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THE SHAPE OF THE EARTH AND OF THE SKY :
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THE SHAPE OF THE EARTH AND OF THE SKY :
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Practical session is an integrant part of the activity to clarify:
1. Activity: Drawings and their classification
Comparison between drawings of adults and children
Interpretation of the drawings, making explicit and collective the implicit individual ideas
The perception of the force of gravity
2. Activity:
Use and construction of several unusual models for understanding better our position on the earth's globe. Working with them we feel at the same time on the Earth and outside it, and this double point of view helps us to understand.
Models: blank spheres, parallel globe, maps, totem of directions …
 Mappamondo di Ecateo VI sec a.C (Ricostruzione) |
 Petri Apiani Cosmographia, libellis MDXL |
| "When the first God created the world, he began shaping the Earth in such a way that every part had the same weight and he made it round". Ovid , Metamorphosis |
"Geography must consider the dimensions of the Earth, besides its shape and position under the sky." Ptolemy |
So, at the ancient times people already knew the roundness of the Earth and Sacrobosco in the 13th century confirmed that:
"If the earth were flat from east to west, stars would rise at the same time for all who inhabit the world, and this is incorrect. Furthermore, if the earth were flat from north to south, stars would always be visible to an observer wherever he went, and this is also incorrect. The earth seems flat to people because of its great wideness."
De Sphaera mundi, Sacrobosco, XIII cent.
…but mental images about the shape of the Earth were various:
"I say that the world - land and sea - is spherical, and Ptolemy's experience and that of others who have written about the world confirm and demonstrate this, as do eclipses of the moon, experiments made from east to west, and the observation of the different height of the Polar Star from south to north.
I have seen so many irregular shapes, and for this reason I made my own idea of the world: I have found that it is not round as they describe it but it has the shape of a very round pear, with the exception of the part where the stem is, that is the highest point. Alternatively we can say its shape is like a very round ball and on a point of which there is a "woman's nipple": this part of the world is the highest and nearest to the sky and it lies under the equinoctial line. On its summit, I believe, is heaven.."
C. Columbus, XVI cent.
At the beginning of the world there was only the dark sky, the Night and the Wind. From their union a giant and silver egg was born. When the silver egg opened, Eros emerged, the God who arouses every longing for love. First of all Eros made order in that primordial egg: heavy things went down to the low cavity and they became the Earth, Gaea; light things went up to form the sky, Uranus. So the Earth and the Sky took different shapes inside the primordial egg. A deep union lasted long between them: in fact Uranus fell in love with Gaea and his embrace was so deep and strong that she couldn't breathe, nor to give birth to the children she carried. The Earth stayed flat under the Sky, completely crushed, without any life. So she asked her children to help her, and Cronos, the youngest of all, came out from the Earth and wounded his father. Crying, the Sky went away from the Earth and they were separated for ever.
Also in the Maori myth at the beginning of the world the Night, and the Earth. were so close together that there wasn't enough space between them, and their many children couldn't breathe or move. So, one of the children decided to separate their parents and pushed his father away from his mother. It made the Earth and the Sky very unhappy. The children, to make the sky happier, put the sun on his back and the moon on his stomach, and many stars on his dark blue coat. But Sky and Earth were separated for ever.
In this workshop we want to research some relations between what we know and what we perceive about the shape of the world and about our perception of the space that surrounds us. Everybody knows that the Earth is a sphere, but experiences about this question with children and adults, students and teachers of every school level demonstrate that the majority of people don't use the concept of earth-sphere. In effect in practical and everyday life everybody lives and acts as if the earth was really flat and at the centre of universe. When we enjoy a sunset, we don't think that the earth is turning around itself, but we think that the sun is moving, and in fact we say : "The sun is setting ". But as teachers we must be aware about the different uses of common sense knowledge and scientific knowledge and about the complex relations on which scientific knowledge is based.
