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. 2025 Nov 19;13:1278. doi: 10.1186/s40359-025-03630-y

How creative self-efficacy influences problem-solving skills in engineering education: the dual mediating role of critical thinking and metacognition

Zhihua Liu 1,#, Huifen Guo 1,✉,#, Zhen Zhou 2,#, Fengqi Ma 1, Yanhan Zeng 3
PMCID: PMC12628857  PMID: 41257912

Abstract

Background

Problem-solving skills are a core competency for engineering students, yet the psychological mechanisms underlying their development remain poorly understood. Creative self-efficacy has been identified as a potential motivational driver of problem-solving skills, but the pathways through which it functions have received limited empirical investigation. This study examines the direct relationship between creative self-efficacy and problem-solving skills and explores the dual mediating roles of critical thinking and metacognition in this relationship.

Methods

A cross-sectional survey was conducted with a sample of undergraduate engineering students (N = 711). Validated self-report scales were used to assess creative self-efficacy, critical thinking, metacognition, and problem-solving skills. Partial least squares structural equation modelling (PLS-SEM) was employed to test the proposed dual mediation model.

Results

Creative self-efficacy was found to have a statistically significant direct effect on problem-solving skills (p < 0.01), although the effect size was weak (f² = 0.031). In contrast, creative self-efficacy had strong effects on both critical thinking (p < 0.001, f² = 0.690) and metacognition (p < 0.001, f² = 0.676). Both critical thinking (p < 0.01) and metacognition (p < 0.001) significantly mediated the relationship between creative self-efficacy and problem-solving skills, though their direct effects on problem-solving were modest (f² = 0.035 and f² = 0.129, respectively).

Conclusions

The findings demonstrate that creative self-efficacy primarily enhances problem-solving skills through its positive effects on critical thinking and metacognition. These results highlight the need for engineering education to strengthen students’ critical thinking and metacognition while fostering their confidence in their problem-solving. These insights offer both theoretical and practical guidance for designing targeted interventions to enhance students’ problem-solving skills.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40359-025-03630-y.

Keywords: Creative self-efficacy, Problem-solving skills, Critical thinking, Metacognition, Dual mediating

Introduction

Problem-solving skills are widely recognized as a defining attribute of engineering education, equipping students to address the open-ended and complex challenges that characterize professional engineering practice [1]. Yet engineering problem-solving differs fundamentally from problem-solving in other domains. Whereas many educational problems can be solved through the direct application of established procedures, engineering problems are often ill-structured, situated within real-world contexts, and constrained by technical, economic, and social considerations [2]. They demand not only the integration of diverse forms of disciplinary knowledge but also the ability to balance creativity with feasibility, and innovation with safety and regulatory compliance. Moreover, engineering problem-solving is inherently generative (students are expected to design, optimize, and evaluate solutions that may not yet exist, often under uncertain conditions) [3]. These distinctive demands mean that successful problem-solving in engineering education cannot rely solely on procedural knowledge; it requires confidence in one’s creativity, the critical thinking to evaluate alternatives rigorously, and the metacognition to monitor and adapt strategies as problems evolve [4]. This domain-specific complexity underscores the importance of investigating how creative self-efficacy, critical thinking, and metacognition jointly support the development of engineering students as effective problem solvers [5].

To account for this interplay, the present study is grounded in social cognitive theory, which posits that personal beliefs, cognitive processes, and behaviors interact reciprocally within specific contexts [6]. Within this framework, creative self-efficacy functions as a motivational driver that shapes how they approach and persist in solving engineering problems. Creative self-efficacy not only sustains students’ willingness to take intellectual risks and explore unconventional approaches but also facilitates adaptive engagement with setbacks and iterative design processes. Yet self-efficacy alone does not guarantee effective performance; its impact must be channeled through cognitive–regulatory mechanisms that guide how ideas are critically evaluated and how strategies are monitored and adapted during problem-solving [7]. Two such mechanisms are particularly salient in engineering contexts. Critical thinking provides the foundation for rigorous evaluation, enabling students to interrogate assumptions, compare alternatives, and weigh evidence against technical, ethical, and contextual constraints [8]. Metacognition, in turn, equips learners with the capacity to plan, monitor, and regulate their cognitive activity, allowing them to adapt strategies as problems evolve and as constraints shift [9]. While conceptually distinct, these constructs are functionally interdependent: critical thinking directs attention to what must be questioned and justified, whereas metacognition governs how strategies are deployed and revised. Together, they serve as vital pathways through which creative self-efficacy is translated into competent problem-solving performance in engineering education.

Despite increasing scholarly attention to creative self-efficacy, critical thinking, and metacognition, two significant gaps remain. First, prior studies often investigate these constructs in isolation, overlooking their potential interdependence in shaping problem-solving outcomes. Mediation models have occasionally considered critical thinking or metacognition separately, but rarely have they examined both simultaneously as parallel mechanisms. Second, much of the existing research has been conducted in general educational settings, with limited attention to engineering-specific contexts where domain constraints, uncertainty, and generativity play a central role. This omission limits our theoretical understanding of how motivational beliefs and cognitive–regulatory processes jointly contribute to engineering students’ problem-solving performance. To address these gaps, this study develops and empirically tests a dual mediation model in which critical thinking and metacognition simultaneously mediate the relationship between creative self-efficacy and problem-solving skills. Within the framework of social cognitive theory, this research advances a more comprehensive account of how self-efficacy is enacted through higher-order cognitive processes to foster effective problem-solving skills in engineering education. The findings are expected to inform curriculum and instructional design, highlighting the need to cultivate not only students’ creative self-efficacy but also their critical thinking and metacognition. Based on the above literature review, the research questions are as follows:

  • RQ1: What is the relationship between creative self-efficacy and problem-solving skills?

