TaST Supplement, Part 2

Teaching as Story Telling Supplement, Part 2

Further examples of lesson/unit plans using the story-form framework

(A variety of examples using the framework are now in print. One source is obviously Teaching as Story Telling . A second is in K. Egan, Primary Understanding (New York and London: Routledge, 1988). As increasing numbers of teachers use and adapt the framework much more interesting and elaborate examples are becoming available. I am building up a library of these and will look for some format whereby they might be made generally available -- perhaps through a newsletter, or some such means.)

Here is the story form framework as it appears in Teaching as Story Telling :

The Story Form Model

Identifying importance:
What is most important about this topic?
Why should it matter to children?
What is affectively engaging about it?
Finding binary opposites:
What powerful binary opposites best catch the importance of the topic?
Organizing content into story form:
Conclusion
What is the best way of resolving the dramatic conflict inherent in the binary opposites?
What degree of mediation of those opposites is it appropriate to seek?
Evaluation:
How can one know whether the topic has been understood, its importance grasped, and the content learned?

Area: Science
Topic: Properties of the Air
1. Identifying importance:
An important function of education is to enrich our everyday environment with meaning. In the case of air, we tend to take it for granted as a kind of emptiness through which we move. One of the delights of education is the discovery of wonder in what is commonly taken for granted. This topic should matter to children because it can enlarge and enrich their perception of the world and their understanding of their experience. It can be affectively engaging through its power to evoke, stimulate, and develop the sense of wonder and engage it with reality.

2. Finding binary opposites:
One usable binary set for a unit on the properties of the air is empty/full. This may seem a bit simple, with no evident affective "pull." But I think we can invest emptiness with the affective components of starkness, nothingness, uselessness to life, and fullness with the opposites -- varied richness, complexity, and supportive of life.

3. Organizing content into story form:
The first sub-section here calls us to organize our opening teaching event. In this we must show dramatically that the air, which is taken as largely empty, is in fact full. We could begin with a single dramatic instance. If we have a lab available we might start with some bangs and flashes with test tubes and oxygen and hydrogen. After the children have agreed that the test tubes are empty, we can use the usual pyrotechnics to point out that they were indeed full of something. But in the ordinary classroom we can also demonstrate that the air is full. A beam of bright light in a darkened room can display a million dust particles calmly moving around. Where did they come from? Where will they go to? Or we might turn on a batterypowered radio. How does the signal reach the radio? Switch it off and move to another part of the room and change radio stations. How many signals are there? Are they all in the room all the time? Having established these kinds of things in the air, we might go on to things that are less easy to demonstrate directly. One might show enormously enlarged pictures of the microbes that inhabit the air. We breathe in gases, of which the air is made up. Huge planets such as Jupiter and Saturn are gases, some liquified, swirling around. They have no surface. If we think of the air as empty then Saturn and Jupiter are not there.
We think of the air as moving in the wind, and it carries clouds along, rustles leaves and shakes branches of trees, holds aloft kites when it moves, lifts flags, and so on. But it itself is taken usually as empty. We can quickly establish, then, that the "empty" air through which we walk is teeming with life, particles of matter, radiation of various kinds, gases, etc. That we cannot see many of these things does not mean that they are not there. Depending on teachers' knowledge and interests one can enrich the view of full air by adding the various particles of matter that stream through the air, and through us and the earth, from the sun and from the stars. If we looked out the classroom window not with human eyes but with various particle sensors or the "eyes" of a radio, or life-detecting receptors then our view of the air would be very different. Far from empty! This then is the impression we must impart dramatically at the beginning of our unit -- a sense of the air as full, and wonderfull.
The second sub-section under 3 is where we organize the content into the developing story form we want to stretch between the poles of empty and full. If a teacher chose to use only one dramatic example of the air not being empty, then the other examples I mentioned might form the basis for this section. If a teacher decided to touch on each quickly to build a sense of just how packed with varied things the air may be (which I think is probably better), then under this sub-section we might work out how to explore each of those topics in more detail.
One could organize these varied contents of the "full" air into a story form in a variety of ways. This is one of those cases where one might build one's exploration on a fictional element. One can tie together all the different kinds of fullness by inventing a brother and sister who "know" that the air is empty and scoff at the idea that it is full of all kinds of things. The brother and sister then can meet creatures who introduce them to various constituents of the air. Each lesson, or segment, may begin with our empty-air pair meeting a new character -- Mr. Radio, Mrs. Neutrino, Miss Microbe, Master Gas, and so on, or perhaps better might be Science Fiction kinds of creatures. One can build up zany characteristics for these as one feels inclined. Each invites our skeptical pair to come with them, and put on special glasses or earphones, or whatever, that will allow them to see the air differently or hear it differently -- perhaps colors for the gases and different sounds for wavelengths, etc. Our hero and heroine can be taken on a journey through the wonders, mysteries, and terrors of the "empty" air. The Microbe might take them on a journey through the year. In winter the air might be fairly clear, but in late spring and summer the winter microbes are blotted out in a teeming fog of pollen, microorganisms, seeds and pullulating life.

