's experiment - are a necessary and unavoidable byproduct of this process.

In physics there are more of those fundamental experiences. These serve functional goals (11; 21) in the educational process, in contrast to the material goals, which, however, are a necessary byproduct. Schooling in a discipline is always a byproduct of the educational process, not necessarily the other way around.

Within and inextricably bound up with the triad subject-method-object, I see on the side of the object:

a) The fact that the subject matter can be framed in terms of mathematics, as has been mentioned above.

b) The experience that - before any measuring, mathematics, or theorizing - the pure phenomena allow us to see order and coherence. For example, evaporation, boiling in a vacuum, diffusion of all states of matter, and gas pressure, all taken together indicate an active striving towards dissolution inherent in all matter. This conclusion can be reached before coming to the kinetic theory of matter.

c) Thinking up more or less pictorial allegories (models, images) - such as waves, fields, or atomic models - leads to a marked clarification of connections. We could speak of the "model-readiness" of nature as considered through the lens of physics.

The following insights are, in addition, fundamental.

a) The experimental method is not without implicit assumptions (closed system, reproducible results, neutrality of the observer, etc.). It is not the method, it is one method.

b) The physicist is limited to a procedure that first analyzes and then synthesizes, and to concepts that are quantifiable.

c) In light of this whole triad, we therefore see that physics opens up only one aspect of nature, because it is only one way to understand nature. Yet we can only be amazed about what it is able to reveal.

Physics doesn't tell us what nature is; it only tells us how nature answers.

Nature's answers comply. And the fact that we are able to comprehend nature is, as Einstein says at one point, what is incomprehensible about her.

It seems to me that such insights are essential in teaching physics, if it aspires to be a formative education, and to achieve this I see no other way than teaching according to the principle of the exemplary. Not because we wouldn't "have enough time" to "cover" the ever-accumulating knowledge, but because we have ample time. In any case, it would be pointless and futile to waste the time we have with accumulating information, for that neither schools us nor educates us. Exemplary teaching method is not a way out, chosen because of resignation. It takes us back to what alone can be seen as real teaching.

The fundamental experiences mentioned so far are purely "functional goals," there are no specific individual outcomes. I would like to believe, however, that certain end results can almost be called fundamental as well, inasmuch as they show the place of the human being in the world in a new light. When I say this I am not thinking we should race ahead and drag unripe and hard-to-understand theories like trophies into the school. An example would be the model of the universe as a closed system, expanding over the past for a billion years.

I am thinking of simpler things that we still haven't come to terms with inwardly: the infinity of space and the Copernican system (22). Up to now, these are "dealt with" so superficially in schools that hardly a single senior in high school would be able to say why he believes the Copernican model. The pedantic assertion that what we see in front of our eyes all day long is "only semblance" is a result of shallow natural science teaching. It is one of those things that contributes to the destruction of a feeling of belonging in this world (31). This happens when natural science is presented superficially and hastily. In this category I also place the approach that sets at the beginning the kinetic theory of heat and ends with the atom bomb, suggesting that the essential nature of matter, which seems so reliable and quiet, carries within it an aggressive tendency. The states of matter turn out to be successive stages of unleashing. And the experiments of nuclear fission show how more power can still be unleashed by the human being, if we are willing to carry the responsibility.

Since the discovery of modern natural scientific thinking, we human beings have ceased feeling at home in the world. But there has been gain as well: being able to calculate things mathematically awakens trust. Both things need to be valued rightly in physics education, which must have as a goal recognizing and demonstrating how physics sheds light on only one aspect of nature. I wouldn't know how we could approach this goal other than through thorough, exemplary consideration of appropriate problems.

4. I will now briefly turn to history, because things look essentially different there, and then return to natural science, more specifically biology, which in a certain way takes a middle position between history and physics. O.F Bollnow (18, 32) and W.Flitner (2) have judged the applicability of the exemplary teaching for history to be strongly limited in possibilities and extent. It is indeed clear that it is most aptly applied where rules and laws are to be discovered, where we find recurrence, experiments with the same outcome, and have certainty that results can be reproduced. When we truly understand the methodology of physics from one example, and when we are able to have enough distance to understand this methodology in the light of the triad (subject-method-object) we can, in principle, discover ourselves what remains because the source, nature, is open to all of us. With this background a student can also easily follow courses in the subject. A student can even have a truly educational awakening when he or she realizes the most important thing, namely, what it is we actually do when we look with the eye of the physicist, both to nature and to ourselves.

It is different with history. Not only are the sources buried, they are also - and this is different from natural science - often twisted by error and lies. Above all, however: the course of human destiny is steered neither by causality nor logic. Historical research tries to find out what happened, when it happened, and what will always happen differently even though similar circumstances may return (Burckhardt, Spengler, Toynbee). In spite of these differences, there seems to be something to the exemplary method even in teaching history, otherwise historians like Heimpel (6, 32) would not speak about it and experienced teachers would not have followed him (23, 34, 35, 45, 55, 56, 67, 78).