  • RQ2: What roles do critical thinking and metacognition play in the relationship between creative self-efficacy and problem-solving skills?

Literature review and hypothesis development

Creative self-efficacy and problem-solving skills

Within the framework of social cognitive theory, self-efficacy has long been recognized as a key contributor to variations in learning and performance [10]. It influences their willingness to engage with demanding tasks and their capacity to sustain effort in the face of challenges [11]. Higher levels of self-efficacy are typically associated with more adaptive learning behaviors and improved problem-solving skills [12]. Extending this framework, creative self-efficacy captures individuals’ belief in their capacity to produce original and useful ideas. This domain-specific belief is especially relevant to ill-structured problem solving, where solutions cannot be derived mechanically but instead require the generation of novel approaches. In engineering education, students with higher creative self-efficacy are more willing to confront open-ended challenges, explore diverse solution strategies, and sustain engagement despite ambiguity [10]. A consistent line of empirical research has established a positive association between creative self-efficacy and problem-solving skills [13]. Students reporting stronger creative self-efficacy demonstrate greater adaptability in approaching open-ended tasks, employ a wider range of solution strategies, and maintain persistence in the face of uncertainty. Importantly, these effects have been observed across both academic and applied contexts, suggesting that creative self-efficacy operates as a robust predictor of problem-solving skills [14]. Prior studies have typically operationalized creative self-efficacy through evaluating problem-solving outcomes using rubric-based assessments, structured case analyses, or scenario-driven tasks [15]. Despite variations in design and measurement, the evidence consistently underscores the predictive role of creative self-efficacy [16]. Yet, this literature has primarily emphasized direct associations, offering limited insight into the cognitive processes that mediate this link. Moreover, relatively few studies have focused explicitly on engineering education, where problem-solving demands the integration of creativity, reasoning, and technical expertise. Addressing these gaps requires a more systematic examination of the direct and indirect relationship between creative self-efficacy and problem-solving skills within the context of engineering education. Thus, the first hypothesis is proposed:

  • H1: Creative self-efficacy is a significant positive predictor of problem-solving skills.

Creative self-efficacy and critical thinking

Creative self-efficacy refers to individuals’ belief in their capacity to produce original and useful ideas [10]. Extensive empirical research has established a robust link between creative self-efficacy and critical thinking among university students [17]. A meta-analysis demonstrated that higher levels of creative self-efficacy correlate with increased creativity and problem-solving skills, suggesting that students with strong creative self-efficacy are more adept at critical thinking tasks [18, 19]. Similarly, it was found that academic self-efficacy positively predicts critical thinking, including open-mindedness, systematicity, and truth-seeking, among university students [8]. In the context of engineering education, it was highlighted that engineering students’ self-efficacy is closely tied to their problem-solving skills and overall academic performance [20]. These findings suggest that students with higher creative self-efficacy are essential for critical thinking [21]. Creative self-efficacy encourages students to approach problems with an open and analytical mindset, facilitating the evaluation of alternative solutions. Despite these findings, evidence within engineering education remains scarce. Engineering students regularly face ill-structured and technically complex problems that require not only the generation of novel solutions but also the critical evaluation and refinement of these ideas. It is therefore plausible that creative self-efficacy operates as a motivational driver that not only stimulates divergent thinking but also supports the analytical reasoning processes integral to critical thinking in engineering problem-solving. On this basis, the following hypothesis is proposed:

  • H2: Creative self-efficacy is a significant positive predictor of critical thinking.

Creative self-efficacy and metacognition

Metacognition, broadly defined as the awareness and regulation of one’s cognitive processes, includes knowledge about strategies, monitoring, and planning activities, and evaluative processes that guide problem-solving and learning [22, 23]. A considerable body of empirical research has shown that self-efficacy is closely related to metacognition [24]. Studies employing validated survey instruments and performance-based tasks consistently demonstrate that students with higher self-efficacy report greater use of metacognitive regulation strategies such as planning and self-monitoring, and they perform more effectively on tasks requiring reflective control of cognition [25]. Prior research suggests that students who feel confident in their ability to generate novel and useful ideas are also more likely to engage in reflective planning, monitor their reasoning, and evaluate alternative approaches [26, 27]. Experimental designs that strengthen creative self-efficacy through mastery experiences, feedback, or collaborative design projects have similarly reported improvements in students’ self-regulatory and reflective learning strategies, suggesting that efficacy beliefs in creativity extend beyond idea generation to shape cognition [28]. Despite this growing evidence, research in engineering education has seldom systematically examined how creative self-efficacy predicts metacognition, particularly given that engineering problem solving requires both creative ideation and strategic regulation of thought. By synthesizing insights from prior survey-based, performance-based, and mediational studies, the present study extends this literature to clarify whether creative self-efficacy directly enhances students’ metacognition in an engineering context. Therefore, the following hypothesis is proposed:

  • H3: Creative self-efficacy is a significant positive predictor of metacognition.

Critical thinking and problem-solving skills

Critical thinking involves the ability to evaluate evidence, identify assumptions, analyze arguments, and make reasoned judgments, thereby enabling students to navigate ill-structured and information-rich tasks [28]. Empirical studies consistently demonstrate that stronger critical thinking skills are associated with superior performance in complex problem-solving tasks [29], as learners who think critically are more adept at clarifying problem structures, generating alternatives, and selecting feasible solutions. Intervention research further shows that instructional programs explicitly targeting critical thinking development significantly improve students’ problem-solving skills, highlighting critical thinking as both a transferable skill and a core determinant of success in engineering contexts [30]. Building on this evidence, the following hypothesis is proposed:

  • H4: Critical thinking is a significant positive predictor of problem-solving skills.