In fact, if we have a real understanding about the concept of earth-sphere, we must be able to connect the spherical form with its geometrical and physical proprieties, but usually we are not. That means that the common sense of a modern man is connected only with his own experience as it was for a primitive man, and that the role of school in learning scientific knowledge is a failure. At school often only isolated notions are taught ( the earth is a sphere) and not relations between this knowledge and other fields of knowledge.
Besides that, we focus our attention on some aspects of the dynamics of individual cognitive processes and on the problem of inducing a conceptual change or re-structure by unusual learning situations.
We don't want to reflect about teaching, but about mental processes of learning: to make explicit what is usually implicit by using simple but significant questions and some unusual models. For this reason we require an active personal involvement of the participants: they don't stay in the perspective of an observer, but of a learner who produces actions, thoughts, perceptions and expectations during a specific learning situation. This allows them to reconsider their conceptions making explicit the implicit ones, to reach a systematic organisation of the results of their strategies of reasoning and perhaps to modify their points of view.
Everybody has an his own perception of the world that surrounds him. Mauro, monk in Venice during XV century made his map of the world never travelling, but standing in his monastery in Venice and hearing from sailors, pilgrims and travellers the histories about their trips and their ideas of the world:
"I'm afraid that my image of the Earth is not correct. Perhaps in reality the world is different from how I have begun to perceive it.. Every man who lived on this earth has contributed to its evolution, because his observations have helped to modify it. For this reason the world is completely built by thought, continually changing during reflections about it by man."
As teachers we have to know which mental habits, concepts and common sense concepts our students have about the knowledge we plan to teach, how we may know those mental habits, how we may help them to re-structure their conceptual framework and build scientific knowledge.
"People will not understand something only because it has been shown to be true. They must be taken from their standpoint and brought forward". Wittgenstein, "Philosophische Untersuchungen, 1953"
Let's discover our mental image of the Earth…
Activity : Let's draw a picture of the earth, clouds and rain.
Pictures help to understand conceptions about a flat or round Earth, and perceptions of high and low.
In the drawings the concept of Earth's sphere is often not used: the perception of a flat surface under our feet and a high sky above us prevails. High and low may be sometimes absolute elements, independent from gravitational force.
In this way , the gravitational field hasn't a correct spherical symmetry and the spherical form is not connected with its geometrical and physical proprieties.
Adults have often an ingenuous thinking about the shape of the Earth, exactly as children
Perhaps we didn't make a long street from the times of Plinius, Historia Naturalis:
"Usually we talk about the Earth's sphere, but the struggle between science and popular opinion is great. They say that men stand all over the world, and their feet are opposed to each other. If matters stand thus, why don't the people at the antipode fall from the Earth? And they probably wonder why we don't fall in the same way! Another question arises: why the Earth itself is hanging in the sky and doesn't fall with us?"
We can't expand our disciplinary knowledge without knowing its foundations … but common sense ideas must not be replaced by scientific theories: we must make explicit and collective the individual 'roots', see gradually the differences between common sense knowledge and scientific knowledge, and to use both in different contexts and for different objectives. From provisional foundations we must construct consistent and true concepts and correlate them into scientific knowledge: Knowledge is a continuous process of accommodation.
Activities: Use and construction of several unusual models
We use our models for understanding better the reality.
Models enable to predict, to facilitate images and explanations, provide practical bases for identifying improvements and facilitate the transfer and construction of knowledge.
Working with our models we feel at the same time on the Earth and outside it, and this double point of view helps us to understand our position in the earth's globe.
Key issues for models and actions:
The path to follow is not a linear one, it goes forwards and backwards according to the interplay of actions and ideas which is at the basis of the work.
1. Blank spheres: where are you?
"The sphere is a model of the Earth and the stick is you. Let's put the stick on the surface of the sphere in the same position you have on the Earth, according to the perception you have of your position. Where and how do you stand on the Earth's surface?"
