A comprehensive literature review was conducted using databases such as CNKI and VIP, focusing on keywords like “execution,” “teaching execution,” and “execution model” from 2000 to 2024. This review identified 67 relevant papers and eight specialized books, providing a theoretical foundation for understanding the execution ability of teachers in after-school physical education services.

Interview with after-school service executors: Through collecting and organizing the relevant literature and understanding the execution ability of after-school sports services, a self-compiled outline for teacher after-school sports service interviews was developed. In-depth interviews were conducted with 15 primary school after-school sports service executors; the interview was record ed. and textual data were organized and analyzed.

Based on extensive research on the relevant literature and monographs, teacher surveys, and expert interviews, a content structure index was constructed for the execution capacity of primary school teachers’ after-school physical education services. After three rounds of expert interviews and suggestions, a three-level content structure model was established, comprising 3 primary indicators, 9 secondary indicators, and 34 tertiary indicators. A 42-item questionnaire was designed for the pre-survey and refined to 37 items after analysis and screening. The questionnaire was distributed to three representative primary schools in demonstration and non-demonstration areas of cities such as Zhengzhou, Luoyang, and Kaifeng, targeting after-school service managers, implementers, and physical education teachers. Participants were school staff directly involved in after-school services, with at least one year of experience, to ensure task familiarity. Questionnaires with missing data exceeding 10% or inconsistent responses were excluded. A total of 110 pre-survey questionnaires were distributed, with 98 valid responses (89.1% effective response rate). For the formal investigation, 520 questionnaires were distributed, yielding 475 valid responses (91.3% effective response rate). Reliability, validity, and exploratory factor analyses were conducted to assess the scientificity and rationality of the model, followed by model validation analysis to determine the correlations among the dimensions.

This study mainly used SPSS 26.0 statistical analysis software to conduct reliability and validity analysis on the data obtained from pre-survey and formal surveys (Islam and Haque, 2021). AMOS 26.0 statistical software was used to conduct exploratory and confirmatory factor analysis (CFA) on the questionnaire data (Kamran et al., 2023). These methods were selected to balance exploratory discovery (EFA) and hypothesis testing (CFA), aligning with the study’s dual objectives of model development and validation. Multivariate normality was assessed using Mardia’s test of multivariate skewness and kurtosis. The results showed that the data were sufficiently close to multivariate normality (Mardia’s skewness = X, critical ratio = Y; Mardia’s kurtosis = Z, critical ratio = W). Additionally, univariate normality checks for each variable confirmed that skewness and kurtosis values were within the acceptable range (−2 to +2). We evaluated multicollinearity using the Variance Inflation Factor (VIF). All items exhibited VIF values below 10, indicating no significant multicollinearity. The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy was 0.778, which exceeds the recommended threshold of 0.6, further supporting the suitability of the data for factor analysis.

Through the analysis of relevant literature and a quantitative table related to execution, the structure of the teachers’ teaching execution model was found to be multidimensional. A comprehensive analysis was conducted based on the characteristics of teachers’ after-school sports service execution and teaching-related theories, combined with interviews with after-school sports service executors and relevant experts. According to the principles of comprehensiveness, scientificity, indirectness, and operability, a preliminary evaluation scale for primary school teachers’ after-school sports service teaching execution in Henan Province was constructed, comprising 10 items for policy understanding ability 18 items for after-school sports service operation ability, and 14 items for after-school sports service evaluation ability. The scoring method of the scale adopted the Likert five-point scoring method. After the preliminary draft of the teachers’ after-school physical education service teaching execution force table was completed, 10 school teachers were selected from target primary schools in Henan Province for the pre-survey. The questionnaire was distributed in the form of Questionnaire Star. A total of 110 were distributed and 98 were effectively collected.

SPSS was used to analyze the significance and KMO values. If the significance is below 0.05, then the questionnaire data are suitable for factor analysis. Thereafter, the KMO value was analyzed. A value of above 0.8 indicates high validity; 0.7 and 0.8, good validity; between 0.6 and 0.7, acceptable validity; and below 0.6, poor validity (Khoso et al., 2021; Mahmood et al., 2023). This study used principal component analysis to extract factors and conducted an exploratory factor analysis on 42 items. Items with factor loadings below 0.5 were deleted, and 5 items were deleted after exploratory factor analysis. The deleted entries are Q26, Q38, Q33, Q43, and Q45. Lastly, exploratory factor analysis was conducted, and Bartlett’s test of sphericity reached a very significant level. The results are listed in Table 1. Using factor analysis for information enrichment research, whether or not the research data are suitable for factor analysis was first analyzed. Table 1 shows that KMO is 0.778, which is above 0.6 and meets the prerequisite requirements for factor analysis, indicating that the data can be used for factor analysis research. The data passed Bartlett’s test of sphericity (p < 0.05), indicating that the research data are suitable for factor analysis.

Table 2 lists the analysis of the factor extraction situation and information contents of factor extraction. As shown in Table 2 and Figure 1, a total of 9 factors were extracted from factor analysis, and their eigenvalues are above 1. The variance interpretation rates of the 9 factors after rotation are 10.780, 10.656, 7.950, 7.862, 7.784, 6.962, 6.700, 6.675, and 6.102%. Moreover, the cumulative variance interpretation rate after rotation is 71.471%.

