Research suggests that the reciprocal relationship between mathematical interest and competence may emerge as early as preschool, with learning interest shaping mathematical abilities during formative developmental stages (Fisher et al., 2012). Preschoolers’ mathematical interest, emotional skills, and pre-school mathematical competencies are intercorrelated (Doctoroff et al., 2016). In primary education, mathematical interest remains predictive of academic performance (Brumm and Rathgeb-Schnierer, 2023), while middle school studies from a social-cognitive perspective confirm its enduring influence on achievement outcomes (Petersen and Hyde, 2017). By high school, mathematical interest fosters advanced cognitive strategies that enhance academic performance (Yu and Singh, 2018). However, given the highly specialized and practice-oriented nature of mathematical applications in medical education, the mechanisms through which learning interest influences medical students’ problem-solving abilities remain unexplored. Thus, we propose:

Regarding teacher-student relationships, active classroom engagement and responsive teacher-student interactions have been shown to enhance educators’ job satisfaction and instructional efficacy, indirectly improving academic outcomes (Holzberger et al., 2013). We therefore posit:

Self-efficacy frequently mediates learning outcomes. Empirical studies demonstrate its role in boosting classroom participation (Jung et al., 2023) and mathematical achievement (Yang et al., 2021), leading to:

The direct influence of learning interest on teacher-student relationships is well-documented. Positive emotional engagement in team settings facilitates collaborative interactions and task completion (Warwas et al., 2009), implying that intrinsic motivation and interest strengthen interpersonal dynamics. Consequently, heightened learning interest fosters supportive teacher-student relationships (Huang et al., 2022), prompting:

Learning interest drives self-efficacy development. From the Social Cognitive Career Theory (SCCT) perspective, self-efficacy shapes occupational attitudes and interests, with both constructs forming core components of professional identity (Armstrong and Vogel, 2009). Medical students’ learning interest enhances intrinsic motivation, thereby elevating academic engagement (Pelaccia and Viau, 2017). We hypothesize:

Situational expectancy-value and control-value theories further indicate that teacher-student interactions modulate students’ perceived support, enabling educators to reinforce the value of learning interests and mitigate negative emotions in mathematics (Rubach et al., 2023). Supportive relationships amplify self-efficacy by fostering motivational resilience (Fasce et al., 2016), leading to:

In the context of medical education, teacher-student relationships and self-efficacy are theorized to mediate the link between learning interest and problem-solving ability. Positive teacher-student relationships create a low-stress, supportive learning environment that bolsters students’ confidence in mathematics. Analyses of PISA data reveal that such relationships predict mathematical achievement by enhancing interest and self-efficacy (You et al., 2021), with academic self-efficacy further driving performance through perseverance and goal-oriented behaviors (Tosto et al., 2016).

Self-efficacy critically shapes problem-solving competence by regulating learners’ emotional states [e.g., reducing anxiety (Wang et al., 2024)] and sustaining scientific curiosity (Cordero et al., 2010). Students with high self-efficacy exhibit greater persistence, employ metacognitive strategies, and explore diverse solutions when confronted with mathematical challenges (Ten Braak et al., 2022). Integrating these mechanisms, we propose:

This study employed a randomized sampling method to distribute anonymous questionnaires at a medical university in Shandong Province, China. A total of 853 questionnaires were issued, with 806 valid responses retained, yielding a valid response rate of 94.49%. The final sample comprised 288 male students (35.7%) and 518 female students (64.3%). In terms of academic standing, 752 participants were first-year students (93.3%) and 54 were second-year students (6.7%).

This study employed a self-designed questionnaire consisting of two parts: a mathematical problem-solving ability test and a survey on factors influencing medical students’ mathematical competence. The ability test section included four publicly available PISA mathematical literacy test questions (e.g., shopping discount calculations and transportation route optimization). Questions 1–2 were selected from “occupational context” items to assess multi-step calculations and quantitative reasoning, while questions 3–4 were drawn from “social context” items requiring mathematical modeling to solve complex problems. All questions were categorized as PISA Level 4–5 (top 20% proficiency level for 15-year-olds). Scoring followed a binary system: fully correct answers received 0.5 points, with incorrect or incomplete responses awarded zero points. Questionnaire validity was ensured through dual verification, with item content rigorously aligned with the PISA “mathematization processes” competency framework.