4. Conclusion:
What is dust? Where does it come from? Where does it go? Children will have some grasp on the elements that fill the air by this time. Mediation is not so appropriate here, given the choice of binary opposites. The resolution is rather the discovery that what was thought to be empty is in fact full. The fullness is one of massive forces, tiny delicate organisms, the endless "dust." Given the fictional element, we might conclude with the brother and sister returning to tell their friends and family how crowded the air is, what wonders it holds unseen. (An imaginative teacher might think up a better fictional story line than this!)

5. Evaluation:
One may use any of a range of traditional evaluation procedures to see whether children understood the variety of things that fill the air. One might additionally or alternatively ask them to write and/or draw an image of the air from the perspective of one or more of the creatures who gave the brother and sister their guided tour. Also they might be encouraged to gather data about what their parents or neighbours know about the thronging contents of the air we breathe.
* * *

Area: Social Studies
Topic: Maps
1. Identifying importance:
I will assume that this is a unit for a third year group, after some basic map skills are developed. We need to hunt around under the everyday routineness of maps in our experience to whatever is affectively engaging and of fundamental importance about our topic. This, of course, is always necessary for teaching in elementary school. Only when we have located the most fundamentally important feature of our topic will we have discovered the place to begin teaching it. And what is most important about mapping? I don't want to make this seem too outrageous, but I think at base it is a moral matter. A map is a representation of places relative to each other. Cultures without maps see themselves as unique and at the centre of the world, as special. Their conceptions of the world typically involve the belief that their local area received special treatment at the hands of gods or sacred ancestors "in the beginning." What the map does is locate us and our place as one among many equivalents. Maps represent one of the more important conceptual revolutions in human cultural history. The history of maps, of earth and sky, go hand in hand with our discovery of our place in the universe, and with the reduction in ego- and ethno-centrism. This is why they are important, and this therefore is where we must begin.

2. Finding binary opposites:
How then can we catch this importance in binary terms? Perhaps one way might be through the binary opposites self/other. This is not to be likened to the sense in which in the "expanding horizons" kind of curriculum it is assumed that children know themselves and can therefore "expand" their understanding from concepts of the "self." This seems to build on a superficial logical scheme that ignores completely some important psychological truths. Young children view the world from the "self," as do adults, but this does not mean they have available some concept of their individual identity that is somehow a secure starting point for conceptual exploration of the world. A complex truth about our understanding of our "selves" is that it seems to grow through our understanding of "others." Our selves become defined only as we define the distinctiveness of others. Those who as adults we recognize as most "egocentric," most tied up with themselves, are usually those who are least sensitive to the distinctiveness of others. So the sense of self/other here is not to be seen as a move from one to the other, but is an attempt to introduce mapping in its cultural role of helping to give some further definition to both together.

