5.1. Key Research Findings
5.1.1. Differential Impact of Teacher Competencies
This study reveals that teacher competencies have varying impacts on the teacher-rated sustainable development of students in online mathematics competition education. Specifically, online teaching efficacy (OTE) has a strong direct effect (H1a, β = 0.204,
p < 0.001), while competition teaching professionalism (CTP) has a weaker but still significant direct effect (H1b, β = 0.121,
p = 0.032). This finding contrasts with traditional classroom teaching research, where teachers’ professional knowledge typically has a more important role (
Ball et al., 2008). Presumably, this results from increased psychological distance and reduced anxiety caused by teacher authority. Pedagogical and content knowledge also facilitated teaching reflection on video-recorded face-to-face teaching practice (
Kulgemeyer & Riese, 2018). However, in online environments, technological mediation introduces new variables that influence how professional knowledge is conveyed and applied, highlighting the crucial role of teachers’ online teaching capabilities in maintaining educational effectiveness. This explanation aligns with the recent findings of
S. Huang et al. (
2022), who emphasized the importance of online teaching efficacy and self-efficacy in engagement. Furthermore,
Dong et al. (
2023) found that teacher adaptability significantly moderated changes in online teaching self-efficacy, particularly during technological transitions.
While CTP shows a relatively weak direct effect on students’ sustainable development (H1a, β = 0.121), its indirect effects through mediating pathways (i.e., H5a and H5b; total indirect effect = 0.068) remain significant and moderate. This indicates that teachers’ professional knowledge influences students through not only direct teaching interactions but also dynamic interactions in the educational process and students’ learning methods. The transformation of teacher competencies requires a process of teacher engagement and practice, highlighting how technology intervention affects the transmission and application of teacher knowledge. Contemporary perspectives on the psychological dynamics of learning and interaction in mathematics learning can support such an explanation (e.g.,
Abrahamson & Sánchez-García, 2016).
5.1.2. Role of Teachers’ Understanding of Gifted Students
Our analysis reveals an unexpected finding regarding the relationship between teachers’ understanding of gifted students (UGS) and the teacher-rated sustainable development of learners. Contrary to our initial hypothesis (H1c), which proposed a direct positive effect, the UGS showed an insignificant direct effect on students’ sustainable development (β = 0.032, p = 0.557). However, this finding provides important theoretical insights about the nature of teacher knowledge translation in online educational environments.
This apparent contradiction between our hypothesis and findings can be explained through several theoretical mechanisms. First, the lack of a direct effect suggests that teacher knowledge requires active operationalization through specific pedagogical approaches to be effective in online environments. This aligns with
Mishra and Koehler’s (
2006) framework, which emphasizes that effective teaching requires the integration of knowledge through practical implementation rather than the mere possession of understanding.
While the direct effect was not significant, our analysis revealed that the UGS demonstrates substantial influence through indirect pathways. Specifically, the UGS shows a strong positive influence on teaching engagement (H2c, β = 0.307, p < 0.001), which in turn affects teaching practice (H2d, β = 0.127, p = 0.020). These sequential relationships culminate in significant total indirect effects on sustainable development (H4c, β = 0.015, p = 0.018). This pattern suggests that the impact of teachers’ understanding manifests primarily through its implementation in teaching processes rather than through direct transmission.
The transformation of theoretical knowledge into practical outcomes appears to require specific mediating mechanisms in online environments. This finding extends
Subotnik et al.’s (
2011) comprehensive development model by highlighting how teachers’ understanding of gifted students must be actively transformed into specific teaching strategies and practices to be effective. Furthermore, this result suggests that future teacher development programs should focus not only on building teachers’ understanding of gifted students but also on developing their capacity to operationalize this knowledge through effective online teaching practices.
5.1.3. Role of Mediating Mechanisms
Teaching engagement and teaching practice play crucial mediating roles in transforming teacher competencies into educational outcomes. Teachers’ understanding of gifted students influences student development through the sequential mediation of teaching engagement (H2c, β = 0.307, p < 0.001) and teaching practice (H3c, β = 0.127, p = 0.020). This chain-mediated effect emphasizes the central position of the teaching process in knowledge transformation. This research has established that the understanding of gifted students (UGS) indirectly affects student development through the chain-mediated pathways of teaching engagement and practice (H4c, β = 0.015, p = 0.018), indicating that traditional gifted education theories need to be transformed through interactive design and dynamic feedback mechanisms in online teaching.
5.1.4. Moderating Effect of Teacher Adaptability
Our research revealed a novel dual moderating mechanism of teacher adaptability in online mathematics competition education. This mechanism manifests through two distinct pathways of enhancement: process enhancement and outcome enhancement.
