The essence of metacognition is “cognition of cognition” (Flavell 1979). Cognition mainly comprises knowledge stored by oneself and strategies used to solve problems, while metacognition involves monitoring, understanding, and adjusting one’s own knowledge and strategies. This helps individuals not only know what is important but also comprehend when, where, and how to appropriately apply various kinds of knowledge and strategies (Csikos 2022; Williams et al. 2016). In cognitive psychology, metacognition plays the role of “executive control”, which supervises thoughts, knowledge, and behavior. This kind of monitoring is achieved through introspection, knowledge of oneself as a cognitive subject, and adjustment of one’s way of thinking (Veenman and Spaans 2005). In short, metacognition describes people’s understanding and control of their thinking, which is a cognitive process that takes their own psychological state, cognitive process, and thinking mode as cognitive objects, and external manifestations are regulation and monitoring of cognitive activities (Efklides 2002; Flavell 1979).

The key components of metacognition are planning before tasks, monitoring during tasks, and evaluation during or after tasks (Efklides et al. 1999). Planning involves the “how” of executing activities, which includes three components: resource allocation, problem decomposition, and strategic planning (Moshman 2018). Resource allocation refers to how resources, such as time allocation, are distributed before the execution of activities to activate relevant knowledge. Problem decomposition involves breaking down a problem into several sub-problems or sub-goals to be solved separately and sequentially, including setting clear objectives and predicting outcomes. Strategic planning entails determining the order of achieving sub-goals in order to choose the most effective strategies, including setting priorities and predicting potential challenges (Efklides 2008). The plan focuses on the implementation aspects and delineates the steps involved in executing activities effectively (Veenman and Spaans 2005). It emphasizes the allocation of resources to optimize knowledge utilization, breaking down complex problems into manageable components, and strategically planning the order of completing sub-goals based on their significance and anticipated difficulties (Guo 2022). This systematic approach aims to enhance the efficiency and effectiveness of the overall execution process.

Monitoring and control refer to the supervision and coordination of cognitive processes (Rivers 2020). Monitoring requires the ability to assess one’s cognitive processes successfully, while control means using these assessments to modify behavior, such as coordinating time, allocating attention, adjusting strategies, tracking progress, and regulating emotions (Dinsmore et al. 2008). Monitoring and control play a crucial role in regulating cognitive processes. The ability to accurately monitor one’s cognitive performance and adjust behavior accordingly is vital for effective learning and problem solving (Paulewicz et al. 2020).

Various studies emphasize the importance of self-monitoring in promoting students’ metacognitive regulation and overall academic success. It is worth noting that high-achieving students demonstrate the adaptive application of knowledge and make wise choices regarding learning strategies (Paulewicz et al. 2020). This is because metacognitive monitoring utilizes metacognitive knowledge to help individuals formulate strategies to achieve cognitive goals (Medina et al. 2017). In recent years, many studies have highlighted the significant role of self-monitoring in areas such as students’ selection of learning strategies and information processing (Rivers 2020). Specifically, students with high academic performance exhibit flexibility in knowledge transformation and the selection of appropriate learning strategies (Grasset et al. 2022). Guo (2022) conducted a meta-analysis to examine the impact of metacognitive prompts (guiding students to adopt monitoring strategies) on self-regulated learning (SRL) and learning outcomes in a computer-based learning environment (CBLE) (Guo 2022). The results demonstrated that metacognitive prompts significantly enhanced self-regulated learning activities and learning outcomes.

Evaluation involves assessing the effectiveness of strategies, which includes the evaluation process, achievement, and the value and applicability of learned knowledge (Schraw and Dennison 1994; Schraw et al. 2014). This system of self-reflection allows individuals to monitor and adjust their thinking. It involves processes such as monitoring cognitive processes, assessing knowledge, controlling thinking, detecting errors, and using strategic thinking (Guo 2021). Through metacognition, individuals become aware of their thoughts, evaluate their understanding, regulate their thinking, identify and correct errors, and utilize effective strategies (Flavell 1979; Moshman 2018).

