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Familiar notions of shape and space

The videotape produced with students from the first to fourth grade at the Doutor Edmundo de Carvalho State School, the Lapa Experimental School, has been used as a benchmark in teaching geometry. After watching the documentary, teachers got to know better the way and pace with which children between the ages of 7 and 10 build up their notions of space and shape. The tape is part of a teacher training project that the Center for Study and Research into the Teaching of Mathematics, of the Pontifical Catholic University of São Paulo (PUC), developed over three years (until August 1999), under the coordination of professor Tania Maria Mendonça Campos.

She explains: “If you want to be successful in teaching mathematics, you have to start with the familiar notions, to go into the abstract part later”. That is what the videotape deals with. Students from the 1st and 2nd grades do not grasp very much the idea of points of reference, nor of perspective. “If you ask them where their desk is, the child will say it is the one with a red knapsack on top, but without locating a point in the room. If you ask where the bathroom is, the reply will be that you have to go all the way down the corridor, without any precise information about left and right being given”, says Tania.

As time goes by, they acquire a greater capacity for locating themselves. Notions of space, indeed, are worked on in the first stage of the project. “At the outset, the children were encouraged to think about the surroundings of the class-room, then we moved on to the patio, and later on we were already asking them about the way they took to get back home”. In the following stage, the project focused on the teaching of geometrical shapes.

Modeling flat surfaces, peaks and ridges in clay, setting up and taking down cubes and cobblestones, the pupils learned to recognize shapes by the number of faces and points, “although they do not realize the relationships between figures spontaneously”. Last, they learned about flat shapes, and strove to reproduce them in drawings. “They keep the same format, prominence and recess, but give no importance to size.”

The research team will shortly be launching a book on the project, encouraged by the success of the videotape. Besides showing the different stages in learning geometry, the researchers will give tips on the use of the computer as a tool for teaching. FAPESP financed the purchase of these computers and offered grants to the teachers. It was the teachers themselves who chose to work with geometry. “Geometry has been much abandoned over recent years, in favor of algebraic structures. It is understandable that there should be shortcomings in the area.”

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