(CZ) O konstruktivismu ve vyučování matematiky
(EN) Constructivism in the Teaching of Mathematics

Práce autorů hlásících se ke konstruktivismu často vyostřují kritiku dosavadní výuky a hlásají nutnost její reformy v konstruktivistickém duchu. Článek prozkoumává způsoby argumentace, o něž se tvrzení didaktického konstruktivismu opírají. Referuje o kritice na adresu konstruktivismu ze strany některých kognitivních psychologů, která dokazuje, že konstruktivismus nezachází se zjištěními kognitivní psychologie korektně. Vlastní analýza autora vede také ke zpochybnění toho, jak autoři jedné ze zakladatelských prací amerického didaktického konstruktivismu zacházejí s empirickými údaji a s jejich interpretací.

The work of authors identifying their ap-proaches with constructivism often sharpens the edge of criticism of teaching hitherto and asserts a need to reform it in a constructivist spirit. This text explores the modes of argu- mentation on which the claims of didactic constructivism rest.
It leaves epistemological claims to one side and concentrates primarily on the kind of didactic measures proposed by authors identified with constructivism. Constructivism in didactics first and foremost challenges the effectiveness of instructive teaching based on exposition and the explanation of concepts and procedures.
The study of the way in which construc-tivism constructs its criticism of so-called transmissive teaching is based on analysis of a number of articles in one of the founding publications of American constructivism in the field of the didactics of mathematics.
The basic attitude in these articles is on the one hand admiration for the kind of discoveries that children arrive at entirely by themselves, without any sort of help, and the ingenuity, inventiveness and intelligence that they show in this activity, and on the other hand horror and outrage at the sort of nonsense and idiotic expressions of incom-petence of which they are capable under the pressure of the school.
The text follows in detail the modes of argument used. One feature is that instead of presenting properly checked empirical data there is a tendency to one-sided disinterpretation of anecdotal tales taken out of context. Even in the treatment of data obtained and recorded in relatively standard ways in these articles, one can still find a range of improper procedures of interpretation based on a priorisms, subjectivism and over-simplification.
Analysis of the articles provokes doubts over the way the authors of the often cited collection, which is considered one of the fundamental sources of didactic construc-tivism, treat empirical data and its inter-pretation. It also suggests certain internal contradictions in the approach of the more onstructivist authors.
Similar shortcomings can be found in the way constructivism treats the findings of cognitive psychology that it claims are its theoretical starting points. The author mentions the criticism of constructivism put forward by a number of cognitive psychologists who argue that constructivism does not treat the findings of cognitive psychology properly.
In the articles analysed there are also instances gross over-simplification of the treatment of the mental representations of pupils, which are then used as a basis for the idea that during instructive teaching the pupil is condemned to passive reception and memorising.