Abstract

Background

Previous research paid more attention to the negative effects of the bullying on psychological distress, such as anxiety and depression. However, few studies explored the underlying mechanism between bullying and mathematics achievement. The purpose of this study was to explore the direct and indirect effects of school bullying on mathematics achievement among Chinese eighth grade students.

Methods

A two-stage stratified sample design was used to select participants. The participants were all eighth grade students from a city of southwest China and 17,527 adolescents (51.7% boys, M_age = 13.34鈥壜扁��0.56 years) were included in this study. Students completed a battery of paper-and-pencil instruments concerning demographic information, school bullying, teacher-student relationships, sense of belonging, and mathematics achievement. The Two-Step Rule was employed to explore the association between school bullying and mathematics achievement.

Results

(1) There was a direct effect of school bullying on mathematics achievement (尾 = -0.203, 95%CI: -0.235, -0.171, p鈥�<鈥�.001); (2) Teacher-student relationships (尾 = -0.096, 95%CI: -0.115, -0.078, p鈥�<鈥�.001) and sense of belonging (尾 = -0.011, 95%CI: -0.021, -0.003, p鈥�=鈥�.010) played separate mediating roles in the link between school bullying and mathematics achievement; (3) Teacher-student relationships and sense of belonging served as chain mediators between school bullying and mathematics achievement (尾 = -0.011, 95%CI: -0.021, -0.003, p鈥�=鈥�.012); (4) Gender moderated the impact of school bullying on mathematics achievement (尾 = -0.081, p鈥�&濒迟;鈥�.001).

Conclusions

These results have implications for educational staff by suggesting that teacher-student relationships and school belonging may be the two pivotal factors that future research should utilize the two factors to develop more evidence-based preventions and interventions. Moreover, more attention should be paid to girls who are victims of bullying.

Introduction

Bullying is usually defined as a specific type of aggressive behavior in which someone intentionally and repeatedly causes another person injury or discomfort [1]. School-bullying is a pervasive phenomenon in the global world. For example, in the 2018 Program for International Student Assessment (PISA) results, it found that 23% of students were being bullied at least a few times a month from their self-reported questionnaires on average across Organization for Economic Co-operation and Development (OECD) countries [2]. In China, some researchers found that the percentage of middle school students who were victims ranged from 1.5 to 13.4% in mainland China [3]. Unsurprisingly, school bullying is a universal problem that has attracted numerous researchers鈥� attention. A number of studies have focused considerable attention on the adverse effect of school bullying on students鈥� physical (such as unspecified psychosomatic symptoms, stomachache, sleeping difficulties) and mental health (such as depression, anxiety, loneliness, suicidal behavior) [4,5,6]. Moreover, the pernicious effects of bulling at school could last well into adulthood [7].

From a policy perspective, the effects of bullying on academic achievement and long- term employment are a reason to worry. For example, in 2016, the national anti-bullying policy of Guidance on the Prevention and Treatment of Bullying and School Violence was issued so as to prevent the occurrence of bullying and violence and reduce the adverse impact of school bullying on academic achievement [8]. According to the extant literature, bullying victimization was significantly negatively associated with students鈥� academic achievement [9, 10]. One longitudinal study found that bullying was a predictor of low academic performance [11]. Mathematics and reading performance at 7-year-old could predict socioeconomic status by age 42 [12]. Mathematics subject is important to educational and economic success in modern society and is becoming ever more so [13]. Therefore, many researchers carried out studies on the link between bullying and mathematics achievement, but the underlying mechanism of the relation between the two variables was not clear [14]. Hence, there is a need to explore the mechanism underlying the association between school bullying and mathematics achievement, which would offer guidance for designing interventions to improve bullied students鈥� math performance.

In order to improve students鈥� mathematics achievement, we must first understand what factors affect math performance. According to Bronfenbrenner鈥檚 ecological systems theory [15], an individual鈥檚 development will be influenced by the environment that is made up of four interrelated systems (microsystem, mesosystem, exosystem, and macrosystem). From the perspective of ecological systems theory, microsystem, the most proximal setting, has a direct effect on individuals, which involves their family, friends, teachers, and so on. For students, outside the family, most of their time is spent in the school and they acquire knowledge of math from their teachers, hence school bullying, teacher-student relationships and sense of belonging in school may be the main factors affected students鈥� mathematics achievement.

