Math achievements in school are a strong predictor of later academic outcomes (Reddy et al., 2012), career aspirations (Shapka et al., 2006), choice of Science, Technology, Engineering, and Mathematics (STEM) professions (Wang, 2013), retention in STEM education (Leuwerke et al., 2004), and socio-economic status in adulthood (Ritchie and Bates, 2013). Yet, depending on population and diagnostic criteria, from 4 to 15% of schoolchildren consistently experience math difficulties (Wang et al., 2024; Jabeen et al., 2021; Morsanyi et al., 2018; Lewis et al., 1994). Moreover, math achievements are shown to decline with age (Gottfried et al., 2007) and be particularly low in girls (Ellison and Swanson, 2010; Else-Quest et al., 2010; Cimpian et al., 2016; Reilly et al., 2015), immigrants (Huang, 2000; Martin et al., 2012), children from poor socio-economic backgrounds (Hopkins, 2005; Short and McLean, 2023; Baird, 2012; Muskens et al., 2024; Jordan and Levine, 2009), and rural living areas (Ababneh and Kodippili, 2020; Butt and Dogar, 2014; Tayyaba, 2012; Betancur et al., 2023). In particular, the math achievement gap between rural and urban regions was observed in 14 countries (Williams, 2005), and it has widened over time (Graham and Provost, 2012). Among possible reasons for this gap are low value placed on math and academic achievement in rural areas (Reeves, 2012), as well as lack of economic (Williams, 2005) and environmental (Betancur et al., 2023; Irvin et al., 2017; Graham and Provost, 2012) resources.

A variety of cognitive, socio-emotional, and socio-demographic factors explain individual and group differences in math achievements (see Myers et al., 2017; Moustafa et al., 2017; Robson et al., 2020; Jordan and Levine, 2009, for review and meta-analyses).

Math anxiety, defined as a tendency to feel tension and fear while solving math tasks, is one of the key socio-emotional traits explaining variance in math achievements. Several studies pointed out the negative association between math anxiety and math achievements across different ages, genders, and cultural contexts (see Ma, 1999; Zhang et al., 2019; Barroso et al., 2021; Caviola et al., 2021 for meta-analysis; Chang and Beilock, 2016; Dowker et al., 2016; Foley et al., 2017; Ramirez et al., 2018; Lau et al., 2024 for a review). Two prominent theories explain the nature of the relationship between math performance and math anxiety: the “Reduced Competence Theory” developed by Ramirez et al. (2018) suggests that math anxiety is triggered by initial low math ability, while the Processing Efficiency Theory developed by Eysenck and Calvo (1992) claims that math anxiety hinders math performance by overloading cognitive resources, in particular working memory (Lau et al., 2024; Dowker et al., 2016; Foley et al., 2017). As both theories are supported by empirical evidence, a bidirectional association between math achievements and math anxiety was proposed (Carey et al., 2016). Recent longitudinal studies provide empirical support for the bidirectional association between math achievement and math anxiety, implying that both mechanisms work simultaneously, causing a vicious circle (Szczygieł et al., 2024; Aldrup et al., 2019; Gunderson et al., 2017).

The link between math performance and math anxiety is related to both individual and socio-cultural factors (Chang and Beilock, 2016; Luttenberger et al., 2018). Numerous researchers are dedicated to revealing the factors that moderate the relationship between math achievement and math anxiety, yet have yielded controversial results. Thus, the link between math anxiety and math achievements was shown to be stronger for Asian students in comparison with their European peers (Zhang et al., 2019). Conversely, another study (Lee, 2009) reveals that in some Asian countries students demonstrate high math achievements despite high math anxiety, whereas in European countries high math achievements are linked to low math anxiety. Interestingly, one study (Kalaycioğlu, 2015) reveals an association between math anxiety and math achievements in Turkey, Greece, and the USA, but not in Hong Kong, England, or the Netherlands. Some studies show that the association between math anxiety and math achievement is especially pronounced in children with high working memory (Ramirez et al., 2013, 2016), whereas others demonstrate that children with high math anxiety and low working memory are particularly vulnerable to poor performance in math (Soltanlou et al., 2019; Doz et al., 2024). Although there is a lack of studies on math anxiety differences in rural and urban populations, we assume that rural children would experience higher levels of math anxiety, as it was found to be associated with poor math performance and lower value of math (Wang et al., 2021), in particular for Chinese schoolchildren (Long and Li, 2024; Fu, 2025).