In recent years, there has been an increased use of eye tracking devices to record and identify the allocation of gaze time during cognitive monitoring (Karatekin 2007; Alemdag and Cagiltay 2018). Eye gaze is regarded as a reliable indicator of the focal point of active information processing, offering the advantage of being an accepted measure of implicit abilities and performance (Karatekin 2007). For example, compared to eye saccades, the distribution of gaze time reflects top-down processing, which is controlled by an individual’s ongoing cognitive processes (Karatekin 2007; Tsai et al. 2019). Roderer and Roebers (2014) used eye tracking technology to explore implicit monitoring processes in children (Roderer and Roebers 2014). Their study identified gaze position and duration as indicators of sustained information processing, and the results demonstrated the usefulness of eye tracking techniques in uncovering implicit and retrieval-limited monitoring processes. Hence, our objective is to gain intriguing insights into monitoring processes by applying eye tracking methods in creative thinking tasks.

Creative thinking is a high-level psychological activity involved in the creative process (Hong and Milgram 2010; Redifer et al. 2021). The term “creative thinking” was first introduced by Wallace and subdivided by Guilford into divergent thinking and convergent thinking, wherein each plays a different role (Guilford 1967; Lubart 2016). Different cognitive models describe creative thinking as a constant interplay between these two types of thinking (Cristofori et al. 2018; De Rooij and Vromans 2020; Fink et al. 2012). In various stages of creative problem solving, divergent and convergent thinking play different roles. They work in unison instead of separately (Runco 1992). In the creative process, individuals employ divergent thinking to generate ideas and then employ convergent thinking to identify criteria and limitations for evaluating and selecting ideas (Lubart 2016; Runco et al. 2023; Simonton 2015).

Divergent thinking, also referred to as “divergent thought”, is a cognitive process characterized by the generation of a multitude of alternative solutions or perspectives during problem solving or task completion. It entails the uninhibited production of numerous ideas, free from judgment or constraints, encompassing the exploration of non-traditional viewpoints and liberation from conventional or linear approaches (Yang et al. 2022). In the early stages, divergent thinking accentuates quantity as opposed to quality, as a broad range of ideas lays the foundation for a diverse repertoire of potential solutions (Runco et al. 2023). The fluidity and flexibility inherent in this mode of thinking enable individuals to explore multiple possibilities without being confined to a singular methodology (Benedek et al. 2016; Hao et al. 2017). Divergent thinking plays a critical role in cultivating creativity and novelty. By deviating from traditional modes of thinking, individuals are more likely to generate innovative and distinctive ideas that surpass the limitations of conventional problem solving approaches (Beaty and Silvia 2012; Silvia and Beaty 2012). To summarize, divergent thinking facilitates the exploration of alternative viewpoints, associations, and connections, thereby fostering original and creative solutions. It enables individuals to transcend orthodox and linear thinking patterns, stimulating the generation of a broad spectrum of ideas that contribute to novel and unique problem solving endeavors.

Divergent thinking plays a pivotal role in the generation of multiple alternative solutions, while convergent thinking is crucial for effectively resolving specific types of problems (Lubart 2016; Patston et al. 2021). Convergent thinking, also referred to as “convergence thinking” or “consensus thinking” is characterized by the pursuit of a singular correct solution, emphasizing accuracy, directionality, and closure. Convergent thinking leverages one’s existing knowledge stored in memory to facilitate a more focused cognitive approach towards a potential solution (Sriraman and Dickman 2017). In order to generate innovative and adaptive ideas for problem solving, a combination of divergent thinking for idea generation and convergent thinking for idea selection is typically employed (Cropley 2006). Indeed, both divergent and convergent thinking are indispensable in the creative process, whereby individuals strive to not only generate a wealth of novel ideas, perspectives, or problem solving approaches, but also integrate, evaluate, and identify the most optimal solutions within the given context.