Beyond its direct influence, critical thinking has also been identified as a pathway through which self-efficacy affects learning outcomes. According to social cognitive theory, self-efficacy shapes individuals’ motivation and persistence when engaging with challenging tasks, thereby influencing the extent of their cognitive engagement. In line with this framework, prior studies have shown that self-efficacy can enhance learners’ willingness to engage in cognitively demanding activities and that this engagement frequently translates into higher levels of critical thinking [21]. Extending this logic to creative self-efficacy, individuals who are confident in their creativity are more likely to invest cognitive effort in scrutinizing ideas, questioning assumptions, and applying systematic reasoning, which are processes central to critical thinking [31]. Recent empirical findings further suggest that critical thinking acts as a mediator between creative self-efficacy and problem-solving skills, partially explaining how self-efficacy is transformed into more effective learning and problem-solving behaviors [32].

Although alternative mediators such as learning motivation or self-regulation are frequently examined, critical thinking offers a more direct lens for understanding how creative self-efficacy translates into problem-solving skills [29]. Engineering problem-solving tasks typically require learners to analyze complex information [33], evaluate alternative solutions, and make reasoned judgments, which are cognitive processes best captured by critical thinking. In contrast, motivational or regulatory constructs may shape students’ engagement and persistence, but do not by themselves explain the quality of the reasoning applied. By highlighting this proximal cognitive pathway, the present model not only clarifies how creative self-efficacy influences problem-solving but also extends existing research by identifying a mechanism that more closely aligns with the demands of engineering education. Accordingly, the following hypothesis is proposed:

  • H5: Critical thinking mediates the relationship between creative self-efficacy and problem-solving skills.

Metacognition and problem-solving skills

In engineering contexts, problem-solving is often an iterative process involving complex, ill-structured challenges [34]. Research indicates that successful problem-solvers engage in continuous self-regulation, which allows them to allocate cognitive resources efficiently, identify knowledge gaps, and adapt their strategies in real-time [35]. A systematic review concluded that metacognition is a potent predictor of learning performance, frequently surpassing the influence of intellectual ability in problem-solving tasks [35]. Furthermore, studies demonstrate a clear correlation between metacognitive training and enhanced problem-solving outcomes [36]. Interventions designed to teach metacognitive strategies, such as self-explanation and reflective journaling, have been shown to significantly improve students’ abilities to analyze problems, design solutions, and troubleshoot effectively [37]. This body of evidence substantiates the claim that metacognitive processes are not merely ancillary but are fundamental components of proficient problem-solving. Based on the established empirical link between metacognition and problem-solving skills in academic literature. Therefore, the following hypothesis is proposed:

  • H6: Metacognition is a significant positive predictor of problem-solving skills.

Beyond its direct effect, metacognition may function as a key variable linking creative self-efficacy to problem-solving performance [38]. Social cognitive theory suggests that individuals with higher self-efficacy are more likely to engage in proactive and strategic behaviors, which, in turn, enhance performance [39]. In the context of creative tasks, students with strong creative self-efficacy are more likely to set challenging goals, critically evaluate their progress, and adapt strategies when encountering difficulties, which are processes closely aligned with metacognition. Prior empirical work supports this mediating role, indicating that metacognition can partially transmit the influence of self-efficacy on task outcomes [40]. Notably, metacognition is selected as a mediator in our model because of its foundational role in higher-order cognitive control and strategy adaptation during complex problem-solving. While factors like motivation initiate engagement, and self-regulation support broader learning processes, metacognition specifically governs the real-time monitoring and steering of cognitive strategies in novel problem contexts, making it particularly relevant to problem-solving skills in engineering. Furthermore, prior studies on creative self-efficacy and problem-solving have underscored metacognition as a pivotal variable linking self-efficacy to problem-solving skills. Given this robust theoretical and empirical foundation, we propose the following hypothesis:

  • H7: Metacognition mediates the relationship between creative self-efficacy and problem-solving skills.

The proposed research model of this study is shown in Fig. 1.

Fig. 1.

Fig. 1

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Proposed research model

Method

Instrumental design and pilot survey

The research instrument was initially developed bilingually in Chinese and English to ensure linguistic appropriateness and conceptual equivalence for the target population. The questionnaire consisted of two parts: the first part collected demographic information, including gender, region of origin, and level of education. The second part comprised a self-report scale designed to measure four core constructs: Creative Self-Efficacy, Critical Thinking, Metacognition, and Problem-Solving Skills. The Creative Self-Efficacy Scale, adapted from [41] and [42], comprises seven items that capture students’ confidence in their ability to tackle challenges creatively; for example, “When a technical problem seems too complex, I can figure out a simple and creative way to solve it.” The Critical Thinking Scale, drawing on the frameworks proposed by [43] and [44], contains five items and examines students’ tendency to question assumptions and challenge received information, as reflected in statements such as “I do not believe that what is presented by others is always true.” The Metacognition Scale, developed from [45], includes five items that assess learners’ ability to monitor and regulate their thinking; one item, for instance, reads: “When I cannot come up with an original approach to a problem, I go back to the assignment and try to figure it out.” The Problem-Solving Skills Scale, adapted from [46] and [47], consists of four items that gauge the extent to which students can approach problems flexibly and from multiple angles, exemplified by “I can understand problems from different directions.” Before the formal data collection, a pilot survey was conducted with a sample of 100 engineering students to examine the clarity, comprehensibility, and appropriateness of the items. Based on the participants’ feedback, minor revisions were made to improve wording, remove ambiguities, and ensure consistency between the two language versions. The refined questionnaire was then finalized for formal administration, ensuring that the instrument was both valid and reliable for capturing the intended constructs. The respondents rated each item using a 5-point Likert scale, ranging from 1 (strongly disagree) to 5 (strongly agree). Details of the questionnaire are provided in Appendix A.

