Cognitive ability, particularly fluid intelligence assessed by matrix reasoning tasks, significantly predict offspring’s logical reasoning development (Anger & Heineck, 2009). Cognitive ability includes fluid intelligence (e.g., memory capacity) and crystallized intelligence (e.g., logical reasoning ability) (Peking University Social Science Survey Center, 2020). Good parenting requires one to know the concept of good parenting, the idea of parenting, the importance of parenting and children’s needs, the components of parenting, and the consequences of parenting (Lanjekar et al., 2022). Teaching methods are necessary to increase the critical thinking disposition and learning competence of students (Oh et al., 2021). Thus, the cognitive ability of parents may be due to the problem-solving methods and logicality demonstrated by parents in front of their children.

Logical reasoning in children’s cognitive development involves forming complete representations of their environment by “filling in” inaccessible information through ruling out known alternatives (Cheng & Kibbe, 2024). For instance, a study recorded the development trajectory of digital knowledge from preschool to primary school, and found that these trajectories significantly predicted children’s later math performance, further highlighting the importance of early cognitive development (Garon-Carrier et al., 2018). Importantly, a higher level of parental education is linked to increased participation in numeracy activities with their children, which positively influences the children’s mathematical skills (Zou et al., 2022). Moreover, the ability of children aged 4–7 years to use exclusion reasoning to track occluded objects is evidence of significant cognitive development, with maternal education being the strongest determining factor Gonz. Moreover, when parents encourage children to engage in strategic and reasoning activities, such as board games, they can significantly improve the children’s logical reasoning skills. In conclusion, parental cognitive ability may influence the development of children’s logical reasoning ability through either direct or indirect ways (Blanch, 2022).

Academic expectation of parents refer to expectations and beliefs regarding their children’s academic achievement, cognitive development, and educational goals (Zhao, 2023). A meta-analysis (Pinquart & Ebeling, 2019) assessed associations between parental educational expectation and child achievement and found that parental expectations predicted change in child achievement in overall achievement, mathematics, language and literacy. When parents communicate positive educational expectation to their children, such as checking homework and staying in contact with teachers (Pinquart & Ebeling, 2019), they influence future-oriented cognitive abilities in children (Zhan et al., 2023). In conclusion, parental academic expectation improve their logical reasoning ability by motivating their children to study harder.

Over the past three decades, a growing number of studies have provided empirical evidence that the home learning environment is an important predictor of differences in children’s academic achievement (Lehrl et al., 2020). Family is the first class of life, with the multiple dimensions of family atmosphere, parent-child interaction and family rules. For instance, as a family environment factor, insufficient parent-child interaction time is associated with lower levels of growth (Waters et al., 2023). Similarly, family learning activities, such as reading, playing, and drawing are correlated with children’s nonverbal reasoning scores and vocabulary scores (Hoyne & Egan, 2022), which underscores the potential role of the home-based learning environment. Also, the family’s digital communication capabilities are significantly related to children’s digital skill learning (Lee et al., 2023).

Parents unable to understand their children’s motivations and who use insults, ridicule, warnings, reminders, threats, and punishments may hamper child development. For instance, these loveless behaviors of parents can lead to children developing self-doubt in terms of emotions and behavior. However, while the family learning environment contributes to early childhood mathematics, no association was found between frequency calculation activities (Stefanie et al., 2021), which suggests a need for further study.

The present study explored parental cognitive ability effects on children’s logical reasoning ability by the double mediating roles of parental academic expectation and family environment in that relationship. Figure 1 presents the conceptual model. We tested the following hypotheses:

H1: Parental cognitive ability is associated with higher children’s logical reasoning ability.

H2: Parental academic expectation plays a mediating role in the relationship between parental cognitive ability and children’s logical reasoning ability for higher levels of children’s reasoning.

H2 (a): Parental cognitive ability is associated with parental academic expectation of children.

H2 (b): Parental academic expectation is associated with children’s logical reasoning ability.

H3: Family environment plays a mediating role in the relationship between parental cognitive ability and children’s logical reasoning ability.

H3 (a): Parental cognitive ability is associated with a pro-learning family environment.

H3 (b): Pro-learning family environment is associated with higher children’s logical reasoning ability.

The data for this study’s results are the 2020 China Family Panel Studies (CFPS) The sample comprised of 1491 children (girls ratio = 53.78%; average grade = 6.023 years, school year standard deviation = 1.825 years). Table 1 reports the study sample demographics. By gender grouping, male (n = 790) comprised 52.98% of the sample. The number of students from the primary school grades was 870, accounting for 58.35%. Students from the western region (n = 524) accounted for 35.15% of the sample. Parents (n = 764) were part of the CFPS (females = 49.08%, mean age = 42 years, SD = 5.2 years).

