How multiple levels of metacognitive awareness operate in collaborative problem solving

Metacognitive awareness is knowing about learners’ own thinking and learning, facilitated by introspection and self-evaluation. Although metacognitive functions are personal, they cannot be explained simply by individual conceptions, especially in a collaborative group learning context. This study considers metacognitive awareness on multiple levels. It investigates how metacognitive awareness at the individual, social, and environmental levels are associated with collaborative problem solving (CPS). Seventy-seven higher education students collaborated in triads on a computer-based simulation about running a fictional company for 12 simulated months. The individual level of metacognitive awareness was measured using the Metacognitive Awareness Inventory. The social level of metacognitive awareness was measured multiple times during CPS through situated self-reports, that is, metacognitive judgements and task difficulty. The environmental level of metacognitive awareness was measured via a complex CPS process so that group members’ interactions were video recorded and facial expression data were created by post-processing video-recorded data. Perceived individual and group performance were measured with self-reports at the end of the CPS task. In the analysis, structural equation modelling was conducted to observe the relationships between multiple levels of metacognitive awareness and CPS task performance. Three-level multilevel modelling was also used to understand the effect of environmental-level metacognitive awareness. The results reveal that facial expression recognition makes metacognitive awareness visible in a collaborative context. This study contributes to research on metacognition by displaying both the relatively static and dynamic aspects of metacognitive awareness in CPS.


Introduction
Metacognitive awareness is "thinking about your thinking".Although early studies of metacognition have focused on individual learning (e.g.Brown, 1987;Flavell, 1979), recent research has expanded its focus to include the role of metacognitive awareness in collaborative learning (e.g.Çini et al., 2020;Goos et al., 2002;Rienties et al., 2009).Although metacognition is an individual process, it also plays an important role in groups, especially in a collaborative group context.At the individual level, metacognitive awareness is the conceptual systems of individuals.For example, we can regulate and control our learning through planning, monitoring, developing information management skills, and evaluation (Lesh & Doerr, 2003).At the social level, metacognitive awareness refers to one's interactions with others (Taub et al., 2021).In practice, through interactions with tutors and peers, learners may be supported to regulate their current thinking, to control their current knowledge level and understanding, and to retest their misconceptions (Kim et al., 2013).An example is the collaborative problem-solving (CPS) task performed by a computer, which provides sharing knowledge construction through interactions in written and spoken language, body movements, manipulation of the task conditions, and facial expressions.At the environmental level, metacognitive awareness involves one's interaction with the learning environment, such as classroom activities, task complexity/difficulty, stages of problem solving, and multiple cycles of feedback in which students criticise and revise each other's thinking (Kim et al., 2013).
There have been attempts to raise and support metacognitive awareness in different ways, such as studying self-directed metacognitive prompts (Bannert et al., 2015), developing metacognitive group awareness tools (Schnaubert & Bodemer, 2019), and examining individual metacognitive awareness in terms of their situation-specific metacognitive interpretations (Çini et al., 2020).Nevertheless, as pointed out by Winne (2018), more is needed to know about learners' metacognitive functions, that is, making judgements about learning, task difficulty, and feelings of knowing that are manifested in real learning situations, such as complex CPS task environments (Dindar et al., 2020a).Metacognition is about learners' perceptions of themselves, others, and learning situations (Flavell, 1979).When individuals work in collaborative groups, they activate their metacognitive awareness.For example, they evaluate their own and group members' ideas through task processing, state their current ways of thinking about problem solving, retest those ideas through information provided by the problem or by other group members, and monitor their thoughts based on feedback (Hurme et al., 2009;Jayapraba & Kanmani, 2013;Yilmaz & Yilmaz, 2019).
Video data have been used to study metacognitive experiences, such as metacognitive monitoring, in face-to-face collaborative learning environments (Malmberg et al., 2017).However, there has recently been enormous development in analysing multimodal sources (i.e.360° video, heart rate, skin conductivity, log data, self-report) to make metacognitive learning processes in collaborative groups visible to both learners and teachers (Järvelä et al., 2021).Due to technological development, video data and heart rate (Sobocinski et al., 2022), physiological arousal events by utilising skin conductance response (Dindar et al., 2020b), physiological arousal recorded from electrodermal activity (Haataja et al., 2022a(Haataja et al., , 2022b)), or facial expression recognition (Taub et al., 2021) have been used to understand metacognitive learning processes and their conditions in real time.Facial expressions are an efficacious nonverbal communication method that gives a lot of information about individuals' emotions.Previously, metacognition and emotions were taken different and separate processes (Efklides, 2006).However, there have been attempts to raise the issue that metacognition and emotions co-exist in developing learning strategies (Efklides, 2006).
Overall, little is known about metacognitive awareness at multiple levels and its influence on CPS and individuals' facial expressions.In light of this, we explored the relationship between multiple levels of metacognitive awareness during CPS and their effects on perceived performance.This study also investigated ways of capturing emotional experiences during complex CPS tasks using facial expressions (fear, surprise, anger, sadness, contempt, disgust, happiness, and neutrality) in conjunction with self-report items to assess their relation to metacognitive awareness.

