Extended reality (XR) provides opportunities for embodied practice and immediate feedback. However, the motivational impact of XR is not monolithic; it varies across its sub-technologies. Virtual reality (VR) offers high immersion that facilitates deep “presence” and flow by isolating the learner from distractions. In contrast, augmented reality (AR) and mixed reality (MR) allow for the integration of digital cues into the physical field, which may better support perceived self-control and the transfer of skills to real-world soccer environments (Cummings and Bailenson, 2016; Radianti et al., 2020). For skill learning such as soccer, XR can stage graded challenges, capture micro-performances, and surface analytic cues that would typically require expert guidance. These affordances shape motivational and self-regulatory processes that underwrite engagement. This study integrates self-determination theory with the challenge–skill balance framework to investigate the drivers of learning engagement in gamified XR for soccer instruction.

According self-determination theory (SDT), satisfaction of autonomy, competence, and relatedness needs fosters high-quality engagement (Ryan and Deci, 2000). Research also indicates that designing gamification elements based on the SDT can address students’ psychological needs for autonomy, competence, and relatedness. This enhances their engagement in learning and achievement of learning goals (Grabner-Hagen and Kingsley, 2023). In XR-supported soccer skill teaching, students are more likely to invest effort and effectively regulate their behavior when basic learning needs are supported through XR’s gamification elements (Deterding et al., 2011; Sailer et al., 2017). This study integrates self-determination theory (SDT) with the challenge–skill balance framework through a “motivation-experience-development” logic. SDT acts as the foundational layer: when XR design satisfies the needs for autonomy and competence, it creates the psychological readiness required for an optimal experience. According to SDT, satisfaction of these needs fosters high-quality engagement (Ryan and Deci, 2024). In this framework, perceived gamification and perceived self-control serve as the environmental and individual precursors that fulfill these needs.

Furthermore, flow theory posits that optimal experience arises when perceived challenges match perceived skills and is accompanied by clear goals and immediate feedback (Csikszentmihalyi, 1990; Engeser and Rheinberg, 2008). XR can help maintain this balance by algorithmically calibrating task difficulty and visualizing evolving skill states. Repeated flow episodes can enhance attentional control and promote appraisal of challenges as opportunities. These processes are closely related to mental toughness—perseverance, self-confidence, and emotional regulation under stress (Gucciardi et al., 2012). Furthermore, this study propose a “state-to-resource” transition to justify the flow-toughness link. While flow is a situational, transient state of optimal experience (Csikszentmihalyi, 1990), mental toughness is a more stable psychological resource (Gucciardi et al., 2012). Theoretically, repeated episodes of flow—where the learner successfully navigates high challenges—act as “mastery experiences.” These experiences gradually crystallize into mental toughness, as the learner internalizes the ability to maintain focus and emotional regulation under pressure.

Accordingly, this study models flow experience and mental toughness as interrelated mediators linking XR and instructional design features, together with self-regulatory capacities, to soccer learning engagement and, ultimately, sports attachment. Methodologically, sequential mediation can generate more precise mechanism testing and align the analysis with the logical teaching timeline (i.e., session-level experiences that precede the development of capabilities), thus providing feasible guidance for designing an XR-based soccer curriculum.

Perceived gamification (PG) is defined as learners’ perception that design elements unique to games, such as points, levels, challenges, leaderboards, rewards, and narratives, constitute an XR course (Deterding et al., 2011; Hamari et al., 2014). Gamification has been proposed as a way to encourage people to engage in behaviors that are both personally and socially beneficial, such as exercising and pursuing an education. Gamification aims to motivate users to perform tasks promoted by the service (Deterding et al., 2011; Huotari and Hamari, 2012). This can be achieved by providing the affordances of a gamified experience and making the target activity more appealing. Previous research has shown that incorporating gamification elements that meet students’ basic psychological needs improves their sports skill performance, learning behavior, and learning engagement (Fernandez-Rio et al., 2020), particularly when clear goals are set and conditional feedback is provided (Sailer et al., 2017). They can also diagnose learning progress and competence. However, PG may also generate “extraneous load,” which will not automatically translate into greater effort unless transformed into an optimal experience or toughness beliefs (Hsia et al., 2025). Gamification learning theory predicts that these elements indirectly influence learning outcomes by shaping antecedent states (e.g., motivation, attention, and flow), thereby driving learning behaviors (Thomas and Baral, 2023). Therefore, the following hypotheses are proposed.

