Online mathematics learning power represents an extension and discipline-specific evolution of traditional learning power theory (Crick, 2006; Crick et al., 2013) in the digital age. Grounded in the double helix theory of learning (McGettrick, 2002) and classical frameworks of online learning power (Broadbent and Poon, 2015; Kember, 2009), it is defined as the systemic capability essential for learners to succeed in mathematics learning within online environments. This encompasses key dimensions such as the active construction of mathematical knowledge, strategic problem-solving for complex issues, the ability to engage in rigorous logical reasoning, and the sustained development of deep mathematical thinking. The formation of this capability is influenced by both individual and environmental factors. Individual factors include learning motivation, self-regulatory skills, and digital literacy (Crick et al., 2015), while environmental factors encompass learning platform design, teacher support, and peer interaction (Kember, 2009). Although the academic community has not reached a consensus on the dimensional structure of online learning power, core elements such as adaptation, cognition, application, and reflection have gained broad recognition (Crick, 2007; Zimmerman, 2002; Artino Jr, 2012; Zheng et al., 2025). The synergistic development of these core abilities helps learners achieve continuous growth in complex and dynamic online environments (Broadbent, 2017). Based on the characteristics of the mathematics discipline, this study conceptualizes online mathematics learning power through four key dimensions: adaptability in mathematics learning, cognitive capability in mathematics learning, applicative ability in mathematics learning, and reflective capacity in mathematics learning, thereby establishing the theoretical analytical framework.

Generative artificial intelligence (GenAI) tools, capable of assuming multiple roles such as teacher, tutor, clerk, and designer, are reshaping the forms and boundaries of student learning and transforming how students learn (Dwivedi et al., 2023). By providing personalized content delivery, instant feedback, and immersive learning environments, these tools stimulate and support learners’ capacity for autonomous exploration and continuous development (Liu et al., 2025). In response to this transformation, learners require corresponding artificial intelligence literacy (Burgsteiner et al., 2016), defined as the ability to understand fundamental AI knowledge and concepts. Long and Magerko (2020), from a human-computer interaction perspective, proposed an AI literacy framework comprising 17 elements, encompassing aspects such as knowing AI, understanding AI, and using AI. Building upon this, Heyder and Posegga (2021) structured AI literacy into three conceptual blocks: functional AI literacy, critical AI literacy, and socio-cultural AI literacy. Ng et al. (2021), drawing on Bloom’s Taxonomy of Educational Objectives, developed a coding framework for core AI competencies through a literature review, identifying four key areas for cultivating AI literacy: knowing and understanding AI, using and applying AI, evaluating and creating AI, and AI ethics. Wang et al. (2023), based on a “technology-cognition-ethics” model, constructed a framework for core AI literacy across four dimensions: awareness, use, evaluation, and ethics. Chiu et al. (2024) proposed a framework consisting of five key components: technology, impact, ethics, collaboration, and self-reflection. United Nations Educational, Scientific and Cultural Organization (UNESCO) has defined the core of AI literacy as knowledge, understanding, skills, and values. Its further elaborated specific competency framework covers multiple dimensions, including a human-centered approach, AI ethics, technology and application, and system design, aiming to provide theoretical support for global AI literacy education.

In the context of higher education, student AI literacy has emerged as a prominent research focus (Dai et al., 2020; Laupichler et al., 2022; Wang et al., 2023). While a unified definitional framework for artificial intelligence literacy is yet to be established, existing research in this area spans numerous dimensions, including awareness, knowledge, skills, thinking modes, attitudes, ethics, values, evaluation, creation, and socio-cultural elements. Generative AI not only assists students in acquiring knowledge diversely and efficiently to enhance learning capacity (Chiu et al., 2023) but also directly supports the development of core competencies such as critical thinking (Long and Magerko, 2020), self-directed learning (Dai et al., 2020), and innovative creation (Ng et al., 2021). Consequently, for online mathematics learning, AI literacy fundamentally reshapes students’ problem-solving capabilities. It enables them to accurately articulate mathematical problems to AI, critically evaluate the logical soundness of AI-generated solutions, and ultimately transform AI output into personal mathematical understanding, thereby achieving deeper learning and cognitive advancement.

