Motivational climate, need satisfaction, self-determined motivation, and accelerometer-measured physical activity among secondary school students in China

Objectives Based on integration constructs from self-determination theory (SDT) and achievement goal theory (AGT), this study aims to investigate the relationship among classroom motivational climate from four perspectives (i.e., autonomy support, relatedness support, task-involving climate and ego-involving climate), three psychological needs (i.e., autonomy, competence and relatedness), self-determined motivation and physical activity (PA) in secondary physical education (PE).Methods The participants consisted of 1,186 Chinese students aged 11 to 16 years from three secondary schools around Shanghai. An accelerometer was adopted to measure moderate-to-vigorous physical activity (MVPA). Questionnaires were used to measure SDT variables (i.e., classroom motivational climate, perceived competence, autonomy, relatedness, self-determined motivation). Structural equation modelling (SEM) was used to analyze the hypothesized relationship.Results A SEM analysis revealed that autonomy support and task-involving climate were positively associated with autonomy, relatedness and competence. Relatedness support was positively related with autonomy and relatedness, whereas ego-involving climate was only associated with competence. The three psychological needs positively affected self-determined motivation, and self-determined motivation positively affected the MVPA time of secondary school students in PE lessons.Conclusion These findings support a model of motivation that integrate SDT and AGT, provides new insight into understanding MVPA in Chinese PE, and establishes a solid basis for intervention research. correlation results showed that classroom climate variables such as autonomy support, relatedness support, task-involving climate, and ego-involving climate were positively related to autonomy, competence and relatedness. Autonomy, competence and relatedness are positively related to intrinsic motivation and identified motivation, but were negatively related to external motivation and amotivation. Intrinsic motivation and identified motivation were positively associated with student MVPA in PE.

50% of their time in PE class to obtain health benefits [7]. However, numerous studies have found that secondary school students do not meet this recommended time in a variety of countries [8][9][10][11][12][13][14].
One review by Hollis et al. [14] has found that secondary school students engage in MVPA for an average of 40.5% of their time in PE class. Hence, promoting adolescent MVPA engagement in PE has become an imperative task.
Motivation is an individual drive to act, and several studies have reported that the motivation of students in PE drives them to engage in physical activities and develop their habit of PA participation [15][16][17]. The relationship between the motivational profiles and PA engagement of students in PE must be investigated to provide evidence to develop strategies in promoting students' PA level in PE classes [6,18]. Self-determination theory (SDT) [19] and Achievement Goal Theory (AGT) [20] are two social-cognitive theories that are widely used for studying student motivation in the PE setting.

SDT and student MVPA in PE classes
SDT [21] is one of the numerous theoretical frameworks that can provide insights into human motivation and psychological development. According to SDT, there is a continuum of motivation which determined behavior: intrinsic motivation (an individual engages in activity out of interest in the activity itself), extrinsic motivation (an individual performs an activity to obtain certain desirable and separate outcomes such as rewards, grades, and praise), and amotivation (an individual perceives no association between behavior and corresponding outcome) [19,22]. The extrinsic motivation is theoretically divided into four specific behavioral regulations that vary in their level of self-determination, including external regulation, introjected regulation, identified regulation, and integrated regulation. External regulation occurs when an individual's behavior is governed by the externally controlled contingencies administered by others. Introjected regulation occurs when an individual's behavior is controlled by contingent consequences administered by the individuals to themselves. Identified regulation occurs when individuals participate to gain benefits that they consider important (e.g., fitness gains or weigh loss). Integrated regulation is the fullest and most complete form of internalization of extrinsic motivation, in which individuals consider the benefits they have gained consistent with their core values and beliefs [22]. However, researchers have suggested that assessing the integrated regulation of adolescents is not needed because they have yet to develop this type of regulation [23,24]. Based on SDT, self-determined forms of motivation, including intrinsic motivation and identified regulation, are associated with positive outcomes, whereas controlling forms of motivation, such as introjected regulation and external regulation, and amotivation, are related to negative outcomes [22]. Empirical evidence has also confirmed that the self-determined PE motivation of students is positively associated with student MVPA during PE [15,17,[25][26][27][28].
Another core tenet of SDT is that individuals have innate needs to be competent, autonomous, and socially related, which are associated with their motivation and further influence their cognitive, affective, and behavioral consequences [19,21]. Autonomy refers to a need of feeling in which an individual has a choice and a sense of freedom before taking action. Perceived competence is described as the ability to achieve desired outcomes effectively. Relatedness refers to the need to contact with and be accepted by significant others (i.e., schoolmates, peers and sibling). According to SDT, satisfying or meeting three innate psychological needs can promote self-determined motivation.
Under the PE context, some studies have examined the relationship between the satisfaction of the three psychological needs and students' MVPA level. They have found that these needs are positively associated with self-determined motivation and further enhanced their MVPA level [29][30][31].
A third fundamental tenet of SDT is that different social context either satisfy or hinder the needs for autonomy, competence, and relatedness. In addition, these situations indirectly influence the forms of motivation further. Under PE context, some studies found that perceived need support (autonomy support, competence support, and relatedness support) from PE teachers [29][30][31][32][33][34][35] positively affects three types of psychological needs to foster self-determined motivation.