Metacognition in Collaborative Problem Solving
CPS is a joint activity in which multiple individuals combine their resources, skills, and efforts to transform a problem state into a desired state (Roschelle & Teasley, 1995).CPS offers a rich source to support or prompt metacognition in cognitive and social processes.In the cognitive dimension, throughout the CPS task, individuals in the group plan, monitor, evaluate, think, and interpret the task at a high level and share these processes with others (Slof et al., 2010;Zimmerman & Schunk, 2011).In the social dimension, the individuals in the group share communicative processes, such as argumentation, negotiation, and perspective taking, including a socio-emotional interaction that fuels the student's collaboration (Hesse et al., 2015;Janssen et al., 2012).However, successful collaboration is hard to accomplish and requires the effective coordination of individual and group processes in both cognitive and social dimensions (Baker et al., 2001;Hadwin et al., 2018), since successful collaboration requires more than group work or task completion and the group may face several challenges (Jeong & Hartley, 2018).For instance, the group may consume more effort than necessary to work together and learn effectively or efficiently, may experience social and emotional problems that inhibit group learning and processes (Kreijns et al., 2003;Näykki et al., 2017), or may not be able to synchronise and perform the essential learning activities between group members for proper learning (Rogat & Adams-Wiggins, 2014).These issues stem from the fact that collaborative group members fail to perceive challenging learning situations and their need for regulation, which inhibits the activation of strategic adaptation behaviour (Järvelä et al., 2016).Here, metacognition plays an important role in collaboration.
Metacognition ensures that individuals and groups control and adapt their cognition, motivation, emotion, and behaviour (Hadwin et al., 2018).The problem is that learners are not often aware of their metacognition, and they tend to be overconfident in terms of their learning (Hadwin & Webster, 2013).More is needed to know about learners' metacognitive awareness in real life situations as well as in social interaction, such as complex collaborative learning (CL) because social interaction influences metacognition and enhances learning success (Artz & Armour-Thomas, 1992;Salonen et al., 2005).Also, social information can influence individuals' metacognitive monitoring and subsequent self-regulation of learning (Schnaubert et al., 2021), and that individual students' metacognitive skills predict engagement in group-level regulation (De Backer et al., 2021).It improves learners' metacognitive awareness of their own and others' learning processes, facilitates knowledge construction, and enables the effective application of strategies (Isohätälä et al., 2020).Thus, regulating CL is essential for success.The literature acknowledges the interaction between individual metacognitive monitoring and group-level CL processes (Efklides, 2008;Hadwin et al., 2017;Näykki et al., 2017) and shows the importance of both individual and group shared processes (Malmberg et al., 2017).Therefore, it has been considered that a key factor in determining the success of the CL process is the learners' metacognitive awareness of both their own and peers' thinking processes as well as their own ability to articulate these ideas in interactions (Järvelä et al., 2021).Metacognitive interaction predicts learning achievement in CL (Haataja et al., 2022a(Haataja et al., , 2022b)).For example, Çini et al. (2020) demonstrated that students' self-reported metacognitive characteristics are associated with their subjective situation-specific task interpretations during CL.After a collaborative session, situated interpretations of task understanding can also predict individual performance on a summative assessment.Problem-solving and metacognitive skills are distinct but also fundamentally connected and interdependent because humans' perceptions about a problem-solving task are a product of their metacognition, which is central in fuelling thinking and cognition.In collaborative learning settings, metacognitive monitoring and related regulatory strategies promote group cooperation and foster successful learning (Järvelä et al., 2015).Van der Stel and Veenman (2010) found metacognition to be a highly effective predictor of learners' achievement in completing complex learning tasks.A few earlier studies have also suggested that metacognitive processes may help learners overcome the challenges (Pugalee, 2001) they have during CPS and enhance their performance (Kramarski & Mevarech, 1997).In the meantime, CPS tasks give students the chance to analyse their own thinking, reflect on it, and improve their metacognitive abilities (Siegel, 2012).
In summary, a higher level of metacognition is required in CL and CPS (Dierdorff & Ellington, 2012;Haataja et al., 2022aHaataja et al., , 2022b)).However, evidence of metacognitive awareness in CPS, with a focus on examining the features and nature of CPS, remains scarce.This study aims to first understand how special features, which are continuous feedback, affect group members' interactions and performance in computer-based CPS simulation.In our study, group members received feedback about their task progress at specific time points during CPS; therefore, feedback was either negative or positive.Further, metacognition is a dynamic process in which learners' metacognitive awareness changes and evolves over time (Molenaar & Järvelä, 2014;Winne, 2010).During CPS, capturing metacognition, which is situated, contextual, and social, provides only a limited understanding of the complex and varying nature of CPS processes (Reiter-Palmon et al., 2017).A common approach to examining these processes has been single-item self-reports, which are completed at multiple time points during a learning task (Dindar et al., 2020c).Trait-based assessment cannot sufficiently explore metacognition in action, since it should be assessed at multiple times and at different stages of the problem-solving process with situated selfreports by examining metacognitive awareness at individual, social, and environmental levels.

Metacognitive Awareness at Multiple Levels
This study conceptualises metacognitive awareness by considering three levels that interact with metacognition: oneself (the individual level), one's interplay with others (the social level), and one's interplay with the learning environment (the environmental level) (Kim et al., 2013), and focuses on a learner as an interdependent intermediary accessing all the levels (Fig. 1).The sources of metacognitive awareness are categorised as internal and external (Vermunt, 1996).Internal sources are one's cognitive and metacognitive components, whereas external sources include others' cognitive and metacognitive components in collaborative activities and environmental components (Kim et al., 2013).

Metacognitive Awareness at the Individual Level
At the individual level, the conceptual systems of individuals contribute to awareness.Individuals elicit metacognition through their knowledge and attributes (Schraw & Dennison, 1994).These internal sources of metacognitive awareness are collected from previous knowledge and experiences and therefore differ in quantity and quality (Çini et al., 2020).Individuals monitor or regulate their own cognitive components and stimulate their metacognitive awareness at the individual level.In this study, individual-level metacognitive awareness was assessed through participants' responses on the Metacognitive Awareness Inventory, a trait-based background questionnaire that assesses two distinct components of metacognitive awareness: knowledge of cognition and regulation of cognition (Pintrich, 2002;Schraw, 1998;Schraw & Moshman, 1995).Knowledge of cognition includes the ability to determine what is known, such as tasks and specific knowledge, by assessing metacognitive beliefs with different types of prior knowledge, such as declarative, procedural, and conditional knowledge.This requires an awareness of one's own thinking processes.The regulation of cognition helps learners regulate and control their learning through planning, monitoring, developing information management skills, and evaluation (Schraw, 1996;Schraw & Dennison, 1994).Here, individuals think about their own strategic planning and control of these processes.For instance, learners with efficient metacognitive skills can choose appropriate learning strategies for a task and adapt them based on learning outcomes.An individual's regulation of cognition includes a continuous selfevaluation of what is known and what still needs to be learned.Eventually, learners support their metacognition at the individual level by regulating and monitoring their cognitive and metacognitive components (Kim et al., 2013).