Participants and data collection

To ensure comprehensive data collection, the questionnaire was distributed via WeChat, a platform that is widely and routinely used among university students in China for communication, study groups, and academic activities. The use of WeChat enabled us to access a large and diverse pool of engineering students across different universities efficiently and cost-effectively. Data were collected from September to December 2024, yielding a total of 756 responses. To ensure data quality, a series of screening procedures was conducted, including the removal of incomplete questionnaires, cases with unrealistically short completion times, patterned or inconsistent responses, and statistically extreme values. After applying these procedures, 45 responses were excluded, resulting in 711 valid cases and an effective response rate of 93%. While WeChat-based distribution may introduce certain limitations in terms of sample representativeness and potential self-selection bias, several measures were taken to mitigate these concerns: the survey was disseminated through multiple independent channels (e.g., student associations, class groups, and faculty networks) to reach students from varied academic and demographic backgrounds, and rigorous data screening was performed to enhance internal validity. In terms of gender composition, 480 respondents (68%) identified as male and 231 (32%) as female. Concerning region of origin, 488 participants (69%) reported coming from rural areas, while 223 (31%) were from urban areas. Regarding level of education, first-year students constituted the largest proportion with 241 respondents (34%), followed by second-year students with 231 (32%), fourth-year students with 138 (20%), and third-year students with 101 (14%), demonstrating a relatively higher representation of students in the lower years. All procedures were conducted in strict accordance with institutional ethical guidelines and relevant regulations; ethical approval was obtained from the university’s ethics committee (approval number: GZHU202341), and informed consent was secured from all participants before data collection.

Results

Common method bias

As this study employed self-reported questionnaires administered at a single time point, the potential influence of common method bias was carefully assessed. First, Harman’s single-factor test [48] was conducted by subjecting all items related to creative self-efficacy, critical thinking, metacognition, and problem-solving skills to an unrotated exploratory factor analysis. The results revealed that the first factor accounted for 37.21% of the total variance, which is below the commonly accepted threshold of 50% [49], indicating that no single factor was predominant. Second, to provide additional robustness, the full collinearity assessment was performed within the SEM framework. The variance inflation factor (VIF) values for all latent constructs were far below the conservative cut-off value of 3.3, further confirming that common method bias is unlikely to undermine the validity of the findings.

Descriptive statistics and correlation analysis

As shown in Table 1, demographic variables exhibited minimal relationships with the main outcome measures. Region of origin, in particular, did not show a significant correlation with any other variable, and level of education only had a very small correlation with problem-solving skills (r = 0.075, p < 0.05). Gender showed weak but statistically significant correlations with academic level (r = 0.109, p < 0.01), metacognition (r = 0.128, p < 0.01), creative self-efficacy (r = 0.092, p < 0.05), and critical thinking (r = 0.103, p < 0.01). However, these coefficients are all close to zero, indicating that demographic characteristics have a negligible practical impact on the key constructs. In contrast, meaningful correlations were observed among the psychological and cognitive factors. For example, creative self-efficacy was strongly related to critical thinking (r = 0.814, p < 0.01) and problem-solving skills (r = 0.705, p < 0.01). Metacognition also showed strong associations with problem-solving skills (r = 0.547, p < 0.01), creative self-efficacy (r = 0.613, p < 0.01), and critical thinking (r = 0.609, p < 0.01). The descriptive statistics reveal that critical thinking, creative self-efficacy, and metacognition achieved the highest average scores, while demographic factors such as academic level and region of origin were comparatively lower.

Table 1.

Descriptive statistics and correlation coefficients

GEN ACL ROO MET PSS CSE CT
GEN 1
ACL 0.109** 1
ROO 0.010 0.049 1
MET 0.128** 0.046 0.055 1
PSS 0.052 0.075* 0.026 0.547** 1
CSE 0.092* 0.047 0.009 0.613** 0.705** 1
CT 0.103** 0.047 0.081* 0.609** 0.692** 0.814** 1
M - 3.044 1.314 4.575 4.085 4.613 4.616
SD - 0.417 0.464 0.644 0.649 0.622 0.565
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M Mean, SD Standard Deviation, GEN Gender, ACL Academic Level, ROO Region of Origin, MET Metacognition, PSS Problem-Solving Skills, CSE Creative Self-Efficacy, CT Critical Thinking

*Correlation is significant at the 0.05 level (2-tailed)

**Correlation is significant at the 0.01 level (2-tailed)

Measurement model assessment

Assessment of convergent validity and internal consistency reliability

The cleaned dataset was first exported from SPSS version 24.0 in “.csv” format and subsequently imported into SmartPLS 4.0 for partial least squares structural equation modelling. The measurement model was evaluated to examine the reliability and validity of the latent constructs before the assessment of the structural model. In line with the recommendations for exploratory research provided by [50], the following threshold criteria were adopted: Cronbach’s alpha greater than 0.80, composite reliability greater than 0.80, average variance extracted greater than 0.50, indicator weights greater than 0.10, and factor loadings greater than 0.70. In addition, each item was required to load more strongly on its associated latent construct than on any other, thereby satisfying the criterion of factor loadings being greater than cross-loadings.