Cognitive tools refer to technological pathways specifically designed to extend and optimize learners’ cognitive processes. These tools are defined as computer applications capable of representing, organizing, or automating specific cognitive tasks, and forming an intellectual partnership with the learner (Lajoie and Derry, 1993). In mathematics learning environments, cognitive tools effectively reduce the cognitive load associated with understanding complex mathematical concepts through visualization, interactivity, and computational support, and fostering deeper conceptual understanding (Jonassen et al., 1998). Typical mathematical cognitive tools, such as MATLAB and the dynamic geometry software GeoGebra, demonstrate enhanced effects on mathematics learning across multiple dimensions (Mackenzie and Allen, 1998; Majid et al., 2013; Feng, 2024; Saha et al., 2010; Arbain and Shukor, 2015; Takači et al., 2015; Bekene Bedada and Machaba, 2022), and consistently enhance student learning motivation (Joshi, 2020). Research (Majid et al., 2013) indicates that MATLAB software, through multiple pathways such as visual demonstrations, mathematical computation support, and project-based practice, can effectively enhance students’ problem-solving abilities, foster positive mathematical attitudes and learning confidence, and exert a positive impact on mathematical achievement and learning motivation. The use of MATLAB in instruction has been shown to improve academic performance in advanced mathematics without imposing additional cognitive burden (Feng, 2024). And GeoGebra software aids students in constructing more intuitive conceptual models in topics such as calculus through its dynamic geometry and function graphing capabilities (Takači et al., 2015). Its use significantly boosts students’ confidence and conceptual understanding in learning calculus (Bekene Bedada and Machaba, 2022), while also markedly enhancing their positive perceptions of the learning process. By deeply integrating technological mediation with cognitive processes, cognitive tools provide robust support for online mathematics learning and enhance its overall effectiveness.

Perceived teacher support refers to students’ subjective experience and evaluation of the emotional care, informational resources, instrumental assistance, and autonomy facilitation provided by teachers during their learning process. According to existing research, teacher support encompasses multiple dimensions, including emotional support (Patrick et al., 2007), informational support (Tardy, 1985), instrumental support (Bekene Bedada and Machaba, 2022), and autonomy support (Reeve and Cheon 2021). Supportive behaviors from teachers in academic or life contexts significantly promote students’ deep learning, with higher levels of teacher support correlating with richer positive experiences for students (Hao et al., 2021). Perceived teacher support shows a significant positive correlation with academic achievement (Zhang et al., 2019), and teachers’ supportive behaviors can effectively predict students’ academic performance (Tao et al., 2022).

As digital literacy increasingly becomes a core competency for learners, teacher support plays a significant role in boosting students’ confidence in applying technology and fostering their digital literacy development (Chen and Ma, 2023). In the fields of mathematics and science, teacher support has emerged as an important predictor of student literacy (Saroughi and Cheema, 2023). By providing informational resources, guidance on using technological tools, and encouraging student participation in highly interactive digital learning environments, teachers effectively promote the comprehensive development of students’ digital literacy (Wang, 2022). Supportive teacher behaviors, such as engaging in cross-curricular collaboration and pursuing professional development, can enhance students’ comprehensive competencies, including information technology literacy (Weidner, 2018). Simultaneously, perceived teacher support has also been proven to be a crucial factor influencing students’ online learning power, impacting aspects such as learning engagement (Yang and Du, 2025), self-directed learning capacity (Bai and Gu, 2022), self-regulation levels (Rui and Liu, 2023), and innovative problem-solving abilities (Hsia et al., 2021). A positive correlation exists between teacher support and learners’ information technology literacy (Chen and Ma, 2023). Effective dynamic resources in online learning can stimulate students’ positive achievement emotions (Pekrun, 2006), thus directly transforming their information technology literacy into comprehensive online learning power.

Based on the preceding theoretical foundation, this study constructs a mediating model (as illustrated in Figure 1). The model positions perceived teacher support as the independent variable and online mathematics learning power as the dependent variable, with a specific focus on examining the parallel mediating roles played by AI literacy and cognitive tools.

This model aims to examine the internal mechanism through which teacher support influences online mathematics learning power, specifically testing the extent to which this influence is realized by enhancing students’ AI literacy and promoting their use of cognitive tools. Accordingly, the following research hypotheses are proposed.

This study was conducted at a comprehensive university in Eastern China. The participants were sophomore-year undergraduate students enrolled in online mathematics courses, including Advanced Mathematics, Probability and Statistics, and Linear Algebra. A total of 813 questionnaires were distributed. After screening and removing invalid responses, 758 valid questionnaires were retained, resulting in an effective response rate of 93.23%. Among the valid sample, 423 participants were male (55.8%) and 335 were female (44.2%). The entire survey process strictly adhered to the principle of voluntary participation and was conducted anonymously. All participants completed the questionnaire independently based on informed consent.