Perceived self-control (PSC) is learners’ perceived ability to maintain attention, suppress impulses, and regulate behavior during training (Tangney et al., 2004; Baumeister et al., 2007). In gamified XR soccer instruction, PSC provides the self-regulatory capacity needed to remain task-focused and persist through graded challenges (Lu, 2023), thereby increasing the likelihood that learners can enter and sustain a flow experience characterized by clear goals and immediate feedback (Csikszentmihalyi, 1990). While XR can present calibrated difficulty and feedback cues, these affordances do not automatically yield flow unless learners can allocate attention, resist off-task impulses, and regulate pacing across repeated practice episodes (Duckworth and Seligman, 2005). Therefore, PSC is theorized as a proximal individual resource that helps learners capitalize on XR-supported challenge–skill balance and feedback salience, strengthening flow experience and, in turn, learning engagement. Utilizing gamified learning platforms to enhance students’ ability to learn soccer autonomously can help them adapt to an autonomous learning environment. This facilitates better acceptance of soccer teaching content (Lyu and Park, 2025). Therefore, the following hypotheses are proposed.

A flow experience (FE) is a state of deep concentration with clear goals and immediate feedback. It is accompanied by a loss of self-awareness and an altered perception of time (Csikszentmihalyi, 1990; Jackson and Eklund, 2002). This state occurs when skills and challenges are balanced and feedback is immediate. XR’s high presence and precise telemetry algorithms can manipulate these states. In physical education, meta-analytic and systematic evidence links flow to improved sports performance and persistence (Harris et al., 2023), which supports its role as a proximal driver of SLE and SA. In sports, FE can improve decision-making speed, technical execution, and persistence, thus enhancing learning engagement (Goh and Yang, 2021).

Meanwhile, adaptive XR soccer instruction fosters frequent FE by maintaining optimal challenge levels. These episodes serve as structured micro-adversities, strengthening mental toughness (MT) through repeated emotional regulation and resource consolidation (Gucciardi et al., 2015). Consequently, FE provides a proximal pathway for MT development. Furthermore, MT mediates the relationship between FE-related commitment and learning engagement (St Clair-Thompson and Devine, 2023). The connection between FE and MT represents the shift from “doing” to “being.” Frequent FE episodes serve as structured micro-adversities. Conceptually, the flow stage is rich in mastery experiences, which can provide a pathway from FE to MT through sequential mediation by accumulating efficacy and coping resources. Therefore, the following hypotheses are proposed.

Mental toughness (MT) is a state-like psychological resource. Its purposefulness, flexibility, and efficiency enable the formulation and maintenance of goal-oriented pursuits (Gucciardi, 2017). Related research has consistently identified MT as one of the most important psychological characteristics related to performance in sports and learning (Crust, 2007). MT represents commitment under pressure, which requires control as a foundation (Liew et al., 2019). These traits contribute to maintaining consistent performance and recovering from setbacks (Gucciardi, 2017). Previous studies (Gucciardi et al., 2015; Covington and Omelich, 1988; Raymond, 2009) have emphasized the importance of considering the dynamic interactions among cognitive, emotional, and motivational domains when conceptualizing MT-related processes. Therefore, gamified XR-related soccer instruction, with its opportunities for graded exposure, safe failure, and repeated mastery, can provide micro-adversities and successes, thus potentially building mental toughness over time. Thus, the following hypotheses are proposed.

Soccer learning engagement (SLE) is defined as the investment of time and attention, as well as the display of continuous learning behaviors related to skill acquisition (Morgans et al., 2014; Ericsson et al., 1993). SLE indicators measure behavioral, cognitive, and emotional investments in soccer learning. Furthermore, emotional investment brought about by digital technology can reinforce users’ behaviors (Wang et al., 2026). Repeated, meaningful investment can strengthen competence, self-goals, and social connections, deepening the sense of identity and attachment to the sport (Funk and James, 2001).

