Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as difficulties in counting as well as developmental dyscalculia. Reported prevalence rate for this problem in general population is 6%-10%. The most common difficulties in counting are: difficulties in logic, difficulties in planning, perseverance of inappropriate (responses) procedures and poor understanding of arithmetic operations. This paper aims to identify the influence of assessed arithmetic skills and to clarify to what extent the assessed cognitive skills affect each other in children with difficulties in counting. The relations between the level of working memory and acquiring of arithmetic skills, between the attention and the conceptual observation, and also between planning ability and acquiring of arithmetic skills have been assessed within the study goals. The tested sample consists of 84 third-grade pupils of general population divided into an experimental and a control group. The subjects of the experimental group were chosen according to the discrepancy between general intellectual competences, general achievement at school and success in the filed of mathematics expressed by school marks. Following tests of neuropsychological test battery were used: (1) Taylor's word list-Rey test; and (2) Trail-making-TMTa/b test. The results have been analyzed regarding qualitative test results, as well as the aspect of previous knowledge in the studies dealing with dyscalculia. The results of the studies indicate that there is statistically a significant difference in effectiveness of assessed cognitive characteristics of working memory, attention and planning abilities between experimental and control group (sample) (p less than 0.01). The subjects of experimental group, i.e., those with difficulties in counting and the results given, show that there is poor effectiveness but positive connection of moderate intensity among assessed cognitive characteristics (p less than 0.01). (Contains 4 tables and 4 figures.)