Do we use fuzzy sets in early school education?
Abstract
Fuzzy sets are most often associated with very complicated, contemporary calculations in mathematics and are the basis of functioning of the most modern devices, such as space probes or unmanned airplanes and submarines. Thus, may we expect the elements of these sets in pre-school or early school education? However, the precise analysis of both educational cycles entitles us to the statement that the elements of fuzzy sets help with the interpretation of not only various areas of mathematics, but also with one of physics, biology and linguistics, and in the integrated education they support the natural science-social education connected with the circles of nearness (house, the nearest landscape, my town, family area), the Polish language education together with art and culture education and mathematical education. In the integrated education the teacher and students use both the measurable undefined values, which we know from everyday Polish language, for example, wysoki / niski, duży / mały, gruby / chudy, szybki / wolny, ciężki / lekki, ładny / brzydki, as well as, mathematical operations with symbols >; < ‘higher than’, ‘lower than’ e.g. x>y, y<x, which mean the comparison of values where lack of clarity is connected with relational reading ipso facto of the not fully defined symbols, while the calculations are connected with the value of equality / equal number. We have to do with a different status of those two operations: they are either included in the theory of multiplicity (in bivalent logic), the classic definition of truth understood as the agreement between words and reality and the objective theory of interpretation of reality or, on the other hand, they are included in the polyvalent logic accepting the third value – possibility, beyond the classic definition of truth, and the value of possibility itself lies beyond the categories of: truth (1) and falsity (0). The comparison of the values is connected with blurring/lack of clarity used in reading of signs x>y, y<x. The measurable undefined values, such as, big / small, fast / slowly, often appear in mathematical tasks when teachers present the new issue to the children and then they explain it in the following way, for instance: the train was going at 140 km/h/ (the measurable defined value). The relational symbols>; <‘higher than’, ‘lower than’ facilitate the children’s abstract thinking and influence, in a creative way, the development of the categories of comparison, abstraction and generalization.References
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