Based on the theory of self-determination, perceived teacher emotional support refers to that an individual feels an emotional connection with the teacher in the classroom, and the teacher is interested and sensitive to his needs and responds positively and enthusiastically to him (Pianta et al., 2008). Students have a sense of security in the classroom, which allows them to explore new things and expand their experiences. Such emotional connections can promote learning motivation (Downer et al., 2010). The more encouragement a child receives from teachers in early childhood (from kindergarten through third grade above) and the more harmonious the teacher-student relationship is, the more likely is that the student achieves good academic and social development (Silver et al., 2005). In high-quality teacher-student interaction, the emotional support of teachers for children is crucial. Hamre and Pianta (2005) found that improving the emotional support of teachers can effectively reduce the risk of first-grade students dropping out of school. The subjects who also had inattention, low academic levels, and easy to have behavioral problems were randomly divided into two groups and were given different levels of emotional support from teachers, respectively. The results showed that the group with the lower emotional support of teachers showed low academic achievement and easy to conflict with teachers. Many previous studies have shown a strong relationship between social support (teacher support, peer support, and parent support) and academic achievement among middle and high school students (Rosenfeld et al., 2000). In a representative large sample study, in Maslow's hierarchy of needs, the need for affective and belonging precedes the need for knowledge. It is difficult for students to succeed academically when they are emotionally unfulfilled. Therefore, exploring the relationship between teacher's emotional support and math performance of junior middle school and primary school students can enhance the understanding of the teacher-student relationship, help them better adapt to school life, and thus lay a certain foundation for their social adaptation in adulthood.

Academic self-efficacy refers to expectation and judgment of the individuals that they are capable of completing specific learning tasks (Bandura, 1986). This study focuses on the embodiment of self-efficacy in the field of mathematics learning, which refers to the judgment of students and evaluation of their ability to complete mathematics learning tasks and achieve learning goals (Hackett and Betz, 1989). Research on gender stereotype threat has demonstrated that the motivation, engagement, and performance of girl students can suffer a negative stereotype, such as men outperforming women on math tests (Rosenthal et al., 2007). Students believe that they are capable of completing learning tasks, which is the foundation of academic achievement and personal success (McWilliams, 2014). Self-efficacy also predicted the math performance of primary and middle school students (Usher et al., 2019). The higher the level of self-efficacy of the student, the easier it is to achieve better academic performance (Komarraju and Nadler, 2013; MacPhee et al., 2013).

According to the self-determination theory proposed by Ryan and Deci (2000), the emotional support behavior of teachers satisfies student needs for competence and belonging (Jin and Wang, 2019). When these needs of students are met, it is conducive to the development of self-efficacy. Perceived teacher support can enhance the sense of self-efficacy in the individuals (Scott and Walczak, 2009) and trigger the internal and external motivation of students (Deci and Ryan, 2004). Students with more perceived teacher support have higher academic self-efficacy (Kim et al., 2018).

Although the predictive effect of teacher's emotional support on math performance has been supported by many studies (Hamre and Pianta, 2005; Chen et al., 2018), the research on its internal influence mechanism is still relatively limited.

In this study, behavioral engagement refers to a process from students simply completing mathematical academic tasks and observing discipline to participating in mathematical learning activities in math class, which is a description of the degree of involvement in mathematics learning (Fredricks et al., 2004). Finn (1993) found that student behavioral engagement can predict performance on standardized achievement tests. The positive prediction effects of student behavioral engagement on student achievement and student dropout rate (Fredricks et al., 2004). Positive classroom interaction between teachers and students is very important to improve the behavioral engagement of students (Cooper, 2014). A study by Lee (2014) on 3,268 middle school students from 121 middle schools in the United States showed that learning engagement can significantly predict the academic achievement of middle school students.

