The family significantly influences children's development, impacting various aspects such as self-concept, physical and mental health, and social adjustment. Social adjustment, crucial for healthy development, involves adapting to the environment, managing behavior, and building interpersonal relationships. Parenting styles play a pivotal role, with negative styles linked to poor social adjustment. Parental Child-rearing Gender-Role Attitudes (PCGA), reflecting parents' beliefs about gender-appropriate behaviors and activities, are a key component of parenting style. Traditional PCGA, emphasizing gender stereotypes, can negatively affect children's social adjustment, while enlightened attitudes fostering gender equality can promote healthy development. Beyond parental influence, cognitive factors such as children's identity with parents are important mediators, as children interpret and internalize parental attitudes. This study examines how PCGA, through the lens of intergenerational identity, influences children's social adjustment in single- and two-parent families.

Existing research highlights the impact of family structure on children's development, with single-parent children potentially facing challenges in social interaction, academics, and emotional regulation. Studies show that negative parenting attitudes and gender-differentiated parenting contribute to poor social adjustment. The influence of PCGA on children's toy choices, play styles, and career aspirations has been documented, demonstrating how rigid attitudes can limit children's opportunities and social interactions. Conversely, enlightened attitudes emphasizing gender equality promote self-exploration and better social adjustment. Ecological systems theory emphasizes the family's role as a microsystem shaping children's development. Intergenerational transmission theory explains how attitudes are passed from one generation to the next, with children interpreting and reacting to their parents' PCGA. This interplay between PCGA, intergenerational transmission, and children's identity helps understand the development of social adjustment.

This study employed a convenience sampling method, distributing questionnaires to children (aged 14-18) and their parents in 20 Suzhou middle schools. A total of 4663 valid questionnaires were collected (931 single-parent families, 3732 two-parent families). The Parental Child-rearing Gender-Role Attitude (PCGA) Scale assessed parents' and grandparents' attitudes (Cronbach's α = 0.93). The Social Adjustment Scale measured social adjustment in children and parents (Cronbach's α = 0.97). Children's identity with parents regarding PCGA was assessed using a 39-item scale (Chen et al., 2018). Data analysis included descriptive statistics, independent sample t-tests, correlation analysis, and structural equation modeling (SEM) using AMOS 23.0. Harman's single-factor test addressed common method bias. SEM examined the mediating role of children's identity with parents and its variability across family structures. Model fit was evaluated using various indices (CFI, TLI, RMSEA).

Intergenerational analysis showed significant differences in masculinity rearing between grandparents and parents, with grandparents scoring higher. There were no significant differences in femininity rearing. However, both masculinity and femininity rearing scores were significantly higher in two-parent families. Social adjustment scores were also significantly higher in two-parent families for both parents and children. Correlation analysis revealed significant positive correlations between parents' PCGA, children's identity with parents, and children's social adjustment. SEM analysis showed that children's identity with parents mediated the relationship between parents' femininity rearing and children's social adjustment. Multi-group analysis revealed significant differences in the model between single- and two-parent families, specifically in the pathway from parents' masculinity rearing to children's identity with parents. This pathway was significant in single-parent families but not in two-parent families.

The findings support the significant influence of family structure and PCGA on children's social adjustment. The intergenerational differences in PCGA reflect societal shifts towards gender equality. The mediating role of children's identity highlights the importance of parent-child relationships in shaping children's social adjustment. The difference in the mediating model across family structures underscores the unique challenges faced by single-parent families. The higher masculinity rearing in single-parent families may reflect a compensatory strategy to help children cope with the pressures of a non-traditional family structure. The study emphasizes the importance of androgynous gender-role education, open communication, and strong parent-child relationships in promoting healthy social adjustment in children.

This study contributes to a better understanding of the complex interplay between PCGA, intergenerational identity, and children's social adjustment in different family structures. The findings highlight the need for androgynous gender role education, strengthened parent-child communication, and appropriate support for single-parent families to improve children's social adjustment. Future research could investigate a wider range of family structures and utilize longitudinal designs to establish causal relationships more definitively.

The study's limitations include the use of convenience sampling, retrospective self-reporting, and focus on a specific geographic area in China. The cross-sectional design limits the establishment of causal relationships between variables. Future research should address these limitations by employing larger, more diverse samples, longitudinal studies, and multiple data collection methods to enhance the robustness and generalizability of findings.