Introduction
Students are the future builders of the social system, and their school years play a critical role in shaping their life paths and personalities. In this context, academic engagement is considered a construct that includes components such as behavioral engagement, cognitive engagement, emotional engagement, psychological engagement, and social engagement. It reflects a sense of belonging and an individual's tendency to participate in classroom activities, acquire skills, and strive for improvement. Hope is the key to academic success. It is associated with capabilities and enthusiasm for learning, and includes elements such as hope for opportunities, hope for acquiring life skills, hope for the usefulness of school, and hope for achieving competence. This is viewed as a motivational, cognitive, and dynamic system within the educational framework that drives individuals toward goals and provides the motivation necessary to reach them.
  Academic buoyancy, as a positive psychological construct, can be influenced by hope for education. It helps students confront academic challenges and obstacles, ultimately leading to greater academic engagement. Given the importance of educational hope for students, as well as the role of academic buoyancy and the relationships among these variables, this study aims to develop a model of academic engagement based on educational hope, with academic buoyancy acting as a mediating factor. Based on previous research, it can be said that academic engagement, the pursuit of success, and having a spirit of hope and vitality in education are significant factors in the field of education. Therefore, it is essential to examine the status of these variables from the perspective of educators in the educational districts of Mashhad.
 
Methodology
This study employed a survey method conducted at secondary schools in District 7 of Mashhad. The target population consisted of school management personnel, including principals, educational deputies, executive deputies, counseling deputies, and teachers. Data were collected during the 2023–2024 academic year from a sample of 572 participants using standardized questionnaires measuring the research variables. The questions were administered through an online questionnaire based on convenience sampling. Participants rated each question on a scale from 1 to 10. The data were analyzed using descriptive and inferential statistical methods via SPSS and Smart PLS software. The reliability and validity of the measured variables were assessed using Cronbach’s alpha coefficients and average factor loadings. The results showed strong internal consistency for academic engagement (α = 0.911) and academic buoyancy (α = 0.878), while hope for education demonstrated an acceptable level of reliability (α = 0.691). Additionally, the average factor loading across the variables and their components was approximately 0.727, indicating acceptable convergent validity.
 
Findings
Nearly half of the educators had between 21 and 30 years of service. Around 80% of the respondents were officially employed, and nearly half of the participants held a master’s degree. More than half of the school staff reported that their schools were equipped with moderate-level facilities and resources. The mean scores of the variables—except for the components of cognitive engagement and hope for gaining more opportunities—were above 5, indicating levels higher than the average. Regarding the variable hope for education, the assumption of equal variances between male and female secondary school students was accepted based on the significance level. Thus, there was no significant difference between the genders in terms of hope for education. For academic buoyancy, the Levene’s test showed a significance level below 0.05, suggesting unequal variances between the two groups. However, since the overall significance level (0.919) was above 0.05, no significant difference in the means was found.
For academic engagement, the Levene’s test yielded a significance level of 0.023, indicating a meaningful difference in means. Ultimately, the results showed that academic engagement varied between boys' and girls' secondary schools, with girls' schools placing greater importance on academic engagement.
Based on the results, the F-value for the variable hope for education in relation to school type was greater than 0.05, meaning there was no significant difference in the means between different school types. However, significant differences were found in the variables of academic buoyancy and academic engagement based on school type. Academic buoyancy showed higher averages in exemplary culture-based schools and schools for gifted students. Academic engagement was higher among students in private and gifted schools compared to other school types.
Based on the results of the structural equation modeling and considering the significance level of P ≤ 0.05, all relationships in the model were found to be positive and significant except the following:

The relationship between hope for gaining competence, hope for opportunities, hope for acquiring life skills, valuation, sense of belonging, cognitive engagement, and behavioral engagement—which were all positive but not statistically significant.
Additionally, the relationship between academic buoyancy and behavioral engagement was negative and non-significant.

Among the hypothesized relationships, the first hypothesis—the relationship between hope for education and academic buoyancy, and the second hypothesis—the relationship between hope for education and academic engagement, were confirmed. However, the third hypothesis, which proposed a significant relationship between academic buoyancy and academic engagement, was rejected due to a low and non-significant path coefficient.
The R² value for academic buoyancy was low, indicating that hope for education has a weak predictive power for academic buoyancy. However, it was found that approximately 45% of the variance in academic engagement can be predicted by the variables hope for education and academic buoyancy.
According to the Q² values in the structural model, hope for education had weak predictive power for academic buoyancy but showed strong predictive power for academic engagement. The SRMR (Standardized Root Mean Square Residual) index was below 0.10, indicating a good model fit; in this study, the SRMR was 0.094, confirming the model’s adequacy.
Finally, the VAF (Variance Accounted For) was used to determine the strength of the indirect effect through the mediating variable. The closer this value is to 1, the stronger the mediation. The results showed that the indirect effect of hope for education on academic engagement through academic buoyancy was statistically significant (value = 0.019), but the effect size was not particularly strong.
Discussion and Conclusion
Ultimately, students who were hopeful about their education did not exhibit a particularly strong motivation to achieve desirable goals and outcomes within the school setting. Although they expressed a certain level of satisfaction with their academic lives, this satisfaction appeared to be unstable. As a result, their academic engagement toward school also showed signs of inconsistency. This finding suggests that while there is a foundation of hope and partial satisfaction, academic engagement remains fragile and could be strengthened to better support students in achieving academic success.