3. Organizing content into story form
The first sub-section of 3 invites us to look for the most dramatic way of catching the importance of the topic using the binary opposites on which we will build our lesson or unit. Maps are graphic means of making easily visible various kinds of data about the world. They are selective and abstract representations, as distinct from unselective and specific photographs. There are many kinds of maps and our unit will explore a number of them. A vivid portrayal of our theme might be possible by starting with maps of the sky. One might begin by showing a picture of an ancient or medieval sky map, or by representing a simplified version on the chalk board or on a hand-out sheet. In this the earth will be in the centre, the planets and moon and sun travelling around the earth and a backdrop of the sky on which the stars are fixed and which turns around the earth as a great sphere, at the centre of which is the Earth. (Archimedes calculated this sphere's diameter to be equal to 10,000 earth diameters.)
The teacher might begin by pointing out how well this map represents what we can see in the sky. Emphasis should be put on the observational care that was required to trace the paths of the planets as different from the stars. And what a puzzle the whole canopy of the heavens was to people without telescopes, spectrometers, and other such instruments.
Then the teacher might introduce the anomaly of the planets' motions. The planets were so called by the Greeks because, compared to the smooth regularity of the stars, they seemed to be "wanderers" around the heavens. Their paths were irregular, going round the earth smoothly for a while but then suddenly reversing their courses, then moving forward again faster. (The more detail the teacher knows about the movement of the other planets relative to the earth -- i.e., what we see of them -- the better. An hour's reading will provide quite enough information for present purposes.) What was the solution? How was the anomaly of the planet's movements explained? Why was their movement the key to one of the most profound conceptual revolutions in Western cultural history? No doubt most children will know the answer, but in this case have very little idea what the question was. The dramatic element here is the question, and the ingenuity and courage required to find it, and for others to accept it.
Now the teacher might show a similar map but with the Earth as a wanderer like others around the sun. What a disturbance was this discovery! We've really never been the same since. The teacher might move on from the map of the Solar System to smaller scale maps of our sun's place among our local group of stars, whose names the children should know. The names of our arm of the Milky Way galaxy and the other arms around ours should be known too, as should the contents of the globular cluster halo that surrounds our galaxy be known, and the names of our local group of galaxies -- even if they are no more exciting than M32 and M33. I think maps of the neighbourhood make more sense when integrated with maps of our local stars and galaxies.
An alternative opening might be to provide the children with a local street map and a map of the solar system, and consider how neither looks like what you can see if you look at the neighbourhood or the sky. Or this could begin the extension of the unit in the second part of 3, where we are invited to use the guiding theme and its binary opposites to select the content that articulates the topic into a developing story form.
Given our theme, it would seem useful to consider a wide array of different kinds of maps, and see how they can establish a sense of the other as equivalent to the self. The local road map can be investigated in terms of its emotional characteristics for the individual students. They might be asked to mark in one color the places that are happiest for them; in another color, the saddest; in another color, the safest; in another color, the scariest. They might then explain each. Then they could be asked to do the same from the perspective of their parents, or the mayor, or a policeman, or whomever. They might similarly consider our solar system from the perspective of creatures from planets more like Mars or one of Jupiter's moons.
One might use this unit to extend the common activity in which children are asked to compose a kind of map of their parents, grandparents, and other ancestors as far back as possible. A slight problem with that kind of map is that it presents the child with a visual image of lots of predecessors and a few siblings all focused on the child. We might augment such maps to include not just the ancestors of the child but a more general map of family relationships, to include cousins, etc. We will thus represent visually a tracery of relations with, in most cases, more people in the child's generation than in predecessors' generations. Research for this might take some time, phone calls to grandma and cousin Jake, and some letters to Hong Kong or Scotland, but the charts could be gradually filled out as the unit progresses.
Other visual representations of relationships between self and other might include categories of animals and forms of life in general, and kinds of material. One would want to avoid the "evolutionary" sense of progressive evolution from monkey thugs to gleaming humans, culminating in the child. Rather it might be better represented as a network of related animal forms, of which humans are one; networks of living forms, of which mammals are one; and networks of materials, and their major concentrations -- a map in which humans might take a slight and incidental role. The child might compose such networks as a result of instruction, of inquiry, and individual research.

