2.1 Data Resource: China Education Panel Survey

The present study adopted the data of Chinese Education Panel Survey (CEPS) (2013-2014), accessing from (https://ceps.ruc.edu.cn/), which focuses on Chinese secondary school students who are in grade 7 and grade 9 (year 13-15), including 1216 male (52.2%), 1068 female (45.9%), while 44 students did not provide their gender information. This survey aims at obtaining relatively comprehensive information on Chinese secondary education from multiple perspectives, such as students, parents, homeroom teachers, subject teachers, and school administrators. The CEPS uses a stratified, multi-stage sampling technique wherein 28 districts from a population of 2870 districts were chosen. From each of these 28 districts, four schools were selected, and four classes of grade 7 and grade 9 were randomly selected from each school. As a result, approximately 20,000 students in 448 classrooms of 112 schools were selected in the CEPS.

This study adopts data from the student perspective. Based on the question of ‘What is your family’s current economic situation?’ Economically disadvantaged stu dents (N=2328) were confirmed as those who answered: “very poor” or “poor”. This study is conducted based on these students’ information.

2.2 Key Measures and Variable Definitions

Academic achievements: all students need to report their most recent test scores for mid-term exams in Chinese, English, and mathematics. Originally a 150-point score in total, each students’ raw score is changed into a standard score with standard deviation=70 and mean=10. The sampling students’ standardized scores in three subjects are the dependent variable of this study.

^{Metheny, McWhirter, and O’Neil (2008)} reviewed the existed 17 tools on measuring teacher support on students’ perspective and proposed a four-dimensional structure of teacher support, which included teachers’ investment in students’ learning, teachers’ emotional support, teachers’ expectations, and teachers’ accessibility of students. In CEPS (2013-2014), teacher support was assessed on two aspects: how often teachers ask questions on subject content and how often teachers praise students. Based on Chinese teaching culture, teachers asking questions is regarded as one of the strategies teachers concerning students’ learning use and could be regarded as teachers’ investment in students’ learning. Thus, teacher support was assessed on two aspects: investment and emotions. In addition, considering the differences of subjects, teacher support was measured using six items. Students are required to rate both descriptions on a 4-Likert scale ranging from 1=strongly disagree to 4=strongly agree.

According to ^{Pitzer and Skinner (2017)}, peer support was regarded as the component of supportive classroom interactions among peers, including warm relations, structural classroom context and supporting autonomy. Consistent with this definition, in the CEPS (2013-2014), peer support was examined on two aspects: warm relations and structural classroom context using two items. It was measured on a 4-Likert scale ranging from 1= strongly disagree to 4=strongly agree.

According to ^{Zimet, Dahlem, Zimet, and Farley (1988)} as well as (^{Chou, 2000}), family support mainly focuses on the supporting willingness, emotional support, decision making support, and the availability of discussing problems that children are facing on. In a line with this content, family support in CEPS (2013-2014) also covers two aspects: emotional support form parent and their availability of discussing problems that children have in schools. Specifically, family support was measured using four items. Students’ responses to the questions were scaled on a 3-Likert format (1=never, 2=sometimes, and 3=always).

According to ^{Martin and Marsh (2006)} and ^{Martin (2013)}, academic resilience mainly concerns on how students cope with the adversity or difficulties within academic settings. Then, the measurement of academic resilience focuses on students’ responses to their emotional issues during learning, academic pressures, or some other setbacks within schools (^{Martin & Marsh, 2006}). Consistent with this method, academic resilience in CEPS (2013-2014) concerned on how students tackle with the negative emotional response and academic pressures. Academic resilience was measured on three aspects, including students’ negative feelings toward school engagement, emotional issue, and academic pressure using three items. All these items were examined on 4-Likert scales (1=strongly disagree, 4=strongly agree).

2.3 Data Analysis

The normality of these four constructs is tested. Based on the suggestion of ^{Hair, Black, Babin, Anderson, and Tatham (2010)}, a skewness-kurtosis test is conducted to assess whether the data follows the rule of normal distribution. The values of skewness and kurtosis range from -1.133 to .496, and from -1.446 to 2.186, respectively, which follow the rule of (^{Kline, 2010}) that the values be within the ranges of |3| and |8|.

In this study, it was used the Partial Least Squares Structural Equation Modelling (PLS-SEM), which is a non-parametric test and is adopted to analyse the data by using SmartPLS3.0 (^{Ringle, Wende, & Becker, 2015}) with several considerations. First, PLS-SEM is a complicated model that includes multiple independent variables and mediated variables, and has been shown to be capable of assessing parameters of complex models (^{Hair, Hult, Ringle, & Sarstedt, 2017}). It allows enormous flexibility on the number of items of the construct and the measurement scales. Second, because the majority of constructs in this study were assessed by different scale criteria, there might be measure errors or systematic errors. This requires rigorous computation of parameters which the PLS-SEM meets (^{Chin, 2010}). Last, academic resilience is always treated as an entity rather than divided into different components. Thus, in this study we are trying to explore the theory rather than confirm it. As such, the PLS-SEM is regarded as the most suitable data analysis technique for our study.