Theoretical framework

The theoretical framework for this study mainly draws from self-determination theory (SDT) and stage-environment fit theory. SDT focuses on the fundamental psychological needs of competence, autonomy, and relatedness. In the domain of education, if the three basic psychological needs are fulfilled, students鈥� school engagement and academic achievement in school will be enhanced [16]. In educational contexts, competence involves the knowledge and confidence needed to achieve specific outcomes. Autonomy is fostered when students view their schoolwork as aligned with their personal interests and objectives, or when they have the opportunity to make choices about their own actions [17]. Relatedness refers to the quality of connections students have with others in a given context [18]. Studies have shown that a strong sense of connection to teachers and peers in school is associated with individuals鈥� academic performance [16]. SDT provides a theoretical foundation for mediated models that links school bullying to academic achievement via sense of belonging (teacher-student relationships and school belonging). According to SDT, meeting the need for relatedness facilitates the internalization process [19], which is in congruence with social capital theory [20]. That is, students who maintain positive relationships with their teachers are likely to receive warmth, care, and respect from them. This supportive environment can encourage students to internalize the academic values and expectations of their teachers, thereby promoting their academic achievement.

Theory and empirical evidence have pointed to the importance of the school as an environmental context that should meet the developmental needs of adolescents [21]. Stage-environment fit theory clearly posits that students perform well when a match between school environment and their psychological needs [22]. In the school context, teachers and peers play a crucial role in fostering a nurturing and supportive atmosphere that satisfies students鈥� fundamental needs, thereby enhancing their academic outcomes. A positive teacher-student relationship is important to students鈥� academic achievement and acts as a protective factor for students with academic risk [23]. Conversely, school bulling is considered as a major threat to creating a safe and caring school environment [24]. Drawing on these theoretical frameworks, mathematics achievement may result from students鈥� interactions with their school environment, that is, school bullying, teacher-student relationships and school belonging are expected to influence students鈥� math performance.

School bullying and mathematics achievement

Considering math is crucial to technological innovation, several studies paid close attention to explore the impact of school bullying on students鈥� performance in mathematics [24, 25] and found that greater exposure to bullying was related with lower mathematics achievement. Furthermore, school bullying had a significantly negatively effect on math performance [26]. According to a two-year longitudinal study, the link between bullying and academic achievement was relatively stable among Chinese students across the two years, and the results showed that school bullying at Grade 3 could predict poor academic performance at Grade 5, but academic achievement at Grade 3 could not predict school bullying at Grade 5 [27]. In addition, Graham found that school bullying could be a central driver of low mathematics achievement [28]. However, a review of the literature indicated that school bullying might be both an antecedent and consequence of poor academic performance [29].

School bullying, teacher-student relationships and mathematics achievement

Teachers are the adults who are nearest to and familiarize with school bullying problems [30]. According to socialization theory, teacher-student relationships are considered more as the outcome of students鈥� externalizing behaviors, that is, students have abilities to affect how teachers interact with them [31, 32]. In addition, social capital theory indicates that a positive teacher-student relationship is a primary form of social capital for students, and can improve students鈥� academic outcomes [20]. Not surprisingly, the links among bullying, teacher-student relationships and academic achievement were explored by a number of researchers. For instance, a meta-analysis including 66 cross-sectional studies showed that students who were involved in bullying were likely to have a poor relationship with their teachers [33]. Moreover, a review concerning longitudinal studies found that school violence was significantly associated with teacher-student relationships over time [34]. Longitudinal research showed that externalizing behaviors (e.g., aggression, conduct problems) negatively predicted teacher-student relationship quality over time [32] and one longitudinal study showed that children who viewed their teacher-student relationships as positive less likely to have bullying-related behaviors [35]. In addition, a meta-analysis review involved 61 studies concluded that overall effect sizes for the associations between teacher-student relationships and academic achievement were small to medium (r鈥�=鈥�.16, p<.01, for both fixed and random effects models) [36]. The reciprocal effect of teacher-student relationships on academic achievement was confirmed by a cross-lagged longitudinal study [37]. However, another longitudinal study found that students鈥� perceptions of teacher warmth would be a significant predictor of students鈥� mathematics competence beliefs, which in turn, predicted changes in mathematics performance [38]. Konishi et al. found teacher-student relationships served as a mediator in the link between school bullying and academic achievement among Canadian students [24]. Therefore, it can be seen that a good teacher-student relationship may act as a possible buffer that could reduce the negative impact of school bullying on mathematics performance among Chinese eighth grade students.

School bullying, sense of belonging and mathematics achievement

A meta-analysis indicated that students鈥� sense of belonging had a negatively association with bullying perpetration [39]. In addition, research found that bullying climate had a detrimental effect on students鈥� school belonging [24]. Furthermore, the results of one study showed that sense of belonging at school was a strong predictor for school achievement [40]. A longitudinal study drew a conclusion that initial level of sense of belonging in sixth grade could predict students鈥� math performance in eighth grade [41]. Students who had higher levels of school belonging reported better academic achievement and lower school bullying scores [42]. In China, the collectivism cultural requires people to consider themselves as a part of social relationships and their cognitions and behaviors are largely influenced by the perceived thoughts and anticipated behaviors of significant others [43]. Hence, for Chinese students, sense of belonging would act as a vital factor to their school-based outcomes.