The process enhancement pathway (H6a, β = 0.156,
p = 0.008) strengthens the connection between teaching engagement and teaching practice. This finding suggests that adaptable teachers more effectively translate their engagement into coherent teaching practices through the flexible implementation and responsive modification of instructional strategies. This addresses what
Mishra and Koehler (
2006) identified as the “wicked problem” of technology integration—the complex challenge of dynamically balancing technological, pedagogical, and content knowledge in constantly evolving environments.
The outcome enhancement pathway (H6b, β = 0.122,
p = 0.024) amplifies the positive impact of teaching practice on sustainable development. This pathway is particularly significant in mathematics competition education, where problems often have multiple solution approaches requiring teachers to adapt their guidance based on students’ thinking processes. This finding aligns with
Leikin’s (
2011) research on multiple-solution tasks, suggesting that teacher adaptability plays a crucial role in supporting the development of students’ mathematical creativity through responsive feedback mechanisms.
The interaction between these two enhancement pathways creates a synergistic effect that promotes overall teaching quality. This dual mechanism extends significantly beyond
König et al.’s (
2020) single-pathway model by revealing how teacher adaptability creates a comprehensive enhancement effect throughout the teaching process. It helps explain why some teachers maintain effectiveness during technological transitions while others struggle despite similar professional knowledge and technological skills. This suggests that professional development programs should focus on enhancing adaptability across multiple dimensions rather than merely building technological or pedagogical knowledge in isolation.
5.1.5. Demographic Analysis
The analysis of demographic factors revealed several significant patterns. Our participants demonstrated distinct characteristics that warrant careful consideration. Most participants were highly experienced educators. While this depth of experience provides valuable insights into established teaching practices, it may limit our understanding of the challenges faced by novice teachers in online mathematics competition education. Although experiences may allow teachers to more deeply dedicate themselves to the teaching process, mechanisms have also illustrated that high relatedness to students could result in a rapid decline in teachers’ psychological well-being (
Collie & Martin, 2023). Therefore, it is reasonable to assume that the contribution of teaching experience to teaching effectiveness may face a plateau effect.
The institutional distribution in our sample showed significant concentration, with 63.32% of participants being from key middle schools. While these schools typically have superior resources and more experienced teaching staff, this concentration may introduce systematic biases into our findings. Key middle schools typically have better technological infrastructure and support systems, resulting in participants potentially overestimating the feasibility of online teaching implementation in resource-constrained environments.
Furthermore, the observed teaching engagement levels (mean = 5.86) require careful interpretation, as they may reflect the advantaged position of key middle schools rather than the broader reality of mathematics competition education. Regular middle schools, comprising 7.61% of our sample, may require additional technological infrastructure and professional development support to maintain competitive standards in online mathematics competition education.
Although demographic features are not examined explicitly in the current study, their impacts have been noticed in mathematics education for decades (e.g.,
Borko & Livingston, 1989;
R. Huang & Li, 2012;
Wardat et al., 2024). Based on the current sample, the current study contributes to the research area with a particular set of demographic features in mathematics gifted education, a less explored direction. Continued efforts are needed to elucidate the complex cognitive, affective, and behavioral mechanisms of teachers and students in such contexts.
5.2. Theoretical Contributions
This research advances existing educational theory in three significant aspects:
First, we establish an innovative theoretical framework integrating teacher competencies and student development. This framework demonstrates how different dimensions of teacher competencies—competition teaching professionalism, online teaching efficacy, and the understanding of gifted students—influence students’ sustainable development through teaching processes. Notably, our findings reveal that online teaching efficacy shows a stronger direct impact (β = 0.204) on students’ sustainable development than competition teaching professionalism (CTP) (β = 0.121). This challenges traditional assumptions about knowledge transmission methods (
Ball et al., 2008), highlighting the crucial role of technology-mediated instruction in educational effectiveness.
Second, we uncover a novel chain-mediation mechanism in gifted education. While teachers’ understanding of gifted students shows insignificant direct effects (β = 0.032), it is effectively transformed into educational outcomes through the mediating pathways of teaching engagement and teaching practice (β = 0.015). This extends
Subotnik et al.’s (
2011) gifted education theory by highlighting the specific transformation mechanisms through which teachers’ understanding of gifted students’ needs manifests in educational outcomes.
Third, we propose an innovative “Dual Enhancement Model” of teacher adaptability in online mathematics competition education. The model demonstrates how adaptability’s influence dynamically varies across different teaching phases, and it explains the varying levels of effectiveness among teachers during technological transitions.