Individual Level Conceptual systems
Social Level Interactions with collaborative group members through written and spoken language, facial expressions Environmental Level Interaction with the learning environment such as feedback during CPS

Metacognitive Awareness at the Social Level
Research has shown that metacognition cannot be explained only at the individual level; it involves a dual-agent organisation of metacognition-a learner and a group in which the learner is engaged (Vauras et al., 2003;Volet et al., 2009).From this perspective, a group is considered a whole agent of metacognitive awareness at the social level.
Students sometimes have trouble understanding their solutions; however, group members, such as their peers, can help with this understanding.This means that, when students collaborate in groups, they serve a metacognitive role for one another by assessing each other's ideas (e.g.Goos et al., 2002;Hurme et al., 2009).For example, speaking aloud about how one's understanding of a topic has evolved can provide another person with new ideas to think about for their own conceptualisation.Metacognitive awareness among the group members operates to jointly monitor, regulate, and control cognitive processes towards a common consensual goal by recognising new strategies, reinterpreting issues, switching tactics, fixing mistakes, and so on (Iiskala et al., 2011).Collaboration involves reciprocal communication and social interactions by nature.Through social interactions with teachers or peers in a collaborative group, the individual's conceptual system, attitudes, and beliefs are stimulated, which significantly contributes to individuals solving problems collaboratively (Lesh & Doerr, 2003;Lester, 2007).Also, social interaction encourages information transmission between cognitive systems, which might alter the circumstances of each person's cognitive schemas (Kirschner et al., 2018).From a metacognitive point of view, through these interactions, learners can be supported to regulate their current thinking, control their current knowledge level and understanding, and retest their misconceptions and metacognitive experiences (e.g.Carr & Biddlecomb, 1998;Kim et al., 2013;Kramarski & Mevarech, 2003;Smith & Mancy, 2018).We know from earlier theories that metacognitive experiences are situated judgements and feelings that emerge during an ongoing task (Efklides, 2011).These experiences are subjective, temporal and dynamic processes that develop as learners complete a task (Efklides, 2011).They vary according to the characteristics of the task being processed.In terms of task difficulty, reciprocal communication can exchange crucial information about a person's assessments of the task's current state (Greeno, 2011;Schnaubert et al., 2021).This can be seen when students collaborate with peers to solve problems, their metacognitive awareness can be improved through peer explanation or peer criticism of a solution or both.Learners' confidence in judgement (metacognitive judgement) may decrease towards the end of a problem-solving task, for instance, if the task is too difficult or if they cannot get along with their collaborative group members.Given the dynamic nature of metacognitive experiences, it is common to assess them using single-item self-reports at multiple time points throughout a learning task (Dindar et al., 2020c).Therefore, in this study, students' perceptions of task difficulty and metacognitive judgement of situated self-reports, which were completed multiple times while collaboratively solving a complex task, were used to measure their metacognitive awareness at the social level (Dindar et al., 2020a).
Although learners' metacognitive awareness of their own and peers' learning processes in interactions has been considered to play a crucial role in specifying the efficacy of collaborative learning process (Järvelä et al., 2021;Näykki et al., 2017), students are typically unaware of their peers' level of metacognitive judgement of task perceptions (i.e.task difficulty) while collaborating.As learners progress through the task, they can gain a greater understanding of their own and their peers' weaknesses and strengths (Bakhtiar et al., 2018).Regarding collaborative learning, it is unknown how learners with different metacognitive conditions can affect and be affected by others' regulation, as well as how regulation in collaboration alters situational metacognitive conditions.However, internal and external conditions for learning, including the social context, shape the ways in which learners perceive a task and make metacognitive judgements (Bakhtiar et al., 2018).
Students are metacognitively active and capable of directly engaging with each other's thinking (Kuhn, 2015), evaluating others' ideas carefully, expressing and justifying their own ideas, and answering group members' questions in productive forms of collaborative learning (Chiu & Kuo, 2010).Thus, students' interaction during collaboration not only focuses on the task content but also includes metacognitive interaction, that is, interaction with their own and other group members' thinking.In metacognitive interactions, students may assess, for instance, whether they comprehend the task correctly or whether the proposed solution seems reasonable.Therefore, learners continuously adapt their strategies and behaviours, regulate their current thinking, and monitor their metacognitive judgements and current levels of task difficulty during a collaborative learning task, which may be evidenced in written and spoken language, body movements, and facial expressions.

Emotion Recognition from Facial Expressions
At the social level of metacognitive awareness, facial expressions can be used as a focus point of assessment in collaborative learning contexts because metacognitive experiences can also be disseminated among collaborating individuals through written and spoken language and facial expressions (Efklides, 2006).Earlier studies have indicated that metacognition in collaborative environments can be related to facial expressions (du Boulay et al., 2010) because facial expressions give clues about the social interaction of the group (Frith, 2009).For example, AutoTutor (D'Mello et al., 2008), an artificial intelligence tool, designed to observe learners' facial expressions and to understand their affective state, captures boredom, engagement, frustration, and confusion as the most relevant emotions to learning.Further, the exchange of metacognitive experiences among group members can contribute to shared metacognitive monitoring, and facial expression can provide valuable information about shared cognition and task progress (Efklides, 2008).Therefore, facial expressions can invite metacognitive interaction in collaborative learning.
Facial expression provides powerful information about one's mental state and thoughts (Ansari et al., 2019) and is a significant way to automatically detect emotions (Azevedo, 2015).Studies suggest that emotions are directly linked to learning processes (Pekrun & Stephens, 2010) and affect learners' ability to understand complex topics (Lajoie et al., 2020).Emotions are typically measured before and after learning sessions using selfreported questionnaires (Marengo et al., 2022).This has been a limitation in terms of capturing the dynamic and shifting nature of emotions (Frijda, 2007).However, current technological advancements make it possible to capture and classify the emotions of individuals unobtrusively, for example, through facial recognition methods along with machine vision (Liu & Wilkinson, 2020).For instance, Taub et al. (2021) analysed whether negative and positive emotions were related to learning processes, such as strategy use, metacognitive monitoring and academic performance.They found that negative emotion, that is, "frustration", positively predicted academic performance and learning processes.Ahmed et al. (2013) found that positive emotions were positively related to learning processes and academic performance.Others have also shown negative relationships between increases in negative emotions (i.e.boredom), performance, and metacognitive monitoring accuracy (Cloude et al., 2020).The studies mentioned above have revealed how emotions play an important role in education.Numerous studies have shown that people of various cultural backgrounds interpret some facial expressions in the same way.In other words, there are emotions that are considered universal despite differences in an individual's cultural background, environment, and language.The facial expressions of disgust, sadness, happiness, fear, contempt, surprise, and anger are universally accepted emotions (Ekman & Friesen, 1976).Tonguç and Ozkara (2020) analysed how students' universal emotions changed during the lecture and found that facial expressions of anger, fear, contempt, and confusion increased while facial expressions of disgust, happiness and sadness decreased in the first stage of the lecture.Ayvaz et al. (2017) analysed the facial expressions of the participants in the e-learning session in an attempt to classify specific physiological variables in facial images using classification algorithms.At the end of the classification process, they made a calculation of the universally recognized emotions of fear, sadness, anger, surprise, happiness, and disgust.
To date, facial expression data has been used mostly on the individual level, disregarding social interactions (Järvelä et al., 2016;Malmberg et al., 2019).However, development in the methodological approach is needed to capture emotions that fluctuate, are dynamic, and change over time during learning and their effect on metacognition, such as metacognitive awareness.In this study, we investigated whether facial expression recognition can be used as a complementary method to understand metacognitive awareness during CPS.

