The new generation of primary school teachers in Italy is prepared in a special University course by following a specific curriculum that include science education. The curriculum is complex and multifaceted, with interplay between theoretical courses, laboratory activities and teaching practice starting from the first year of the course. The old generation, that of teachers currently in service, has been prepared in a special section of the high-school and has received a preparation oriented to methodology rather than to disciplines. Most teacher in Italy have very little grounding in science and many students essentially never had any science teaching.
The objective of my work as a teacher under the Programme “Skills for Development” (a National Operational Programme financed through the European Social Fund) was to try to recover the gap in knowledge of science teachers at this time employed by primary schools. This experience took place in six primary schools (with an average of 20 teachers per school) with the aim of promote a strong integration between the development of knowledge and practical activities and to help teachers acquire experience of what a science experiment is. These activities provided teachers with available objects of every day life they could use in the class-room and with the knowledge to back them up.
The inspiration for experimental activities came from following the historical development of knowledge about some fundamental phenomena, their first qualitatively explanations and the subsequent and more quantitative analysis.
Below are two examples.
Rainbows on a disk-like raindrop
The study of raimbow is the study of the deflection of light rays by a spherical drop. Even in the textbooks of primary school children are said to the rainbow is formed by light from the sun hitting a small water droplets suspended in the air. Each individual droplet of water acts as a tiny prism which both disperses the light and reflects it back to your eye. The rainbow we normally see is called the primary rainbow and is produced by one internal reflection within the drop while a double reflection yields the secondary rainbow. It is a problem in optics that was first clearly discussed by Rene Descartes in 1637. A simple schematic representation for a single primary rainbow reflection inside the drop of water is reproduced in the figure: light is refracted as it enters the raindrop, then how it is reflected by the internal, curved, mirror-like surface of the raindrop, and finally how it is refracted as it emerges from the drop. The maximum deflection does not depend on radius R of the sphere, but only on the refractive index. As the index of refraction of water varies depending on the color, the angle of the light emitting from the drop changes slightly depending on the color. The angle for maximum deflection for light in a drop of water is between 40° and 42°. Under 40° all the colors are refracted, and then the white light remains white, while for higher angles of 42° light can not get out of the drop.
The following is a simple and costless "demonstrator", a small experiment to be done in class with little effort and success. The materials are those that one can easily find at home.
· a transparent plastic lid of a container for CD or DVD
· a torch
· a screen (a piece of rigid paper, a wall, …)
· a thick brown sheet of paper
1. Construct, with thick brown paper, a cone with a small hole in the top 2 mm high and with the base slightly larger than the opening of the torch.
2. Place the paper cone on the torch.
3. Fill the lids of water (you can also add a little white tempera).
4. Point the torch on the outer edge of the lid.
To see the light that propagates in the water it needs a thin, collimated beam of light. But this is hard to find at home as well as at school. Instead of a pointer that generates an intense white beam you can build the apparatus described above: the light that comes out of a hole of few mm in diameter placed at the top of the cone is more than sufficient to achieve the desired effect.
The first thing you may notice is the deviation that the light undergoes when passing from air to different fluid and vice versa. The game will then be to find the right angle to create the total reflection within the container. When you are able to do, the light can be cast on a wall or a distant screen, placed in the right position, to see the colors. It is clear that the rainbow is a cooperative effect of many raindrops and that our result is the best we can do with our “apparatus”.
Instead of the lid you can use a transparent spherical container (e.g. one container for fish or a flask) but is a little more difficult to find and use. In any case, since the light path is to be made in a plane passing through the center of the sphere (otherwise everything gets complicated) a cylindrical vessel is enough.
Making a spherical drop
Archimedes of Syracuse, who lived in the third century BC, enunciated in the well-known work on floating bodies the celebrated principle that a body immersed in a fluid received a boost from the bottom up of intensity of weight of a mass of fluid with volume equal to that of the submerged part of the body. So the weight of a body immersed (partially or totally) is not what you measure out liquid, but the weight of the volume of fluid displaced by the submerged part. In a situation of equilibrium, the weight force is balanced by the “buoyancy”, the upward force caused by fluid pressure. This is true not only for solids but also for a fluid immersed in another fluid. Oil sinks in alcohol but floats in water. In agreement with the Archimedes’ principle, in a density-matched water/alcohol mixture, oil is subject to internal attractive forces only and take its natural shape, that of a sphere! This is part of the experiment published between 1863 and 1865 by Joseph Plateau that concerns the more general problem of a spinning liquid drop.
· A glass
· A teaspoon
· Alcohol, oil, water
1. Place a drop of oil in a glass.
2. Fill the glass of alcohol
3. Slowly add a little water with the help of a teaspoon (very carefully, so that the water drips down the walls of the glass)
When we add water to the alcohol, the oil in the glass will begin to swell and when the water will be sufficient will rise from the glass in one or more spherical droplets that remain suspended, wrapped in another liquid (the right alcohol/water mixture) with the approximately same density.
H. M. Nussenzweig (1977) The Theory of the Rainbow. Scientific American 236: 116-127
J. Plateau (1873) Statique experimentale et theorique des liquides soumis aux seules forces moleculaires, Gauthier-Villars, Paris, France.
The Mathematics of Rainbows at the The Rainbow Lab.
"The optics of a water drop" of Philip Laven (experimental data for the refractive index of water as a function of wavelength);
"Unweaving the Rainbow" from The Wolfram Demonstrations Project;
"Light Refraction with a Waterdrop" from The Wolfram Demonstrations Project;
The apparatus for Plateau's experiment.