5.3. Practical Implications
Our empirical findings provide insights that may inform approaches to enhancing online mathematics competition education. Based on our research results, we propose several potential recommendations that should be considered in light of the study’s limitations:
First, the results suggest that educational institutions might benefit from establishing professional development programs that address multiple dimensions of teacher competency. Given that both competition teaching professionalism and online teaching efficacy demonstrated positive relationships with sustainable development, institutions should consider developing comprehensive training programs that strengthen teachers’ mathematical competition knowledge while simultaneously enhancing their digital teaching capabilities. These programs could include collaborative problem-solving workshops, mentoring from experienced competition teachers, and hands-on training with online educational platforms and tools. However, these recommendations should be implemented with a careful consideration of institutional contexts and resources, as our study primarily reflects the experiences of teachers from well-resourced key middle schools in China. Teachers’ well-being should be taken into consideration in their close association with students. For example, researchers have demonstrated that teachers’ sense of relatedness with students could accelerate the decline in teachers’ psychological well-being over time (
Collie & Martin, 2023).
Second, educational institutions should implement differentiated support strategies based on school type and existing resources. In the digital reform of education, teachers have actively adopted emerging technologies, like AI, and researchers have also identified reasons behind teachers’ unwillingness to adopt AI to assist student learning, which appeals to further teacher training and student support from institutions (
Collie & Martin, 2025). For key middle schools, the focus should be on advancing sophisticated pedagogical approaches and fostering higher-order thinking skills. These institutions should establish professional learning communities that facilitate systematic knowledge-sharing and collaborative innovation among educators. This approach enables experienced teachers to mentor colleagues while promoting the continuous evolution of teaching practices. For regular middle schools, the emphasis should be on strengthening fundamental infrastructure and building core competencies. These institutions would benefit from comprehensive support systems that include technical resources, structured training programs, and standardized teaching protocols. The focus should be on developing adaptable teaching methodologies that can accommodate diverse student needs while maintaining high educational standards. Training institutions should focus on developing standardized online teaching procedures while maintaining the flexibility to adapt to different student needs and learning paces. It is also worth noting that our research topic should be extended to investigate whether contextual factors like school types would drastically change our conclusions.
Third, institutions must establish robust evaluation and support systems to enhance teaching effectiveness. This should begin with the development of comprehensive teacher evaluation mechanisms that assess both competition teaching expertise and online teaching capabilities. The evaluation criteria should include measures of student engagement, learning outcomes, and teaching innovation (see
Wafudu & Bin Kamin, 2024, for an example of teaching quality assurance in vocational education). Furthermore, institutions should create resource-sharing platforms that facilitate the exchange of teaching materials, methodologies, and best practices among teachers. These platforms should include both synchronous and asynchronous communication channels to support ongoing professional dialogue and collaboration. Additionally, institutions should implement incentive mechanisms that recognize and reward teaching innovation and effectiveness, particularly in the online environment.
Fourth, given the significant moderating role of teacher adaptability (β = 0.156, p = 0.008), institutions should prioritize developing teachers’ adaptive capabilities through structured support systems. This can be achieved by establishing regular professional learning communities where teachers can share experiences, challenges, and solutions related to online mathematics competition teaching. These communities should meet regularly to discuss emerging challenges and innovative solutions in online teaching. Additionally, institutions should provide structured feedback mechanisms that help teachers identify areas for adaptation and improvement in their teaching practices. This feedback should come from multiple sources, including peer observations, student evaluations, and self-reflection protocols.
5.4. Limitations and Future Research Directions
While this study makes significant contributions to understanding online mathematics competition education, several limitations should be acknowledged, and corresponding future research directions can be identified.
A significant limitation of this study is the absence of comparison groups, which restricts the interpretability of our findings. The current study only focused on teachers from gifted education, and the sampling in the current study relied on convenient samples accessible to the researchers, which indicates that their eligibility for the current study relied mostly on the participants’ self-reporting. This limitation prevents us from making definitive claims about whether the relationships identified are unique to online mathematics competition education or might apply equally to other educational contexts. Future research should address this limitation through comparative designs that include multiple teacher groups and teaching formats, allowing for a more nuanced understanding of context-specific effects.
For research practice, researchers should expand the population under investigation to include regular and offline mathematics learners at comparable educational stages, where potential moderators like student types (gifted vs. non-gifted) and learning media (online vs. offline) could be explored. In online learning, timing is usually explored to reflect whether synchronous and asynchronous teaching, feedback, and collaboration demonstrate substantial differences (e.g.,
Zeng & Luo, 2024). For example, asynchronous learning was found to be more effective than a synchronous mode (
Zeng & Luo, 2024), which should be considered in future research to examine our research contexts and beyond. Timing may allow students to better understand their learning content and solve problems when it comes to abstract and complex problems in mathematics competition learning. Such contextual factors were found to be critical predictors of academic achievements, for example, socioeconomic factors (
Collie & Martin, 2024;
Collie & Hascher, 2024). Introducing such factors into investigations and explanations should help future researchers make contributions to understanding contextualized learner and teacher populations.