Metacognitive Awareness at the Environmental Level
At the environmental level, metacognitive awareness is one's interactions with the learning environment, such as classroom activities, task complexity, and stages of problem solving.The learning environment supports and develops an individual's focus of awareness at different levels in the conceptual and metacognitive demands of the task processes through specific problem-solving tasks and classroom activities (Lesh & Doerr, 2003).Studies have revealed that planning, monitoring and evaluation practices in the learning environment can increase metacognitive awareness and help students control and regulate the learning process and products (Karaoğlan Yılmaz et al., 2018;Yılmaz & Keser, 2017).Metacognition is invited or activated intensively during difficult problems (Helms-Lorenz & Jacobse, 2008;Iiskala et al., 2011;Prins et al., 2006;Stahl et al., 2006;Vauras et al., 2003).In this study, complex CPS simulation is considered an ill-defined problem that provides comprehensive metacognitive awareness to and typically involves complex real-world contexts, such as running a fictional shirt company.These types of tasks related to real-world situations require creating mathematical models that encourage learners to think about thinking, both their own and others', and to regulate, control, or monitor possible alternatives (English, 2008;Hamilton et al., 2008).CPS can be considered a temporal and iterative process that is shaped by the interplay of external conditions (e.g.task complexity) and individuals' internal metacognitive experiences, such as feelings of difficulty and metacognitive judgement (Dindar et al., 2020a).
Multiple feedback about learners' performance during CPS tasks provides them with a place to implement and develop various metacognitive processes (Lesh & Doerr, 2003).In particular, social conditions, such as collaborative learning and CPS, that require learners to develop their metacognitive thinking are defined as environmental levels that stimulate and discuss learners' metacognitive awareness at both the individual and social levels (Kim et al., 2013;Magiera & Zawojewski, 2011).Thus, CPS environments are intentionally created to provide students with sufficient knowledge to self-evaluate their understanding (individual) and demand that they work in groups where various perspectives are provided (social) (Hamilton et al., 2008;Lesh & Doerr, 2003;Magiera & Zawojewski, 2011).Multiple cycles of feedback in which students criticise and revise each other's thinking are typically necessary in CPS; therefore, the productivity of metacognitive functions is provoked (Lesh & Doerr, 2003).These CPS feedback show how actively and dynamically students monitor and adjust their own and others' thinking during the course of problem solving (Lesh & Doerr, 2003).To this end, they interact with "the following four problemsolving processes: (1) exploring and understanding the problem, (2) organising and integrating information with personal knowledge, (3) planning and executing a solution, (4) monitoring the plan and reflecting on how to improve it" (Stewart et al., 2021, p. 716).In this study, CPS was used as a methodological tool for understanding metacognitive awareness on multiple levels, and its specific design feature provided continuous feedback about students' goal attainment, which was used as an environmental level for supporting metacognitive awareness.

Aim
This study investigates how metacognitive awareness at the individual, social, and environmental levels are associated with CPS.The following research questions were addressed: (1) What is the relationship between individual and social levels of metacognitive awareness and their impact on perceived task performance in CPS tasks?
(2) What is the role of environmental levels in stimulating learners' metacognitive awareness at the social level in CPS tasks?

Participants
The participants were 77 higher education students, three of whom belonging to different groups withdrew and their data were excluded from the dataset (n females = 41; n males = 33; M age = 27.8;SD age = 5.43) from international degree programmes (f Master's = 52; f PhD = 16; f Bachelor's = 6) at the University of Oulu, Finland.The participant profile included different nationalities; the most common ones were Chinese (n = 12), Finnish (n = 7), Pakistani (n = 5), Vietnamese (n = 4), Mexican (n = 3), and Polish (n = 3).The participants took part in a CPS task in groups of three (n = 22) or two (n = 4).Participation in a CPS task was voluntary.Students' collaborations during the CPS task were video recorded.

The CPS Task
The students' CPS task comprised a simulation of running a shirt production company called Tailorshop simulation (a computer-based complex problem simulation) (Danner et al., 2011;Dörner et al., 1983).The tool has been used by several studies to measure individuals' complex problem-solving skills (Barth & Funke, 2010;Danner et al., 2011).In Tailorshop, participants run a fictional shirt production company for 12 simulated months.The simulation task includes 22 variables (Fig. 2), 12 of which the participants can directly manipulate.The remaining variables can be manipulated only indirectly through changes in the variables that can be directly manipulated.The main goal is to enhance the company's value as much as possible at the end of the task.The company's value depends on the complex relationship between the variables in the simulation.In each simulated month, participants, as a group, make decisions about how to manipulate the variables and input their decisions into the simulation.When the group proceeds to the next month, the simulation updates the company's value on the screen based on the group's input.The simulation provided group members with feedback about their success (i.e. company value increase or decrease) during at the end of each month of the simulation.