4. Conclusion
We might conclude such a unit by combining the lessons of the various maps giving definition to the child's relationships to other things, places, and life forms. This is achieved with a certain dramatic flair by Carl Sagan in one of the widely available parts of his Cosmos series. In the context of considering the life of stars he concludes that we are made of "star stuff," we are parts of the Cosmos, not separate observers of it. Showing a videotape of this might make an excellent conclusion. Lacking that resource one might look for a way of bringing home the same message; that we are intimately related to the natural and material world (while we might also be unusual or different in some significant ways). The mediation between self and other can be made in terms of what we share. We could conclude with lists of each feature of ourselves that we can name, and then list as many "others" as we can that share features similar to each one. So we might have a list beginning "hair on our heads," "nails," "carbon," "exhale carbon dioxide," "like temperatures between 15o and 30o C.," "grow for approximately 16-20 years," etc. etc.

5. Evaluation
Again, the traditional forms of evaluation may be used to assess the degree to which the basic content of the unit has been grasped. What we should additionally look for in this scheme is evidence of greater definition of "self" and "other," and perhaps greater sympathy for "others" as extensions of "self." This is in part a moral matter, bordering on what might be called mystical experience. It might be observed informally in children's sensitivity to their environment, but I cannot think of any way of getting a precise reading of it. That one cannot evaluate it precisely in no way effects its value as an educational goal, of course.
* * *

Area: Mathematics
Topic: Multiplication of double digit numbers
1. Identifying importance:
Multiplication involves manipulation of numbers which are abstracted from any things in the real world to which they might refer. But when the manipulation is completed and referred back to concrete elements of the world, the world is found to conform with the results. Mathematics is a kind of magic, a set of rules removed from the concrete stuff of reality but which yet catches something seemingly invariable about the shifting concrete stuff of the world.

2. Finding binary opposites:
To catch this sense of importance one might choose opposites such as concrete/abstract, seeing the bases of multiplication in the gradual abstraction of mathematics from concrete elements of the everyday world

3. Organizing content into story form:
We might begin by emphasizing how mathematics became both increasingly sophisticated and easy as it removed itself from concrete kinds of calculation. We might begin with the techniques that laid the foundation for this increasing abstraction. We can point out to the children that for thousands of years in the early human civilizations, while art, literature, and philosophy made great strides, only the very crudest developments took place in arithmetic. The ancient Greeks, who achieved great things in geometry, contributed little of significance to arithmetic. After this short unit, the teacher might announce, they will be superior to Plato and Aristotle in their arithmetical abilities.
Two simple but immensely important discoveries or inventions were required before multiplication could be easily performed. These were the discovery of place or positional setting (such that 4 has a different value in 42 from in 24) and the second was the invention of the zero. On these all our hugely complex technological civilization relies.
On ancient counting boards a number such as 42 would be represented by two columns with four marks in one and two in the other: e.g.