In recent years, the field of eye tracking has emerged as a valuable tool for gaining deeper insights into human cognitive processing. Extensive research has demonstrated the association between eye movements and cognitive processes (Benedek et al. 2017; Ceh et al. 2021; Maheshwari et al. 2022b; Walcher et al. 2017). Studies have indicated that eye movements can serve as indicators of an individual’s thinking processes. Particularly in problem solving scenarios, analyzing an individual’s eye movement patterns can facilitate an understanding of the potential solutions they may generate. Maheshwari et al. (2022a) conducted a study that further confirmed the relationship between thinking patterns and eye movements (Maheshwari et al. 2022a). They compared the attention patterns of individuals performing the Alternative Uses Task (AUT) and the Remote Associates Task (RAT), and observed that individuals exhibited significantly longer average fixation durations on task materials during divergent tasks compared to convergent thinking. This finding suggests that individuals allocate more time to attending to experimental materials in order to generate a greater quantity of ideas. Similarly, Walcher et al. (2017) found a higher rate of fixations in conditions involving divergent thinking compared to those involving convergent thinking (Walcher et al. 2017). Another empirical study discovered a recombination of higher fixation rates and scan rates that corresponded to participants’ actual observations of objects during cognitive manipulations, indicating a potential coupling between eye activity and internal cognitive processes (Benedek et al. 2017). While most research on eye tracking and problem solving has focused on graph-based problems, where eye tracking is employed to investigate participants’ problem solving strategies, it remains crucial to explore the role of eye movements in tasks unrelated to graphs (Grant and Spivey 2003; Jankowska et al. 2018). More comprehensive research is warranted to gain a thorough and comprehensive understanding of the role of eye movements in effectively solving non-graph-based problems.

The impact of metacognition on creative thinking has long been a topic of interest for educators and psychologists. Supporting students in developing innovative thinking skills through metacognitive strategies has also been a focus of educational research. Some scholars propose that creative thinking is a metacognitive process model that is monitored and regulated by metacognition (Beaty and Silvia 2013; Feldhusen 1995; Mokhtari and Reichard 2002; Pesut 1990). Puryear (2015) assumed that metacognition plays an important role in creative thinking by acting on the thinking process (Puryear 2015). According to sequential effects, later ideas are typically more creative than earlier ones (Beaty et al. 2014a, 2014b), because the initial phase of divergent thinking requires flexible thinking to discover potentially valuable information from memory, whereas the later stage necessitates continuous evaluation, revision, and improvement of potential solutions (Avitia and Kaufman 2014; Sidi et al. 2020). In this process, individuals consciously reflect on and monitor their own thinking processes and strategy choices through metacognition, enabling them to generate ideas more flexibly (Beaty and Silvia 2013). Metacognition allows individuals to adjust their thinking methods and explore different perspectives and problem solving approaches when generating ideas. Individuals can self-assess and scrutinize their generated ideas, leading to revision and improvement. This process helps individuals identify and correct potential errors or shortcomings, thereby enhancing the quality and effectiveness of solutions (Sidi et al. 2020). This requires the use of both top-down control processing and bottom-up associative processing to generate more creative ideas (De Rooij and Vromans 2020; Liu et al. 2023). Bottom-up spontaneity is insufficient for divergent thinking, as the process also requires monitored retrieval to select appropriate concepts while suppressing irrational connections. Monitored retrieval and idea selection, along with the suppression of irrational associations, play a crucial role in cognitive processes and creative thinking (Liu et al. 2023). These cognitive mechanisms enable individuals to refine and enhance the quality of their ideas by actively monitoring and controlling the retrieval of relevant information from their memory and by selectively choosing the most appropriate ideas (Saggar et al. 2021).