Without wanting to take anticipate any results in this area, which really is the research domain of the history teacher and historian, I would like to mention an idea of Dilthey's, which seems important to a layperson. It is commonly known that we human beings will not find out anything about ourselves by reflecting on how we would like to be, but rather by venturing into situations that force us to act. That's how we will experience something essential and usually unexpected about ourselves, and afterwards we can reflect and use the experience for the future. Dilthey speaks about the corresponding experience, not of the individual, but of the human species as such. He says (36), "no amount of reflecting on ourselves will give us self-knowledge ... only in understanding the historical reality that we create will we become aware of our capacities, good or bad."

Hence we now know much more about ourselves than we did in 1913, or even in 1932. And a person who reflects historically over longer periods of time than the span of a single lifetime is likely to be less surprised by upcoming events than someone who lives one day at a time. Human beings are in certain respects persistent, just as we are changeable and forgetful. We have so many hidden characteristics, and yet they are out in the open. No doubt we should be able to gain some clues from history about the characteristics of our being that are persistent. At least we should be able to decipher and collect examples of them, and thereby prevent our secular forgetfulness. Isn't that a fundamental goal of history teaching, and is there no subject matter that can stand as an example? We wouldn't even need to think of examples that the philosophy of history would consider high points. A simple contemporary example would be that the history teaching of all nations should make sure that what happened in concentration camps is not forgotten. Not in order to incite revenge, but to warn against possibilities we all carry within us.

How little this functional goal of history teaching has to do with physical causality becomes apparent when we understand that history takes on meaning and contour when a second factor is added. It is just like life itself. In the life of an individual we see on the one hand how a person can fall back time and again into the same patterns. In spite of this chain of same reactions, there can be a meaningful thread in the life the person leads, a "path of healing," so to speak. In a similar way we can ask in history not only how human beings always remain the same, but also: where is it all leading to? Perhaps a historian will say that this is none of his business, that it isn't scholarly, just like the physicist can object that much of what I termed "fundamental" is not within his domain, but belongs to philosophy. But subject teachers cannot confine themselves to their subjects if they want to be real teachers. If you stay within the limits of physics, or any other subject for that matter, you will only be able to instruct, not educate. (Lichtenberg: If you only understand chemistry, you won't understand that rightly either. Pascal: I don't want to be called a mathematician.)

5. We are used to connecting biology with physics and chemistry in the same way that we connect physics with mathematics. It doesn't have to be this way. Mathematics can also be related to music, and biology has elements of history. This becomes apparent from something the biochemist F. Knoop (quoted by Butenandt, 37) said about life being characterized "by a continuity of chemical movement, beginning with the first living cell and continuing through the millennia into the single individuals living today." This developing and differentiating stream of living beings is unique, like human history, and cannot be grasped in categories of causality but rather in morphological categories. The multitude of present-day forms only represents a cross-section of this stream. The conceptual system of modern physics and chemistry is inadequate to comprehend it (at least that is the way it seems to the layperson, especially when he is a physicist). Moreover, the events of human history cannot simply be understood as a natural continuation of the organic evolution of form (39).

The above-mentioned essay by Butenandt therefore carries a very modest title, "What does life mean from the viewpoint of biological chemistry?" (italics not in the original). And it contains the sentence, "Let us be conscious of the fact that we are not able to grasp the full reality of life with this procedure. What we find depends on the methodology we apply. If we apply the methodology of chemistry, the answer can only be expected to come from the realm of chemical processes."

Accordingly, Portmann's (38) assertion that there are two fronts in biological research is convincing to the layperson. The first goes into ultramicroscopic detail in penetrating genetics and physiology, researching structure and function of living substance. The second, promoted by Portmann himself, is a new morphology that keeps to what the naked eye can see, understanding shape, form, and gestures as "signs of the way the inner being manifests itself."

What does the teaching method based on the principle of the exemplary have to do with fundamentals in teaching biology? I wonder if it means the following. First, that by doing an exemplary physiological experiment, every one of us can learn that chemical questions will generate only chemical answers and, second, that an adequate way of grasping life would require another conceptual system, probably morphology. This would apply both to forms as they appear to us today, and to their natural history. (Bertalanffy's (40) "organic" conception of life and Konrad Lorenz's (41) behavioral research tend in the same direction, at least for the layperson.) These would be functional goals, because they take the triad subject-method-object into account.