However, such designs, especially those requiring Structural Equation Modeling techniques that help model multiple variables, should entail a more balanced sample consisting of the abovementioned sub-groups. It will also be interesting to explore the relevant research themes through more traditional quasi-experimental designs to test if interventions can improve teachers’ and students’ competencies. This limitation should not undermine our innovative contributions made by exploring a specific context in gifted education.
Another important limitation concerns our measurement of the outcome variable “sustainable development”. This variable was measured through teacher self-reports, which are subject to the discrepancy between learning gains and observers’ ratings, rather than through the independent assessment of student outcomes. Thus, this approach introduces potential bias, as teachers may overestimate their students’ development or may be influenced by their perceptions of their own teaching effectiveness. Furthermore, each dimension of student development (performance, problem-solving, creative thinking, and motivation) was measured with only a single item, limiting the depth and reliability of these assessments.
Researchers have noted the discrepancy between learners’ ratings and their actual gains (e.g.,
Lin et al., 2023), but most admit the value of establishing perceptual data, encouraging the incorporation of more objective measurements. This issue is similar to our situation, whether it be self- or others’ observation, since measuring the predictors and outcomes from the same perspective may involve common method bias. However, given the advantages of questionnaire measurements, researchers must be aware of the potential risk and interpret our findings with caution to strike a balance among methodologies. Future research should incorporate more robust outcome measures, including direct assessments of student performance, multi-item scales for each dimension of development, and the longitudinal tracking of student outcomes. Ideally, such research would also include student self-reports and independent evaluations to provide a more comprehensive and objective assessment of sustainable development. Qualitative results are also welcomed to consolidate the perceptual outcomes of digital gifted education explored in this study.
The cross-sectional nature of our study presents another limitation, as it may prevent us from establishing causal relationships between the variables examined. The data represent a single point in time, making it impossible to determine whether teacher competencies lead to effective teaching processes and student development, or whether successful experiences with students might enhance teachers’ sense of competence and engagement. Additionally, our reliance on self-report measures introduces potential social desirability bias, as teachers may report their competencies, practices, and students’ development in an overly positive light. These methodological limitations suggest that our findings should be interpreted as correlational rather than causal, and that the practical implications derived from these findings should be viewed as preliminary until confirmed by more robust longitudinal and mixed-methods research.
The sample representation is also limited. Our study primarily drew participants from key middle schools in China, with 63.3% of the participants coming from key middle schools. This gender and institutional concentration may limit the generalizability of our findings to other contexts. However, as reflected in
Lin et al. (
2023), the psychological mechanisms revealed in our particular research context may bring enlightenment and be extended to broader contexts. Future research should increase representation from regular middle schools and training institutions to ensure broader institutional diversity in the sample. Additionally, researchers should consider conducting comparative studies across different regions and school types to understand how contextual factors influence teaching effectiveness.
Another significant limitation is that we measured overall teaching experience rather than specifically assessing teachers’ experience with online teaching. The transition from face-to-face to online teaching involves substantial adaptation, and teachers’ level of experience with online instruction likely influences their effectiveness in this environment. Future research should explicitly measure both overall teaching experience and online teaching experience as separate variables, examining how the relationship between teacher competencies and student outcomes might be moderated by familiarity with online teaching formats. This would provide more nuanced insights into the development of teaching effectiveness in digital environments.
Moreover, our study focused exclusively on mathematics competition education for gifted students in online environments. Future research should explore how these same teaching processes operate in regular mathematics education and face-to-face contexts. Such comparative studies would help identify which aspects of our findings are specific to online mathematics competition education and which may be generalizable to broader educational contexts. This expansion would contribute to a more comprehensive understanding of effective teaching processes across various educational settings and student populations.
Despite these limitations, our study provides valuable insights into the dynamics of online mathematics competition education and lays the groundwork for future research in this important field. Subsequent studies may consider not only addressing these limitations but also exploring some emerging areas, such as the role of artificial intelligence in mathematics competition education, the impact of various online teaching platforms on learning outcomes, and the development of innovative assessment methods for online mathematics competition education (e.g.,
Almarashdi et al., 2024). Reflecting on another notable branch of research into educational technology, students’ and teachers’ intentions to use technology, their technostress, attitudes, and other influencing factors should receive future attention (e.g.,
Dai et al., 2024;
Wang et al., 2025;
Lin & Yu, 2024), especially when emerging technologies are prepared for pedagogical designs. Such research should benefit technological integration into mathematics gifted education.