AGT and student MVPA in PE classes
Another prevailing theory is AGT, which describes social and cognitive factors associated with adolescent motivation. Two important elements are used in AGT, namely, individual's goal orientation (i.e., individuals' competence toward an activity) and social environment (i.e., motivational climate) [20,36]. In this study, we only adopted the construct of motivational climate, which relates to a psychological environment that directs the goals in achievement situation in PE [36][37][38]. Motivational climate refers to the social environment that is created or fostered by significant others such as PE teachers in achievement environment [16]. According to AGT, motivational climate is divided into two climates, namely, task-involving and ego-involving climate. Task-involving climate is characterized by self-references, mistake as part of integral learning, cooperation, effort, and task-mastery, whereas ego-involving climate is characterized by normative comparison, less effort, and competition with others [38]. Under PE context, previous studies have found that a task-involving climate created by teachers is positively related to the satisfaction of the three psychological needs, whereas the egoinvolving climate is not related or negatively related to autonomy, competence and relatedness [39,40].

Theoretical integration of SDT and AGT
Certain similarities and differences have been found between SDT and AGT. Both theories emphasize the construct of perceived competence and the influence of classroom climate. However, the two theories view them differently. On the one hand, AGT operates only with perceived competence. On the other hand, SDT involved autonomy and social relatedness as additional elements except for the perception of competence. Second, SDT does not divide the competence support climate into taskinvolving and ego-involving climate, which are crucial elements in motivating students in PE [36,41].
Some studies have suggested that the two models should be integrated to provide a comprehensive understanding of the motivational mechanisms involved in the class [24,36]. Therefore, the present study integrated the SDT and AGT to investigate relationship among the four types of PE climate, psychological needs (i.e., autonomy, competence and relatedness), self-determined motivation, and MVPA time of students in PE. Based on the literature, this study proposes the hypothesized model described in Figure 1. Specifically, we hypothesized that: (1) self-determined motivation is positively associated with student MVPA in PE. (2) Self-determined motivation can be positively predicted by the satisfaction of the three basic psychological needs. (3) Autonomy support, task-involving PE climate, and relatedness support are positively related to the satisfaction of the three psychological needs, whereas ego-involving climate is negatively related. (4) The three basic psychological needs and self-determined motivation mediate the relationship between the PE climate created by PE teachers and MVPA of adolescent students in PE.

Participants and setting
The university ethics committee and relevant educational authorities approved the study. For convenience, three secondary schools were selected from shanghai, a city in the eastern part of China. Secondary school has four grades (i.e., Grades 6 to 9) and three or four classes were selected randomly from each grade. A total of 1,344 students from 42 classes were invited to participate in this study, and consent forms were sent to them and their parents. Of the 1,344 students, 1,221 volunteered to participate, with 1,199 students providing both MVPA and survey data (98.2% response rate) Participants were taught a 40-minute co-educational PE class on alternate days by 18 certified PE teachers with 8 to 15 years of teaching experience in school settings. Data were collected in 42 different PE classes, including three track and field lessons, five game lessons, three aerobics lessons, six basketball lessons, five football lessons, four table tennis lessons, six volleyball lessons, three badminton lessons, three kung fu lessons, and four jump rope lessons. In a typical PE classes, a 5-to 10-minute warm-up was provided at the beginning of the class. Then the teachers instructed sports skills and organized students to practice during the middle period of the class (25 to 30 minutes).
Finally they provided cool-down activities and closure to the lesson (5 minutes).