The second front is emerging again in our time, having been dormant since the time of Goethe. For teachers it is important to realize that this second front, the morphological approach, is pedagogically the first. Because that is where the child is at home. It is where the child can have the most intensive, inward experiences of the kind we have characterized as exemplars. Such experiences are not seldom destroyed in school by treating plants or animals too early from a purely physical perspective, as if that would do them justice. I remember being disconcerted when I saw a teacher putting a white flower in ink, which proceeded to rise in the plant. In doing so he violated the plant (as I would put it now). A biology teacher will usually take no notice of this, because he has gotten used to suppressing such objections as irrelevant. In other words he acts as if physicalist categories would be adequate for life. No child will believe this. Children can only express their disbelief through aversion, and I'm inclined to go along with them.

So we should wait longer than is currently done with physical and chemical questions and foster the morphological approach, because, as Portmann says (38), "Cytoplasmic research, which penetrates into the realm of the invisible, necessarily leaves the familiar world of the senses - the everyday world we experience - behind. It goes into a different realm and does not encompass the sphere of human experience in which the richness of nature's creations fosters our life of feeling and nourishes our creative imagination. When we do research down into the sub-microscopic level, penetrating into the molecular structure, we leave the realm in which we are at home."

The functional goal, which the biology teacher can attain while still remaining in the sphere where we are at home, seems to me to be that "every living form goes beyond what it needs for survival" (38), which is to say that a columbine, a peacock's tail, or bird song should never be understood merely as means to an end, but as something that Portmann calls the self-presentation of organisms ("Selbstdarstellung des Lebewesens"). This is what Stifter means when he says "The artist produces his work in the same way that a flower blooms, and even one in the desert, where no gaze falls upon it."

Isn't this the pure soil where teachers should start? Shouldn't we linger here long and give the children time to experience the selected exemplary examples? The wrong way to start is to fall into the routine of "all right, it is winter, time to start teaching human biology, let's take the skeleton out of the biology closet." It is still being done this way around fifth grade, but you couldn't find a deader way to begin teaching about life. And from there on to all the skeletons, to the bellows that simulate the lungs, and to all the rest of the system. As an example of an alternative way I quote Portmann, where he aims at something truly pedagogical. In his essay about leaf forms (42; page 24) he says, "Whenever we devote ourselves lovingly to nature, even just to a simple collection of leaves, we awaken healing forces of the soul." The words "healing forces of the soul" show how a truly pedagogical chord is sounded here, in a way that is almost forgotten in our schools today. Modern education rarely keeps in mind that the objects we observe can have a healing effect. The main aim is thinking analytically about the subject matter and practicing that skill. But education will only be truly formative when there is no rift that cuts us off from the deeper wellsprings of our souls.

A misunderstanding could arise here, namely, that I would wish to ban the exact analytical research of living substance from the world altogether or at least from schools. On the contrary, I believe this approach can open up something essential, simply by virtue of the fact that it teaches us to see more exactly and penetrate our observations with thinking. The microscope - which Kierkegaard (43) so rightly mocked, saying, "If Christ had had a microscope, he would have used it to check out the apostles" (1846) - cannot reveal the essence about things. It is true that when we have only dim notions about certain processes in space and time, a microscope can bring certainty.

There is something decidedly more important that analytical research can show us. When we slap our leg, we are basically all convinced we are touching the same old body we have always lived in. But we now know from chemical isotope research, as Butenandt reports (37), that all structures of living organisms, including bones and teeth, are constantly being built up and destroyed. So we cannot think of our body in mechanistic terms, because it is in flux equilibrium.

So the body of an organism is not what the physicist calls a body, but it is a process. We would recognize our mistake sooner if the process were to run more quickly. If we want to compare a human body to something physical, we shouldn't think of a stone or statue but - and even this would not yet be exhaustive - of a whirlwind that sucks up and again drops dust as it moves along, or a cumulus cloud, a fountain, a flame, or a river.

Such an understanding is fundamental because it also encompasses the human body. A true grasp of this reality changes radically how we appear to ourselves and others appear to us. We look differently at youth and old age, at healthy and sick people. And the corpse appears as a trace someone has left in the sand. We recognize that our bodily state in space and time is not static, but rather see it as "only" the idea of a formative process that continually incorporates matter and then discards it again. That such a view "creates demands for the transformation of biology teaching at all levels is something that is hardly recognized today, and it will definitely create hefty demands in the near future" (Portmann, 38; Walther Klumpp has given valuable suggestions for high school, 44).

6. We can divide the fundamental experiences of a subject, which can only be won by the teaching method relying on the principle of the exemplary, into two categories: those that strengthen our feeling of being at home in the world and those that weaken it. The natural sciences are able to do both. Rational understanding of certain natural processes awakens trust, while this trust is shaken again by the demystification accompanying the analytical process. To avoid the feeling of loss becoming dominant, we need to, first, observe carefully and, second, always remain awake to scientific methodology. When we do that, it turns out that the feelings of loss, barrenness, and fright are only erroneously called forth because we take one aspect for "reality" and add up the various (often contradicting) results, instead of recognizing them as different perspectives on one and the same thing. We are then protected against seeing living phenomena only as physical or chemical processes and viewing history only as a biological process.