Procedure
Prior to the CPS task, the participants were administered the Metacognitive Awareness Inventory questionnaire (Schraw & Dennison, 1994), which asked the students to report their metacognitive beliefs regarding 52 items on a 7-point scale that ranged from strongly disagree (1), neither agree nor disagree (4), to strongly agree (7).The adjusted inventory included the following component categories: knowledge of cognition (declarative knowledge -8 questions, procedural knowledge -4 questions, and conditional knowledge -5 questions) and regulation of cognition (planning -7 questions, information management skills -9 questions, monitoring -7 questions, debugging strategies -5 questions, and evaluation -6 questions).The scores for each item on the Metacognition Awareness Inventory were summed to obtain a composite score for metacognition.The internal consistency of the scale, measured by Cronbach's alpha, was 0.75 for metacognitive knowledge and 0.78 for metacognitive regulation.The internal consistency for the subcomponents of metacognitive knowledge ranged from α = 0.92 to α = 0.76, and the internal consistency for metacognitive regulation subcomponents ranged from α = 0.84 to α = 0.72.
During the CPS task, the simulation prompted participants to complete situated selfreport questionnaires about their metacognitive judgements (i.e. the extent of confidence in attaining the task goals) and perceived task difficulty at specific times: at the beginning of the task and after simulated months 3, 6, 9, and 12. Table 1 displays the situated selfreports at each time point.The metacognitive judgement questionnaire asked, "How confident are you that your team is attaining the current task goal?" (Hadwin & Webster, 2013).Participants responded to the questionnaire by choosing a value between 1 (I am not confident at all) and 5 (I am very confident).The task difficulty questionnaire was based on Efklides et al.'s (1998) model.In the questionnaire, the participants were asked to rate the task's difficulty ("This task seems to be …") from 1 (not difficult at all) to 10 (very difficult) in a single-item questionnaire.
At the end of the CPS task, two separate single-item questionnaires were used to measure perceived group performance ("How was your group's performance during the task?") and perceived individual performance ("How was your individual performance during the task?").Answers to the perceived group performance questionnaire ranged from 1 (we performed very poorly) to 10 (we performed very well).Similarly, the range for perceived individual performance was the same as for the perceived group performance question.Overall, the average CPS duration for the groups was 96 min (SD: 28.08).

Facial Expression Detection
Different combinations of independently moving muscles on human faces are activated to produce different facial expressions.Ekman and Friesen (1976) created the Facial Action Coding System (FACS) to recognize face movements.This system defines 46 action units for each distinct facial muscle movement.The FACS simply categorizes the physical motions required to produce various facial expressions (not their meanings or reasons behind them).Differences in facial expressions based on various emotions are described using Ekman and Friesen's (1986) universally recognised categories, that is, pan-cultural facial expressions of emotions.The Cognitive Services Pack provided by a cloud-based emotion recognition service (Microsoft Azure Face API; application programming interface) can identify people's face and emotional expressions after processing pictures.This software identifies the seven basic universally recognised emotional groups (fear, surprise, anger, sadness, contempt, disgust, and happiness) described by Ekman and Friesen (1986) as well as neutrality.
The average accuracy rate of the emotion recognition services provided by Microsoft Azure is 97%, according to the confidence rates (Al-Omair & Huang, 2018).The system performs three main processes: facial acquisition, feature extraction, and emotion classification.Facial acquisition and feature extraction focus on the location of facial images and the extraction of facial expressions (Ansari et al., 2021, p. 23).The emotion classification process classifies facial expressions according to various emotions.Microsoft Azure Face API analyses the frames from a video and provides the system with emotions based on facial expressions categorised into neutral, fear, surprise, anger, sadness, contempt, disgust, and happiness.They can be found in all cultures and correspond to distinctive patterns of physiognomic arousal.Since our participants were international students, universal facial expression emotions were examined.In this study, video data for 26 groups were clipped when the participants received feedback from the simulation.The duration of the video clips was determined to be five seconds.All clipped videos were intended to be analysed for individuals' facial expression emotions related to the feedback from CPS using Microsoft Azure.Since Microsoft Azure could not process video clips, we used Python script programming language to take sample images from video clips and transferred them into Microsoft Azure for analysis.This software detects human faces in the images and then returns the rectangular coordinates of the locations and facial expressions with their scores.Participants' relative positions (left-middle-right) did not change during the recording.Facial expressions scores matched with participants by using their detected face coordinates.Images with less than 3 faces of successful matching were excluded to eliminate possible matching errors.

RQ1. What is the relationship between individual and social levels of metacognitive awareness and their impact on perceived task performance in CPS tasks?
To analyse the collected data, SPSS and AMOS 26 software programs were used.Structural equation modelling (SEM) was conducted to specify different relationships between variables in the model and to examine the effect of variables for the first research question.The model fits the data consummately (× 2 = 65.777,df = 44, p = 0.018; GFI = 0.875; AGFI = 0,778; CFI = 0.968; TLI = 0.953; NFI = 0.913; RMSEA = 0.082 (acceptable fit indices, please see Hu & Bentler, 1999;Tanaka & Huba, 1985)).All significant relationships among the study variables in the SEM analysis are shown in Table 2. Table 2 highlights the SEM model with all estimated coefficients.SEM yielded a positive relationship between perceived individual performance and metacognitive judgement (β = 0.65, p < 0.01).An indirect relationship was also observed between metacognitive judgement and an individual's perceived group performance through the mediation of perceived individual performance.The direct effects associated with perceived individual and group performance were positive and statistically significant (β = 0.71, p < 0.01).We also observed that metacognitive awareness at an individual level, which is the response of the Metacognitive Awareness Inventory, was positively associated with perceived group performance (β = 0.18, p < 0.026).Lastly, the perception of task difficulty has a significant and negative direct effect on perceived group performance (β = -0.15,p < 0.048).

