*2.2. Measures and Procedure*

An online survey was administered from June to October 2020. Participants were recruited through online advertisements on websites and social media (Facebook and WhatsApp) via a snowball sampling strategy.

All participants were informed about the aims and procedures of the study by a brief description of the study; they gave their informed consent (via the survey) before filling out the survey. Participation was voluntary and anonymous. The survey took about 20–25 min to complete.

The study was conducted in accordance with the Declaration of Helsinki and was approved by the Bioethics Committee of the University of Palermo (no. 13/2020).

Collected parental sociodemographic data were: gender, age, nationality, region, marital status, level of education, work regimen before and during COVID-19 pandemic, habits before and during the COVID-19 pandemic, social relations after the COVID-19 emergency, the use of social networks, psychological support needs during the COVID-19 pandemic, discomfort during the COVID-19 emergency, and ideas relating to the process of the pandemic. Concerning the children, data included gender, birth order, pathologies, or disabilities.

Parental distress was measured by the balance between risks and resources (BR2; [52]). It was a self-report questionnaire. Specifically, the BR2 instrument reliably measured parental balance between risks (parental distress-enhancing factors) and resources (parental distress alleviating factors). This tool was composed of 39 bipolar items, in which parents were asked to read carefully each sentence and express their degree of agreement, using a 10-point answer scale of values ranging from −5 to +5. Of these, 14 items defined common antecedents as risk factors, indicating predictors of job and parental burnout (e.g., "It is difficult for me to reconcile my family life and my professional life") and 25 items defined specific antecedents showing aspects strictly related to parental burnout (e.g., "Due to my parenting responsibilities, I can never find time for myself"). The total score ranged between −195 and +195. A positive score revealed the prevalence of parental resources, whereas a negative score indicated the risk of parental burnout; the "0" scores revealed equal levels of risks and resources. The original version was translated and adapted to the Italian context with the author's permission. The original administration procedure was used. The results of the EFA showed that the principal component analysis identified two factors that explained the 47.21% variance. The mean sampling adequacy (Bartlett's test) was 6889.42 (*p* < 0.001) and the Kaiser–Meyer–Olkin (KMO) was 0.917.

The internal consistency was verified through the Cronbach's Alpha test, given that the Cronbach's Alpha reliability is considered within an acceptable range, of around 0.70. The reliability values were of α = 0.96 for the global scale, α = 0.89 for the common antecedents subscale, and α = 0.94 for the specific antecedents subscale.

The parental perception of children's EF was measured through the executive functioning self-report (EF-SR) [54]. This was composed of 20 items, conceptualizing, as a system of perceptions, about their child's cognitive abilities in the management of environmental conditions, such as working memory (e.g., "My child is not good at remembering sequences of items, for example, numbers or words"), attention (e.g., "My child has difficulty ignoring extraneous thoughts when he/she performs a task"), shifting (e.g., "My child has difficulty moving from one task to another (for example from a math task to a science task"), planning (e.g., "My child has troubles performing tasks that have more steps") and inhibitory control (e.g., "My child has difficulty with concentration while working in the classroom"). All items used a four-point Likert scale ranging from 1 (always) to 4 (never) to quantify the frequency of use. Higher scores indicated minor difficulties on EF tasks.

A total score (from 20 to 80) and sub-scores (from 4 to 16) for each area were obtained. The reliability values were of α = 0.95 for the global scale, α = 0.87 for the working memory subscale, α = 0.80 for the attention subscale, α = 0.86 for the shifting subscale, α = 0.76 for the planning subscale, α = 0.79 for the inhibitory control subscale.