Participants reported the sociodemographic information of the children, including gender, grade, household registration, and region of residence. The children completed a logical reasoning ability test (serial test items), and parents completed a cognitive ability test (serial test items, memory test items). The parents also answered questions about their academic expectations for their children. These measures and items were as follows.

The China Family Panel Studies (CFPS) database of 2020 is publicly available. The database samples are from 162 counties in 25 provinces/municipalities/autonomous regions. Since publicly available, there was no need for ethics approval to utilize these data for study.

Based on the above theoretical analysis of parental cognitive ability, academic expectation, family environment and children’s logical reasoning ability, this paper introduces the OLS model for the analysis. The basic regression model is constructed as follows: (1) CLRAi=β0+β1PCAi+βicontroli+δz+εi (2) CLRAi=β0+β1PCAi+β7AEi+β9FEi+βicontroli+δz+εi

To further investigate the indirect effects of parental cognitive ability, academic expectation, family environment and children’s logical reasoning ability, the mediation effect model was established as follows: (3) AEi=β0+β1PCAi+βicontroli+δz+εi (4) FEi=β0+β1PCAi+βicontroli+δz+εi

In the above expression, i represents different individuals, representing the collection of control variables, which is the intercept term, representing the random error term, representing the province fixed effect.

The correlation analysis of the four variables of parental cognitive ability, academic expectation, family environment and children’s logical reasoning ability found significant pairwise correlations among the four variables (Table 2).

As in Table 3, parental cognitive ability had a positive impact on children’s logical ability, and which was not limited by gender and household registration, but grade was significantly positively correlated with children’s logical reasoning ability. From the regression results of the whole variable in column 2, the coefficient of parental cognitive ability score (PCA) was 0.596, and this coefficient was significant at 1‰; this indicates that parental cognitive ability score has a significant positive promotion effect on children’s logical reasoning ability, in support of Hypothesis 1.

Among the mediation variables, the coefficient for academic expectation (AE) was 0.014 (p < 0.01) The coefficient of family environment (FE) was 0.516 (p < 0.01). These findings indicate a significant positive correlation between academic expectation and the logical reasoning ability of children (supporting Hypothesis 2(b)), and also for the family environment variable (supporting Hypothesis 3(b)).

As in Table 4, the coefficient of parental cognitive ability (PCA) was 0.634 to suggest that parental cognitive ability can promote children’s logical reasoning ability by improving their academic expectation, supporting Hypothesis 2. Moreover, the coefficient of parental cognitive ability (PCA) is 0.054 (p < 0.01), suggesting that parental cognitive ability can promote children’s logical reasoning ability by improving the family environment, supporting Hypothesis 3.

The results of this study have far-reaching implications for education, offering practical strategies for schools, parents, and policymakers to enhance children’s logical reasoning ability. Firstly, from the school education perspective, schools should value the critical role of parents’ cognitive levels in the development of children’s logical reasoning ability. By organizing parent workshops and school-family cooperation projects, schools can offer strategies and tools to assist parents in more effectively participating in their children’s learning journey (Lehrl et al., 2020; Zeng, 2024). Moreover, schools can encourage interactive games between parents and children to enhance the children’s thinking skills.

Secondly, on the home education front, parents should actively utilize available educational resources, such as reading educational books and engaging in educational activities, to improve their cognitive ability. As the first teachers of their children, parents should create a conducive learning environment at home, provide necessary learning materials, and maintain a quiet and tidy study space (Niklas et al., 2018). Encouraging children to study diligently to achieve excellent results is also essential.

Thirdly, from the social support perspective, there should be a commitment to providing educational resources and support, especially for low-income families, to help parents improve their cognitive ability (Miller & Eakin, 2011). Concurrently, policies should be established and implemented to eliminate the unequal impact of social factors like gender and household registration background on children’s educational opportunities, thereby promoting the development of logical reasoning skills in all children within an equitable environment.

The cross-sectional design of this study limits the determination of causality. Future research should adopt a longitudinal design, incorporating multi-wave data to reveal the long-term dynamics among the study variables. The self-report measure used for this study has social desirability limitations, and needs to be backed by direct observational data in future studies. Also future studies should pay attention to children’s individual differences, such as self-efficacy and learning motivation, which significantly affect logical reasoning ability.