Sports attachment occurs when students develop an identity with and dependence on soccer due to the influence of learning soccer in an XR environment. This attachment likely determines how they explore the entire sports and learning system (Moss and St-Laurent, 2001). While Bowlby’s (1979) original attachment theory focused on interpersonal bonds between child and caregiver, it is adapted here to the sporting context. In technology-mediated physical education, the XR environment and the sport itself act as a “secure base.” When the XR system provides consistent feedback (competence) and autonomy, the learner feels secure enough to explore complex skills. This psychological safety fosters an affective bond, sport attachment, similar to the emotional security described in traditional attachment theory, which drives long-term adherence and participation beyond the classroom. Exploring sports situations in qualitatively different ways affects the mental representation of attachment (Carr, 2009). Soccer provide individuals with opportunities to explore and develop their cognitive, physical, and social selves. The achievement of goals in sports has been shown to influence this pattern of exploration (Elliot and McGregor, 2001). Therefore, the following hypotheses are proposed.

Previous studies have typically regarded gamification as a unified approach, failing to specify the mechanisms that generate optimal experiences. This has resulted in inconsistent direct impacts on engagement. Flow and mental toughness were often examined separately rather than as interacting processes, obscuring how transient optimal states could develop lasting resources. To address these issues, this study created a research model (Figure 1) based on the aforementioned hypothesized framework. The model advances theory by distinguishing between the situational optimal state (flow) and the enduring self-regulatory trait (mental toughness), showing how the former facilitates the development of the latter.

The model advances theoretical development by linking need-supportive design and challenge calibration into a single, comprehensive explanation of extended reality (XR) soccer learning (Makransky and Petersen, 2021). This study clarifies the trajectory of the gamification effect, demonstrating a fully mediated path from perceived gamification to learning engagement (Zeng et al., 2024). In addition, the study identifies a continuous path through which the experience of flow consolidates into mental toughness. This refines the distinction between the optimal situational state in teaching and the enduring self-regulatory ability (Hsieh et al., 2024). Finally, the study links learning engagement and investment to sports attachment. This extends the logic of sports socialization to technology-based courses with the explicit educational goal of fostering sports attachment (Nite and Edwards, 2021).

This model aligns with the available evidence in the XR context. In education and sports, XR evaluations and trials have shown that interactive, adaptive tasks improve skill-related outcomes (Darwish et al., 2023; Doolani et al., 2020). This strengthens the rationale of the motivation-behavior association in the model.

This study uses a quantitative, survey-based approach to empirically evaluate the proposed research model. Since the necessary data are unavailable in public databases, original data must be collected. The measurement scales were derived from existing literature and adapted based on the context of gamified, XR-related soccer education (see Table 1). The scale consists of 32 items. Previous research (MacKenzie et al., 2011) has shown that formative measurement can fully represent higher-order constructs. To capture the relative importance of these dimensions, all items are measured using a five-point Likert scale ranging from “strongly disagree” (1) to “strongly agree” (5). The adaptation process combined content validation and linguistic procedures (expert review, pilot testing, and bilingual translation/back-translation) to ensure that the items retained the conceptual meaning of the original scales while being appropriate for XR-based soccer instruction.

At the beginning of the questionnaire, detailed examples of XR applications in soccer learning were provided. Then, the first part of the questionnaire asked respondents about their demographic characteristics. The second part required them to answer questions about all the variables. To ensure high-quality cross-cultural adaptation and semantic validation, we followed Brislin’s (1970) back-translation model. Because the original scales were developed in English, a bilingual sports-education researcher first translated all items into the local language, after which an independent bilingual expert back-translated them into English. Discrepancies were resolved by consensus to achieve semantic and conceptual equivalence before finalizing the wording. To ensure a wide range of respondents and accurate linguistic adaptation, this bilingual procedure was followed before the questionnaire was written and distributed in English.

Content validity was determined through a formal expert panel review. Four experts were selected based on the following criteria: (1) holding a doctoral degree in physical education or teaching technology; (2) having at least five years of experience in XR implementation or sports psychology; (3) having published peer-reviewed papers in these fields. These experts used the content validity index (CVI) to evaluate the clarity, relevance, and representativeness of each item. After making revisions according to the experts’ opinions, the questionnaire was finalized.

Before the main study, a pilot test (N = 60) was conducted to evaluate the instrument’s psychometric properties. Internal consistency was confirmed with Cronbach’s alpha values ranging from 0.82 to 0.91 for all constructs. exploratory factor analysis (EFA) demonstrated that all items loaded onto their respective factors (>0.60) with no significant cross-loadings, indicating acceptable preliminary validity. The pre-test results were not included in the total sample size.