More specifically, two-steps analysing procedures are conducted to examine model hypotheses. First, we use the PLS algorithm technique for testing the outer model and its reliability and validity. Then, the bootstrapping technique is conducted to confirm the structural model relationships as well as compute the effect size of each path by using the blindfolding technique (^{Hair, Sarstedt, Hopkins, & Kuppelwieser, 2014}).

3.1Measurement Model Assessment

To test the measurement model’s reliability and validity, the Cronbach’s alpha, composite reliability (CR), average variance extracted (AVE), and discriminant validity are estimated. Table 1 shows the results from the SmartPLS3.0.

As outlined in Table 1, only the factor loading of item ’a1201’ is below .7, so it seems this item needs to be deleted (^{Hair, Ringle, & Sarstedt, 2011}). However, all constructs’ value of AVE is over .5 and all constructs’ value of CR is over .7, thus, in this study, we keep this item in the resilience. As to Cronbach’s alpha, its value ranges from nearly .6 to .886, and four constructs’ alpha values are below .7 (^{Nunnally & Bernstein, 1994}). However, we cannot conclude that we get a weak reliability of these constructs because (1) the Cronbach’s alpha is too sensitive to the number of items in each construct and (2) the CR estimated the combined reliability of all items to the latent variables and its values (all over .7) show good reliability of each construct.

If the square roots of the AVE of each construct is over the correlation coefficients of two constructs, then we can confirm the construct has good discriminant validity (^{Fornell & Larcker, 1981}). As shown in Table 2, all constructs’ discriminant validity meet this rule, which reveals a reasonable discriminant validity for the constructor.

It proposed that the standardized root means square residuals (SRMR) and NFI are two indicators of the model fit to assess to what extent the data fits the model in SmartPLS3.0 (^{Henseler, Hubona, & Ray, 2016}).

In this study, the SRMR=.064 is less than 0.1 (^{Hu & Bentler, 1995a}) and NFI=.705 is less than the suggested .8 (^{Hu & Bentler, 1995b}). Thus, basically, this is a fitted model.

3.2 Structural Model Assessment

Using the bootstrapping technique with 1000 resamples, the path coefficients in this model are estimated, as shown in Table 3. Besides the hypothesis of H1a and H3a, all the other hypothesis paths are significantly supported. Students’ perception of academic resilience is significantly impacted by teacher support (β=.16), peer support (β=.131), and family support (β=.083). The result also reveals that students’ academic achievements are significantly influenced by peer support (β=.102) and academic resilience (β=.123).

To test the mediation effect of academic resilience, we adopt ^{Chin (2010)}’s two-steps bootstrapping procedures. The effects, firstly, between family support, peer support, and teacher support and academic achievement without the mediator variable are assessed (see the section of Direct effects without mediator in Table 4). The results indicate that academic achievement has a significant relationship between peer support (β=.119) and teacher support (β=.065). However, the relationship between family support and academic achievement is not significant.

Then, we add academic resilience as the mediator variable and the three coefficients of family support, peer support, teacher support, and academic achievement are declined. As shown in Table 3 and Table 4, the relationship between peer support and academic achievement is still significant, declined from .119 to .102, but the relationship between teacher support and academic achievement changes into insignificant, the coefficient declined from .065 to .029. Meanwhile, all indirect effects between family support, peer support, teacher support, and academic achievement are supported. Thus, we conclude that academic resilience has a partial mediated effect between peer support, family support and academic achievement and has a full mediated effect between teacher support and academic achievement.

The structural relations are presented in the Figure 1.

Figura 1 Structural model relations 

4.1 The Direct and Indirect Effects of Peer Support

This study reveals that peer support has a positive effect on low-income household children’s academic resilience. This finding is consistent with some existing research conducted in the western context that, when students get strong support from their friends, they are more likely to have a high level of academic resilience (^{Robinson et al., 2015}; ^{Stewart & Sun, 2004}). However, the finding is inconsistent with an investigation in China by ^{C. Li, Zhang, and Li (2008}) who found no significant effect between peer social capital and resilience. One possible reason is the difference in defining the construct of peer support. In our study, we assess two aspects of peer support -friendly to individuals and good for learning- while, in Li et al.’s research, they measured peer capital on both positively and negatively aspects.