-- --
-- --
--
--

The problem was that 420 or 4002 would also look like that. One could not transcribe numbers and manipulate them abstractly until one had a symbol for zero.
The solution came from a Hindu early in the Common Era. Sunya , meaning "void" or "nothing" was used to take the place where no other number symbol fitted, and thus allowed the development of an unambiguous way of representing place value. Around the tenth century the Arabs translated sunya into the Arab sifr , which meant "empty." When this concept reached Italy about the beginning of the thirteenth century, it was Latinized to zephirum . Over the next hundred years zephirum became the Italian zero . (In Latin, however, the term cifra was used for centuries thereafter. This has come into English as cipher , as in "a mere cipher," suggesting no power or significance. For some, however, the number cifra had some mystical significance, so we have also the word decipher , meaning to resolve a puzzle or break a code. I think, incidentally, that this kind of etymology should form a part of the story we are telling about multiplication.)
After this introduction we might tell the children about the fifteenth century German merchant who wanted his son to learn all the tools necessary to run a sophisticated business. He asked a professor at the local university where was the best place to send the boy. The professor said that if he wanted to learn addition and subtraction, beyond what the fingers could accommodate, it would be enough to send him to the local university. But if he wanted the boy to learn also how to do the most sophisticated forms of multiplication and division, he would have to send him to an Italian university, where such advanced knowledge had been recently developed. So the son was sent to Padua, and there he learned how to do multiplication. And this is how he learned how to multiply 46 by 13: (actually it was even more complicated than this, but we can use modern notation)
First multiply 46 by 2. Answer = 92
Next multiply 46 by 4, which is equal to 92 x 2. Answer = 184
Next multiply 46 by 8, which is equal to 184 x 2. Answer = 368.
Next add 368 + 184 + 46. Answer = 598.
This fifteenth century breakthrough to multiplication, it will be evident, was a slightly modified addition. The children might enjoy performing a multiplications using this method. Then ask them how they would use it to multiply 9,387 x 6,221? How long would it take? This can lead to a demonstration of the much simpler techniques of multiplication invented since. We can with these perform in minutes what used to take days and even weeks of laborious calculating. The more abstracted from the counting board, and from the things the numbers represent, the more easily arithmetical operations work.
One may develop this point by demonstrating how it is the positioning of the numbers that enable more sophisticated, and easy, methods of multiplication to develop. The role of the zero in setting positions can be seen to be crucial. When multiplying 46 x 13, for example, we can easily establish the numerical value of the 4 and the 6 by holding them in their appropriate place by the use of the zero (46 x 10 = 460).
The abstraction is important, but equally important is to make clear to the children what the abstractions are abstractions from. One of the best ways to do this, I find, is through the history of mathematics, showing the concrete context in which certain techniques were developed and the practical problems they helped to resolve. (For which Tobias Danzig's Number: The language of science , New York: Free Press, 1954, is useful. It is from this source that I have taken much of the above. A math text book for children designed on such principles would seem most desirable.)
Practice with the modern techniques would then be useful. Once in the context of multiple addition, and having seen other techniques for doing this, the regular practice with modern techniques should be more meaningful.
4. Conclusion:
After the technique is mastered, one might conclude with some playful exploration of the abstraction of multiplication -- play that exposes some of the curious features of mathematics. The teacher can show alternative ways of multiplying. For example, to multiply by 5, 25, or 125 one can multiply by 10, 100, or 1000 and then divide by 2, 4, or 8. Do some examples of this and see if the class can see why they work.
If one wants to multiply two numbers between 10 and 20, try this method. Add the first number to the second digit of the second number, then multiply that number by 10, then multiply the second digits of both numbers, and add the two answers: e.g.,
13 x 18 -- 1. 13 + 8 = 21

21 x 10 = 210
3 x 8 = 24
Add 210 + 24 = 234

(For other techniques and tricks and games that will add to the sense of mathematics as an abstract magical playground see Gyles Brandreth, Number- Play , New York: Rawson Associates, 1984).

5. Evaluation:
One might use the usual means of evaluating whether children have mastered the basic techniques of multiplication with examples for them to work out. In addition one might provide a problem and ask them to multiply the numbers using as many different techniques as possible. Whether or not they cheerfully engage in number games, "magic squares," tricks and puzzles using numbers, will provide evidence of how successful one has been in trying to inculcate a sense of the magical abstract playground of mathematics.
* * *

Area: Language Arts
Topic: Jokes
For reasons I have given in Primary Understanding: Education in early childhood (New York: Routledge, 1988, pp. 222-25), the form of the story that can play an important role in the early development of logic is the joke. The joke remains, despite books of jokes, primarily an oral form. Certain jokes pass from generation to generation of school children, surviving sometimes with only superficial changes through decades and even centuries.