Consistent with established research methods, the hypotheses in this study were tested using survey data. To capture a representative range of experiences, the inclusion criterion “XR-integrated football teaching” was strictly defined as participation in courses in which at least 30% of the teaching time involved skills training using immersive XR devices. Over a three-month period, researchers recruited respondents through university forums and social media pages created specifically for this study, focusing on universities offering XR-integrated physical education courses. While this resulted in a convenience sample, we addressed institutional representativeness by targeting students from 15 different universities across various regions. XR technology in education is evolving rapidly. Therefore, respondents had to be students over 18 years old who had experienced XR-integrated soccer teaching within the past two years, as a more distant technological experience may be completely different from the present.

Of the 700 completed questionnaires initially collected, 80 were excluded due to incompleteness or invalidity (e.g., two questionnaires had the same IP address, and the completion time for some was less than half the average time). Thus, the final sample used for structural validation and hypothesis testing consisted of 620 valid questionnaires, with a qualification rate of 88.57%. Accordingly, the sampling frame represents higher education institutions that have already adopted XR-integrated soccer instruction. The results should therefore be generalized to comparable XR-adopting settings rather than to the full population of universities or sports.

Of the 620 samples, males slightly outnumbered females (57.1% male and 42.9% female). The age distribution was concentrated in the traditional college student age range: 65.0% were aged 18–25, 25.0% were aged 26–29, and 10.0% were aged 30 and over. Undergraduates accounted for the largest proportion (42.1%), followed by postgraduate students (36.0%). On average, XR courses accounted for a high percentage of all soccer learning courses. Eighty-six percent of respondents reported that XR was integrated into more than 40% of soccer courses, and 62.9% reported that XR was integrated into more than 60% of soccer courses. The average proportion of time spent on soccer among all sports also showed a similar concentration. Seventy-seven point 9% of respondents reported that soccer accounted for more than 40% of all sports, and 51.0% reported that it accounted for more than 60%. These results suggest that respondents have recently engaged meaningfully with XR-integrated soccer pedagogy, which supports this study’s focus on contemporary implementation. Notably, Kline and Santor (1999) recommended that the sample size be at least 10 times the number of measurement items. The final sample exceeded the general adequacy criterion for a structural model with 32 indicators (≥320 observations), thereby ensuring sufficient statistical power for the PLS-SEM analysis (Yu et al., 2025).

Kline and Santor (1999) suggested that the sample size should be at least 10 times the number of measurement items. Since the six variables in this study involve 32 measurement items, the sample size available for analysis should be greater than 320 to support the statistical power of subsequent analyses. The 620 valid samples in this study provide strong power and precision for structural estimation and hypothesis testing (Yu et al., 2025).

This study selects structural equation modeling (SEM) for data modeling and analysis. SEM estimates relationships among interrelated variables while accounting for measurement errors. There are two approaches, including covariance-based structural equation modeling (CB-SEM) and partial least squares-structural equation modeling (PLS-SEM). CB-SEM focuses on theory validation, while PLS-SEM uses a causal-predictive approach to explain the variance of the dependent variable (Chin et al., 2020). PLS-SEM is highly effective for studies with small sample sizes, non-normal data distributions, and complex models involving intricate interdependencies among structures (Hair et al., 2021). Its variance-based approach addresses the limitations of traditional CB-SEM techniques, providing robust analysis even when sample size and data normality are restricted (Hair et al., 2019). In addition, PLS-SEM can simultaneously accommodate both formative and reflective concepts, ensuring an overall evaluation of the model.

PLS-SEM was adopted as the primary validation approach owing to its suitability for early-stage theory development (Shiau et al., 2019) and its emphasis on predictive assessment (Benitez et al., 2020). This method concurrently models latent constructs, accounts for measurement error in exogenous and endogenous variables, and estimates all hypothesized relations within a single framework, thereby attenuating statistical bias and diminishing the risk of inferential error. Following the two-step procedure (Hair et al., 2021), we first evaluated the measurement model using SPSS and SmartPLS, and subsequently estimated and tested the structural paths.

The PLS-SEM measurement procedures include examining empirical dimensionality with principal component analysis, evaluating reliability and convergent validity with Cronbach’s α values, composite reliability, and average variance extracted, and assessing discriminant validity with Fornell–Larcker criteria and HTMT ratios. These procedures determine construct quality before the structural assessment.

