Background: The researches emphasize the importance of the relationship between psychological hardiness and differentiation of self with cognitive flexibility and self-regulation with academic engagement. Thus, the purpose of this study was to predict cognitive flexibility and academic engagement based on self-regulation, psychological hardiness and differentiation of self by mediating family functioning in students.
Materials and Methods: For this purpose, in a descriptive-correlational study 499 of the second-high school students of Tehran in the academic year, 2019-2020 were selected by random cluster sampling method. The statistical population includes four hundred and ninety students of Tehran who were selected by the multistage cluster random sampling method. Data collection tools included the Cognitive Flexibility Inventory (CFI), The Maslach Burnout Inventory, Self-Regulation Questionnaire, Psychological Hardiness scale, The Differentiation of Self Inventory (DSI), and The McMaster family assessment device. Data were analyzed using the Structural Equation Modeling method using the SPSS software version 20.0 and Amos software version 24.0.
Results: The most frequent were in the 17-year-old group (11th level) with 169 participants and the least abundant belongs to the 18-year-old group (12th level), with 167 participants. The findings showed that there was a significant full effect relationship between self-regulation and academic engagement (p <0.001). According to the results, there was a significant full effect between the differentiation of self with cognitive flexibility (p <0.037). The results showed that there was a significant full effect between self-regulation and academic engagement (p <0.001). 
Conclusion: Based on the results, the students who are at a lower level of differentiation of self may be frustrated by the family's excitement, which leads to emotional breakdown or confusion with others.