In addition, cognitive flexibility positively predicts creative problem solving performance (Takeuchi et al. 2010; Zabelina and Robinson 2010). Cognitive flexibility is the ability to adapt and switch between cognitive processes, strategies, or perspectives (Martin et al. 2011). It allows individuals to approach problems from multiple angles, explore alternative perspectives, and generate creative ideas. This is achieved through shifting attention, breaking mental set, integrating perspectives, and overcoming functional fixedness (Diamond 2013). Cognitive flexibility breaks rigid cognitive patterns, embraces fresh perspectives, integrates diverse viewpoints, and enables innovative problem solving by thinking beyond predefined functions. Overall, cognitive flexibility enhances adaptability and creativity in approaching various challenges (Cristofori et al. 2018). Cognitive stability can also predict analytical thinking performance (Razumnikova 2007), mainly by increasing working memory capacity and consolidating task information to promote effective analysis (Nijstad and Stroebe 2006).

Although researchers have investigated the relationship between metacognition and creativity from various theoretical perspectives, few empirical studies have explored and verified it from a dynamic procedural perspective. Empirical research showed that excellent creators are better at intentionally participating in the metacognitive process (Liu et al. 2023). This includes planning and managing their time before tasks, monitoring their cognitive processes while performing the tasks, and evaluating their thinking state to adjust strategies in a timely manner for better problem solving (Zimmerman 1998). Intentional monitoring promotes creative performance. Conversely, better creators are skilled at consciously using metacognition to monitor their cognition (Akin et al. 2007; Urban et al. 2021). Studies have also found that artists are better at monitoring the painting process (Fayena-Tawil et al. 2011; Kay 1991). For example, previous studies asked students who had no design experience to design logos for drinks. The product designers reported stronger improvements from initial sketches to final sketches (Jaarsveld and Leeuwen 2005). Similarly, Wetzstein and Hacker (2004) found that participants who received prompts encouraging self-reflection made greater progress in designing drawings and solutions compared to those who did not receive prompts (Hong et al. 2016; Wetzstein and Hacker 2004). Jia and colleagues (2019) conducted a review of previous research on the role of metacognition in creative thinking (Jia et al. 2019). The review found that although an increasing number of studies suggest the potential importance of metacognition in creative thinking, there is still a lack of consensus among empirical research findings; for example, in a study conducted by Preiss et al. (2016) with university and vocational Chilean students as participants (Preiss et al. 2016), it was found that metacognition did not significantly predict creative performance. The review emphasizes the need for future studies to explore the underlying mechanisms through which metacognition influences creative thinking.

The core of this “synchronous linkage” changing relationship lies in the fact that creative strategies guide thinking and encourage individuals to imagine or invent new products by combining, changing, or applying existing concepts (Bai et al. 2021). Specifically, in a creative thinking task, individuals must focus their attention on the creative problem and the strategies they know may contribute to solving the problem, as well as evaluate the quality of the solution or creative idea that they generate. These complex processes require the use of working memory. This is because working memory is an executive system responsible for an individual’s ability to plan and monitor the encoding and storage of information, guiding individuals to shift their focus of attention (Baddeley et al. 1998). Secondly, it relies on the conscious or unconscious control of metacognition over these thoughts, attention, memories and actions (Hargrove and Nietfeld 2015). Metacognition plays a crucial role in managing cognitive processes involved in creative thinking. It contributes to the generation, evaluation, and selection of ideas, understanding thinking strategies, assisting individuals in regulating attention, refocusing on pertinent aspects, and avoiding interference or biases (Veenman and Spaans 2005). It organizes and utilizes existing knowledge and memories, integrating them with novel ideas. Metacognition also aids in promoting planning, monitoring, and adjusting behaviors, fostering flexibility and an experimental mindset (Koriat and Levy-Sadot 2000).

Eye tracking technology is considered an effective tool for measuring an individual’s attention process and pattern, providing strong support for exploring an individual’s cognitive dynamics (Pi et al. 2018). For instance, previous studies have confirmed that the longer an individual looks at material information, the more attention he or she pays to that information (Michinov et al. 2015).