(CZ) Tři pokusy řešit neřešitelné
(EN) Three Attempts to Tackle the Insoluble

Stať poukazuje na skutečnost, že pedagogika si někdy vytyčuje nesplnitelné cíle a ilustruje tuto myšlenku třemi zcela odlišnými přístupy k vyučování matematice. První, jehož původcem je americký psycholog Jerome S. Bruner, vyústil v celosvětové hnutí u nás nazývané modernizace vyučování matematice. Přes velmi promyšlenou kurikulární koncepci bylo toto pojetí neúspěšné. Pravým opakem tohoto přístupu jsou snahy amerického matematika Paula Lockharta, který chápe matematiku jako umění, navrhuje osnovy zrušit a pěstovat lidské stránky matematiky. Třetí pojednávané pojetí je singapurské chápání matematiky jako řešení úloh s výrazným pracovním nasazením učitelů i žáků. Matematické vzdělávání by si mělo vzít ze zmíněných přístupů poučení, pedagogika by měla přitom hlouběji reflektovat podmínky konkrétní práce učitelů a žáků ve třídách.

The article argues that educational theory sometimes sets itself impossible goals (for example in the Project America 2000: An Educational Strategy) and illustrates this claim with reference to three completely di-fferent approaches to teaching mathematics. The first is the American psychologist Jerome Bruner‘s conception of school mathematics as a structure. The international movement started in 1960 by his book The Process of Education proved totally unsuccessful. The reason for the failure was the unhistorical set and logical basis of school mathematics and lack of understanding by many teachers. The complete opposite to this approach is represented by the efforts of the American mathematician Paul Lockhart, who sees ma-thematics as an art. In his view to do mathe-matics is to engage in an act of discovery and conjecture, intuition and inspiration, and so mathematics curriculum does not need to be reformed, but to be scrapped. According to this view there is no need to bend over backwards to give mathematics relevance; it has relevance in the same way that any art does - that of being a meaningful human experience. Teaching is not about informa-tion, but about having an honest intellectual relationship with students. Mathematics is about problems, and problem must be made the focus of the student‘s mathematical life. Lockhart‘s conception is appealing but in the author‘s opinion unrealistic. The third approach is the Singapore mathematics curriculum framework with mathematics understood as the solving of tasks with an emphasis on intense working commitment by teachers and students. The elements of this conception are concepts (numerical, algebraic, geometrical, statistical, proba-bilistic and analytical), skills (numerical calculation, algebraic manipulation, spatial visualisation, data analysis, easurment, use of mathematical tools, estimation), processes (reasoning, communicaton and connections, thinking skills and heuristics, applications and modelling), attitudes and metacogni-tions. Mathematical teaching should learn something from all these approaches, with educational theory geared to deeper reflexive consideration of the conditions of the concrete work of teachers and pupils in classes.