Among cognitive factors, general fluid intelligence is strongly associated with math performance (Semeraro et al., 2023; Romero et al., 2024; Blanch, 2015; McGrew and Wendling, 2010; Peng et al., 2019; Primi et al., 2010; Ren et al., 2015; Cormier et al., 2017; Green et al., 2017; Peng et al., 2019), presumably because math requires more abstract thinking than other school subjects (Romero et al., 2024), and due to the high role of fluid intelligence in the development of basic arithmetic skills, number line estimation (Hornung et al., 2014) and the ability to consider multiple relations between different variables (Miller Singley and Bunge, 2014). Moreover, recent genetic and neuroimaging findings show shared neurobiological underpinnings of fluid intelligence and mathematical performance (for review, see Shuang and Mengmeng, 2022). In particular, nonverbal intelligence predicts math achievement in primary (Tikhomirova et al., 2017), secondary (Bouchefra et al., 2022), and high (Tikhomirova et al., 2016) school. The link is especially strong for achievements on high-stakes exams (Tikhomirova et al., 2016) and complex tasks (Peng et al., 2019), as well as for older children and children from families with high SES (Peng et al., 2019). Furthermore, nonverbal intelligence has been found to predict children’s math performance through the mediation of number sense and basic arithmetic ability (Zhou et al., 2022).

Regarding socio-demographic factors, parental, especially maternal education is strongly linked with children’s math performance (Bellon et al., 2022) due to both genetic (Hart et al., 2009) and environmental factors, such as learning materials, stimulation, parental responsiveness (Zadeh et al., 2010), parenting style (Macmull and Ashkenazi, 2019), parental math anxiety (Maloney et al., 2015), and early exposure to an enriched environment at home (Slusser et al., 2018; Zadeh et al., 2010; Blums et al., 2016). The effect of maternal education was also observed in the Chinese cultural context. Specifically, high school students whose mothers hold a graduate degree demonstrate significantly higher math scores than those whose mothers have no formal education (Fan, 2024).

Gender is also linked with math performance, as boys typically outperform girls in math (Lu et al., 2023; Hyde and Mertz, 2009). Recent Chinese studies demonstrate that boys show notably better learning attitudes toward math than girls (Yang et al., 2024) and have higher math achievements (Wang et al., 2022). Due to the prime role of sociocultural factors, such as gender equality and social expectations (Hyde and Mertz, 2009), the magnitude of the link varies across different cultural contexts (Lu et al., 2023). Based on that evidence, we expect that gender differences will be more pronounced in rural contexts, as they are typically associated with more traditional values and roles (Dunstan et al., 2021).

Age is another socio-demographic factor that is strongly linked to math achievements, as math achievements tend to decline as children grow up, in particular during the transition from primary to secondary school. Older students value mathematics less, have a less positive self-concept in mathematics, use learning strategies less frequently, and achieve lower mathematics performance compared to younger students (Rončević Zubković et al., 2021). Moreover, age moderates the association with gender and math, as the gender gap in math achievements and math anxiety widens over time (Rončević Zubković et al., 2021).

Overall, studies suggest an intricate interplay between math achievements, math anxiety, cognitive abilities, and socio-demographic factors. However, few papers are focused on cultural differences in that complex association. In particular, the specificity of that interplay for rural and urban living areas remains largely unexplored. The present study aims to investigate the association between math performance, nonverbal intelligence, math anxiety, maternal education, gender, and age separately for urban and rural areas of China. In particular, four objectives guided the study:

In line with these objectives, the following hypotheses were formulated:

Table 1 summarizes the socio-demographic description of rural and urban subsamples of Chinese schoolchildren. Overall, both subsamples have similar gender structures (49% females in urban areas and 50% females in rural areas), whereas urban children are younger (t-stat = −34.9, p-value < 0.001) than their rural peers. Notably, the youngest age group (10–11 years old) is underrepresented in the rural subsample dramatically (7%), while the oldest group (14–15 years old) comprises more than half of the subsample. Conversely, in the urban subsample, only 9% of children fall in the oldest age group. The sample difference in age structure reflects the corresponding population difference evoked by the recent decrease in the birth rate in rural Chinese areas. As would be expected, urban schoolchildren come from more educated families. 50% of rural mothers do not complete high school, while among urban mothers, the proportion of the lowest educational level is less than 25%.