7. For biology, and perhaps for physics, there may be yet another entryway that could almost be called magical. It arises through an experience that opens us to all other aspects of a discipline. This entryway has nothing to do with the particular methods of the discipline, neither is it an outcome. It is a onetime event, bound to the particular grace of a lesson, a name, a mood, a teacher. It can hardly be planned, and comes close to an "encounter" in the true sense of the word. It often has to do with opening the way to the right insight, with clearing away misunderstandings and prejudices, partly those that school has put there.

I know the case of a girl who had previously been unable to find a connection to biology, but suddenly found it the moment a teacher took her by the hand, went into the garden, and just showed her the flower called "Love in a Mist" (Nigella). The name and the shape told her in one moment not only what this flower is, but provided a key to all others.

The colorful flash of a single, first drop of dew in the grass can spark insight into the nature of physics, namely that everything having to do with apparatuses is of a secondary nature, derivative, and a means to something else. This insight, when arrived at in the right mood, can dissolve mountains of dark misunderstandings into nothing.

Experiences such as these bring us to the question - which needs to be researched - whether the principle of the exemplary can also be applied in the teaching of literature and language, say in the experience of poetry or any other field of art. Who knows, perhaps original vistas may open up here, a flash of insight in one particular case could work as a catalyst and not as a mirror, or as a direct example. Perhaps one could speak of "enchantment."

8. So what is the essence of the exemplary in teaching? Is it perhaps the breakthrough of the principle of self-directed learning into deeper, almost existential layers? Is it the attention toward the fundamentals of a particular discipline, what it attends to and also ignores? Is it the sober assessment of how the revelations of physics, biology, or history can make us lose our feeling of being at home in the world, only to re-establish this feeling by making transparent what we actually do in a particular discipline and what it does to us? And, is it looking directly at what needs to be discarded?

All this would entail quite a different aim (even though sometimes the same topics would be involved) from the usual benumbed confinement to a particular discipline. We always have to fight this tendency in ourselves, and also fight the compulsion to amass material.

Who knows whether in 50 or 100 years we will even shake our heads or smile any more. If we do, we will definitely shake our heads about a school system that believed any good would come out of amassing half-understood information presented as gospel truth. At the beginning of this article I spoke about "courage to leave gaps," which is easy to misunderstand. What I meant to say was: courage to be thorough, to be original.

In place of the idol of broad and static completeness, which makes us work too frantically to fill a storehouse of knowledge, we clearly look for something new. We boldly aim for the sources. The aim is not to cover every last detail, but to reach the inexhaustible sources.

This is a translation of Martin Wagenschein's German language essay "Zum Begriff des exemplarischen Lehrens" (published in his book Verstehen lehren, Weinheim: Beltz Verlag, 1997, 11th edition, pp. 27-59; the essay was originally written in 1956). Translation by Jan Kees Saltet and Craig Holdrege. Copyright 2008 The Nature Institute. A different translation of sections of this essay has been published under the same title in the book Teaching as a Reflective Practice: The German Didaktik Tradition (edited by Ian Westbury et al. Mahwah, New Jersey: Lawrence Erlbaum Associates, 2000, pp. 161-76). We borrowed the title for the essay from that translation and are grateful to the translator (Gillian Horton-Krüger) for finding such a felicitous expression for Wagenschein's difficult-to-translate phrase "exemplarisches Lehren."

References

[Translator's note: we have left the references, which are German language publications, in German and in Wagenschein's original format. Only where he made editorial comments have we translated into English ]

(1) Albert Einstein, Leopold Infeld: Die Evolution der Physik. Rowohlts Deutsche Enzyklopädie, Bd. 12.

(2) Wilhelm Flitner: Der Kampf gegen die Stoffülle: Exemplarisches Lernen, Verdichtung und Auswahl, Die Sammlung, 1955, S. 556 ff.

(3) Ernst Mach: Über den relativen Bildungswert der philologischen und der mathematisch-naturwissenschaftlichen Unterrichtsfächer der Höheren Schulen; (Vortrag 1881); in: Populärwissenschaftliche Vorlesungen, Leipzig, 1923, 5. 313 - 355.

(4) Lichtenberg, Aphorismen.

(5) Abgedruckt in den Zeitschriften: „Bildung und Erziehung", V. (1952), S. 58 ff.; „Die Höhere Schule", IV (1951), 5. 6 ff.; „Die Pädagogische Provinz", 1951, 5. 623 ff.