As environmental variables, supportive factors from teachers can significantly affect the learning engagement of students (Brewster and Bowen, 2004). A study on middle school students in Hong Kong showed that teacher support was stronger than parental support and peer support in predicting the academic engagement and academic achievement of the students (Chen, 2005). As a kind of independent support “choice” provided by teachers can positively predict motivation, interest and cognitive, and behavioral and emotional engagement of the students in learning (Flowerday and Schraw, 2000, 2003; Flowerday et al., 2004). Meanwhile, existing studies have also found that emotional support from the teacher plays an important role in enhancing motivation, participation, cooperation, and emotional well-being of the students in learning (Meyer and Turner, 2007).

Perceived teacher support indirectly affects primary school math learning engagement of students through academic self-efficacy (Liu et al., 2018). Students can feel the care, trust, and respect of the teacher for them (Roth and Weinstock, 2013), which can stimulate positive emotions of the students, thus generate positive self-evaluation and further enhance their sense of academic self-efficacy. Self-efficacy directly affects the way of thinking, behavior, and emotions (Goetz et al., 2010). The Self-efficacy beliefs of the Secondary school student related to learning and performance in math significantly predicted their behavioral and affective engagement in math positively while predicting their behavioral and affective disaffection negatively (Ozkal, 2019).

According to social cognitive theory and self-determination theory, environment, personal factors (such as cognition, emotion, and motivation), and behavior interact. The emotional support of a teacher, as an environmental factor, can enhance individual self-efficacy (Scott and Walczak, 2009), show stronger learning vitality, and focus on their learning tasks (Jin and Wang, 2019). Figure 1 shows the hypothesized model.

We hypothesize the following:

The convenience sampling method was adopted to select students from grades 3 to 5 and grades 7 to 8 of middle and primary schools in Henan and Gansu provinces of China, as the subjects for group testing. In total, 1,294 valid questionnaires were collected, with an effective rate of 91.5%. Among them, there were 657 boys (50.77%), 637 girls (49.23%), 233 students (18.01%) in the third grade, 219 students (16.92%) in the fourth grade, 285 students (22.02%) in the fifth grade, 223 students (17.23%) in the seventh grade, and 334 students (25.81%) in the eighth grade, with an average age of 12.05 ± 1.83 years old.

Our data analyses were conducted using SPSS 20.0, and the SPSS macro PROCESS (Hayes, 2013), and Amos 24.0. First, descriptive data were obtained using SPSS 20.0, and then Pearson's correlations were calculated to assess the correlations between the variables. Second, in accordance with Anderson and Gerbing (1988), we performed a two-step procedure to analyze the mediation effects. We first used two measurement models to test whether each latent variable could be well-represented by its indicators. We next determined whether the results from the measurement model were satisfactory; the two structural models could be tested using maximum likelihood (ML) estimation in the AMOS 24.0 program. Although the χ² statistic is often reported, because of its dependence on sample size (Gessaroli and De Champlain, 1996), other indicators are commonly used to determine how well the model fits. According to Hu and Bentler (1999), the model fits well when CFI > 0.90, TLI > 0.90, and RMSEA <0.06.

Finally, the multi-mediation analyses were all conducted using the PROCESS macro in SPSS 20.0 (Preacher and Hayes, 2004; Hayes, 2013). The number of bootstrap samples for the bias-corrected bootstrap confidence intervals was 5,000.

Data collected by the self-report method may have a common method deviation, and Harman single factor test was adopted in this study (Podsakoff et al., 2003). It was found that there were seven factors with eigenvalues >1, which explained 61.861% variation. The variance explained by the first factor was 35.859%, less than the 40% threshold. Therefore, the common method deviation of data in this study is not serious.

To test the discriminative validity of the variables in this study, confirmatory factor analysis was conducted for each variable using the AMOS 22.0 software. The results in Table 1 show that, compared with the single-factor model, two-factor model and three-factor model, the four-factor model adopted in this study is the most appropriate. The combination effect is ideal, and the fitting indexes of the four factors model all reach the standard, and the fitting degree of the model is good.