1. Identifying importance:
Jokes work by establishing a, usually metaphoric, connection between things otherwise not connected. They don't simply reflect connections already there, but they make the connection. The degree to which the connection is incongruous or unexpected or asserts a logic that is thinkable but absurd, the more likely we are to respond with an explosive laugh. The laugh seems a result of our holding for a moment categories or images of the world that suggest a world working quite differently from the way we are convinced reality works. This applies at least to certain kinds of jokes; those that create deliberate confusion usually by insisting on the wrong interpretation of a homonym. Lewis Carroll was a master of this kind of joke. In their simplest form they can appear as those question and answer jokes: "When is a door not a door?" "When it's ajar." Lewis Carroll takes the deliberately confused answer "seriously," and explores the worlds built on a sliding logic of metaphor ricochetting off the wrong side of homonyms. Playing with such jokes encourages flexibility in the use of metaphor, and so in a foundation of our mental lives, introduces us to logic, and can give us practice with the composition of narratives.

2. Finding binary opposites:
A useful structuring pair might be congruity/incongruity. At the heart of many jokes is the contrast between what things go together in our expectations and what things don't, and the sudden intrusion of something that does not fit, but yet makes a kind of sense. It is a kind of sense that threatens the categories of our expectations. The incongruity often serves to reassert the normal course of events by its craziness, but in the moment of the joke it creates a wild, new, different world.

3. Organizing content into story form:
The first part of this section invites us to think of a dramatic embodiment of the binary opposites that catch the importance of the topic. One way of getting at this might be to begin with a set of the children's favorite jokes. Such as:
"How do you make a Venetian blind?"
"Put a bag over his head."
* *
"Why did the chicken cross the soccer field?"
"The referee called foul (fowl)."
* *
"How do you stop a herd of gooseberries from charging?"
"Take away their credit cards."
* *
"How can you tell a gooseberry from an elephant?'
"Pick them up. The elephant is usually the heavier one."
* *
"Why does a mouse when it spins?"
"The higher it gets the fewer."
* *
Teachers might begin with a brief analysis of these. The first two are cases of deliberate misunderstanding of a homonym. The second, third, fourth and fifth also get some of their humor from being parodies of joke forms as well as using the form they parody. The third involves another homonym confusion. The fourth is based on a double incongruity; the expectation of the usual joke-ending being undercut by a "serious" response. The final example is for connoisseurs/eusses of incongruity. If the teacher and many children are simply bewildered by it, they should be prepared for a few children unable to unwrap themselves from rolling on the floor with laughter.
This analysis should be quite brief. The teacher might then take the jokes further, Lewis Carroll style, by asking the children, perhaps in groups, to take their favorite joke, and continue the narrative further. The teacher might prepare a few examples, perhaps including one directly from Lewis Carroll. The teacher might do some extempore in funny voices -- the T.V. commentator-style of high-seriousness might continue -- "having hoisted the elephant onto my back, however, the animal showed much reluctance to dismount. This required my taking it home with me. Fortunately I drive a covertable car, but some awkwardness ensued at the front door of my house, where my wife said ..." (The teacher might invite the children to supply the wife's response, and the next step in the narrative.
The lesson might continue by getting the children, possibly in groups, to write or make notes about their favorite jokes. Each group might choose one for telling to the class. After a brief analysis, the class might be invited to take the world of the joke seriously, and explore it further.

4. Conclusion:
A concluding activity might be to take a homonym at random and get the children to invent a joke, based on deliberate confusion of the meanings of the homonym. Take, for example, channel, as in narrow passages of water and as in T.V. The task is to invent a question whose answer is wildly incongruous, but coherent in the metaphoric slippage between meanings of the homonym. Immediately children will suggest confusions between "crossing the channel" in a boat or on T.V. Or questions such as "What channel is the wettest?" or "What channel shows most boats?" will emerge. Keep at it long enough for a good joke to emerge, and then extend it à la Lewis Carroll into a weird-world narrative.

5. Evaluation
The amount of laughter might form a unique evaluation instrument to such a lesson. The degree of engagement should also provide an index of success. If children are invited to write their favorite joke and extend the incongruous world created by the joke, then teachers might evaluate their ability to generate metaphoric connections and imaginatively pursue their products.
* * *

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