Teacher-student relationships and sense of belonging

The effects of bullying and teacher-student relationships on mathematics achievement may be further mediated by school belonging. In the present study, school belonging refers to 鈥渢he extent to which students feel personally accepted, respected, included, and supported by others in the school social environment鈥� [44]. The definition showed that the teacher-student relationship was one of the operational aspects and a critical contributor to students鈥� school belonging [45]. Cemalcilar indicated that teacher-student relationships made a difference to students鈥� sense of belonging at school [46]. Students who perceived teacher support would have a greater sense of belonging at school [45]. Wentzel assumed that students who expected to experience a sense of belonging at school should first need to foster relationships with their teachers [47]. A longitudinal study showed that teacher-student relationships could positively predict students鈥� school belonging according to growth curve analysis [48]. Furthermore, Uslu and Gizir found that teacher-student relationships were one of the most important predictive factors of students鈥� school belonging [49]. That is, students who were in warm teacher-student relationships tended to regard teachers as a prominent emotional and cognitive resource [50] and they were likely to report high classroom engagement, which in turn could promote their school belonging [51]. Moreover, Zimmer-Gembeck et al. showed that sense of belonging at school mediated the link between teacher-student relationships and school engagement [21]. Similarly, Wang and Holcombe conducted a short-term longitudinal study and the results suggested that sense of belonging at 8th grade mediated the link between teachers鈥� social support at 7th grade and academic achievement at 8th grade [18].

Taken together, sense of belonging may not only mediate the association between bullying and mathematics achievement, but also serve as a potential mediator between teacher-student relationships and mathematics achievement. The hypotheses were in accordance with the self-determination theory [16]. The theory assumes that students鈥� needs for sense of belonging at school are satisfied, which may assist them to enhance their motivation, engagement and learning [52].

Gender differences

Previous studies have explored the gender differences in the association between school bullying and academic performance. A longitudinal analysis showed that victimization had a stronger relationship with academic achievement among boys than girls [53]. Whereas, Hoglund found that, for girls, the link between peer victimization and achievement was stronger when compared to boys [54]. However, there was some evidence showed that the direct effects of bullying victimization on academic achievement in the multi-group model were not statistically significant regardless of gender [55]. Additionally, a meta-analysis indicated that there were no significant gender differences in the coefficients between school bullying and academic achievement [10]. Hence, it is imperative to examine whether the correlation between school bullying and mathematics performance is differed across gender groups, so as to provide assistance to the risk group whose math performance is deeply affected by school bullying.

The current study

The present study attempted to construct a multiple mediation model (Fig.听1) in order to explore the underlying mechanism between school bullying and mathematics achievement. Based on prior studies and related theories, the following research questions were proposed. First, does bullying have a direct and adverse effect on mathematics achievement? second, do teacher-student relationships mediate the association between school bullying and mathematics achievement? third, does school bullying have an indirect effect on mathematics achievement through sense of belonging? fourth, do teacher-student relationships and sense of belonging serially mediate the association between school bullying and mathematics achievement? fifth, does gender moderate the direct link between school bullying and mathematics achievement?

Fig. 1

The proposed multiple mediation model. Note. SB鈥�=鈥塖chool bullying; TSR鈥�=鈥塗eacher-student relationships; SOB鈥�=鈥塖ense of belonging; MATH鈥�=鈥塎athematics achievement

Method

Participants

The data in our study were from a large-scale compulsory education quality assessment project in a provincial capital city of southwest China. It is a city where multiple ethnic groups live together, which has a population of nearly 30听million. The study employed a two-stage stratified sample design to select students to participate. First, schools were chosen through probability proportionate to size (PPS) sampling, then students were randomly selected from the schools. The ultimate result was that 169 secondary schools and 18,130 eighth grade students were chosen to be participants. The informed consent was obtained from the students and their legal guardians. A total of 283 students were unwilling to take part in this study. Among them, four students who took the math examination but did not accomplish the questionnaire were excluded and 316 students had missing responses in questionnaires. Independent samples t-test was applied to compare the means of variables between those who completed the instruments without any omission and those who had missing responses in instruments. A combination of t value and Cohen鈥檚 d showed that there is no practical significance between the two groups. Hence, considering that the sample size was large enough, we deleted students whose responses were incomplete, and then the valid sample was 17,527. Students were 51.7% boys and 48.3% girls. Their mean age was 13.34 years (SD鈥�=鈥�0.56) and their ages ranged from 10 to 18 years. Based on students鈥� self-report, 41.2% of them were boarding school students, who lived in the school premises, and 58.8% were day school students lived with their families. 49.5% of students were only children and 50.5% reported that they had siblings. Most of students answered the optional questions on parents鈥� education level and job occupation. On average, 50.2% of fathers and 54.1% of mothers had lower secondary education or below; 26.6% of fathers and 26.1% of mothers had upper secondary education; 22.9% of fathers and 19.4% of mothers had tertiary education or above. 3.0% of fathers and 15.1% of mothers had no work, 42.0% of fathers and 35.7% of mothers engaged in manufacturing and transportation, sales and farming, 38.0% of fathers and 41.5% of mothers were employed as civil servants or professionals, such as teachers, doctors and bankers, 16.6% of fathers and 7.4% of mothers were employed in professional and technical occupation, such as government officials, managing directors, and entrepreneurs.