The survey on factors influencing medical students’ mathematical problem-solving ability comprised 22 items adapted from existing literature. Part 1 collected demographic information (gender, grade, residence, and major) through four questions. Part 2 measured three dimensions of mathematical competence—learning interest, self-efficacy, and teacher-student relationships—using 18 items. Each item adopted a 5-point Likert scale, scored from 0.5 to 2.5 points to enhance response differentiation (Bu et al., 2023).

To reduce potential response bias in self-reported data, this study implemented three measures: anonymous responses, randomized item sequencing, and attention-check questions (reverse-scored items), leading to the exclusion of 5.5% invalid questionnaires. Reliability analysis demonstrated strong internal consistency, with an overall Cronbach’s α coefficient of 0.919. Subscale coefficients were 0.801 for self-efficacy, 0.855 for learning interest, and 0.876 for teacher-student relationships (mean α = 0.844). Validity was verified through exploratory factor analysis (EFA). The Kaiser-Meyer-Olkin (KMO) measure reached 0.916, and Bartlett’s test of sphericity yielded χ² = 11,246.7 (p < 0.001), confirming sampling adequacy. The cumulative variance explained was 66.29%, with factor loadings aligning closely with the predefined dimensions: Factor 1 (self-efficacy: loadings 0.72–0.89) explained 30.53% variance; Factor 2 (teacher-student relationships: loadings 0.65–0.83) accounted for 13.08%; Factor 3 (learning interest: loadings 0.61–0.79) contributed 9.04%. The remaining four factors each explained <5% variance (reflecting measurement error variability), but all cross-loadings remained below 0.40, confirming the structural validity of the hypothesized three-dimensional framework and the questionnaire’s robust psychometric quality.

Data analysis was conducted using SPSS v29.0 for descriptive statistics and Spearman’s rank-order correlation with a two-tailed significance threshold of α = 0.05. A serial mediation model was constructed via Model 6 in Hayes’ PROCESS macro v4.2 for SPSS. To evaluate the practical significance of findings, this study reported standardized regression coefficients and 95% confidence intervals (CIs). Additionally, Cohen’s d effect sizes were calculated, interpreted using Cohen’s (1988) heuristic benchmarks: d = 0.20–0.50 (small), 0.50–0.80 (medium), and > 0.80 (large). Notably, Cohen emphasized these thresholds as “conventional reference points,” and recent scholarship has cautioned against their uncritical application across contexts (Panjeh et al., 2023).

Common method bias (CMB) was tested using Harman’s single-factor test. Results showed 7 factors with eigenvalues greater than 1, with the first factor explaining 30.529% of variance—below the 40% critical threshold—indicating no significant common method bias. Potential biases (e.g., systematically inflated self-efficacy scores or elevated correlations due to uniform scoring formats) were mitigated by: (1) combining Likert scales with objective calculation tasks, (2) including reverse-scored items, and (3) enforcing anonymous responses. While CMB might modestly inflate correlation magnitudes, the clear differentiation of factor loadings and strong alignment between empirical data and theoretical dimensions support the robustness of core conclusions.

In the surveyed sample, grade level, geographic residence, and academic major were included as control variables in subsequent regression and mediation analyses. Gender distribution showed 35.73% male and 64.27% female participants, with a higher proportion of females. First-year undergraduates accounted for 93.30% of the sample, reflecting a deliberate focus on first-year medical students. Geographic residence distribution was predominantly rural (335 participants), followed by cities (273 participants) and towns (198 participants). Academic majors were represented in descending order as Clinical Medicine, Biomedical Engineering, Medical Imaging, Health Administration, Anesthesiology, Emergency Management, Labor and Social Security, and Public Health. The skewed distributions of grade levels and majors (e.g., overrepresentation of first-year students and specific disciplines) may confound the relationship between academic interests and competencies due to variations in curricular intensity, requiring statistical control.

On the gender dimension, no significant differences were observed in scores for mathematical self-efficacy, mathematical learning interest, teacher-student relationships, or mathematical problem-solving ability. On the grade dimension, no significant differences were found for mathematical self-efficacy, mathematical learning interest, or teacher-student relationships, but first-year students scored higher than second-year students in mathematical problem-solving ability (p < 0.05). On the residence dimension, no significant differences emerged for mathematical self-efficacy, but medical students from towns scored higher than those from cities and rural areas in mathematical learning interest (p < 0.05), while urban medical students scored higher than those from towns and rural areas in teacher-student relationships (p < 0.05). On the major dimension, no significant differences existed for mathematical self-efficacy, but Emergency Management majors outperformed other disciplines in mathematical learning interest and teacher-student relationships (p < 0.05), and Anesthesiology majors scored higher than others in mathematical problem-solving ability (p < 0.05) (see Table 1).

