TaST Supplement, Part 2
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
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:
- 1 What content most dramatically embodies the binary opposites, in order to provide
access to the topic?
- 2 What content best articulates the topic into a developing story form?
What is the best way of resolving the dramatic conflict inherent in the binary
What degree of mediation of those opposites is it appropriate to seek?
How can one know whether the topic has been understood, its
importance grasped, and the content learned?
Topic: Properties of the Air
1. Identifying importance:
An important function of education is to enrich our everyday environment
In the case of air, we tend to take it for granted as a kind of emptiness
which we move. One of the delights of education is the discovery of
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
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
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
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
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,
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
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.
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
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!)
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
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
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
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."
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
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
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
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
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
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
movement of the other planets relative to the earth -- i.e.,
what we see of them --
An hour's reading will provide quite enough information for
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
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
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
of creatures from planets more like Mars or one of
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.
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
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.
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
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
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
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
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.
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.
* * *
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
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
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
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
. 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
, 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
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
One may develop this point by demonstrating how it is the positioning
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).
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
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.
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.
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:
13 x 18 -- 1. 13 + 8 = 21
(For other techniques and tricks and games that will
add to the sense of mathematics as an abstract
magical playground see Gyles Brandreth, Number-
, New York: Rawson Associates, 1984).
- 21 x 10 = 210
- 3 x 8 = 24
- Add 210 + 24 = 234
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
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
to generation of school children, surviving sometimes with
only superficial changes through decades and even
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
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
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
is the contrast between what things go together in our expectations and what
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
The incongruity often serves to reassert the normal course of events by
but in the moment of the joke it creates a wild, new, different
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
"Put a bag over his head."
"Why did the chicken
cross the soccer
referee called foul
"How do you stop a herd
of gooseberries from
away their credit
"How can you tell a
gooseberry from an
up. The elephant is usually
the heavier one."
"Why does a mouse when
"The higher it gets
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
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
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
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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