Procedure

Students who were willing to participant the survey were all arranged in the assigned classrooms in their own school. Each of them would complete a paper-and-pencil test and a battery of questionnaires on the same school day. First, it would take students two hours to accomplish the mathematics test in the morning. Then, in the afternoon, students filled out a series of questionaries regarding school bullying, teacher-student relationships and sense of belonging in twenty minutes. The teachers who were responsible for handing out the papers would explain the purpose of the study to students and let them know some common do鈥檚 and don鈥檛s during the survey. Then each student was received a paper-and-pencil test or a series of questionnaires. All research methods were carried out in accordance with relevant ethical guidelines and regulations. The survey was approved by the school governors and the Guizhou Normal University Human Research Ethics Committee. In addition, students could participant in voluntarily and their answers were guaranteed to be confidential.

Measures

The present study used a battery of self-report questionnaires concerning school bullying, teacher-student relationships, and sense of belonging, which came from PISA students鈥� questionnaire [56, 57]. The original scales were translated into Chinese by two professors of psychology in our university. Then, a college teacher, who had the Master Degree in foreign linguistics and applied linguistics, back-translated the Chinese-version scales into English. Last, the two professors compared the back-translated version of the scales to the original ones and discussed each item of the scales with the college teacher, in order to make sure conceptual equivalence between the translated scales and the original ones [58]. A pilot study was conducted among eighth grade students in a school so as to ensure the psychometric properties of the instruments in our study.

School bullying

The school bullying scale came from the PISA 2018 students鈥� questionnaire [57]. The items on bulling were employed to measure the incidence of bullying-related behaviors in the past 12 months among students. It was a self-reported instrument that contained 4 questions (e.g., Other students left me out of things on purpose) and asked students to select their own answers from the given options (鈥渘ever or almost never鈥� = 1, 鈥渁 few times a year鈥� = 2, 鈥渁 few times a month鈥� = 3, 鈥渙nce a week or more鈥� = 4). A higher score indicated that bullying occurred more frequently. The scale has previously been found to have an acceptable internal consistency (伪鈥�=鈥�0.736) among Beijing, Shanghai, Jiangsu and Zhejiang students in China [57]. In our study, the model fit indices of the scale were acceptable: 蠂²(2, 17527)鈥�=鈥�190.246, p鈥�<鈥�.001, CFI鈥�=鈥�0.987, TLI鈥�=鈥�0.960, RMSEA鈥�=鈥�0.073, and SRMR鈥�=鈥�0.016. Moreover, the Cronbach鈥檚 伪 coefficient of the scale was 0.725.

Teacher-student relationships

The teacher-student relationship scale with eight items was modified from PISA 2012 students鈥� questionnaire, which was developed to evaluate the degree of caring, warm, supportive, and respectful interactions between teachers and students. Among the eight items, the four items (Students get al.ong well with most teachers; Most of my teachers treat me fairly; If I need extra help, I will receive it from my teachers; Most of my teachers really listen to what I have to say) came from PISA 2012 students鈥� questionnaire and its internal consistency reliability was 0.870 among Shanghai students in China [56]. The other four items (Most of my teachers criticize me when I can鈥檛 answer the questions correctly; Most of my teachers trust me; Most of my teachers respect me; I like most of my teachers), which came from the previous education quality assessment, were added to meet requirements of the experts in Bureau of Education. Students were asked to give their options according to the eight items regarding their relationships with teachers at school. It was a four-point Likert scale assigning 1 (strongly disagree) to 4 points (strongly agree) to each category and one negatively worded item was reverse-coded. Students who had a higher score would perceive a more positive teacher-student relationship. In our study, the fit indices of the scale construct were acceptable: 蠂²(20, 17527)鈥�=鈥�2156.795, p鈥�<鈥�.001, CFI鈥�=鈥�0.961, TLI鈥�=鈥�0.946, RMSEA鈥�=鈥�0.078, and SRMR鈥�=鈥�0.027. In addition, the Cronbach鈥檚 伪 coefficient in this study was 0.860.