MVPA in PE
Student MVPA in PE was measured by using Actigraph GT3X accelerometers, which had been confirmed to be a valid instrument in measuring the PA of children and adolescents [42,43]. A onesecond epoch was used to avoid underestimating short periods of high-intensity activity; specific cutoff points for Chinese children and youths aged 9 to 17 years were used to determine activity level thresholds, defining MVPA as counts per minute ≥ 2800 [44].

Self-determined Motivation
Motivation in PE was assessed using the Sport Motivation Scale (SMS) [45]. The SMS included four dimensions (intrinsic motivation, identified regulation, external regulation, and amotivation), each with four items. The stem, "I take part in PE class…," precedes the items. Examples included "because PE is exciting" (intrinsic motivation), "because I want to learn sport skills" (identified regulation), "because I'll get into trouble if I don't" (external regulation), and "but I don't see why we should have PE" (amotivation). Participants responded through a seven-point scale ranging from 1 (strongly disagree) to 7 (strongly agree). Evidence on internal consistency and construct validity were found adequate in previous studies [45,46]. To examine student self-determined motivational levels [40], a self-determination index (SDI) was adopted by using the formula, SDI = (2 * intrinsic motivation) + (identified regulation) -(external regulation) -(2 * amotivation) [12,17].

Basic Psychological Needs in Physical Education
The Psychological Needs Satisfaction Scale in PE lesson [47] was used to assess student autonomy, competence, and relatedness. Every subscale of the three psychological needs had three items, resulting in a total of nine items. Sample items (competence) include (a) "I think I am good at PE," (b) "I feel I am good in sport skills," and (c) "I feel I am able to do most of games well in PE". Students responded to these items on a five-point Likert scale ranging from "strongly disagree (1)" to "strongly agree (5)". The composite reliability coefficients for autonomy, competence, and relatedness were acceptable [47].

Motivational Climate in Physical Education
Students' perception of the motivational climate in PE were assessed using the Motivation Climate in Physical Education Scale (MCPES) [48], which consists of four subscales (18 items) that measured the climate of autonomy support, relatedness support, task-involving, and ego-involving. The stem, "I take part in PE class…," precedes the items. The scale has 18 items, with five terms assessing autonomy support (e.g. "Students have significant freedom to make choices during PE lessons") and five items assessing task-involving climate (e.g., "It is important for the students to try their best during PE lessons"). Relatedness support (e.g., "Our PE class is united when practicing during PE lessons") and ego-involving climate (e.g., "It is important for students to show that they are better in PE than others") had four items each. Students responded to these items on a five-point Likert scale ranging from "strongly disagree (1)" to "strongly agree (5)". Internal consistency and construct validity with a sample of secondary school students were found to be adequate [36].

Translation procedures
Before the data collection, questionnaires were translated and validated. Translation and backtranslation of scales were conducted by two bilingual experts individually. The original English version was then compared with the back-translated version, and different opinions were discussed by the two translators until they were unanimous. The Chinese version of the questionnaire was sent to five experts for advices. Accordingly, certain modifications were made based on suggestions from the experts. For instance, the item "what's most important is that we progress every year in our skill" was changed to "what's most important is that we progress every year in our motor skill". The item, "Our PE class has a good sense of unity", was changed to "We have a good sense of unity in PE class" because the new item was more in line with the language habits of Chinese adolescents.

Data collection
Data was collected by the first author and three research assistants from December 2018 to January 2019. Prior to starting each PE class, the research purpose was explained, and instructions on how to wear the accelerometers were provided. Before the beginning of the typical PE class, participating students were asked to wear the Actigraph GT3X accelerometers. The accelerometers were fastened to the right hipbone by an elastic belt for the entire lesson. A research assistant monitored the students to ensure that they did not remove the accelerometers during the PE classes. All accelerometers were returned when the class was over. Therefore, the valid wearing time of an accelerometer was defined as being 100% of PE class time. After class, the Actigraph data were downloaded to individual computer via the ActiLife software 6.11.5, and raw accelerometer counts were converted into minutes spent for MVPA per class. After the class, the questionnaires were distributed to the students. The survey was completed within approximately 15 minutes. The questionnaires were collected immediately upon completion.

