Scenario-based perceived intelligence of an educational social robot, academic self-efficacy, and learning engagement in adolescents: a three-wave longitudinal study

Educational social robots are increasingly discussed as potential learning technologies, but judgments formed from a written description should not be equated with perceptions arising during actual human–robot interaction. This three-wave longitudinal study examined whether adolescents’ scenario-based perceived intelligence of a hypothetical educational social robot was indirectly associated with later learning engagement through academic self-efficacy, and whether physical activity moderated the association between academic self-efficacy and later learning engagement. Data were collected in November 2025, February 2026, and May 2026 from adolescents attending six collaborating secondary schools in Central, South, and North China. Convenience cluster sampling was conducted at the class level. After data cleaning and longitudinal matching, 1,340 adolescents were retained for analysis (M_age = 16.27, SD = 1.34; 620 boys and 720 girls). At T1, participants read a standardized written scenario describing a hypothetical educational social robot; no actual robot interaction occurred. T1 also assessed baseline academic self-efficacy, baseline learning engagement, and demographic variables. T2 assessed academic self-efficacy and physical activity, and T3 assessed learning engagement. Confirmatory factor analysis, correlation analysis, and PROCESS Model 14-based conditional process analyses were conducted using observed composite scores. The five-factor measurement model showed good fit, χ²(692) = 1232.953, χ²/df = 1.782, CFI = 0.968, TLI = 0.966, RMSEA = 0.024, and SRMR = 0.027. Before the mediator and moderator terms were entered, T1 scenario-based perceived intelligence was positively associated with T3 learning engagement after covariate adjustment (β = 0.137, p < 0.001), supporting H1 at the total-effect level. T1 scenario-based perceived intelligence was also positively associated with T2 academic self-efficacy (β = 0.174, p < 0.001), and T2 academic self-efficacy was positively associated with T3 learning engagement (β = 0.575, p < 0.001). In the full conditional process model, the adjusted direct association was not significant (β = 0.038, p = 0.085), whereas the standardized indirect effect through academic self-efficacy was significant (effect = 0.100, 95% CI [0.074, 0.128]). T2 physical activity moderated the academic self-efficacy–learning engagement association (β = 0.075, p < 0.001), but the interaction explained only a small additional proportion of variance (ΔR² = 0.005). The index of moderated mediation was 0.013 (95% CI [0.005, 0.022]). Among adolescents who evaluated a written hypothetical scenario rather than interacting with a robot, higher scenario-based perceived intelligence was positively associated with later learning engagement at the total-effect level and was indirectly associated with later engagement through academic self-efficacy; the adjusted direct association in the full conditional process model was not significant. Higher physical activity was associated with a somewhat stronger academic self-efficacy–engagement relationship, although the moderation effect was small. These findings concern anticipatory evaluations of a described educational robot and should not be interpreted as evidence of a causal psychological mechanism operating during actual educational human–robot interaction.