First, Harman’s single-factor approach and a partial least squares (PLS)-based collinearity surrogate model were adopted to assess common method bias. An unrotated principal component analysis of all 32 indicators (Maćkiewicz and Ratajczak, 1993) yielded six components with eigenvalues greater than 1. Collectively, these components explained 76.91% of the variance. The first unrotated component accounted for only 32.21%. This pattern indicates that the variance was not dominated by a single underlying factor attributable to the common method. The full collinearity diagnosis of the structural model further supports this finding. The variance inflation factors in the endogenous structure ranged from 1.109 to 1.326, which is far below the conservative benchmark of 3.3 (Hair, 2014). Taken together, common method bias is unlikely to significantly distort the estimated relationships, which provides a preliminary basis for the structural plausibility of subsequent validation (Benitez et al., 2020).

To provide an additional, more stringent diagnostic, this study also estimated an unmeasured latent method-factor model in which each indicator loaded on both its theoretical construct (R₁) and a common method factor (R₂) (Wang et al., 2025). The substantive loadings remained high, with an average R₁² of 0.765 across items, whereas the method-factor loadings were very small, with an average R₂² of 0.002 and all individual R₂² values below 0.015. This pattern indicates that the shared method factor explains only a negligible proportion of variance beyond the substantive constructs and converges with the Harman and collinearity tests in suggesting that common method variance is unlikely to bias the reported relationships (see Appendix A for details of the CMB test).

Secondly, the reliability and convergent validity of all six constructs (Table 2) were satisfactory in PLS-SEM (Hair, 2014). Cronbach’s alpha values exceeded the adequacy threshold of 0.70. Composite reliability was uniformly high, surpassing the 0.70 benchmark and evidencing strong internal consistency. Average variance extracted (AVE) for each construct was greater than 0.50, supporting convergent validity under conventional criteria. Collectively, these findings indicate that the measurement model possesses adequate psychometric properties for subsequent structural estimation and hypothesis testing within the proposed framework.

Thirdly, the Fornell–Larcker matrix substantiated discriminant validity. Specially, for each construct in Table 3, the square root of its AVE on the diagonal exceeded all inter-construct correlations, thereby satisfying the classical criterion (Fornell and Larcker, 1981). These results were consistent with previously reported AVE estimates, confirming that each latent variable captured more variance from its own indicators than from other constructs. Overall, the results supported the distinctiveness of the constructs and alleviated concerns about multicollinearity in the subsequent PLS-SEM analysis.

Finally, the HTMT ratios indicated that all pairs of constructs had clear discriminant validity. Table 4 shows that the values ranged from 0.222 to 0.437, well below the conservative benchmark of 0.85 commonly adopted in behavioral research, suggesting that each construct was empirically distinct from the others (Henseler et al., 2015). Combined with the previously reported Fornell–Larcker results, the HTMT evidence supported conducting the structural analysis without taking corrective measures to address construct ambiguity.

After validating and verifying the measurement model, the structural model can be evaluated to test the paths and examine the hypotheses. In PLS-SEM, evaluation of the structural model is based on multiple criteria, including the coefficient of determination (R²), predictive relevance (Q²), assessment of collinearity, effect size (f²), and path coefficients.

Specifically, the structural model exhibited a moderate level of explanatory power and predictive relevance (Table 5). The explanatory power of the endogenous variance was weak to moderate. The R² values were 0.214 for FE, 0.246 for MT, and lower for sports attachment (SA = 0.166) and soccer learning engagement (SLE = 0.145). The adjusted R² had minimal shrinkage, indicating stable estimates (Hair, 2014). Out-of-sample prediction is supported by positive Q² predict across all constructs, meeting the criterion whereby values greater than zero indicate predictive relevance. Proximal states (FE and MT) were relatively more predictable than downstream outcomes (SA and SLE) (Shmueli et al., 2019). The error metrics were consistent with this pattern: FE (RMSE = 0.893; MAE = 0.690) and MT (RMSE = 0.886; MAE = 0.689) had the lowest RMSE and MAE respectively, while SA (RMSE = 0.956; MAE = 0.748) and SLE (RMSE = 0.950; MAE = 0.770) had higher RMSE and MAE, respectively. This indicates that the mediating variables had better point predictability than the distal outcomes. Taken together, these metrics suggest that the cross-validated predictive performance of the model is acceptable and that the model’s strongest prediction accuracy is concentrated on the proximal psychological constructs that are most directly specified by design and self-regulatory antecedents (Benitez et al., 2020).