The purpose of the study was to investigate the interplay among socio-demographic variables, math anxiety, and nonverbal intelligence, and to examine their association with math achievement among schoolchildren in urban and rural areas of China. Overall, despite no differences in nonverbal intelligence and subtle differences in math anxiety between rural and urban areas, urban schoolchildren dramatically outperform their rural counterparts in math, with the highest effect size of almost 1 standard deviation for the oldest age group. In previous studies, the math achievement gap between urban and rural areas was also observed for Jordanian (Ababneh and Kodippili, 2020), Peruvian, Indian, Vietnamese (Betancur et al., 2023), Pakistani (Butt and Dogar, 2014; Tayyaba, 2012), and Chinese (Wang et al., 2020) schoolchildren. A review (Williams, 2005) shows that the urban–rural math achievement gap is observed across 14 countries out of 24. Possible explanations include lower family SES (Williams, 2005), lower academic commitment and career aspirations (Reeves, 2012), the lack of access to early childhood education (Betancur et al., 2023) and to advanced math courses (Irvin et al., 2017), the lack of federal funding and high-quality teachers in rural areas (Graham and Provost, 2012), as well as better school environment in big cities, such as higher emphasis on achievements and discipline (Ababneh and Kodippili, 2020). Moreover, lower quality of rural schools may lead to a negative perception of the school environment by rural schoolchildren, resulting in school refusal and underachievement (Sorrenti et al., 2024). Lack of instructional quality in rural schools may also hinder achievement motivation in math (Scherer and Nilsen, 2016).

In both cultural contexts, nonverbal intelligence shows a moderate positive association with math achievement, with no substantial difference in magnitude between rural and urban schoolchildren (r = 0.21 and r = 0.16, respectively). These results are consistent with previous findings on the association between RPM score and math achievement in schoolchildren in Eastern Morocco (r = 0.381; Bouchefra et al., 2022) and with a meta-analysis showing r = 0.41 between fluid intelligence and math achievement across different studies (Peng et al., 2019). On the other hand, math anxiety shows a moderate negative association with math achievement, with no differences for rural and urban areas (r = −0.32 and r = −0.37, respectively). Similar results were obtained in previous studies. Thus, two recent meta-analyses (Ulum and Küçükdanaci, 2022; Barroso et al., 2021) provide the estimates of r = −0.42 and r = −0.28, respectively. A negative link between math anxiety and math performance was also observed in the Chinese cultural context (Fu, 2025). Maternal education was shown to be positively yet weakly associated with math achievements in urban, but not rural, schoolchildren. The absence of the maternal education effect may be partially explained by the underrepresentation of parents with higher education in rural areas or inaccurate measurement. Furthermore, one previous study reports a stronger link between family SES and math achievements for urban schoolchildren (Miller et al., 2013). Presumably, in a rural context, even educated parents do not have enough time, resources, or aspiration to provide their children with a stimulating learning environment at home, leading to their inability to improve the math achievements of their offspring.

In rural areas, math achievement deteriorates dramatically with age, whereas in urban China, this deterioration is less pronounced, leading to a widening of the achievement gap over time. The continuous enlargement of the rural/urban gap was observed in a previous study on US schoolchildren (Graham and Provost, 2012). The low quality of rural schools and their lack of monetary and human resources may contribute to such a dynamic (Graham and Provost, 2012), as well as lower achievement aspirations in the rural population (Reeves, 2012).