Data analysis
The main analysis was conducted using IBM SPSS Amos 21.0. Confirmatory factor analysis (CFA) was initially conducted on the study inventories to inspect the adequacy of the measurement model.
Structural equation modeling (SEM) was used to examine whether the hypothesized theoretical model specified in Figure 1 fitted the data in this study. Model fit to the data was inspected using chi-square statistic X 2 value, goodness-of-fit index (GFI), incremental fit index (IFI), comparative fit index (CFI), standardized root square residual (SRMR), and root mean square error of approximation (RMSEA).
According to Hu and Bentler [49], the CFI and IFI had values close to or greater than 0.90, and RMSEA and SRMR had values of 0.06 and 0.08 or less, respectively, showing an acceptable model fit. The bootstrap-generated bias-corrected confidence approach was used to explore the mediated relationship among variables.

Demographic characteristics
Out of the 1,199 participants, 11 students were found to have missing data, and two students were outliers because of accelerometer malfunction. All these data were consequently eliminated because

Scale reliability and validity
Mardia's multivariate kurtosis coefficient was used to examine the normality of each variable, and the results indicated that the data distribution was abnormal. CFA was implemented to test the construct validity of scales. CFA was conducted by using the maximum likelihood estimation method with the bootstrapping procedure because it does not require the normal distribution of the data.  Table 1). These results indicated acceptable internal consistency of the all subscales.

Descriptive analysis and bivariate correlations
Descriptive statistics and bivariate correlation for scales was presented in Table 1. Except for external motivation (M = 2.84, SD = 1.58) and amotivation (M = 1.44, SD = 1.14), the mean scores of other variables were higher than the midpoint.
Given that the present data indicated abnormal distribution, the bivariate correlation for each variable was calculated by Spearman. Bivariate correlation results showed that classroom climate variables such as autonomy support, relatedness support, task-involving climate, and ego-involving climate were positively related to autonomy, competence and relatedness. Autonomy, competence and relatedness are positively related to intrinsic motivation and identified motivation, but were negatively related to external motivation and amotivation. Intrinsic motivation and identified motivation were positively associated with student MVPA in PE.

Testing hypothesized structural modelling
SEM was used to test the relationship among the latent variables outlined in Figure 1. The results of path analysis revealed a good fit to the data, X 2 = 2048.997, df = 357, P < 0.0001; CFI = 0.918; IFI = 0.918; SRMR = 0.067; RMSEA = 0.058 (Figure 2). The R 2 value revealed that autonomy support, relatedness support, and task-and ego-involving climate explained the 55%, 65% and 30% of the variance in autonomy, relatedness and competence scores, respectively. Autonomy, competence, and relatedness predicted 33% of the variance in self-determined motivation. Finally, self-determined motivation accounted for 1.4% of the variance in students' MVPA in PE. Most of the regression weights were significant and positive except for three paths, namely, the path from relatedness support to competence (β = 0.072, P > 0.05), the path from ego-involving climate to autonomy (β = 0.028, P > 0.05), and the path from ego-involving climate to relatedness (β = 0.042, P > 0.05).
To examine the mediating effect, the 11 direct paths presented in Table 2 were added to the hypothesized model. After the 2000 bootstrap samples were extracted from the raw data, the results supported the partial mediation for task-involving climate (β = 0.149, P <0.01; Bootstrap 95% CI = 0.093-0.221) to self-determined motivation through autonomy, competence and relatedness. The partial mediation was supported for ego-involving climate (β = 0.051, P < 0.01; Bootstrap 95% CI = 0.025-0.088) to self-determined motivation only through competence.

Discussion
The present study aimed to examine the relationship among the PE climate (i.e., autonomy support, relatedness support, task-involving climate and ego-involving climate), three basic psychological needs (i.e., autonomy, competence, and relatedness), self-determined motivation, and MVPA of secondary school students. Findings showed that the autonomy support and task-involving climate students perceived were positively related to all three psychological needs, whereas relatedness support positively predicted autonomy and relatedness, and ego-involving climate were only positively related to competence. Autonomy, competence, and relatedness positively predicted selfdetermined motivation toward the MVPA. Finally, the self-determined motivation positively predicted the MVPA of the secondary school students.