As presented in Table 2, all constructs exhibited Cronbach’s alpha and composite reliability values greater than 0.80, average variance extracted values exceeding 0.50, and indicator weights above the threshold of 0.10. Moreover, all measurement items demonstrated factor loadings that were higher than their corresponding cross-loadings. These results indicate that the measurement model possesses acceptable levels of internal consistency reliability, convergent validity, and is therefore appropriate for further analysis of the structural model.

Table 2.

Indicator weight, loadings, CA, CR, and AVE

Constructs/Items Indicator Weight Factor Loadings/Cross Loadings
MET CT CSE PSS
Metacognition (MET): CA = 0.904, CR = 0.936, AVE = 0.727
 MET1 0.215 0.933 0.776 0.576 0.698
 MET2 0.218 0.947 0.802 0.599 0.694
 MET3 0.208 0.923 0.774 0.594 0.643
 MET4 0.214 0.923 0.745 0.574 0.692
 MET5 0.209 0.914 0.764 0.604 0.641
Critical Thinking (CT): CA = 0.936, CR = 0.952, AVE = 0.798
 CT1 0.222 0.720 0.867 0.559 0.615
 CT2 0.223 0.756 0.911 0.599 0.584
 CT3 0.226 0.768 0.925 0.597 0.604
 CT4 0.222 0.706 0.881 0.551 0.626
 CT5 0.227 0.755 0.880 0.546 0.653
Creative Self-Efficacy (CSE): CA = 0.895, CR = 0.918, AVE = 0.617
 CSE1 0.169 0.447 0.435 0.637 0.452
 CSE2 0.179 0.494 0.472 0.813 0.449
 CSE3 0.149 0.410 0.399 0.769 0.370
 CSE4 0.147 0.402 0.379 0.758 0.384
 CSE5 0.184 0.485 0.505 0.786 0.463
 CSE6 0.213 0.577 0.608 0.843 0.493
CSE7 0.226 0.614 0.634 0.868 0.531
Problem-Solving Skills (PSS): CA = 0.835, CR = 0.888, AVE = 0.666
 PSS1 0.369 0.714 0.667 0.531 0.842
 PSS2 0.252 0.469 0.465 0.402 0.767
 PSS3 0.271 0.514 0.484 0.427 0.818
 PSS4 0.328 0.622 0.595 0.503 0.835
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The factor loadings are indicated by bold and italic values

CA Cronbach’s alpha, CR Composite reliability, AVE Average variance extracted

Assessment of discriminant validity

Table 3 presents the results of the Heterotrait-Monotrait ratio (HTMT) analysis used to assess discriminant validity among the study constructs. All HTMT values were below the recommended threshold of 0.85, indicating satisfactory discriminant validity. Specifically, the HTMT values ranged from 0.579 (between creative self-efficacy and problem-solving skills) to 0.830 (between metacognition and critical thinking). These results provide evidence that the constructs are empirically distinct, thereby supporting the adequacy of the measurement model.

Table 3.

Results of the Heterotrait-Monotrait ratio (HTMT) analysis

Constructs Metacognition Critical Thinking Creative Self-Efficacy
Metacognition
Critical Thinking 0.830
Creative Self-Efficacy 0.635 0.639
Problem-Solving Skills 0.726 0.690 0.579
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Structural model fit quality assessment

Table 4 presents the fit quality of a structural model, evaluating how well various constructs (Metacognition, Critical Thinking, Creative Self-Efficacy, and Problem-Solving Skills) are explained by the model. The indicators include the Coefficient of Determination (R²), Predictive Relevance (Q²), Goodness of Fit (GoF), Standardized Root Mean Square Residual (SRMR), and Normed Fit Index (NFI). The values suggest a moderate to strong explanatory power for the constructs, with R² values indicating a reasonable amount of variance explained. The Q² values show varying levels of predictive relevance across the constructs. The GoF, SRMR, and NFI metrics indicate an acceptable overall fit of the model to the data, with SRMR suggesting a good fit and NFI supporting a reasonable model adequacy.

Table 4.

Fit quality of the structural model

Indicators Constructs Value
Coefficient of Determination (R2) Metacognition 0.403
Critical Thinking 0.408
Problem-Solving Skills 0.565
Predictive Relevance(Q2) Metacognition 0.291
Critical Thinking 0.323
Creative Self-Efficacy 0.000
Problem-Solving Skills 0.363
Goodness of Fit (GoF) 0.567
Standardized Root Mean Square Residual (SRMR) 0.063
Normed Fit Index (NFI) 0.848
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Hypothesis testing

Table 5 delineates the outcomes of hypothesis testing within a partial least squares structural equation modelling framework, assessing the interrelationships among creative self-efficacy, critical thinking, metacognition, and problem-solving skills. The total effects reveal statistically significant positive associations, with creative self-efficacy exhibiting a robust direct influence on critical thinking and metacognition, as evidenced by high t-values and effect sizes indicative of strong relationships. The impact of creative self-efficacy on problem-solving skills is moderately significant. In contrast, the direct effects of critical thinking and metacognition on problem-solving skills are weaker but still statistically supported. The specific indirect effects highlight the mediating roles of critical thinking and metacognition in the relationship between creative self-efficacy and problem-solving skills. The mediating effect of critical thinking is significant, with a moderate effect size, suggesting a partial mediation pathway. Conversely, metacognition demonstrates a stronger mediating effect, supported by a higher t-value and effect size, indicating a more pronounced indirect influence on problem-solving skills through metacognitive processes. Statistical significance is corroborated by t-values surpassing critical thresholds (t > 1.96 and p < 0.05), with confidence intervals reinforcing the reliability of these findings. Effect sizes, ranging from weak (0.02–0.15) to moderate (0.15–0.35), provide a nuanced evaluation of the magnitude of these relationships, enhancing the validity of the proposed model for inclusion in academic discourse.