Erörtert in: Wilhelm Flitner: „Grund- und Zeitfragen der Erziehung und Bildung", Stuttgart 1954, S. 125 ff.

(6) Hermann Heimpel: Selbstkritik der Universität; Deutsche Universitäts-Zeitung, IV, Nr. 20, S. 5 ff.

(7) Wilhelm Weischedel: Sinn und Widersinn der Wissenschaft. Deutsche Universitäts-Zeitung X. Heft 18, S. 6 ff.

(8) Martin Wagenschein: Gegen das Spezialistentum. Die Pädagogische Provinz, 1953, Heft 3. See also (100).

(9) Derselbe: Ein mathematisches Unterrichtsgespräch. „Bildung und Erziehung", 1949, Heft 10, S. 721 - 729. See also (100).

(10) Karl Menninger: Mathematik in Deiner Welt, Göttingen, 1954, S. 51. (11) Martin Wagenschein: Das Exemplarische Lehren als ein Weg zur Erneuerung des Unterrichts an den Gymnasien (mit besonderer Beachtung der Physik). Hamburg (Verlag der Gesellschaft der Freunde Hamburg 13, Curiohaus) 1953, 3. Aufl. 1964. See also(100).

(12) Derselbe: Das Exemplarische in seiner Bedeutung für die Überwindung der Stoff-Fülle, „Bildung und Erziehung" 1955, 5. 519. - See also (100).

(13) Georg Kerschensteiner: Wesen und Wert des naturwissenschaftlichen Unterrichts, 3. Auflage, S. 116.

(14) Richard Goldschmidt: Einführung in die Wissenschaft vom Leben der Ascaris; Berlin, 1927 (Bd. 3 der Sammlung „Verständliche Wissenschaft").

(15) Johannes Kepler: Ad Vitellionen paralipomena (1604) - Zusätze zur Optik des Vitelo. - Auszug in Ostwalds Klassikern der Exakten Naturwissenschaften, Bd. 198, Leipzig 1922, S. 13.

(16) Max Picard: jenes Bild, das sich auf das Urbild bezieht; in: Wegweiser in der Zeitwende, Hrsg. v. E. Kern, Ernst Reinhardt Verlag. München, Basel, 1956, S. 79. See also his book: Die Welt des Schweigens, 2. Aufl., Erlenbach-Zürich, 1950, S. 74.

(17) Elisabeth Rotten: Erziehung als Begegnung; Pädagogische Blätter, (Berlin), VI, 1955, S. 245 - 251.

(18) Otto Friedrich Bollnow: Begegnung und Bildung; Zeitschrift für Pädagogik, 1(1955), S. 10 - 32.

(19) John Tyndall: Die Wärme, betrachtet als eine Art der Bewegung; Braunschweig, 1867, S. 114.

(20) Martin Wagenschein: Natur physikalisch gesehen; Frankfurt, 1953, 4. Aufl. 1967, 5. 58 ff.

(21) Derselbe: Konstruktive Stoffbeschränkung im physikalischen Unterricht; Der Mathematische und Naturwissenschaftliche Unterricht, VII, S. 165 - 172. See also(100)

(22) Derselbe: Die Erde unter den Sternen, München 1955; 3. Aufl. Weinheim, 1965.

(23) Konrad Barthel: Über exemplarisches Lernen im Geschichtsunterricht; „Die Sammlung", 1956, 5. 35 - 47.

(24) Eduard Spranger: Die Fruchtbarkeit des Elementaren; in: Pädagogische Perspektiven, Heidelberg, 1952, 5. 87 ff.

(25) Derselbe: Der Eigengeist der Volksschule, Heidelberg, 1955, S. 98.

(26) Werner Heisenberg: Das Naturbild der heutigen Physik, Rowohlts Deutsche Enzyklopädie, Bd. 8.

(27) Carl Friedrich von Weizsäcker: Zum Weltbild der Physik, 6. Aufl. Stuttgart 1954.

(28) Theodor Litt: Naturwissenschaft und Menschenbildung. 3. Aufl. Heidelberg 1959.

(29) Clemens Münster und Georg Picht: Naturwissenschaft und Bildung, Würzburg 1953.

(30) I'm indebted to Eduard Spranger for this felicitous choice of words.

(31) Hinweis auf die Funktionsziele der Geologie und Astronomie in Martin Wagenschein: Das Exemplarische in seiner Bedeutung für die Überwindung der Stoffülle. Bildung und Erziehung VIII (1955), 5. 519 ff. See also (100).

(32) Otto Friedrich Bollnow: Diskussionsbemerkung in „Bildung und Erziehung" VIII (1955), 5. 538.

(33) Hermann Heimpel in: Erich Weniger: Neue Wege des Geschichtsunterrichts, Frankfurt a. M., 1949, S. 81 - 84.