Normality tests (Kolmogorov–Smirnov: D = 0.135–0.324; Shapiro–Wilk: W = 0.750–0.949; all p < 0.001) revealed significant deviations from normal distribution across all variables, thus justifying the use of Spearman’s rank-order correlation analysis. Correlation analysis revealed significantly positive correlations between medical students’ mathematical problem-solving ability and self-efficacy, learning interest, and teacher-student relationships (see Table 2). Specifically, the correlation coefficients between problem-solving ability and self-efficacy, learning interest, and teacher-student relationships were 0.142, 0.113, and 0.132, respectively. While statistically significant (p < 0.01), the small magnitude of these coefficients may reflect the context-specific nature of medical mathematics and the overall low performance in problem-solving ability (mean score = 1.38), which likely limited the strength of associations. In contrast, stronger correlations were observed: self-efficacy correlated with learning interest (r = 0.629) and teacher-student relationships (r = 0.419), while learning interest correlated with teacher-student relationships (r = 0.429), all with p < 0.01.

Using mathematical learning interest as the independent variable (X), mathematical problem-solving ability as the dependent variable (Y), and teacher-student relationships (M1) and mathematical self-efficacy (M2) as mediator variables, the analysis revealed the following: The total effect of learning interest on problem-solving ability was 0.034 (p < 0.001), with a 95% confidence interval of [0.016, 0.053] calculated via bootstrapping (5,000 samples), indicating that a 1-standard-deviation increase in learning interest corresponds to a 0.034-SD improvement in problem-solving ability (Cohen’s d = 0.12, small effect). The direct effect of learning interest on problem-solving ability was nonsignificant [β = 0.010, p > 0.05, 95% CI (−0.014, 0.035)]. For the teacher-student relationship (M1) mediation path (learning interest → teacher-student relationships → problem-solving ability), learning interest positively predicted teacher-student relationships (β = 0.328, p < 0.001), but the latter’s predictive effect on problem-solving ability was nonsignificant (β = 0.025, p > 0.05), yielding a nonsignificant indirect effect of 0.008 [95% CI (−0.011, 0.020)]. For the self-efficacy (M2) mediation path (learning interest → self-efficacy → problem-solving ability), learning interest positively predicted self-efficacy (β = 0.533, p < 0.001), and self-efficacy significantly predicted problem-solving ability (β = 0.026, p < 0.05), with an indirect effect of 0.014 [95% CI (0.0003, 0.029), Cohen’s d = 0.18, small effect]. For the chained mediation path (learning interest → teacher-student relationships → self-efficacy → problem-solving ability), teacher-student relationships positively predicted self-efficacy (β = 0.227, p < 0.001), with a chained indirect effect of 0.002 [95% CI (0.0003, 0.005), Cohen’s d = 0.04, small effect]. Detailed paths are shown in Figure 1, and results are summarized in Tables 3, 4.

The total indirect effect (0.0243) accounted for 70.66% of the total effect. The nonsignificant standalone mediation via teacher-student relationships suggests that isolated improvements in teacher-student interactions have limited impact on medical mathematics competency unless integrated with clinical-contextualized teaching to activate cognitive support mechanisms. The self-efficacy mediation path was significant, explaining 40.79% of the total effect. The chained mediation path (teacher-student relationships → self-efficacy) explained 5.68%, highlighting the potential of leveraging “teacher-student support → self-efficacy” as an educational enhancer. Overall, self-efficacy is the key mediator linking learning interest to mathematical competency, whereas the weak effects of teacher-student relationships and the chained path suggest prioritizing self-efficacy over isolated relational improvements.

Academic major significantly negatively predicted both teacher-student relationships (β = −0.056, p < 0.001) and problem-solving ability (β = −0.014, p = 0.006), reflecting that high-intensity training in mainstream disciplines (e.g., Clinical Medicine) generally suppresses relational and mathematical development. However, disciplinary heterogeneity exists: Emergency Management majors exhibited superior teacher-student relationships and learning interest due to integrated mathematical modeling curricula, while Anesthesiology excelled in problem-solving ability owing to explicit mathematical applications (e.g., pharmacokinetic calculations). These findings indicate that the overall negative trend across medical disciplines may be moderated by subject-specific differences (see Table 3).

