The article discusses the problem of the influence of digital space and the digital environment on the cognitive processes of primary school children and adolescents. The authors cite and theoretically analyze the characteristics of a personality included in digital space. The contradictions in the ideas about the influence of digital space on the personality are noted: on the one hand, digital space can have a negative impact on the formation of cognitive processes, on the other hand, stimulate their development. The authors empirically investigated such parameters as verbal and logical thinking, behavioral features in the digital environment, attention characteristics and strategies for overcoming stressful situations. It was revealed that the respondents of all groups of the sample have developed classification skills rather than the skills of establishing semantic analogies. The results of the study showed that adolescents with high Internet activity choose impulsive, manipulative and aggressive actions as coping strategies, less often they choose such as seeking social support and cautious steps.