Table 5.

Hypothesis testing

Hypothesis O STDEV t-value CI f2 Hypothesis Testing
2.5% 97.5%
Total Effects
 H1: CSE → PSS 0.155 0.046 3.371** 0.073 0.252 0.031 weak Accepted
 H2: CSE → CT 0.639 0.040 15.884*** 0.561 0.714 0.690 strong Accepted
 H3: CSE → MET 0.635 0.040 15.810*** 0.554 0.713 0.676 strong Accepted
 H4: CT → PSS 0.227 0.068 3.366** 0.093 0.358 0.035 weak Accepted
 H6: MET → PSS 0.439 0.064 6.866*** 0.313 0.564 0.129 weak Accepted
Specific Indirect Effects
 Mediating Effect of Critical Thinking
H5: CSE → CT → PSS 0.145 0.043 3.354** 0.060 0.231 Accepted
 Mediating Effect of Metacognition
H7: CSE → MET → PSS 0.279 0.045 6.223*** 0.194 0.369 Accepted
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O Original sample, STDEV Standard deviation, t-value = t-statistics, CI Confidence intervals, f2 = effect size. T >1.96 at P < 0.05 (*), T >2.576 at P < 0.01 (**), and T >3.29 at P < 0.001 (***). f2 = 0.02–0.15 are weak; f2 = 0.15–0.35 are moderate; f2 >0.35 are strong.

MET Metacognition, CT Critical Thinking, CSE Creative Self-Efficacy, PSS Problem-Solving Skills

Discussion and conclusion

Discussion

The relationship between creative self-efficacy and problem-solving skills

The present study identified a statistically significant positive relationship between creative self-efficacy and problem-solving skills among engineering students (p < 0.01). However, the effect size was weak (f² = 0.031), indicating that although creative self-efficacy contributes to students’ problem-solving skills, its influence is relatively limited. This finding is consistent with prior research that recognizes creative self-efficacy as a meaningful, yet not dominant, predictor of problem-solving outcomes [51]. In engineering education, problem-solving is often situated within highly structured contexts, shaped by technical requirements, established methodologies, and performance standards [52]. Under such conditions, students’ creative self-efficacy may be overshadowed by the demands of domain-specific knowledge, logical reasoning, and procedural accuracy. The modest effect observed in this study may therefore reflect the multifactorial nature of problem-solving, where creative self-efficacy alone is insufficient unless complemented by metacognition, critical thinking, and the strategic regulation of knowledge. Furthermore, instructional structures and external task constraints may attenuate the extent to which creative self-efficacy is expressed in practice.

Nevertheless, the mechanism linking creative self-efficacy and problem-solving skills is not confined to engineering education. From a theoretical perspective, Bandura’s social cognitive theory posits that self-efficacy is a domain-general belief system that shapes motivation, persistence, and adaptive behavior across various learning environments [53]. Creative self-efficacy, as a specific manifestation of this construct, can therefore exert influence in any educational setting that requires the generation, evaluation, and application of ideas [54]. In broader contexts such as the social sciences, humanities, and teacher education, creative self-efficacy may facilitate divergent thinking, sustained engagement with ill-structured problems, and the willingness to take intellectual risks [55–57]. These processes mirror those observed in engineering, but are not limited to it. From the perspective of curriculum design, strengthening students’ creative self-efficacy may enhance their ability to approach complex and ambiguous tasks across disciplines. For instance, in humanities and social science courses, students with higher creative self-efficacy may be more confident in offering alternative interpretations or synthesizing novel perspectives [58]. In teacher education, fostering creative self-efficacy may prepare future educators to design adaptive pedagogies and to innovate in classroom practice [59]. Although disciplinary conventions and assessment structures may moderate the strength of this relationship, the mechanism itself appears to be broadly applicable.

Role of critical thinking in the relationship between creative self-efficacy and problem-solving skills

This study demonstrates that critical thinking mediates the relationship between creative self-efficacy and problem-solving skills in engineering students. Creative self-efficacy strongly predicted critical thinking (p < 0.001, f² = 0.690), and critical thinking, in turn, significantly predicted problem-solving performance, albeit with a modest effect size (p < 0.01, f² = 0.035). These findings align with prior research, indicating that students with high creative self-efficacy are more inclined to challenge assumptions, explore alternatives, and engage in systematic reasoning [60]. Yet, the relatively weak direct effect of critical thinking on problem-solving suggests that critical reasoning alone does not guarantee success in engineering contexts. This points to the importance of educational strategies that not only promote critical thinking but also embed it within authentic engineering tasks.

In laboratory courses, problem-based learning can be implemented by requiring students to analyze open-ended engineering problems step by step [61]. First, identify the underlying assumptions; then, generate at least two alternative design pathways. Finally, compare the trade-offs using explicit evaluation criteria, such as feasibility, cost, or sustainability. This structured process not only promotes divergent idea generation but also forces students to justify their decisions through evidence-based reasoning. Reflective activities can be embedded as mandatory components of coursework [62]. Students may be asked to keep a design journal in which they document the rationale for each major design choice, explicitly note the alternatives they considered, and reflect on why certain options were rejected. Similarly, post-project debrief sessions can be conducted where groups present both the strengths and weaknesses of their solutions, encouraging critical appraisal of their own and others’ reasoning processes. Peer evaluation can also be systematically integrated into project milestones [63]. During prototype reviews or simulation demonstrations, students can be assigned structured critique tasks, such as identifying two strengths, two weaknesses, and one improvement suggestion for each peer project. This structured feedback format ensures that critique goes beyond superficial comments and trains students to critically assess evidence, assumptions, and design logic.