Sense of belonging

The sense of belonging scale came from the PISA 2018 students鈥� questionnaire [57]. The scale was to assess students鈥� sense of belonging at school, which comprised 6 items (e.g. I feel like I belong at school; I feel lonely at school) rated on a four-point Likert scale ranging from 1 (strongly disagree) to 4 (strongly agree) and 1, 4 and 6 were negatively worded items. Students who got a higher score indicated that they had a greater sense of belonging. Prior studies have found that the reliability of the sense of belonging scale was acceptable (伪鈥�>鈥�0.79) among Beijing, Shanghai, Jiangsu and Zhejiang students in China [57, 59]. In our study, the model fit indices of the scale: 蠂² (9, 17527)鈥�=鈥�1692.307, p鈥�<鈥�.001, CFI鈥�=鈥�0.937, TLI鈥�=鈥�0.895, RMSEA鈥�=鈥�0.103, and SRMR鈥�=鈥�0.037. It demonstrated unsatisfactory fit indices (TLI鈥�<鈥�0.90 and RMSEA鈥�>鈥�0.08). The follow-up data analysis found that method effects associated with negatively worded items were present [60] and wording effect had an impact on estimating the validity and reliability of self-report questionnaires [61]. The wording effects are common in rating scale responses, yet the instrument remains effective for measuring students鈥� sense of school belonging. The reliability coefficient was 0.794.

Mathematics achievement

The test aimed to measure eighth grade students鈥� mathematical achievement in the fall term, which was developed by a group of expert math teachers. We applied four stages to develop math items, including construct definition, item generation, item review and piloting of items [62]. The test blueprint was designed according to the textbook and the Full-time Compulsory Education Mathematics Curriculum Standards (2011 version). One expert teacher developed math items in line with the test blueprint. Then, four expert teachers were invited to review and correct math items, and compile the test framework, which ensured the quality of the test. Last, a pilot test was carried out among eighth grade students in a school to make sure the feasibility of the test.

There were a total of 28 items in the instrument, which involved four main content areas: number and algebra (10 items), space and graphics (11 items), statistics and probabilities (3 items), practice and comprehensive application (4 items). The test consisted of ten multiple-choice items, nine constructed-response items with completion and short answer and nine constructed-response items with extended response. It took students 120听min to complete the test. Rasch analysis was undertaken to examine the targeting of the test. The results showed that the distribution of student abilities was well matched to the distribution of item difficulty. The internal consistency reliability of the math test was 0.931 in this study, which was acceptable because 0.931鈥�>鈥�0.80 [63].

Control variables

According to the previous study, it can be known that gender, only child status and boarding status are related with students鈥� academic achievement [64, 65]. Hence, gender, only child or not and a boarding school student or a day student were treated as control variables. We dummy coded the three demographic variables as 0 (boys, non-only child, a day student) and 1 (girls, only child, a boarding school student). The variables were controlled in the multiple mediation analysis and the moderation analysis for its potential effects on mathematics achievement.

Data analysis

The descriptive statistical analysis was used to test the central tendency and the dispersion of the continuous variables and the Pearson bivariate correlation was adopted to measure the strength and direction of the relationship between two variables. The students in our study came from 169 schools and students within same school might share some perceptions of the same learning environment, which had an impact on students鈥� outcomes. Given the nested nature of the data (students nested in 169 schools), we used the TYPE鈥�=鈥塁OMPLEX command in Mplus 8.0 to control for the intragroup variance of the clustered data structure [66]. In addition, the intraclass correlation was applied to estimate the correlation among students鈥� scores with the nested structure.

The Two-Step Rule was conducted to examine the indirect effects of school bullying on mathematics achievement through teacher-student relationships and sense of belonging [67]. The study first employed confirmatory factor analysis (CFA) to evaluate the measurement model pertaining to school bullying, teacher-student relationships and sense of belonging. If the measurement model could be identified, then, latent structural equation modeling would be used to evaluate the multiple mediation model. The first step was to assess the direct effect of school bullying on mathematical achievement. The next step was to explore the indirect effects of school bullying on mathematics achievement in the serial mediation model (Fig.听1). A moderation analysis was applied to test gender as a moderator of the association between school bullying and mathematics achievement. Furthermore, the significance of the direct, indirect effects and moderation effect was estimated by the bias-corrected bootstrapping method, using 5000 bootstrap draws in the computation. The effect was considered significant if zero was not contained in the 95% confidence interval [68].

SPSS 22.0 was used to analyze the reliability of measurement instruments and the descriptive statistics. In addition, intraclass correlations, CFA, the mediation analysis and the moderation analysis were estimated in Mplus 8.0 [69]. In general, the following fit indices are applied to assess model fit: comparative fit index (CFI), Tucker鈥揕ewis Index (TLI), standardized root mean squared residual (SRMR) and root mean square error of approximation (RMSEA). The model fit is considered to be acceptable when a cutoff value of CFI and TLI is greater than 0.90, SRMR with a coefficient is less than 0.08 [70], and for the RMSEA, a cutoff value is less than 0.08 [71].