Self-determined motivation
Results of the present study indicated that the self-determined motivation of secondary school student was positively related to their MVPA during PE and supported our first hypothesis. This finding was also consistent with the tenet of SDT [22] and previous studies in PE context [15,17,28].
However, the findings of the present study revealed that self-determined motivation only explained 1.4% of the variance in student MVPA, which was lower than the results of previous studies under the PE context, ranging from 2% to 4% [15,17,28]. The PE lessons structure, nature of the Chinese PE curriculum, and Chinese educational culture may contribute to the low interpretation rate of variance in student MVPA. First, the Chinese PE curriculum is compulsory, and each student must attend PE classes. Moreover, the class content and PE activities are arranged by secondary schools and teachers, and students cannot choose activities in PE class. Therefore, student motivation is a nonfactor in PE classes, possibly resulting in the small contribution of self-determined motivation to student MVPA. Second, education in China is based on Confucian principles, which have educated students to be obedient and place emphasis on self-control and personal restraint [50,51]. This practice may lead to students' lack of knowledge of their own motivation and interests, thus weakening the effect of their self-determined motivation on their MVPA participation. Although selfdetermined motivation only explained 1.4% of the variance in student MVPA, it remained important, as students with self-determined motivation were likely to continue to participate in MVPA out of the PE class. Based on this finding, PE teachers are advised to adopt certain instructional strategies (e.g., cooperative learning) and activities to stimulate students' interest and improve students' selfdetermined motivation, which ultimately enhances MVPA in PE.

Psychological needs
Results showed that the three psychological needs of autonomy, competence and relatedness positively predicted self-determined motivation. Students were more likely to be intrinsically motivated to participate in MVPA when they perceived further competence to exhibit their sport skills, had more opportunities to choose, and were more connected with peers or classmates in PE classes.
This finding supported the secondary hypothesis, and it was aligned with the previous PE-related studies under the SDT framework [24,31,33,35,39,40,52,53]. Furthermore, three psychological need satisfaction mediated the relationship between PE climate created by teachers and selfdetermined motivation, which was consistent with the tenet of SDT [22]. The importance of the psychological needs of autonomy, competence and relatedness were suggested by the direct and indirect relationships. The fourth hypothesis was partly supported.
Among three psychological needs, relatedness was the strongest predictor of self-determined motivation in this study. This finding was consistent with the studies of Standage et al. [24] and Cox et al. [53], but it was different from other studies [33, 46,52] that found perceived competence as the most important variable to self-determined motivation. Deci and Ryan [21,22] argued that the relative effect of each psychological need satisfaction on self-determined motivation might vary depending on the functional significance of the context. The strongest influence of relatedness may be related to the emphasis of PE on student cooperation in China. The Chinese Curriculum Standard for Physical Education and Health of the primary and middle schools indicated that one of the objectives of the PE curriculum was to develop student social adaption [54]. Certain pedagogical models that addressed student collaboration (e.g., cooperative learning approach) were recommended to PE teachers to develop students' collectivism and cooperative consciousness [54].
More opportunities were provided for students to interact with peers in PE classes, possibly allowing them to find PE fun and exciting; thus they are more willing to participate in PE activities. The low importance of student autonomy and competence in SDT in this study is also understandable because of the students' insufficient autonomy in PE classes and the weakening importance of sports skills and sports performance in the current PE learning assessment system [54].