The study utilized a self-developed questionnaire comprising 27 items, all rated on a five-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree). All scales were adapted from established instruments and modified to fit the online mathematics learning environment. To ensure content validity, the items were reviewed and revised by experts in the field of education. A pilot survey (N = 110) was then conducted for item analysis and reliability testing, after which the final scales were formed upon meeting all required criteria. For perceived teacher support (PTS), a 6-item scale was adapted from Lai (2015) and Pan (2022) and covered the dimensions of emotional support (1 item), behavioral support (2 items), technical guidance (1 item), and feedback support (2 items). For AI literacy (AI), a 5-item scale was modified from Wang et al. (2023) to assess technology application capabilities in mathematics learning contexts. For cognitive tools (CT), a 4-item scale was developed from the perspective of commonly used mathematics learning software and was designed to assess proficiency in data processing, computational programming, geometric visualization, and statistical applications. For online mathematics learning power (OMLP), a 12-item scale was developed by integrating theoretical frameworks from Claxton (2002), Crick (2006), and Crick et al. (2015) and encompassed the dimensions of adaptability, cognitive capacity, application capacity, and reflective capacity. All items are detailed in the Appendix.

Using SPSS 25.0, we performed the Kaiser-Meyer-Olkin (KMO) test of sampling adequacy and Bartlett’s test of sphericity (Kaiser, 1974) on the questionnaire items. The results showed a KMO value of 0.973, well above the recommended threshold of 0.90, and a significant Bartlett’s test of sphericity (χ² = 22330.037, df = 351, p < 0.001). These indices collectively confirm that the data were highly suitable for factor analysis, thus providing a solid foundation for the subsequent confirmatory factor analysis (CFA).

Convergent validity is a key metric in confirmatory factor analysis (CFA) used to assess the effectiveness of scale measurement. A standardized factor loading of 0.70 is typically considered the minimum threshold for an item to effectively measure a latent variable (Hair et al., 2010). We conducted CFA on the four latent variables of perceived teacher support, AI literacy, cognitive tools, and online mathematics learning power using AMOS 21. The factor loading results for the observed items across all dimensions further confirmed the scales’ good convergent validity and reliability. The six items in the perceived teacher support dimension had loadings ranging from 0.765 to 0.921; the five items in the AI literacy dimension had loadings between 0.777 and 0.867; the four items in the cognitive tools dimension exhibited notably concentrated high loadings, distributed between 0.775 and 0.968; and the twelve items in the online mathematics learning power dimension also showed stable loadings in the range of 0.780 to 0.886. All item loadings substantially exceeded the 0.70 threshold, providing preliminary evidence of good convergent validity.

Table 1 presents the reliability and convergent validity test results for the four latent variables. The data indicate that the Cronbach’s α coefficients for perceived teacher support, AI literacy, cognitive tools, and online mathematics learning power are 0.951, 0.914, 0.937, and 0.968, respectively. All Cronbach’s α values exceed the recommended threshold of 0.70 (Fornell and Larcker, 1981; Nunnally and Bernstein, 1994), demonstrating excellent internal consistency reliability for each scale. In terms of convergent validity, the composite reliability (CR) values range between 0.918 and 0.967, all meeting the requirement of being greater than 0.7. The average variance extracted (AVE) values all surpass the critical threshold of 0.5, specifically 0.779, 0.691, 0.808, and 0.709, respectively, indicating good convergent validity for each variable (Fornell and Larcker, 1981) and confirming their effectiveness in measuring the corresponding latent constructs.

Table 2 reports the descriptive statistics and correlation analysis results of the variables. The descriptive statistics show that the mean values of the variables range between 3.714 and 4.501, with perceived teacher support having the highest mean (4.501) and cognitive tools having the relatively lowest mean (3.714). The standard deviations range from 0.553 to 1.082, with cognitive tools exhibiting the largest standard deviation (1.082), while the standard deviations of the remaining variables are relatively close and small, indicating a relatively concentrated data distribution. The correlation analysis results reveal that all variables show significant positive correlations (p < 0.01), with correlation coefficients ranging from 0.488 to 0.760. Among them, perceived teacher support and AI literacy demonstrate high correlations with online mathematics learning power (r = 0.754, r = 0.760, respectively), providing preliminary correlational support for further investigation into their influence mechanisms.