Role of metacognition in the relationship between creative self-efficacy and problem-solving skills

The results of this study further reveal that metacognition serves as a significant mediator in the relationship between creative self-efficacy and problem-solving skills among engineering students. Specifically, creative self-efficacy demonstrated a strong positive effect on metacognition (p < 0.001, f² = 0.676), and metacognition, in turn, significantly influenced problem-solving skills (p < 0.001), though the effect size was weak (f² = 0.129). Mediation analysis confirmed that the indirect effect of creative self-efficacy on problem-solving skills through metacognition was statistically significant (p < 0.001), reinforcing the importance of self-regulatory processes in facilitating problem-solving. These findings are consistent with prior research that emphasizes the reciprocal relationship between self-efficacy and metacognitive processes [64]. Students with higher creative self-efficacy are more likely to plan, monitor, and evaluate their cognitive strategies, especially when tackling complex or unfamiliar tasks [65].

Similar to the findings related to critical thinking, the relatively weak direct effect of metacognition on problem-solving suggests that while essential, metacognitive awareness alone may not yield substantial gains in performance unless it is applied in conjunction with other cognitive and contextual supports [35]. In engineering contexts, where problems are often ill-structured and require iterative design, teamwork, and integration of technical knowledge, metacognitive skills need to be embedded within task-specific strategies to be most effective [66]. While creative self-efficacy exerts only a limited direct effect on problem-solving, its influence is significantly enhanced through its impact on both critical thinking and metacognition. These two mediators act as vital conduits through which creative self-efficacy can be translated into problem-solving skills. Therefore, engineering curricula must not only aim to boost students’ creative self-efficacy but must also deliberately cultivate their critical thinking and metacognition [67].

Conclusion

This study examined the relationship between creative self-efficacy and problem-solving skills in engineering education, with a particular focus on the mediating roles of critical thinking and metacognition. The results revealed that while creative self-efficacy has a statistically significant direct effect on problem-solving skills, the effect size is weak, suggesting that creative self-efficacy alone may not be a strong predictor of problem-solving performance in engineering contexts. Both critical thinking and metacognition emerged as significant mediators in this relationship. Creative self-efficacy strongly predicted both critical thinking and metacognition, each of which subsequently had a significant impact on problem-solving skills. These findings indicate that the influence of creative self-efficacy on problem-solving is largely indirect and operates through metacognition and critical thinking. The results underscore the importance of fostering not only students’ creative self-efficacy but also their capacity for critical reflection and metacognitive control.

Implications

Theoretical implications

Grounded in social cognitive theory, this study unpacks the broad causal chain linking self-efficacy to engineering problem-solving skills by identifying two complementary mediating mechanisms, critical thinking and metacognition, and testing their distinct effects through empirical analysis. The findings offer two key theoretical contributions. First, the results demonstrate that self-efficacy should not be understood merely as a proxy for motivation or effort, but rather as a driver that activates specific cognitive strategies (critical thinking) and regulatory mechanisms (metacognition) [68], thereby shaping complex problem-solving performance. Second, by examining these two closely related cognitive constructs within the same model, the study avoids the confounding issues often present in single-mediator analyses and clarifies their unique functions: critical thinking primarily facilitates problem representation and strategy generation [69], whereas metacognition governs monitoring and regulation [70]. This dual-path approach strengthens construct differentiation and enhances the explanatory precision of social cognitive theory in the context of engineering education. These insights refine the theoretical understanding of how self-efficacy is translated into problem-solving and suggest a more granular cognitive architecture within social cognitive theory. They also provide a conceptual foundation for future research and educational interventions that target both cognitive and metacognitive processes to more effectively foster problem-solving skills in engineering students.

Practical implications

This study offers several actionable implications for engineering education, particularly in designing classroom practices that enhance creative self-efficacy through critical thinking and metacognition. First, dual-dimension (Critical Thinking - Metacognition) training tasks can be operationalized through structured assignments. In design-based problem-solving courses, students may be required to submit two deliverables: a technical solution to the engineering problem and a short analytical brief. The brief should include a justification of why specific approaches were chosen, a critique of alternative solutions, and an evaluation of potential weaknesses in their design. Simultaneously, students can be asked to document the strategies they applied, when they realized their initial approach was insufficient, and how they revised their methods. This dual reporting mechanism ensures that critical thinking and metacognition are not peripheral but integral to problem-solving tasks. Second, metacognitive engineering journals can be systematically integrated into project-based learning [71]. Instead of only recording results, students should be instructed to maintain weekly logs that capture the evolution of their thinking processes. A practical template might include prompts such as: What was the most significant challenge I encountered this week? How did I monitor my progress while addressing it? What specific adjustments did I make, and why? Grading a portion of the journal based on the depth and clarity of reflection, not just completion, encourages students to take the exercise seriously and to internalize metacognitive practices as part of their engineering identity. Third, real-time critical interventions can be embedded into lectures and tutorials [72]. Instructors may intentionally present flawed or suboptimal engineering solutions during class demonstrations, such as circuits with inefficient layouts or code with logical oversights. Students, working individually or in small groups, can then be tasked with identifying errors, debating alternative approaches, and proposing corrections. This practice not only sharpens their ability to detect weaknesses but also builds confidence by giving them opportunities to critique and improve upon expert-provided material. Fourth, collaborative projects can incorporate a structured role rotation system [73]. For instance, in group design challenges, each member can rotate through roles such as “critic,” who systematically questions assumptions and highlights potential flaws; “reflector,” who monitors group progress and documents decision-making strategies; and “executor,” who focuses on implementing the agreed-upon solution. Requiring teams to submit a short record of each role’s contribution ensures accountability and guarantees that all students practice critical and metacognitive skills in addition to technical execution.