Results

Preliminary analysis

In Table听1, results showed that intraclass correlations of teacher-student relationships, school belonging and mathematics achievement were greater than 0.1, indicating that the nested data structure had an impact on these variables. The TYPE鈥�=鈥塁OMPLEX command in Mplus 8.0 was used to control for potential effects of the clustered data structure in all models. Boarding school students were more likely to get high scores in math than day students (r鈥�=鈥�.123^**), and only children had better mathematics performance than non-only children (r鈥�=鈥�.137^**). Moreover, students who had higher levels of school bullying would tend to have lower math scores (r = -.171^**), lower scores of teacher-student relationships (r= -.397^**) and sense of belonging (r = -.431^**).

Table 1 Mean, standard deviations (SD), intraclass correlations (ICC) and correlations among all the variables

Measurement model

In accordance with Bollen鈥檚 Two-Step Rule [67], the first step is to identify the measurement model, which is regarded as a confirmatory factor analysis (CFA) model. CFA was conducted to explore the construct validity of the measurement model containing three interrelated latent variables (school bullying, teacher-student relationships, and sense of belonging). The results indicated an acceptable fit to the data, which was consistent with the proposed three-factor structure, 蠂²(132, 17527)鈥�=鈥�7870.625, p鈥�<鈥�.001, CFI鈥�=鈥�0.930, TLI鈥�=鈥�0.919, RMSEA鈥�=鈥�0.058, and SRMR鈥�=鈥�0.039. The factor loading of each item in the three scales was showed in Table听2, and the identification of the measurement model provided support for the subsequent chain mediation model.

Table 2 Factor loadings in confirmatory factor analysis of school bullying, teacher-student relationships, sense of belonging

Mediation analysis

Before the serial mediation model was analyzed, the study first tested the direct effect of school bullying on mathematics achievement, while controlling for gender, boarding and only child. The results indicated that the direct effect model was acceptable: 蠂²(17, 17527)鈥�=鈥�344.417, p鈥�<鈥�.001, CFI鈥�=鈥�0.949, TLI鈥�=鈥�0.924, RMSEA (90% CI)鈥�=鈥�0.033 (0.030鈥�0.036), and SRMR鈥�=鈥�0.033. The results also suggested that school bullying had a significantly negatively influence on mathematics achievement after controlling for gender, boarding and only child, 尾 = -0.203, p鈥�&濒迟;鈥�.001.

Secondly, teacher-student relationships and sense of belonging were included in the association between school bullying and mathematics achievement, with gender, boarding and only child being controlled and the Fig.听2 presented the standardized regression coefficients. The fit indices of the serial mediation model were acceptable: 蠂²(201, 17527)鈥�=鈥�5929.791, p鈥�<鈥�.001, CFI鈥�=鈥�0.930, TLI鈥�=鈥�0.920, RMSEA (90% CI)鈥�=鈥�0.040 (0.039鈥�0.041), and SRMR鈥�=鈥�0.038. Furthermore, the indirect effects of school bullying on mathematics achievement were assessed by a bias-corrected bootstrap test so as to understand the statistical significance of the indirect paths. As the results showed in Table听3, the three indirect path coefficients were significant for the 95% bootstrapped confidence interval of each indirect path did not include 0. The standardized coefficient was 鈭掆��0.203 for the total effects, and 鈭掆��0.119 for the overall indirect effects. The indirect effects accounted for 58.62% of the total effect. Among the indirect effects, indirect path 1 (SB 鈫� TSR 鈫� MATH) was 47.29% (尾 = -0.096, p鈥�<鈥�.001), indirect path 2 (SB 鈫� SOB 鈫� MATH) was 5.42% (尾 = -0.011, p鈥�=鈥�.010) and the chain mediating path 3 (SB 鈫� TSR 鈫� SOB 鈫扢ATH) was 5.42% (尾 = -0.011, p鈥�=鈥�.012).

Table 3 Bias-corrected bootstrap test on the mediating effects

Fig. 2

The standardized results of the multiple mediation model

Moderation analysis

The moderation analysis was conducted with gender as grouping variable, mathematics achievement as the dependent variable, school bullying as the predictive variable, and boarding and only child as covariates. The results suggested that the moderation model was acceptable: 蠂²(33, 17527)鈥�=鈥�470.287, p鈥�<鈥�.001, CFI鈥�=鈥�0.933, TLI鈥�=鈥�0.919, RMSEA (90% CI)鈥�=鈥�0.039 (0.036鈥�0.042), and SRMR鈥�=鈥�0.065. As can be seen in Table听4, the effect of bullying on mathematics performance was significant regardless of gender. Whereas, school bullying had a stronger link with mathematics achievement for girls (尾 = -0.252) than for boys (尾 = -0.171). Moreover, the effect of school bullying on mathematics achievement for girls was significantly different for the boys (尾 = -0.081, p<.001), indicating that gender moderated the effect of school bullying on mathematics achievement.