RQ2. What is the role of environmental levels in stimulating learners' metacognitive awareness at the social level in CPS tasks?
a. How does feedback predict facial expressions?b.How does feedback predict metacognitive judgements?c.How does feedback predict task difficulty?
Multilevel models are based on considering hierarchical and clustered data structures.This analysis starts with reckoning "the unconditional, null, or one-way random effect analysis of variance (ANOVA)" (Mohammadpour, 2013, p.215;Raudenbush & Bryk, 2002) and estimates the variance structure using a parsimonious, parametric structure.The ability to predict cross-level effects is an advantage of second or higher levels of multilevel modelling, alongside an alternative research strategy that requires the analysis of each level separately from the others.Since we worked with potentially multilevel data (individuals were nested within groups and participants' responses at different times), we assessed variance across the levels by computing intra-class  Shrout & Fleiss, 1979) for each dependent variable.For the second research question, ICC scores were calculated using SPSS package version 26, and all dependent variables' ICC values are higher than 1% except "sadness" emotional expression (Table 3).Therefore, three-level multilevel modelling was used, which ensures a useful framework for thinking about problems with this type of hierarchical structure (Buxton, 2008): Level 1 (time: participants' responses to the metacognitive judgement and task difficulty questionnaires, and their facial expressions at the feedback times); Level 2 (individuals) and Level 3 (groups in collaborative learning).In all sub-questions, the independent variable is feedback.In our study, group members received feedback about their task progress at specific time points during CPS; therefore, feedback was either negative or positive.Positive feedback indicates that the group has increased the company value in the simulation compared to the previous month, whereas negative feedback indicates that the company value has decreased compared to the previous month.In this analysis, we coded the feedback as positive (binary digit 1) and negative (binary digit 0).For "sadness" facial expression emotion, two-level multilevel modeling was used since its ICC value in Level 3 is zero.The results show that feedback had a positive and statistically significant (p ≤ 0.05) association with the two facial expressions, and metacognitive judgement: Feedback predicted students' facial expressions of "sadness" (b = -0.047,SE = 0.002, t (671) = -2.96,p < 0.01, R 2 = 0.13) and "neutral" (b = 0.28, SE = 0.014, t (618) = 1.91, p = 0.05, R 2 = 0.18), and their metacognitive judgement (b = 0.13, SE = 0.058, t (235) = 1.94, p < 0.05, R 2 = 0.29).However, the perception of task difficulty was not predicted by feedback (b = -0.010,SE = 0.088, t (232) = -0.12,p = 0.90, R 2 = 0.005).

Discussion
This study explored how individual, social and environmental levels of metacognitive awareness operate in CPS.In this study, both perceived individual and group performance were considered.This study also uncovered the effect of the environmental level of metacognitive awareness-the "feedback" feature of a complex CPS environmenton the social level of metacognitive awareness.Besides, facial expression recognition

The Relationship Between Individual and Social Levels of Metacognitive Awareness and Their Impact on Perceived Task Performance in CPS Tasks (RQ1)
The first research question investigated the relationship between individual and social levels of metacognitive awareness and their impact on perceived task performance in CPS tasks.An indirect relationship was observed between metacognitive judgement and an individual's perceived group performance through the mediation of individual perceived performance.Confidence judgements about performance comprise a key subjective experience in self-regulated learning (Hadwin & Webster, 2013).Accurate judgements are significant for selecting the most appropriate self-regulation processes to achieve task goals, whereas inaccurate judgements, in the form of overconfidence or insufficient confidence, may inhibit regulation and achievement (Cavalcanti & Sibbald, 2014).Recently, Dindar et al. (2020a) investigated the relationship between metacognitive experiences and performance in a computer-supported CPS context.Their findings revealed that metacognitive judgement, emotional valence, and mental effort were related to group CPS performance.
Overall, these findings highlight the importance of metacognitive experiences in successful CPS.In our study, the CPS simulation informed the participants about their group progress at specific intervals.It can be assumed that such feedback allowed participants to review their strategies for dealing with the problem situation through negotiation with their group members (Isohätälä et al., 2020).In this regard, the negotiation of group progress in relation to feedback may have yielded a positive correlation between metacognitive judgements and perceived individual performance.
Previous studies have shown that learners' individual metacognitive awareness does not predict learning outcomes at the individual level (Çini et al., 2020).However, this study examined the effects of different aspects of metacognitive awareness on collaborative performance and found a direct effect of individual metacognitive awareness on perceived group performance at the individual level.Although scholars agree that metacognition plays an important role in learning and that there are differences between high-and lowperforming students, the types and details of metacognition differences in regard to performance remain unclear and need to be studied further (Chikersal et al., 2017).A number of studies have also indicated that metacognition is directly linked to performance and thus can be used as a predictor of performance (Kuzle, 2017;Ohtani & Hisasaka, 2018).Keith and Frese (2005) indicated that metacognitive activity mediates performance differences.Overall, earlier findings and the current study highlight the importance of metacognitive experiences in performance.However, our findings underline that perceived performance and individual metacognitive awareness in CPS nest together.Consequently, this study agrees to the study of Çini et al. (2020) and implies that learners who are metacognitively aware are more strategic, predict their performance more accurately, and are more successful than students who are not aware.
The results of our first research question also showed that one of the social levels of metacognitive awareness-the perception of task difficulty measured from situated selfreports during CPS-predicts collaborative perceived group performance at the individual level.Earlier studies have shown that academic performance is strongly related with learners' perceptions of task difficulty and on-task mental effort, among others (Papamitsiou & Economides, 2015;Yen et al., 2015).Students' problem-solving process involves not only applying and regulating manifold problem-solving strategies but also monitoring and controlling the encountered problem-solving process (Stewart et al., 2019).The problemsolving process needs high-level thinking skills, such as reflecting, developing strategies, regulating, evaluating, planning, analysing, and interpreting, indicating the need for metacognitive awareness at every step.Metacognitive awareness enables learners to reason, reflect, and monitor students' thinking processes.This awareness becomes fundamental in the problem-solving process.Previous studies have shown the effect of metacognitive awareness and problem-solving skills on learners' performance (Areepattamannil & Caleon, 2013;Karatas & Baki, 2013;Selcuk et al., 2013;Tavakoli, 2014;Young & Fry, 2008).Scholars have also highlighted the importance of problem-solving skills in the development of metacognitive awareness (Abdullah et al., 2014;Breed et al., 2014;Lee & Schmitt, 2014;Liu & Liu, 2020;Shen & Liu, 2011;Yildirim & Ersozlu, 2013).Overall, metacognitive awareness has been underscored as a key element of effective problem solving.