This study found that Hypotheses 1 and 2 were unsupported, while Hypotheses 3, 4, 5, and 6 were supported—that is, neither college students’ mathematical learning interest nor teacher-student relationships directly predicted mathematical problem-solving ability. On one hand, interest reflects a trait-like preference for work activities, environments, or outcomes, which drives goal-oriented behaviors (Hyland et al., 2022). When students exhibit strong interest in mathematics, they are more likely to engage in proactive learning, exploration, and conceptual understanding, fostering not only deeper knowledge acquisition but also innovative thinking in problem-solving. Prior research indicates that interest exerts a stronger influence on mathematical performance compared to physics, chemistry, or biology (Jansen et al., 2016). Conversely, students lacking mathematical interest often struggle with motivation, leading to difficulties, disengagement, and reduced learning efficacy (Merrick and Maher, 2009). However, this study’s focus on medical students introduces a critical distinction: mathematics in medical curricula serves as a tool rather than a core discipline, potentially diluting interest’s direct effects due to confounding from professionally oriented motivations (Machalow et al., 2022). After controlling for grade, residential environment, and major-related variables, the direct effect of mathematical interest on problem-solving ability became nonsignificant. While academic interest is known to positively influence achievement through enhanced effort and persistence—with stronger interest-achievement linkages in natural sciences (Jansen et al., 2016)—mathematics in medical education is often perceived as a “service discipline,” where clinical motivations may weaken its interest-ability association via motivational filtering (Sun et al., 2024). For example, medical students’ academic interest shows minimal impact on medical academic performance (Wu et al., 2019), and in psychology, initial personal interest fails to predict undergraduates’ grades (Harackiewicz et al., 2008). This study expands the scope of interest-achievement research, suggesting that disciplinary attributes may moderate interest-ability relationships, with implications for medical curriculum integration.

Additionally, aligned with the expectancy-value model, medical students’ mathematical motivations are dominated by career goal commitments. Even with positive teacher-student relationships, if students perceive mathematics as minimally relevant to future clinical practice, intrinsic motivation becomes suppressed by motivational filtering, blocking the direct translation of relational support into mathematical competency (Wu et al., 2020).

This study found that teacher-student relationships did not exhibit a significant independent mediating role in the relationship between college students’ mathematical learning interest and problem-solving ability, thus Hypothesis 7 was unsupported. While prior research indicates that learning interest significantly positively predicts teacher-student relationships (Kwok et al., 2022)—a bidirectional interaction where both participants influence each other’s cognition, emotions, motivations, and behaviors (Korthagen et al., 2014; Holen et al., 2018). Such relationships in medical education are predominantly centered on clinical skills rather than mathematics, likely weakening their mediating role in mathematical competency (Wei and Cheng, 2022). Academic achievement ultimately requires students’ own efforts; for instance, studies analyzing the mediating role of self-efficacy in the relationship between proactive personality and academic performance among college athletes found that proactive personality enhances grades only through self-efficacy (Li et al., 2022). This explains why teacher-student relationships alone cannot directly predict problem-solving ability and must operate via self-efficacy’s mediation.

The study confirmed that mathematical self-efficacy serves as a significant independent mediator between learning interest and problem-solving ability, supporting Hypothesis 8. Learning interest exerted a stronger indirect effect on problem-solving ability through self-efficacy alone compared to the chained mediation via teacher-student relationships. Strong mathematical self-efficacy correlates closely with problem-solving ability (Arens et al., 2022), as students with high self-efficacy typically possess superior mathematical thinking skills, foundational knowledge, confidence (Guo et al., 2023), well-being (Datu and Mateo, 2020), and academic efficiency. This finding identifies a low-cost intervention target for medical education: short-term cognitive-behavioral training to enhance self-efficacy may be more feasible and impactful than restructuring teacher-student dynamics (Ashraf et al., 2024).

The study also validated Hypothesis 9, demonstrating a chained mediation effect (learning interest → teacher-student relationships → self-efficacy → problem-solving ability). Strong learning interest fosters teacher-student interactions, which in turn boost self-efficacy—a critical predictor of academic achievement (Wei et al., 2022). Even in hybrid learning environments, teacher support remains pivotal for elevating self-efficacy (Weber and Harzer, 2022).

In summary, medical students’ learning interest enhances problem-solving ability exclusively through self-efficacy, with both the independent mediation of self-efficacy (β = 0.014, 95% CI [0.0003, 0.029]) and the chained mediation (teacher-student relationships → self-efficacy) exerting significant positive effects. By focusing on medical students, this study expands the scope of research on learning interest and academic performance, revealing that mathematical learning interest cannot directly improve problem-solving ability but requires the amplification of mathematical self-efficacy.