(34) Wolfgang Lautemann: Möglichkeiten der Stoffbeschränkung im Ge-schichtsunterricht der Oberstufe der Höheren Schule; Geschichte in Wissenschaft und Unterricht, 1955, Heft 10.

(35) Helmut Beumann: Die Geschichte des Mittelalters auf der Oberstufe der Höheren Schule; Geschichte in Wissenschaft und Unterricht, 1955, Heft 11.

(36) Dilthey: Zitiert nach J. Wach: Das Selbstverständnis des modernen Menschen, Universitas, X, 1955, S. 449.

(37) Adolf Butenandt: Was bedeutet Leben unter dem Gesichtspunkt der biologischen Chemie?, Universitas X (1955), S. 475 - 482 Auch in Kröners Taschenbuchausgabe Bd. 230, S. 97 - 108.

(38) Adolf Portmann: Aufbau eines neuen Erlebnis der Natur; Biologie auf zwei Fronten. Stuttgarter Zeitung 31. 12. 1955, S. 35.

(39) Derselbe: Zoologie und das neue Bild des Menschen, Rowohlts Deutsche Enzyklopädie, Bd. 20, S. 26.

(40) Ludwig v. Bertalanffy: Das biologische Weltbild, 2 Bde., Bern 1949 Derselbe: Die Evolution der Organismen, in Kröners Taschenbuchausgabe, Bd. 230, S. 53 - 66.

(41) Konrad Lorenz: Er redete mit dem Vieh, den Vögeln und den Fischen, Wien, 1953

Derselbe: So kam der Mensch auf den Hund, Wien, 1953.

(42) Adolf Portmann: Ein Naturforscher erzählt, Basel, 1955 S. 16 - 24 (43) Kierkegaard, Tagebücher, ausgew. v. Theodor Haecker, 4. Aufl. München, 1949, S. 246/7.

(44) Walther Klumpp: Das Grundphänomen in der Biologie; Der mathematische und naturwissenschaftliche Unterricht, VI (1953/1954), S. 104 - 109.

(45) Ernst Wilmanns „Fragen zum ‚Exemplarischen Geschichtsunterricht" in: Geschichte in Wissenschaft und Unterricht, 7. jhrg., H. 4, 1956, S. 223 - 232.

The author learned about following references after the first publication (1956) of this essay.

From Journals:

(46) Wilhelm Flörke: Geochemische Betrachtungen im Chemieunterricht, in: Praktische Schulphysik („Praschu"), 1955. Heft 10.

(47) Arthur Berg: Exemplarischer Unterricht, in: Lebendige Schule, 1956, 5. 139.

(48) Friedrich Walsdorff: Interpretation in der Schule und auf der Universität, in: „Gymnasium", 1956, S. 206.

(49) K. Keller: Die spezifische Arbeitsweise der Höheren Schule, in: Die Höhere Schule, 1956, Heft 5.

(50) Josef Adelmann: Das Exemplarische in der Lehrweise. In: Pädagogische Welt, 1956, 5. 475.

(51) Gert Otto: Kirchengeschichte im Religionsunterricht, zugleich ein Beitrag zum exemplarischen Lernen, in: Die Sammlung, 1957, 5. 3.

(52) Hans Knübel: Exemplarisches Arbeiten im Erdkundeunterricht, in: Geographische Rundschau, 1957, 5. 56.

(53) Werner Jäkel: Das Beispielhafte, in: Die Sammlung, 1957, S. 90.

(54) Karl Pabelick: Bildung durch exemplarisches Lehren und Lernen, in: Neue Wege zur Unterrichtsgestaltung, 1957, 5. 193.

(55) Konrad Barthel: Das Exemplarische im Geschichtsunterricht, in: Geschichte in Wissenschaft und Unterricht, 1957, S. 216.

(56) Joachim Rohlfes: Funktionsziele; zur Frage des Exemplarischen Lehrens im Geschichtsunterricht. In: Geschichte in Wissenschaft und Unterricht, 1957, S. 421.

(57) Martin Wagenschein: „Vielwisserei Vernunft haben nicht lehrt« (Heraklit), in „Die Deutsche Schule", 1957, S. 393. See also(100).

(58) Derselbe: Was das Exemplarische Lehren nicht ist, in: Anregung, Zeitschrift f. d. Höhere Schule (München), 1957, S. 5. See also(100).

(59) Derselbe: Das Fallgesetz, in: „Die pädagogische Dimension der Physik", Braunschweig 1962, 2. Aufl. 1965, 5. 270 - 275.

(60) Arnold Stenzel: Erdkunde-Sendungen im Schulfunk, in: Schulfunkheft des Süddeutschen Rundfunks, August 1957, 5. 288.

(61) Edgar Hunger: Was heißt philosophische Vertiefung des Unterrichts?, in: Die pädagogische Provinz, 1957, S. 437.