Notably, high nonverbal intelligence and low or medium math anxiety are negatively associated with deterioration of math achievement with age in urban populations. Thus, there is a weaker association between achievement and age in subgroups of urban schoolchildren with high nonverbal intelligence or low or medium math anxiety, whereas a stronger negative association is observed for the rest. Low math anxiety is positively associated with higher math-specific grit (i.e., readiness to put efforts into math learning) (Yu et al., 2021) and enjoyment of mathematics (Dowker et al., 2016). On the other hand, high math anxiety leads to avoidance of math (Ashcraft, 2002), procrastination in performing math work (Yu et al., 2021), and an “affective drop” (Ashcraft and Moore, 2009). Presumably, children with low math anxiety are more likely to maintain aspiration for high math achievements, which hinders the decline of a math score with age. Conversely, high nonverbal intelligence may help to manage more complex math tasks that emerge in higher grades (Miller Singley and Bunge, 2014).

Interestingly, for the rural subpopulation, only high nonverbal intelligence attenuates the negative link between age and achievement, while math anxiety level does not moderate the relationship. One possible reason for the lack of the math anxiety effect in rural areas is a much stronger impact of other negative factors, such as poor quality of teachers and low learning motivation. While interventions aimed at reducing math anxiety may be effective in preventing math achievement decline in cities, they may not be effective in rural areas due to specific obstacles. Fostering the quality of the teaching practices and positive school environment may be a more efficient intervention for rural schools (Scherer and Nilsen, 2016; Sorrenti et al., 2024).

Meanwhile, age shows a positive association with fluid intelligence for both subgroups, reflecting the development of working memory and abstract reasoning skills (Chan, 2004). Math anxiety slightly increases with age as well, as was shown in our previous study (Linna et al., 2024).

Regarding gender differences, in the youngest age group, boys surpass girls in math in urban areas, which is consistent with several studies on the gender gap (Ellison and Swanson, 2010; Else-Quest et al., 2010; Cimpian et al., 2016; Reilly et al., 2015), while no gender differences are observed for other groups. On the contrary, in both rural and urban areas, girls outperform boys in nonverbal intelligence. Previous studies have demonstrated that, at a younger age, girls surpass boys in working memory (Niazi and Adil, 2021) and fluid intelligence (Buczyłowska et al., 2019) tasks, but the difference becomes negligible with age (Buczyłowska et al., 2019). At the same time, in urban areas, girls exhibit higher math anxiety, whereas no gender differences in math anxiety level are observed for the rural subsample. Higher prevalence of math anxiety in girls was demonstrated by numerous studies (Marakshina et al., 2023, 2024; Xie et al., 2019; Schmitz et al., 2022; Primi et al., 2014; Sadiković et al., 2018; Linna et al., 2024). Further investigations are needed to explore why gender differences in math achievements and math anxiety are not pronounced in rural Chinese schoolchildren. One possible reason is that, in rural areas in general, there is less cultural emphasis on math achievement, which makes gender stereotypes about math less salient.

Several limitations have to be acknowledged. First of all, a cross-sectional design does not allow us to observe developmental trajectories directly and purely distinguish the developmental effect from the cohort effect. Further longitudinal studies on the interplay among math achievement, math anxiety, nonverbal intelligence, and socio-demographic variables are needed to justify our findings. Another possible direction for future studies is to investigate the origins of the rural/urban achievement gap in the Chinese context, the reasons for its substantial growth with time, and the effectiveness of different interventional strategies aimed at reducing the gap. Longitudinal and interventional studies may be particularly useful for this purpose.

Age imbalance between rural and urban areas should also be considered a limitation, although age was controlled in the analysis. The number of young students in rural areas is small, mainly because of the impact of the birth rate.

Overall, the current study replicates several well-established findings (i.e., a positive association between math achievement and nonverbal intelligence, a negative association between math achievement and math anxiety, a math achievement gap between rural and urban areas, and higher math anxiety and nonverbal intelligence in girls) for the cultural contexts of rural and urban China. Meanwhile, the study also reveals some intricate differences between rural and urban areas that bring novelty to the field, such as the presumably protective effect of low math anxiety on math achievement decline for urban but not rural schoolchildren and more pronounced gender differences in urban areas in comparison with rural regions.