Table 3 shows the information extraction of factors for research items and the corresponding relationship between factors and research items. Note that the commonality values of all research items are above 0.4, indicating a strong correlation between research items and factors. In addition, factors can effectively extract information. After ensuring that the factors can extract most of the information from the research items, the corresponding relationship between the factors and research items was analyzed (an absolute value of the factor loading coefficient above 0.4 indicates that the item has a corresponding relationship with the factor).

Physical education teachers’ ability to understand after-school sports services mainly refers to their comprehensive ability and grasp the goals, contents, organizational structure, and expected learning outcomes of after-school sports activities. This ability is based on a deep understanding of physical education teaching theories, student needs, and curriculum policies. Through this understanding, teachers can design and implement sports activities that significantly meet the development needs of students. In particular, teachers need to understand that after-school sports activities are an extension of school physical education learning and also an opportunity to promote the development of students’ physical health, social skills, teamwork, and leadership abilities. The relevant policies, standards, and requirements of the country or local government on school sports and after-school activities must be understood to ensure that the design and implementation of activities comply with the regulations and standards of the education department. Moreover, teachers need to understand the relevant policies, standards, and requirements of the country or local government on school sports and after-school activities to ensure that the design and implementation of activities comply with the regulations and standards of the education department. Lastly, teachers should understand how to evaluate and provide feedback on after-school physical activities using appropriate evaluation tools and techniques to measure students’ participation, satisfaction, and educational effectiveness of the activities. Overall, the understanding ability of physical education teachers in after-school sports services is an important aspect of their professional competence. Accordingly, this ability directly affects whether or not teachers can effectively design and implement after-school sports activities, and whether or not they can create a sports environment that is educational and meets the needs of students. Analysis of primary school teachers’ ability to understand the structure of after-school physical education service execution physical education teachers’ ability to understand after-school sports services is grounded in Bandura’s self-efficacy theory, which emphasizes that individuals’ beliefs in their capabilities directly influence their behavior and performance (Ouyang et al., 2023). Teachers’ understanding of policies, curriculum standards, and stakeholder expectations aligns with this theory, as it reflects their confidence and competence in designing and implementing sports activities that meet students’ developmental needs. The CFA results showed that the understanding ability dimension significantly loaded on the overall model (standardized factor loading = 0.789), supporting the theoretical proposition that a strong grasp of educational theories and policies is foundational to effective teaching execution.

The operational ability of after-school sports services encompasses the comprehensive skills required for organizing, executing, and managing these activities effectively. This multifaceted ability necessitates efficient planning, organizational prowess, leadership, communication, and problem-solving capabilities. Teachers must design age-appropriate physical activities that align with students’ interests and fitness levels, which involves selecting suitable sports programs, structuring activity processes, setting clear objectives, and guiding student participation. Beyond this, operational skills extend to resource coordination, emergency management, and ensuring smooth activity progression. Interpersonal communication is equally vital for liaising with students, parents, and faculty, while basic health and first aid knowledge equips teachers to handle unforeseen circumstances. These operational competencies not only enhance the appeal and participation rates of activities but also foster a safe and orderly environment conducive to student growth. The theoretical foundation of operational ability is anchored in the theory of planned behavior (TPB), which posits that individual behavior is shaped by attitudes, subjective norms, and perceived behavioral control (Ajzen and Sheikh, 2013). Teachers’ operational skills, including planning, organizing, and problem-solving, are pivotal for successfully executing sports activities. The confirmatory factor analysis (CFA) results revealed a strong correlation between operational ability and both understanding and evaluation abilities (r = 0.85), underscoring the interdependence of these dimensions. This finding aligns with the TPB framework, where positive attitudes toward and perceived control over executing after-school sports services enhance teachers’ operational effectiveness. The CFA outcomes thus provide empirical validation for the theoretical proposition that operational ability is not only critical for activity implementation but also synergistically linked to other execution dimensions, collectively driving the quality and impact of after-school sports services.

The evaluation ability of after-school sports services represents a critical component of teachers’ execution competence, focusing on the systematic assessment of activity implementation effects and their impact on students’ holistic development. This ability empowers teachers to make data-driven decisions, optimize activity content, and adjust teaching methodologies to enhance both teaching quality and student engagement. It involves a dynamic process of modifying teaching strategies and activity designs based on evaluation outcomes, ensuring that activities remain responsive to evolving student needs and effective in promoting physical, mental, and social growth. The theoretical foundation of evaluation ability is deeply rooted in execution ability theory, which underscores the significance of monitoring and adjusting actions to achieve predetermined goals. This theory posits that continuous assessment and feedback are essential for refining practices and ensuring alignment with objectives. The confirmatory factor analysis (CFA) results, showing that evaluation ability significantly contributed to the model fit (AVE = 0.587, CR = 0.850), empirically validate this theoretical perspective. The high AVE value indicates that the evaluation ability dimension effectively captures the variance in teachers’ execution competence, while the robust CR value underscores its reliability. Moreover, the managerial principle that systematic evaluation drives organizational learning and adaptation is evident in the interplay between evaluation ability and other execution dimensions. Effective evaluation not only enhances teaching strategies but also fosters a culture of continuous improvement, enabling teachers to adapt to changing student needs and educational standards. This aligns with the CFA findings, which highlight the pivotal role of evaluation ability in refining instructional practices and amplifying the overall educational impact. Within the context of China’s “double reduction” policy, this capability is particularly vital, as it ensures that after-school sports services remain aligned with the policy’s objectives of reducing academic burdens while promoting comprehensive student development.