In this study, the subjects were divided into four groups: primary school boys, primary school girls, junior middle school boys, and junior middle school girls; and descriptive analysis was performed, respectively. Tables 2, 3 present the descriptive results of each variable and the correlation coefficients among the variables. The results showed that teacher's emotional support was positively correlated with academic self-efficacy, math behavioral engagement, and math performance. Academic self-efficacy is positively correlated with math behavioral engagement and math performance. There is a positive correlation between math behavioral engagement and math performance. This is consistent with the results of previous studies.

All subjects were divided into primary school boys, primary school girls, junior middle school boys, and junior middle school girls for structural equation model analysis.

This study investigated the ways by which teacher's emotional support, academic self-efficacy, and math behavioral engagement affected the math performance of Chinese primary and middle school students. The results showed that teacher's emotional support could directly affect math performance of Chinese primary and middle school boys and girls, which was consistent with the study hypothesis H1 and previous research findings (Kashy-Rosenbaum et al., 2018). According to the ecosystem theory (Bronfenbrenner, 2009), school is the micro-system that has the closest influence on the development of students besides the family environment. As an important part of the school microsystem, the interaction between teachers and students will affect the academic performance and behavior of the student. The emotional support of the teacher satisfies the psychological needs of the student and stimulates learning motivation in the student. They are more willing to invest time and energy in learning tasks, and the more likely they are to achieve academic success.

The test results show that academic self-efficacy and math behavioral engagement play an intermediary role in the teacher's emotional support and math performance of Chinese primary and middle school boys and girls, respectively. Hypothesis 2 and 3 are verified. This is consistent with the results of previous studies. Emotional support of teacher behavior satisfies the needs of the student for competence and belonging (Jin and Wang, 2019). Self-determination theory (Ryan and Deci, 2000) believes that when these needs of students are met, it is conducive to the development of self-efficacy. The higher the level of self-efficacy of the student, the easier it is to achieve better academic performance (Komarraju and Nadler, 2013; MacPhee et al., 2013). Positive classroom interaction between teachers and students is very important to improve the behavioral engagement of the students (Cooper, 2014). As an important aspect of classroom interaction, the emotional support of the teacher plays an important role in enhancing the learning engagement of the student (Liu et al., 2018), and Lee (2014) found that middle school behavioral engagement of students can predict the performance of standardized achievement tests.

Academic self-efficacy enhanced the degree of math behavioral engagement and played a continuous intermediary role in the impact of teacher's emotional support on the math performance of Chinese junior middle school boys and girls. Hypothesis 4 is verified. This is consistent with the results of previous studies. Students can feel the care, trust, and respect of the teacher for them (Roth and Weinstock, 2013), which can stimulate positive emotions of the students, thus generate positive self-evaluation and further enhance their sense of academic self-efficacy. The increase of self-efficacy has a direct impact on the engagement of the student in learning behavior (Goetz et al., 2010), learning engagement can significantly predict academic achievement (Lee, 2014).

This study reveals the important role of teacher's emotional support, academic self-efficacy, and math behavioral engagement in math performance, and explores the chain mediating role of academic self-efficacy and math behavioral engagement. The strength of this study is to help broaden the knowledge about the contextual and individual motivational variables that can influence mathematical achievement. Therefore, the study addresses an important area and provides some new information/data. The results show the importance of the style and behavior of the teacher, which is of guiding significance for improving student engagement and math performance as well as education and teaching of teachers. The social system, school management, and teaching activities should be considered to promote teachers to adopt a supportive style of teaching.

But there are several weaknesses. Some statistical model indicators do not fit very well, probably because the data were collected by online channels. It is a cross-sectional study as it lacks longitudinal data and cannot accurately infer the causal relationship between variables. In the follow-up, it will investigate whether the relationship between teacher's emotional support, academic self-efficacy, math behavioral engagement, and math performance will change over time.