The study explores the relationship between the strategies of parental involvement in education and the ability of schoolchildren to proactive behavior (agency), which allows them to adapt more successfully to changing external conditions. The data was obtained through the Internet survey of students engaged in extracurricular activities about the transition to remote formats of education during the pandemic and lockdown. The latent profile analysis was applied to better understand the differences between respondents in terms of changes in interaction with parents. The results showed that the joint activity of children and parents may be associated with the shaping of the so-called ‘cooperative agency’, whereas the strategy (related to giving more freedom to children, along with the facilitation support) is associated with other behavioral characteristics, which might be called ‘autonomous agency.’ We also found that the lack of interaction with parents, as well as strict control by parents, do not contribute to successful adaptation to the crisis conditions, which might be due to the lack of support of a child’s proactive behavior. It is also shown that the practice of discussing with parents the prospects of participation in educational and research projects is crucial both for shaping proactive behavior and also for expanding the perceived opportunities in crisis periods.