Examples
Example 1. Teachers sometimes teach children that “a parallelo-
gram is a quadrilateral with two sets of parallel sides facing each
other” and then distribute printouts showing a parallelogram, say-
ing “What kinds of characteristics does this quadrilateral have?”
and “Measure the length of the sides, compare the angles, and
examine the properties.” Once the students are finished with their
examination, the teacher will explain the properties, stating: “As
you can see, in a parallelogram, the lengths of the facing sides are
equal, as are the facing angles.” This type of teaching is absolutely
inadequate.
The reason for this inadequacy is that the above properties
are not limited to a single parallelogram, but rather to the proper-
ties of all parallelograms. The children must be made to consider
as many different parallelograms as possible, so that they see these