Table 4 Moderating effect of gender on the relationship between school bullying and mathematics achievement

Discussion

Two models were conducted to examine the factors that made a contribution to mathematics achievement among Chinese eighth grade students in this study. The first model examined whether teacher-student relationships and sense of belonging mediated the association between school bullying and mathematics achievement. The second model was to examine the moderating effect of gender on the direct relationship between school bullying and mathematics achievement.

First, the results of preliminary analysis found that boarding school students demonstrated higher mathematics scores than day school students, which was in line with the previous study [64]. Boarding school students reside on campus and spend a significant amount of time with their peers in the school environment. Martin et al. proposed that boarding can be viewed as a form of extra-curricular activity that could enhance students鈥� identification with and commitment to the school, leading to improved academic performance [64]. This may be one potential explanation for the superior mathematics performance of boarding school students. The findings indicated that only children performed better in mathematics achievement than non-only children, aligning with prior research [65]. According to the resource dilution model, parental resources are limited and significantly influence an individual鈥檚 educational attainment, with this effect diminishing as the number of siblings increases [72]. In China, there is a strong emphasis on children鈥檚 education, and only children can benefit from undivided parental attention and access to a greater share of educational resources. Consequently, only children are likely to experience high parental academic expectations, which, in turn, can motivate them to achieve better academic outcomes.

Second, after controlling for gender, boarding and only child, the direct effect of school bullying on mathematics achievement was significant, indicating that students who reported they were bullied frequently were likely to score lower on the math test than those who reported they were bullied infrequently. The result was consistent with previous studies [24, 25]. One possible reason is that students who are being bullied may have negative attitudes towards school and become less engaged in the classroom, resulting in a poor academic performance [11]. Mathematics performance is regarded as a critical aspect of academic achievement tests and in China, to some extent, academic performance is the vital school evaluation standard [3]. Hence, students with good academic performance tend to receive adequate attention and support from teachers, which may protect them from being victims of bullying. This suggests that bullying can have a detrimental impact on mathematics achievement, while good performance in mathematics may serve as a protective factor against bullying.

Third, the findings showed that teacher-student relationships mediated the association between school bullying and math performance. The result is consistent with the previous study [24], and is partially supported by the socialization theory [31, 32]. The theory indicates that students with bullied experiences tend to have externalizing behaviors and these behaviors may elevate their likelihood of receiving more negative attention from their teachers, resulting in a poor teacher-student relationship. This is also partially supported by a longitudinal study that teacher-student relationships predicted and was predicted by school bullying [35]. A study has showed that culture has an impact on individuals鈥� development, and in a collectivistic culture, an individual often relies on its in-groups and bases its actions on the norms of these groups [72]. As a result, students from collectivistic countries tend to report better teacher-student relationships than those from individualistic countries [72]. From a perspective of Coleman鈥檚 theory of social capital [20], norms function as a form of social capital that can stimulate individuals鈥� behaviors. That is, in the school context, norms of a close teacher-student relationship may encourage students to engage in behaviors that enhance academic achievement. Consequently, integrating these theoretical perspectives provides a scientific explanation for why bullied students in our study who maintained better relationships with their teachers performed better on mathematics tests. This underscores the significance of positive teacher-student relationships as a critical component in bullying prevention programs in Chinese schools.

Fourth, sense of belonging was a significant mediator between school bullying and math performance, which is consistent with the previous research [16, 42]. Therefore, it provides an evidence for stage-environment fit theory, and the theory assumes that if the fundamental need of belonging is not met, students will be hard to obtain academic success [22]. From the perspective of self-determination theory [16], having high levels of school belonging indicates that students鈥� emotional need for being part of a group is satisfied and their academic performance was enhanced through their engagement in school. Furthermore, for Chinese students of collectivist cultures, they tend to see themselves as a part of a group and their achievement motivation may not be characterized by an individual鈥檚 competitive drive [43]. Hence, bullied students with high school belonging are likely to try their best to get good academic performance. In other words, sense of belonging may be a vital social resource that can buffer the adverse effects of bullying on Chinese students鈥� mathematics achievement.

Fifth, the results of indirect effects suggested that the association between school bullying and mathematics achievement was mediated by teacher-student relationships and school belonging simultaneously, which has rarely been verified in the previous research. However, the prior studies and the ecological system theory provide support for the sequential mediating roles of teacher-student relationships and sense of belonging. A meta-analysis, including 51 studies concerning school belonging, found that teacher support had a large effect (r鈥�=鈥�.46) on sense of belonging [44]. In addition, a longitudinal study found that the role of teachers鈥� support for mutual respect in the classroom could predict students鈥� sense of belonging at school [48]. Furthermore, according to ecological system theory [15], teacher-student relationships were critical for child development and a positive relationship may have the ability to mitigate the effects of adverse environment on students. In our study, the multiple mediating analysis provided a perspective for individuals to understand the underlying mechanism between school bullying and mathematics achievement, which the impact of school bullying on academic achievement was often overlooked [25]. Moreover, the indirect effect of school bullying on mathematics achievement via teacher-student relationships and school belonging was significant, indicating that being bullied more often may destroy teacher-student relationships, which in turn, may cause a weak sense of belonging and therefore lower mathematics scores. On the whole, the findings are in support of our proposed model and indicate that school bullying may have both direct and indirect effects on mathematics achievement.