How Feedback Predicts Facial Expressions
It is known that during CPS, knowledge construction and knowledge application within a group can be facilitated through group members' facial expressions in addition to other ways, such as their interactions in written and spoken language, drawings, manipulation of tools and artefacts, and body movements.A few earlier studies have shed light on the relationship between learners' facial expressions and metacognition.For example, Taub et al. (2021) found relationships between emotions and metacognitive processes; they showed that a mean evidence score of "surprise" negatively predicted the accuracy of metacognitive judgements.Facial expression emotions are also considered essential components of metacognitive experiences, signalling positive or negative feelings about a learning task (Efklides, 2011).Similarly, Cloude et al. (2020) found a negative relationship between metacognitive monitoring accuracy and changes in negative emotions (boredom).The second research question in the current study addressed the role of the environmental level of metacognitive awareness at the social level in CPS tasks.Therefore, the "feedback" feature from the complex CPS was used to understand its effect on learners' facial expressions.In learning contexts, feedback, in general, refers to all the information provided to students in relation to the actual state of learning and the outcome (e.g.Hattie & Timperley, 2007;Narciss, 2008).However, the implementation of feedback does not necessarily facilitate learning.Pekrun (2000, p. 156) claimed that "success and failure feedback may situationally produce achievement-contingent emotions (joy, disappointment, pride, shame, etc.)".In our study, feedback was either positive or negative.Positive feedback indicates that the group has increased the company value in the simulation compared to the previous month, whereas negative feedback indicates that the company value has decreased compared to the previous month.Our findings are in line with studies that associated negative feedback with negative emotions (Schrader & Grassinger, 2021).
However, contrary to previous research (e.g., Fong et al., 2018), we did not find a significant relationship between positive feedback and positive emotions.This can be explained by the metacognitive standards (i.e.criteria students set for accomplishing the task) the groups have set for themselves.In the simulation, the group objective was to increase the company's value as high as possible.It can be assumed that the groups did not perceive the feedback from the simulation as a standalone result for a specific month.Rather, they utilised positive feedback to decide on their next group strategy to increase the company's value in the next simulated month.This is because the company value could increase or decrease drastically in any month based on the group strategy.Thus, a glimpse of success indicated by feedback in a specific simulation month comes with the risk of failure and the opportunity for higher success in the next month.In this regard, we can speculate that positive feedback served as a cue to direct the groups' mental effort in the next phase of the task.In the current study, we observed a positive relationship between positive feedback and neutral emotions.This finding supports our speculation.Our findings indicate a potential research agenda for studying the relationship between positive feedback and metacognitive standards.We argue that positive feedback elicits positive emotions if it refers to a match between task progress and the metacognitive standards set for the task.Further, it can be hypothesised that during unfolding collaborative tasks, group emotions might not indicate positive valence until success is guaranteed.

How Feedback Predicts Metacognitive Judgements
The three-level multilevel modelling showed the effect of feedback on participants' responses to their metacognitive judgement in the CPS environment.Previous studies have found that feedback can be an important element in improving and enhancing students' metacognitive judgements, especially when combined with knowledge about the importance of such training tracking accuracy (Händel et al., 2020).It can also increase preservice teachers' metacognitive awareness (Altıok et al., 2019), predict larger training effects for metacognitive strategies (Theobald, 2021), develop metacognition (Taub et al., 2014), and lead to more accurate monitoring (Baars et al., 2014).According to Winne and Hadwin (1998), metacognitive monitoring is the key to self-regulating one's learning since there is no benchmark against which to implement regulation without the cognitive evaluations it generates.The judgement of performance is one of the most frequently used assessment methods for metacognitive monitoring (Blissett et al., 2018) because learners rely on their metacognitive judgements to regulate their performance.The results of our study showed that positive feedback predicts learners' metacognitive judgements.This is not surprising because receiving feedback about the performance provides planning and self-regulation, making evaluations based on various criteria, self-evaluation, questioning the thinking process, and expressing their own opinions (Blakey & Spence, 1990;Costa, 1984;Taub et al., 2014).We can conclude that immediate feedback about performance is a successful method for improving regulation by activating relevant metacognitive awareness.Metacognitive judgements are inferential and individuals base these judgements (i.e.confidence judgements) on a variety of monitoring cues that support these findings (i.e.information sources; Koriat, 2015).This is one reason supporting such findings.It is common for individuals to frequently misinterpret cues and make inaccurate metacognitive judgements of their task performance (Ackerman & Goldsmith, 2011).In our study, the CPS simulation informed the participants about group progress at specific and regular intervals.It can be assumed that such feedback allowed participants to re-evaluate their problem-solving strategies through negotiation with their peers (Isohätälä et al., 2020).Therefore, negotiation of group progress in relation to feedback may have resulted in a positive relationship between confidence ratings and perceived group performance.Studies (Khosa & Volet, 2014) have found that collaboration enhances metacognitive judgement since metacognitive judgement improves high-level cognitive activity as a result of productive discussion and questioning among group members.Providing feedback during a task may prompt learners in task-specific monitoring processes and facilitate accurate judgements about task performance (Hattie & Timperley, 2007).Thus, we suggest that feedback should be embedded in collaborative learning to foster successful group collaboration and effective metacognitive judgements.
Additionally, subjective emotions serve as the informational foundation for judgements and behaviours (Koriat & Levy-sadot, 2000).Therefore, emotional valence is considered an essential component of metacognitive evaluations (Efklides, 2006).Hadwin and Webster (2013) found that positive emotions positively predicted confidence in goal attainment.When inconsistency is detected, it offers students the opportunity to strategically adapt their thoughts, emotions, actions, or judgements of confidence, which is a metacognitive self-evaluation that informs the difference between an individual's actual performance (Hadwin & Webster, 2013).However, a closer look at the results of the relationship between "positive feedback and facial expression" and metacognitive judgement indicates that facial expression "neutrality" is an indicator of metacognitive judgement.In other words, facial expression recognition makes it visible and, thus, can add a new data channel and methodological tool to understanding metacognitive awareness.