Moreover, direct effect path estimations support a mechanism whereby design evaluations stimulate proximal states, which then mobilize engagement and attachment. FE is jointly predicted by PG (β = 0.333, p < 0.001, f² = 0.127) and PSC (β = 0.232, p < 0.001, f² = 0.062), with gamification having a stronger impact. MT is shaped by PSC (β = 0.261, p < 0.001, f² = 0.077) and PG (β = 0.235, p < 0.001, f² = 0.058) and reinforced by FE (β = 0.160, p < 0.001, f² = 0.027), which confirms the link between flow and toughness. Additionally, SLE increases with enhanced perceived self-control (β = 0.204, p < 0.001, f² = 0.038) and toughness (β = 0.178, p < 0.001, f² = 0.028), though FE contributes less (β = 0.083, p = 0.035, f² = 0.006). Taken together, these patterns support H2a, H4a and H3. Conversely, the direct path from PG to SLE is not supported (β = 0.041, p = 0.390), which does not support H1a and suggests that gamification operates via mediating factors rather than directly. SA is promoted by SLE (β = 0.234, p < 0.001, f² = 0.058), FE (β = 0.189, p < 0.001, f² = 0.037) and MT (β = 0.135, p = 0.001, f² = 0.018), thus establishing behavioral and experiential pathways to attachment. These effects support H5, H6 and H7. Notably, the confidence intervals of all significant paths do not contain zero, and multicollinearity is negligible with a VIF ranging from 1.109 to 1.326. This is well below the common threshold for PLS-SEM (Hair et al., 2021) (see Table 6).

Furthermore, one of the objectives of this study was to explore the mediating roles of FE and MT in the relationships between PG, PSC, and SLE. Following the suggestions of Preacher and Hayes (2008), the bootstrapping method was employed to test the indirect effects during the process of testing the mediation hypotheses. The significance of the indicator weights was tested by evaluating the t-values. At a 5% significance level, an indicator weight is considered statistically significant if its t-value is greater than 1.960 (two-tailed test).

The mediation effect tests in Table 7 indicate that PG exerts its influence on SLE exclusively through psychological pathways. The indirect effects through FE (β = 0.028, p = 0.040), MT (β = 0.042, p < 0.001), and the chained mediation through FE and MT (β = 0.009, p = 0.007) are all significant, supporting H1b, H1c, and H1d, while the direct path from PG to SLE is not significant. This suggests that flow and toughness achieve full mediation. In contrast, PSC demonstrates a distinct pattern. The indirect effect through MT is found to be significant (β = 0.046, p < 0.001), supporting H2c, and the serial path through FE and MT is also found to be significant (β = 0.007, p = 0.012), supporting H2d. However, the path through FE alone is not found to be significant (β = 0.019, p = 0.054), not supporting H2b. In view of the identified direct effect of PSC on SLE, this configuration is consistent with the complementary partial mediation effect, meaning that self-control can mobilize engagement both directly and through toughness.

The mediation results also demonstrate that FE promotes SLE through a relatively small direct effect and a significant indirect effect via MT (β = 0.028, p = 0.004), supporting H4b, which confirms that the theoretically postulated link between flow and toughness serves as a channel for guiding behavior. For all supported indirect effects, the confidence intervals do not contain zero, which supports their reliability under the bootstrapped PLS-SEM estimates (Preacher and Hayes, 2008).

Concurrently, the estimation results of the relationships among constructs in the structural model are summarized through Figure 2. PSC is a direct and indirect driver of engagement, while PG is an indirect driver through FE and MT. Additionally, a clear path linking engagement and attachment is evident.

The structural model results show that perceived gamification and perceived self-control significantly predict flow experience, while flow and mental toughness contribute to sports attachment. The model explains 14.5% of the variance in soccer learning engagement (SLE; R² = 0.145) and 16.6% of the variance in sports attachment (SA; R² = 0.166). These R² values are modest, indicating that the psychological mechanisms captured by the model account for a limited but non-trivial portion of the variability in students’ engagement and attachment. Rather than suggesting that SLE and SA are predominantly determined by flow-related processes, these results imply that substantial variance is likely driven by other contextual, interpersonal, and dispositional factors that fall outside the scope of the present model. The path from flow experience to SLE is positive but small (β = 0.083), which suggests that, although flow contributes to engagement, its unique incremental effect is relatively weak once other predictors are taken into account.