Above all the study deals with the solvation of the problem of acceleration of the children’s development in the area of mathematical skills and habits from a long-time view. To solve this problem two of the author’s researches have been made use of, and that in the 2 nd —5th forms of the basic schools in the years 1957 and 1983, in comparison with an analoggical research carried out by Václav Příhoda in 1931. The researches investigated the mathematical connections of adding and the substraction without passing over ten (2 nd form), and with passing over ten (3rd form), the elementary connections of the multiplication (4th form) and of the division (5th form). The analysis of the research — expressesd by the number of mistakes commited by the investigated learners in the area of those investigated connections (at least 1100 pupils in individual forms) confirmed unambiguously a gradual increasing of the level of acquiring these connections in the time periods 1931-1957-1983. The improvement manifestated itself in an expressive gradual decreasing of the number of mistakes. The sequence of connections according to the number of mistakes in individual etaps was found relatively stable; there were some exceptions there which can be explained by the change of methodological processes. Another task of the study was to contribute to the solvation of the problem whether the level of the numerical counting skills and habits has not been weekened on the behalf of the emphasis put on the learners’ logical thinking development due to the sets basis of teching mathematics at the basic school. The research has confirmed that in the investigated area of the elementary numerical connections no decreasing of the level appeared, even some improvement could be stated. The methodology applied here does not allow, however, to distinguish the influence of a changed conception from general trends of acceleration in the children’s development.