3.2.1. Psychometric method
(1) Physical Activity Rating Scale (PARS-3)
The Physical Activity Rating Scale (PARS-3) compiled by Liang Deqing, which is widely used in the field of physical activity, is mainly used to assess an individual's physical activity level [24]. ARS-3 consists of three modules: activity intensity, activity duration, and activity frequency. Each module is divided into 5 levels, scoring 1–5 points, physical activity amount = intensity x time x frequency, the amount of physical activity can be converted into the highest 100 points, the lowest 0 points, the formulation of the physical activity scale standard: small activity amount ≤ 19 points; Small activity ≤ 20–39 minutes; Medium activity ≤ 40–59 min; Greater activity ≤ 60–79 min; Large activity ≤ 80–100 minutes. Studies have proved that the scale has good reliability and validity in middle school students [25]. In this study, Cronbach's α coefficient and KMO value of this scale were 0.506 and 0.651, indicating that the scale questionnaire in this study had good reliability and validity.
(2) Academic achievement Scale
Using the academic achievement questionnaire compiled by Wen Chao et al. [26], middle school students were asked to evaluate their academic performance in Chinese, mathematics and English. Using a 5-point score (1 is very bad, 2 is lower than average, 3 is medium, 4 is above average, and 5 is very good), the average score of the three subjects is finally calculated. In addition, considering the combined calculation of the test scores of the two subjects, this study converted the original test scores (mean 50, standard deviation 10) during data processing. The higher the score, the stronger the academic achievement of the subjects [27]. Studies have proved that the scale has good reliability and validity in middle school students [28]. In this study, the Cronbach's α coefficient and KMO value of this scale were 0.875 and 0.718, indicating that the scale questionnaire in this study had good reliability and validity.
(3) Social support scale
The perceptive social support Scale was originally compiled by Zimet [29] and later translated and revised by Jiang Qianjin, a Chinese scholar, to reflect the degree of perceptive social support, with emphasis on individuals' self-understanding and self-feeling of different sources of social support [30]. The scale consists of 12 questions and consists of three dimensions (family support, friend support, and other support). The scale is scored with 7 Likert points, from 1 to 7 points is "strongly disagree" to "strongly agree". The total score of understanding social support is summed up by all items, and the total score between 12 and 36 is low support state, the total score between 37 and 60 is intermediate support state, and the total score between 61 and 84 is high support state. A higher score indicates a higher level of social support. Studies have proved that the scale has good reliability and validity in middle school students [31]. In this study, Cronbach's α coefficient and KMO value of this scale were 0.879 and 0.948, indicating that the scale questionnaire in this study had good reliability and validity.
(4) Learning engagement Scale
The Utrecht Work Engagement Scale-Student compiled by Schaufeli et al., and revised by Fang Laitan et al. (2008) was adopted [32.33]. The revised scale includes three dimensions of vitality (6 questions), dedication (5 questions) and concentration (6 questions), with a total of 17 questions. Likert-7-point score is adopted, with 1 representing "never" and 7 representing "always". The total score of learning engagement is summed up by all items. The higher the score of each dimension, the higher the level of learning engagement. Studies have proved that the scale has good reliability and validity in middle school students [34]. In this study, the Cronbach's α coefficient and KMO value of this scale were 0.920 and 0.954, indicating that the scale questionnaire in this study had good reliability and validity.
3.2.2. Mathematical statistics
After the questionnaire was collected and the invalid data were screened again, SPSS21.0 software and the SPSS macro program Process plug-in compiled by Hayes were used for statistical analysis of the data in this study. First, SPSS21.0 software was used to conduct descriptive statistics (mean ± standard deviation) and difference test (P < 0.05) on the test data of demographic information, physical activity, academic achievement, social support and learning engagement. Second, common latent factors are used in SPSS21.0 software to test for common method bias. Third, SPSS21.0 was used to examine the Pearson bivariate relationship between physical activity, academic achievement, social support and learning engagement of middle school students. Fourthly, the PROCESS plug-in model 6 and Bootstrap (5000 times) sampling technique were used to examine the independent mediating effect between social support and learning engagement, and the chain mediating effect between physical activity and academic achievement. In this study, P < 0.05 was set as a statistical result with significance.