Peer support also shows a positive impact on students’ academic outcome, in agreement with the study of ^{Ramirez et al. (2014)} but against the finding of ^{Elias and Haynes (2008)}. This disagreement may be because (^{Elias & Haynes, 2008}) measured peer support by focusing on peer threat. They used items with a negative tone, for instance, “do you get picked on and teased by your friends?” or “do you feel left out by your friends?” (p. 480).

By regarding academic resilience as a mediator, the impact of peer support to low-income household children’s academic achievement remains significant, which means academic resilience, has a partial mediation effect on this relationship. Thus, we may conclude that peer support has a positive effect on children’s academic achievement, partially through increasing children’s academic resilience. This finding could contribute to the development of the theory of how peer support improves children’s academic outcomes by raising their academic resilience.

4.2 The Direct and Indirect Effects of Family Support

This study echoes the prevalent conclusion that family support has a positive effect on children’s academic resilience, irrespective of their family’s economic status ( ^{C. Li, Zhang, & Li, 2018}; ^{Sanders et al., 2015}). However, it is interesting that family support has no significant impact on academic outcome of those from a low-income family and this result is inconsistent with some other studies (^{Liew et al., 2018}; ^{Ramirez et al., 2014}). There are two possible reasons for this. First, according to the code theory (^{Bernstein, 1962}), low-income families are more likely to use restricted code to express some simple opinions and the understanding of their speech relies on their specific context, while the middle and upper-class families always use the elaborated code, which includes complete and relatively complicated meanings. The elaborated code is more powerful than a restricted code in expressing someone’s thoughts and does not depend on the specific context. In the school context, teachers prefer to use the elaborated code to transfer knowledge, thus, the working-class or low-income family’s children cannot engage in school education as effectively as those from the middle or upper-class family. Second, the Chinese culture may influence parents’ emotional engagement in children’s learning. For instance, an experimental research revealed that, compared with the USA parent, the Chinese parent shows a low level of emotional intensity and low emotional experience (^{Davis et al., 2012}). This means the Chinese parent is not good at expressing their emotions in their daily life. This effect may influence family support having no significant impact on children’s academic achievement in the Chinese context.

4.3 The Direct and Indirect Effects of Teacher Support

Our study is consistent with the existing findings that teacher support could improve students’ academic resilience (^{Johnson, 2008}; ^{Werner, 1990}). Furthermore, this study confirmed that, if children from the low-income family gain more praise from their teachers, they are more likely to have a high capacity for coping with adverse conditions (^{Sanders et al., 2016}). It is interesting to note that academic resilience fully mediated the effect of teacher support on children’s academic achievement. This means before adding the academic resilience, teacher support significantly impact children’s academic outcomes; however, this effect changes to insignificant after we added the teacher support as the mediator. Based on this finding, we suggest teacher support may have a positive impact on low-income children’s academic achievement but through influencing the children’s academic resilience.

4.4 Academic Resilience and Low-income Children’s Academic Achievement

This study’s findings are consistent with many current findings that academic resilience has a positive effect on children’s academic achievement, regardless of family economic status (^{Sattler & Gershoff, 2019}; ^{D. Wang et al., 2017}). In addition, though, there are two new findings: academic resilience partially mediated the effect of peer support and fully mediated the effect of teacher support. In another recent study, academic resilience mediated the effects of social support on educational aspiration and plan to drop out, and of family support on academic effort and plan to drop out (^{Wu, Tsang, & Ming, 2014}). Our study complements these findings in two aspects: 1) we measure academic achievement directly using English, Chinese, and mathematics testing scores; 2) we prove the effects of peer support and teacher support.

4.5 Implications of the Present Study

Several implications can be proposed for theory and practice improvement. By adopting an ecological framework of academic resilience that encompasses peer, teacher, and family support, this study deepens our understanding of to what extent and by which path these social supports improve academic achievement by extending to children from low-income household in China.

Practically, to improve low-income household children’s school performance, the following two suggestions should be considered carefully: 1) pay more attention to family, such as parents offering more diverse support and learn how to express emotions to their children; 2) provide suggestions to children on how to make friends and how to keep healthy friendships, in recognition that peers are vital for improving both academic resilience and outcomes.

4.6 Limitations and Future Research

There are at least two limitations in this research. First, because it is based on the secondary data, this study is data-driven rather than theory-driven, thus some vital information of participants cannot be obtained. In addition, this is a cross-sectional design, it can only be used to conclude correlational results and cannot obtain causality effects between variables. Finally, the low-income household children were figured out by their own response, while teenagers may have bias perceptions toward their family’s economic conditions. Therefore, it may have measurement errors in classifying the family in poverty.

In future, more studies should focus on casual effect of academic resilience on both its sources and impacts by using longitudinal study or experimental study. Meanwhile, future studies could focus on comparative research on minorities and majorities, local and international.