The measurement model of this study performs well on key metrics such as reliability, convergent validity, and discriminant validity. Meanwhile, the confirmatory factor analysis of the overall measurement model indicates that although the χ²/df value (4.99) is slightly elevated due to the sensitivity of the large sample size, other absolute and relative fit indices perform excellently (CFI = 0.943, TLI = 0.937, RMSEA = 0.073, and SRMR = 0.049). To assess common method bias, an unmeasured method factor was included in the confirmatory factor analysis. Comparison with the original model showed negligible fit index differences (ΔCFI = 0.001, ΔRMSEA = 0.001), both below established cut-offs (Cheung and Rensvold, 2002). The full model comparison results are provided in Supplementary Table S1. The results indicate that common method bias posed no serious threat to measurement validity.

The findings indicate that perceived teacher support contributes to online mathematics learning power through a composite set of pathways. It exerts a direct effect on learning power (β = 0.377, p < 0.001), and its effect is also transmitted through both independent and sequential mediation via AI literacy and cognitive tools. The total indirect effect (0.409) slightly exceeds the direct effect. Further analysis revealed distinct contributions of different teacher support dimensions: behavioral support showed the strongest predictive effect on fostering students’ AI literacy, whereas emotional support emerged as the most critical factor in promoting the use of cognitive tools. These findings support the core propositions of social cognitive theory (Bandura, 1977) and are consistent with prior research in online learning (e.g., Chen and Ma, 2023; Saroughi and Cheema, 2023; Wang, 2022; Bai and Gu, 2022; Yang and Du, 2025). They confirm that external environmental support, specifically perceived teacher support, contributes directly to learning outcomes, while also contributing indirectly through the synergistic interplay of individual-internal competencies (AI literacy) and tool-application abilities (cognitive tool proficiency).

AI literacy and cognitive tools differ in their strength of contribution to online mathematics learning power. The direct effect of AI literacy (β = 0.433, p < 0.001) is larger than that of cognitive tools (β = 0.164, p < 0.001). Furthermore, the mediating pathway via AI literacy contributes the majority (81.2%) of the total indirect effect, exceeding the indirect contribution of the cognitive tools pathway (7.1%). This suggests that, in digital learning environments, students’ literacy in using AI for problem-solving holds greater importance than their skill in mastering specific cognitive tools. Additionally, AI literacy significantly and positively predicts cognitive tools (β = 0.382, p < 0.001), suggesting that students with higher AI literacy are more likely to use cognitive tools effectively.

The direct effect of perceived teacher support on cognitive tools is relatively limited (β = 0.174, p < 0.01). Its contribution to cognitive tools is largely mediated by AI literacy, with the serial mediation pathway accounting for 11.7% of the total indirect effect. This implies that in fostering students’ technology application, teacher support primarily acts by developing their internal AI literacy, which in turn contributes to more effective tool use, ultimately contributing to online mathematics learning power.

This study developed and validated a multiple mediation model encompassing “perceived teacher support → AI literacy/cognitive tools → online mathematics learning power”. Thereby, it extends the application of social cognitive theory to online mathematics learning environments and outlines the mechanism “external support contributing to learning outcomes through key digital competencies” in the intelligent era. Serial mediation analysis revealed that AI literacy not only exerts a strong direct predictive effect but also serves as a critical foundation for the use of cognitive tools. Furthermore, the research clarifies how specific dimensions of teacher support, particularly behavioral support and emotional support, make distinct contributions to these digital competencies: behavioral support is most predictive of AI literacy, whereas emotional support more strongly predicts cognitive tools. These findings enrich social support theory in online mathematics education and provide a theoretical framework for future research to examine how teacher support contributes to learning outcomes in different disciplinary contexts.

The findings of this study offer specific practical implications for online mathematics teaching in higher education.

Educators should adopt instructional strategies that integrate direct support, literacy cultivation, and tool guidance. During instruction, teachers should provide direct support through clear learning objectives, well-structured learning plans, and timely feedback. In the early stages of teaching, teachers should foster AI literacy through behavioral support by creating varied opportunities. For example, teachers can design well-guided AI tasks that enable students to use GenAI tools for mathematical problem-solving, model validation, and outcome evaluation. Teachers can also provide structured reflection templates to guide students in critically examining AI outputs and transforming them into personal mathematical understanding.

When students using cognitive tools or tackling advanced tasks such as programming, teachers should encourage them to actively utilize AI as a learning assistant. For instance, when students encounter difficulties while using MATLAB or GeoGebra, they can be encouraged to break down the problem, pose questions to AI tools such as code interpreters or conversational AI, and leverage AI to generate code snippets, debugging suggestions, or functional explanations. This approach helps lower technical barriers and enhances both confidence and efficiency in using cognitive tools.

Through this phased and targeted support, teachers can effectively promote the development of students’ key digital competencies, which in turn contributes to their online mathematics learning power.