A contribution to tackling the problem of arithmetical facts in the elementary grades of the Basic Nine-Year School is one of the contributions elaborated by the author on the basis of a more extensive research into a more general question concerning instruction in the elementary grades of the primary stage of the Basic Nine Year School. The author makes a partial comparison of the results of a research into the difficulty of arithmetical facts carried out by V. Příhoda in 1931 with the results of his own research made in 1957. In so doing he shows that the sequence of facts considered by V. Příhoda to have a psychological basis does not substantially differ from the sequence that can be arrived at by means of a logical analysis. At the same time the author makes a statistical analysis of errors in addition and points out that these errors are very seldom entirely fortuitous. Besides he finds the connection between the number of errors and the speed of counting. As regards the method of research applied, the author shows that collective investigations together with quantitative as well as qualitative analyses of results may be very well applied in didactic researches. Of great importance, however, is the methodological approach to the problems investigated, for a different methodological approach may result in a different interpretation of the results of the research.