(62) Derselbe: Über den Schichtenaufbau der Funktionsziele, in: Die Pädagogische Provinz, 1957, S. 613.

(63) M. F. Wocke: Exemplarischer Erdkundeunterricht, in: „Die Deutsche Schule", 1958, 5. 163.

(64) Gert Otto: Methodik des evangelischen Religionsunterrichts, in: Zeitschr. f. Päd. 1958, Heft 3.

(65) Derselbe: Gegenwartsprobleme zwischen Theologie und Pädagogik, in: „Lutherische Rundschau", Stuttgart, VIII (1958), Heft 2.

(66) Martin Wagenschein: Über die Aufmerksamkeit, in: Zeitschr. f. Päd., 1959, Heft 1. See also(100).

(67) Horst Rumpf: Das Exemplarische als Weg zu geschichtlicher Wirklichkeit, in: Geschichte in Wissenschaft und Unterricht, 1959, 5. 479.

(68) Martin Wagenschein: Zur Klärung des Unterrichtsprinzips des exemplarischen Lehrens, in: Die Deutsche Schule, 1959, S. 393.

(69) Derselbe: Was bleibt unseren Abiturienten vom Physikunterricht?, in:

Zeitschr. f. Päd. 1960, S. 29. See also(100).

(70) Derselbe: Das exemplarische Lehren als fächerverbindendes Prinzip, in: Die päd. Provinz, 1960, 5. 628. See also(100).

(71) Derselbe: Mathematik aus der Erde, in: Die Deutsche Schule, 1961, 5. 5. See also(100)

(72) Derselbe: Die Tragik des Mathematik-Unterrichts, in: Frankfurter Hefte, 1961, Heft 1, 5. 3 - Kurzfassung in: Internat, Zeitschr. f. Erz. Wiss. VII (1961), Nr. 2, 5. 163. See also(100).

(73) Horst Rumpf: Das Schauen als Weg zur Wirklichkeit, in: Neue Sammlung, 1961, Heft 2, S. 120.

(74) Alexander Wittenberg: Ist echte gymnasiale Bildung ohne Studium der alten Sprachen möglich? In: Neue Sammlung, 1961, Heft 2, S. 141.

(75) Walter Jung: Gibt es unendlich viele Zahlen? In: Neue Sammlung, 1961, Heft 2, S. 148.

(76) Martin Wagenschein: Erwägungen über das exemplarische Prinzip im Biologie-Unterricht, in: Der mathematische und naturwissenschaftliche Unterricht, XV (1961/2), 5. 1. See also(100).

(77) Alexander Wittenberg: Mathematik am Gymnasium, in: Neue Sammlung, 1961, Heft 6, S. 474.

(78) Horst Rumpf: Häufen oder aufspüren? Zum Gespräch über die exemplarische Geschichtsdidaktik, in: Geschichte in Wissenschaft und Unterricht, 1962, Heft 2, 5. 86. See also (101).

(79) Konrad Barthel: Zeitgeschichte und exemplarisches Lehren, in: Geschichte in Wissenschaft und Unterricht, 1962, Heft 4, S. 221.

(80) M. F. Woche: Das Problem eines exemplarischen Erdkundeunterrichts, in: Die Deutsche Schule, 1962, Heft 12, 5. 578.

Note (1966)

A further continuation of the list of journal articles would go beyond the scope of this essay. Thankfully references 97 und 100 below fill this gap. (See, however, Additional References (1969) below.)

From Books and Edited Volumes

(81) Heinrich Roth: Orientierendes und exemplarisches Lehren, in: Pädagogische Psychologie des Lehrens und Lernens, Schrödel, Hannover, 1957.

(82) Josef Derbolav: Das »Exemplarische« im Bildungsraum des Gymnasiums, Schwann, Düsseldorf, 1957.

(83) Eduard Spranger: Der geborene Erzieher, Quelle und Meyer, Heidelberg, 1958, 5. 29 f.

(84) Hans Scheuen: Die Exemplarische Lehre, Max Niemeyer, Tübingen, 1958.

(85) Wolfgang Edelstein: Exemplarisches Lernen - Beispiel Latein, Heft 14 der Schriftenreihe der Odenwaldschule (Oberhambach über Heppenheim a.d.B.).

(86) Edgar Hunger: Die Bildungsfunktion des Physikunterrichts, Vieweg, Braunschweig, 1959.

(87) Martin Wagenschein: Die Aufgabe des Physik-Unterrichts, in: Die Pädagogik im XX. Jahrhundert, Her. v. W. Scheibe, Ernst Klett, Stuttgart, 1960, 5. 216 - 222. See also (100).

(88) Theodor Ballauf - Ernst Meyer: Exemplarisches Lehren, Exemplarisches Lernen, Ernst Klett Verlag, Stuttgart, 1960.