Influence of PE climate
The finding of this study showed that autonomy support positively predicted the three psychological needs. Specifically, students felt autonomous, competent, and related when perceiving autonomy support with low control. This finding supported the third hypothesis and was congruent with previous studies in the context of PE [33,34]. Furthermore, the magnitude of the standardized regression coefficients from autonomy support to the three psychological needs was found to be the highest among the four types of classroom climate, suggesting that autonomy support mostly influenced the satisfaction of the three psychological needs. However, the Chinese traditional teaching style was authoritarian or controlling in PE classes [55]. The mean score of student perceptions of autonomy support climate was lower than relatedness support and task-involving climates in our study also confirmed this fact.
With regard to relatedness support, research findings indicated that student learning in a PE environment where good relationship among students were established felt more autonomous and related in PE, which was consistent with previous research [53]. Unlike the third hypothesis, the path from relatedness support to student competence was insignificant, revealing that the relatedness support PE teachers created could not predict student perception of competence in PE. The possible reason was that the harmonious relationship and emphasis on cooperation among students might weaken competition among students [56], distracting student attention from their competence and performance in PE.
Research findings showed that the student perception of task-involving climate was positively and significantly related to psychological need satisfaction of autonomy, competence, and relatedness.
Students felt more autonomous, competent, and related when they perceived that PE teachers emphasized their effort and self-reference on success or progress. These findings were aligned with previous study in the context of PE [39] and sport context [57]. However, unlike the third hypothesis, the results showed that ego-involving climate was positively associated with competence and not significantly related to autonomy and relatedness. Such a climate resulted in competition among students, which might help improve their sports competence [58]. The nonsignificant influence of ego-involving climate on relatedness and autonomy was also accepted because this type of climate does not address student connectedness and autonomy.
Given the importance of the motivational climate on autonomy, competence and relatedness, the class climate that focused on autonomy, competence, relatedness of students is needed to promote student psychological needs. PE teachers should provide autonomy support and are suggested to put special effort in giving students more freedom to make choices, involving them in decision making, and respecting their personal volition during PE classes. Relatedness support should be cultivated, and PE teachers should set challenging goal for cooperative groups, and emphasize the importance of team progress so as to pull students together as a group. Although ego-involving climate contributed to improving students' perceived competence, its adoption by PE teachers is prudent because it emphasizes the normative comparison among students [59]. Finally, PE teachers are suggested to create the task-involving climate that emphasizes effort, progress on self-referenced criterion, learning new things during the PE lessons by a variety of teaching strategies and methods (e.g., TARGET approach [37]).

Strengths and limitations
The present study has several important strengths. First, it was the first to examine the relationship among the PE climate from the four dimensions, the satisfaction of psychological needs, motivation, and accelerometer-determined MVPA in secondary school students. Second, objective measures were adopted to evaluate the MVPA of secondary school students to eliminate the bias of subjective scales.
Third the present study provided the new insight into understanding how the manners by which students perceived the PE climate created by PE teachers had different influence on autonomy, competence and relatedness. However, this study has some limitations. First, the results of the current study should not be interpreted as causal to cross-sectional research. Therefore, longitudinal and intervention studies must be conducted in the future. Second, Participants were from three secondary school in Shanghai, China. Thus, the results of this study might not be used to generalize situations in other populations. Future research should expand the population beyond Shanghai to other regions or countries. The third limitation was the use of the SDT index to assess the students' motivation. Future study should focus on analyzing the relationship among the intrinsic motivation, integrated motivation, identified motivation, introjected motivation, external motivation, amotivation and MVPA in PE. Fourth, this study did not consider the influence of demographic variables such as gender and age when analyzing the relationship between SDT variables and MVPA. Future studies should consider the influence of demographic variables.

Conclusions
The results of this study emphasized the importance of classroom climate created by PE teachers. The

Acknowledgements
We thank all children, parents and teachers at the participating schools for their excellent cooperation during the data collection.

Authors' contributions
LW originated the research idea and wrote the manuscript. RC contributed to data analysis and writing the manuscript. BW and YZ contributed to collecting data. All authors read and approved the final manuscript.

Availability of data and materials
The datasets used and/or analyzed during the present study are available from the corresponding author (wlj711@aliyun.com) on reasonable request. Note. SDI = self-determined motivation index; MVPA = moderate-to-vigorous physical activity * P < .05, ** P < .01 Figure 1 Hypothesized model of motivational process in PE Note. SDI = self-determined motivation index; MVPA = moderate-to-vigorous physical activity.

Figure 2
Self-determination process model with standardized coefficients for participants. Note. SDI = self-determined motivation index; MVPA = moderate-to-vigorous physical activity; Broken lines represent nonsignificant standardized parameter estimates; Solid lines represent significant standardized parameter estimates.