Page: 332-338 Author: Kuřina, F. Key words: understandig of mathematics, problem solving, transmission of knowledge, construction of knowledge, thinking, application
The main goal of mathematics education - the development of thinking -and the main activity of school practice - the solving of problems - are compared. The traditional method of problem-solving consisting of four parts (analysis, construction, proof and discussion) is compared with Hadamard's conception of four chronological stages in the process of creation: preparation, incubation, illumination and verification. The transmission of new knowledge by means of lectures leads only to the reproduction of information. The alternative, i.e. construction of knowledge in the minds of students, is promising but difficult to put into practice. It offers a way of getting over what Felix Klein and Jaroslav Šedivý have formulated as the problem of two kinds of forgetting (connected with the beginning of university studies and the beginning of teaching practice).