Limitations

Despite its theoretical and empirical contributions, this study has several limitations that warrant consideration. First, the sample displayed an uneven distribution across levels of education, which may limit the representativeness of the findings. However, supplementary descriptive statistics and correlation analyses suggested that grade level exerted only a negligible influence on the key variables and outcomes, thereby mitigating concerns about systematic bias. Second, the study relied on a cross-sectional design, which precludes inferences regarding causal directionality and developmental trajectories. Future research would benefit from employing longitudinal or experimental designs to capture the temporal dynamics among self-efficacy, critical thinking, metacognition, and problem-solving skills. Third, although this study was conducted with engineering students, the underlying mechanisms identified are theoretically applicable across disciplines. Nonetheless, further empirical research is needed to verify whether these relationships hold consistently in other academic contexts. Finally, because data were collected via WeChat, mode-specific self-selection may limit external validity. Replication with alternative sampling frames/platforms would help corroborate these findings. The sample underrepresents senior students, potentially constraining generalizability to advanced cohorts who engage in more authentic, open-ended engineering tasks.

Supplementary Information

Supplementary Material 1. (21.4KB, docx)

Acknowledgements

We extend our heartfelt gratitude to Professor Ma for their invaluable assistance in this study’s data-collection process. We appreciate Mr. Zhou’s support and financial assistance during the manuscript-writing process. Their contributions have been invaluable to our research endeavor.

Abbreviations

CSE

Creative Self-Efficacy

PSS

Problem-Solving Skills

CT

Critical Thinking

MET

Metacognition

CA

Cronbach’s Alpha

CR

Composite Reliability

AVE

Average Variance Extracted

O

Original Sample

STDEV

Standard Deviation

CI

Confidence Intervals

R²

Coefficient of Determination

Q²

Predictive Relevance

GoF

Goodness of Fit

SRMR

Standardized Root Mean Square Residual

NFI

Normed Fit Index

HTMT

Heterotrait–Monotrait ratio

M

Mean

SD

Standard Deviation

GEN

Gender

ACL

Academic Level

ROO

Region of Origin

Biographies

Zhihua Liu

is a doctoral candidate at the School of Education, Guangzhou University. His primary research focuses on education, encompassing digital educational spaces and problem-solving skills. Additionally, he has a keen interest in comparing AIGC in education.

Huifen Guo

is a doctoral candidate at the School of Education, Guangzhou University. Her primary research focuses on higher education, encompassing student performance, fostering innovation capabilities, creativity training, and measurement. Additionally, she has a keen interest in comparing VR, XR, AIGC, and the Metaverse.

Zhen Zhou

serves as the teacher of the School of Mechanical and Electrical Engineering at Guangzhou University. His primary research focus lies in educational management, covering aspects such as student performance, employment, psychological well-being, and further studies. He is particularly intrigued by leveraging intelligent technologies to enhance student learning performance.

Fengqi Ma

is a professor, the Dean of the School of Education at Guangzhou University, and a doctoral supervisor. His primary research areas include principles of higher education, management of higher education institutions, and research on higher education curriculum and teaching.

Yanhan Zeng

is an associate professor at the School of Electronics and Communication Engineering, Guangzhou University, with primary research areas in electronic information engineering, creative talent cultivation, and engineering problem-solving.

Authors’ contributions

Z.H. and H.F. wrote the manuscript and coordinated the project. Y.H. and Z. designed and conducted the experiments and provided funding for this research. H.F. and Z. contributed equally to this work and shared the corresponding authorship. F.Q. supervised the entire research process and provided critical feedback.

Funding

This study was supported by the 2023 Special Task Project of Humanities and Social Sciences Research by the Ministry of Education, China (Grant No. 23JDSZ3200); Guangzhou Higher Education Teaching Quality and Reform Project (Grant No. 2022ZXRCPR001); Guangdong Province Undergraduate Higher Education Teaching Quality and Reform Project: Excellence in Integrated Circuit Design Talent Experimental Class; the Macao funding schemes granted by the Science and Technology Development Fund (FDCT) “Research on intelligent learning system & telephoto learning machine and their key technologies in Macao for K-12 students” (Grant No. 0071/2023/RIB3); the Joint Research Funding Program between the Macau Science and Technology Development Fund (FDCT) and the Department of Science and Technology of Guangdong Province (2024) (FDCT-GDST) (Grant No. 0003-2024-AGJ).

Data availability

The authors are authorized to disseminate the data, accessible upon reasonable request addressed to the corresponding author.

Declarations

Ethics approval and consent to participate

This study was conducted in full compliance with the principles outlined in the Declaration of Helsinki. Ethical approval for the research was obtained from The Ethics Review Committee of the School of Education, Guangzhou University (approval number: GZHU202341), and all participants provided informed consent before participation in the study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Zhihua Liu, Zhen Zhou and Huifen Guo co-first authors of this article.

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