The stick must be parallel to our vertical line. In this way, if the activity is outside in a sunny day, our shadows have the same direction of the stick's shadow.
Participants try to use scientific knowledge more than own perceptions to answer the questions.
Using their common sense, they often don't find points of reference and sometimes there is a real "conflict" between the two points of view.
For somebody it is difficult to find the point where to put the stick, and its direction. Usually different solutions are found. Some sticks are not oriented towards the centre of the Earth, some others go to various directions. Some sticks are on the top of the sphere, some others not.
Everybody speaks about his own resistances and difficulties doing the work: for instance to put the stick on the top of the sphere, where usually people thinks North Pole is.
In effect, we are on the top of the Earth in the sense that the whole Earth is under our feet .
2. Parallel globe: where is Norway?
ACTION 1:
"Knowing the direction south-north, indicate with a gesture of your hand where Norway is in respect to where we are. Imagine I need to follow your indication to go there."
Usually the direction of the hands is towards a high point and indicates the polar star, not Norway. Norway is in the north but its position is lower then ours. If the question was "where is Italy?", the hands would probably indicate a lower direction because we associate "south" with low and "north" with high. This is because usually geographical maps are on the walls of the class rooms: we would have to use them on the floor, because the directions of space are on the plane of the horizon.
The surface of our Horizon is so large that we perceive it flat, but in reality the Earth is a sphere and we are on the highest point, on top of that. The whole Earth is under our feet. Each one is higher than the other.
We all know the Earth is spherical, but if we think we are on a sphere we feel dizzy. Walking on spheres is a feat for acrobats, not for normal men!
ACTION 2:
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Using a special globe, as a model of the Earth, let's put on it a stick representing yourself on the Earth. For the majority of the people it is now clear that the stick must be on the top of the globe! In this model we can see all the spatial references are parallel with the real ones: Horizon plane, Local meridian, Vertical of an observer, Rotation axes… For this reason it is called "parallel globe". When it is correctly oriented with local place on the top, we can read on a goniometer the local latitude. Its axes is not fixed, so it may assume different positions according to the position of the observer. It's better to use it outside, in the sun, because the sun acts on it in the same way as on the real planet and in real time. The direction of its rays is obviously the same, and so are the shadows. So a parallel globe becomes not only a model but also an instrument, from which we can get a lot of astronomical information. By placing and moving some sticks on its surface and looking for their shadows, we can find:
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Besides we can simulate to be at North Pole, or at the Equator and control if the Globe still works in this limit situations. We can also use the Globe by night to control the height of Polar Star and the local latitude.
This is a "Ptolemaic model". The Earth is fixed and the sun moves around it, exactly as it does around the Earth producing changes in light and shadow on the model as on the real planet.
The power of this model is that at the same time we can observe and perceive the same phenomena inside and outside from the Earth. This double point of view helps us to understand our position on the globe and astronomical movements.
3. maps: where does it come from?
The world seen from the southern hemisphere: the higher part has become the lower part
"Fertile perspectives may be revealed
to whom looks common places
from a new point of view"
(L.L.Whith)
In the same way, in the 16° century, during the first travels of Jesuits in China, on the world seen from China East became west. At the same time the world appeared different to Chinese people looking at western maps with respect to their own maps:
"When they saw the world so great and China so small, ignorant people began to deride that representation, but the more clever men, seeing such a beautiful order of parallels and meridians, equinoctial and tropical lines, customs of peoples and the names, believed everything was true."
Father Ricci, Jesuit in Nanchino,16° sec.
4. Totem of directions: where do you want to go?
Let's imagine we can make a trip where we prefer. Let's write our destination on an arrow of paper and put it on a vertical cylinder, exactly orientated towards the direction of that place.
At the end of the work, this was a way to reflect on and test the new knowledge . It appeared that everybody understood that every direction is towards lower points. This was visible by one glance at the totem, on which all the arrows pointed in right directions.