(89) Hans Knübel: Exemplarisches Arbeiten im Erdkundeunterricht, Westermann, Braunschweig, 1960.

(90) Heinrich Newe: Der Exemplarische Unterricht als Idee und Wirklichkeit, Ferdinand Hirt, Kiel, 1960.

(91) Ernst Meyer: Praxis des Exemplarischen, Ernst Klett, Stuttgart, 1961

(92) Martin Wagenschein: Die Erfahrung des Erdballs, Heft 1/1967 der Schriftenreihe „Der Physikunterricht", Klett, Stuttgart.

(93) Derselbe: Die pädagogische Dimension der Physik, Westermann Verlag, Braunschweig, 1962, 2. Aufl. 1965. Inshes.: S. 2 14 - 220 und S. 270 - 275 (Nr. 59 dieses Verzeichnisses).

(94) Derselbe: Pädagogische Aufsätze zum mathematischen Unterricht; als Heft 4 („Exemplanisches Lehren im Mathematikunterricht"), 1962, der Schriftenreihe „Der Mathematikunterricht", Hrsg. v. E. Löffler, Ernst Klett Verlag, Stuttgart. (Also contains the references 9, 70, 71, 72.)

(95) Wolfgang Klafki: Das pädagogische Problem des Elementaren und die Theorie der kategorialen Bildung, 2. Aufl., Julius Beltz, Weinheim, 1963.

(96) Martin Wagenschein und Konrad Barthel: Exemplarisches (paradigmatisches) Lehren; Mathematik, exakte Naturwissenschaften und Geschichte. - Kap. 3 von: Pädagogisch-psychologische Praxis an höheren Schulen, Hrsg. von Kurt Strunz, Ernst Reinhardt Verlag, München und Basel, 1963. See also (100).

(97) Berthold Gerner (Hrsg.): Das exemplarische Prinzip, Wissenschaftliche Buchgesellschaft, Darmstadt, 1963, Nr. 1518; 4. Aufl. 1970 (Sammelband; 21 Autoren, umfassendes Literaturverzeichnis von über 200 Titeln).

(98) Alexander Wittenberg: Bildung und Mathematik, Mathematik als exemplarisches Gymnasialfach, Ernst Klett Verlag, Stuttgart, 1963.

(99) Derselbe: Redécouvnir les Mathématiques: Delachaux & Niestlé. Neuchatel, 1963.

(100) Martin Wagenschein: Ursprüngliches Verstehen und exaktes Denken, Klett Stuttgart, 1965; 2. Aufl. u. Bd. II, 1970. (Contains all of Wagenschein's journal articles cited in this article.)

(101) „Auswahl", Reihe A, Bd. 6; H. Schroedel Verlag, Hannover, 1965. (102) Horst Rumpf: Die Misere der Höheren Schule. Luchterhand, Berlin-Neuwied, 1966. (Contains reference 78.)

(103) Ernst Meyer (hrsg.): Didaktische Studien, Exemplarisches Lehren - Exemplarischies Lernen, Ernst Klett Verlag, Stuttgart, 1969.

(104) Martin Wagenschein: Der Sechs-Stern, in: „Vertrauen und Verstehen", Festschr. f. 0. F. Bollnow, Kohlhammer, Stuttgart, 1968, S. 229 - 244.

Additional References (1969)

Two articles are of particular interest, because they help to resolve some of the widespread misconceptions about example-based learning:

Konrad Barthel: Mißverständnisse des Exemplarischen. In: Geschichte in Wissenschaft und Unterricht, 1964, Heft 2.

Fritz Loser: Sachunternicht als Sprachunterricht (Das exemplarische Lehren und sein Beitrag zu einer pädagogischen Theorie des Lehrens und Lernens), In: Pädagogische Rundschau, 1968, Heft 8, S. 393 - 411.

Additional Reference (1972)

(105) Richard Kluge: Erkenntniswege im Physikunterricht, Klett, Stuttgart 1970.

Additional Reference (1974)

(106) Richard Kluge: Spielzeuge als Zugang zur Physik, Diesterweg, Frankfurt, 1973.

Notes

1 The "Tübingen Resolution" was a recommendation brought forward by distinguished scientists - Carl-Friedrich von Weizsacker, Walter Gerlach, Eduard Spranger and others - to reform high school curricula in Germany by reducing the abundance of content-matter and deepening scientific understanding.

2 Translators' note: Wagenschein uses the term "exemplarisches Lehren." He means a holistic principle of teaching that leads to deep understanding. He later used the term "genetic-socratic-exemplary teaching and learning," thereby emphasizing that the focus of this concept is the process of learning (qualified as ‘genetic') and teaching (qualified as ‘socratic') and not the subject matter.

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