Finally, the moderation results found that the direct effect of school bullying on mathematics achievement was moderated by gender, which was consistent with the previous study [54]. For boys, school bullying had a negative relationship with mathematics achievement; whereas, for girls, the direct path coefficient was stronger. A potential explanation lies in the influence of cultural factors on peer relationships. China, deeply rooted in traditional Confucian values, emphasizes emotional harmony and restraint in interpersonal interactions. In collectivistic cultures, children are expected to maintain strong social connections and exhibit high sensitivity to others鈥� opinions and evaluations [73]. One study has found that Chinese females report stronger attachments to their peers compared to males [74], highlighting the critical importance of peer relationships for girls. Hence, girls who experience bullying may exhibit lower commitment to their studies, leading to a more significant adverse impact on their mathematics performance relative to boys. Although the descriptive analyses showed that boys were more likely to be bullied than girls, the negative relationship between bullying and mathematics performance is larger among girls. That is to say, when girls become victims of school bullying, their mathematics performance tends to suffer more severely compared to boys.

Limitations and future directions

In order to consider the measurement errors in the multiple mediation model, sum scores of variables were replaced with latent factors, which could better reflect the truth of the data in the present study. However, this study has some limitations. First, this is a cross sectional study and the relationships between the variables in our study do not mean casual associations. Therefore, a longitudinal study is needed to explore the cause-and-effect associations among these factors in the future. Second, the data in our study were collected from a battery of self-report questionnaires. Although eighth grade students have abilities to understand the items of measurement instruments and provide a reliable data source, common method bias can be caused by data from the same source that may affect the validity of the findings. Therefore, future studies are encouraged to incorporate teachers鈥� reports or peer nominations so as to mitigate the negative effect of common method bias on empirical results. Third, considering the GDP, culture of the city, as well as the educational level and occupational status of the students鈥� parents, the sample demonstrates high representativeness, allowing the findings to be generalized to most cities, despite being selected from a single city. Nevertheless, the robustness of the results is further confirmed through large-scale data analysis.

Practical implications

From a practical perspective, the present results are encouraging for educational staff and administrators, who play a pivotal role in enhancing the school environment as perceived by students. The results indicated that positive teacher-student relationships and high levels of school belonging can partially mitigate the adverse effects of a bullying climate on mathematics performance. Consequently, these factors may be crucial in an ecological approach to improving bullied students鈥� mathematics achievement. First, effective interventions should focus on restructuring the school climate to foster positive interactions between students and teachers, ensuring that students perceive their teachers as caring, supportive, and fair. This can optimize students鈥� perceptions of their school environment, thereby enabling all students to succeed academically. Second, measures that enhance students鈥� school belonging may serve as effective interventions to protect mathematics performance from being undermined by school bullying. Additionally, the cultural context of collectivism should be considered when interpreting the role of students鈥� sense of belonging in mitigating the impacts of school bullying on learning outcomes in China [75]. Furthermore, school administrators can create environments conducive to learning by providing additional academic support for students who need it, such as teacher-supervised peer tutoring sessions. Third, the moderated analysis revealed that the adverse effect of school bullying on mathematics performance is larger among girls than those of boys. Given that bullying among girls often occurs within female friend groups [76], schools should be vigilant and emphasize this aspect in their anti-bullying education programs. Teachers should pay particular attention to bullied girls, especially in collectivist cultures. Last, it is important to note that past research has identified positive teacher-student relationships and high levels of school belonging as key protective factors in effective anti-bullying prevention programs [35, 40]. Therefore, future research should utilize the two factors to develop more evidence-based preventions and interventions.

Conclusions

The present study aimed to reveal the underlying mechanism between school bullying and mathematics achievement among Chinese eighth grade students. The multiple mediational model was verified, which made a contribution to understand the two protective roles of teacher-student relationships and sense of belonging against school bullying and its negative effects on mathematics achievement. The findings could provide some practical implications for the school staff to reduce negative effects of school bullying on students鈥� mathematics achievement. First, a close teacher-student relationship is a prominent factor among eighth grade students, for it can not only buffer the pernicious effect of school bullying on students鈥� mathematics achievement directly, but also can reduce the adverse effects of school bullying on students鈥� math performance via sense of belonging indirectly. Second, among bullied eighth grade students, girls will be more likely to have poor math performance than boys. Hence, the staff in school should pay more attention to girls who suffer from school bullying.