How Feedback Predicts Task Difficulty
Finally, the second research question revealed the relationship between feedback and task difficulty in the CPS environment.Task perceptions require the main metacognitive knowledge for regulation (Winne & Hadwin, 1998).Task understanding is thoughtful and cognitive; however, the perception of task difficulty involves a judgement about the difficulty level of the task, such as how difficult it is to comprehend the task (Pintrich, 2000).Recognising the learners' task difficulty perceptions is important for understanding learners' metacognitive awareness (Efklides, 2006;Helms-Lorenz & Jacobse, 2008;Iiskala et al., 2011;Prins et al., 2006;Vauras et al., 2003;Winne & Hadwin, 1998).Task difficulty is affected by a task's conceptual and metacognitive requirements (Efklides, 2006;Stahl et al., 2006).When learners' perceptions of task understanding are weak and they find the task difficult, it becomes challenging for them to implement learning strategies.The act of being metacognitively aware prompts learners to think about and assess the perception of task difficulty.A fundamental premise of collaborative learning is that students are interested in collaboration if they are unable to complete a task without the contributions of others (Johnson et al., 1981).Considering CPS, task difficulty should be high enough to invite learners to work together; there is no need for them to collaborate if they can accomplish the task alone (Iiskala et al., 2011).In line with this assumption, difficult tasks activate higher levels of shared metacognitive processes in CPS than simple tasks do (Efklides et al., 1998).Therefore, task difficulty is another crucial element in the elicitation of metacognition (Çini et al., 2020).Our study investigated the effect of feedback on the perception of task difficulty.According to the results of this study, learners' perceptions of task difficulty are not affected by feedback about their immediate performance in a complex CPS environment.In other words, feedback does not predict learners' perceptions of task difficulty during collaboration.In our study, the CPS simulation had intricate relationships between the variables, indicating a very challenging task.One possible explanation for the insignificant correlation between task difficulty and feedback is that there was no time limitation for the group members to complete the CPS task.Consequently, it can be assumed that the groups had sufficient time to determine the relationships between the variables in the CPS simulation, regardless of task difficulty level.However, it could also be that learners become more aware of task difficulties in the context of collaborative learning over time (Çini et al., 2020).

Limitations and Implications for Future Research
The current study has limitations related to dataset, CPS task and facial expression analysis.Our dataset in this study is somewhat modest to analyse cross-level interactions, which were excluded from our study.The first limitation concerning the CPS task is that metacognitive awareness was investigated at multiple levels in a highly complex CPS task.Therefore, the findings may not be generalisable to CPS conditions that include different levels of task difficulty.The second limitation is that the collected data came from a simulation task, which is different from real-world problems and is specific to the participants.Thus, it might have a novelty effect not seen in another context and the findings might not be applicable to CPS tasks with different kinds of problem states.The third limitation involves the sample, with most of the participants being adults; thus, the current findings might not be generalisable to younger populations at lower education levels.Finally, perceived CPS performance was measured only at the end of the CPS task.Thus, the findings exhibit the overall relationships between metacognitive awareness at multiple levels, facial expression emotions, and perceived CPS performance rather than temporal covariations.
In relation to facial expressions, a limitation of this study is that participants can be aware of facial expressions and the effects of their expressions in a video review condition.Knowing that they are being filmed can cause an individual not to react naturally, thus controlling their expressions.For this reason, the results may be limited.Another limitation is that in collaborative groups, participants can mostly express negative emotions due to the low level of interaction between group members.That is, they do not exhibit positive facial expressions when there are socioemotional interactions involving a confusing situation (Kwon et al., 2014).In our study, sadness and neutrality were especially predicted by feedback, which could be due to the study's exploratory setting.Furthermore, the facial expression recognition tool analyses faces in 2D; hence, the analysis has difficulties capturing large variations in pose and subtle facial expressions.Further, facial expression analysis to categorise gender and age does not work well for individuals with darker skin tone (Buolamwini & Gebru, 2018).Thus, datasets are generally condensed to include races in Europe and North America (Shankar et al., 2017), which leads to biases and difficulty in detecting other races.In recent years, the effect of student emotions on learning has been studied (Taub et al., 2021).These emotions can be achievement emotions, epistemic emotions, academic emotions, or basic emotions.In facial expression recognition, sadness might be linked to action units similar to those in confusion (epistemic emotion), frustration (academic emotion), and boredom (achievement emotion) whereas facial movements of enjoyment (epistemic emotion), hope (achievement emotion) and elatedness (academic emotion) can be detected as happiness.To solve the issue, further studies might consider examining emotions as positive and negative.
Future studies should examine how computer-mediated systems that provide feedback dynamically respond to behavioural signals.Students' metacognitive judgement and emotional status via facial expressions could also be studied.Thus, future research should consider comparing on-task feedback-related emotions with end-task feedback-related emotions to test this hypothesis.Supporting positive emotions and preventing negative emotions are essential factors that future studies should consider when designing feedback.Future studies should also explore how multiple levels of metacognitive awareness and emotions vary in different types of collaborative groups, not just in CPS tasks.Further, how facial expressions predict social levels of metacognitive awareness, such as metacognitive judgements and task difficulty in collaborative groups, could be elaborated.Also, future studies could consider using other data channels (e.g., EDA measures) to understand metacognitive awareness in CL.Finally, individual and group performance was measured only as perceived at the individual level and at the end of the CPS task.Therefore, the current results show the overall relationships between metacognitive awareness at multiple levels, facial expression emotions, feedback, and perceived CPS performance rather than the actual individual and group performance.Future studies should measure actual individual and group task performance and investigate their temporal covariations along with other variables.

Conclusion
This study shows the importance of metacognitive awareness in CPS, and it finds an association between metacognitive levels at individual, social, and environmental levels in CPS and CPS task performance.This is in accordance with the theoretical understanding that metacognition is related to learners' perceptions of selfs, tasks and learning situations (Flavell, 1979) and that metacognitive awareness helps individuals regulate and control their thinking in a way that directly promotes their performance (Schraw & Dennison, 1994).Hence, multiple levels of metacognitive awareness represent an integrative framework.Further, the results indicate that the collaboration context is a rich source to support metacognitive awareness via individuals themselves and individuals' interactions with group members and the learning environment.Students frequently struggle to evaluate their solutions in collaborative environments like CPS, but peers can help in this assessment by playing a metacognitive role for one another (e.g.Goos et al., 2002;Hurme et al., 2009) via written and spoken language and/or facial expressions, as was seen in this study, and further practical implications could be developed.

Declarations
Ethics Approval The study was carried out in accordance with the recommendations of the American Psychological Association's Ethical Principles of Psychologists and Code of Conduct.All participants gave written informed consent before participating in the study, with the understanding that they could quit at any time.

Conflict of interest
The authors declare that they do not have any conflict of interest.
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Fig. 1
Fig. 1 Multiple levels of metacognitive awareness

Fig. 2
Fig. 2 Variables in the Tailorshop simulation

Fig. 3
Fig. 3 Structural equation model results.Solid arrows indicate direct relationship.Standardized estimates are provided beside each arrow

Funding
if there was an easier way to do things after I finish a task [ ] if I learned as much as I could have once I finish a Open Access funding provided by University of Oulu including Oulu University Hospital.This research was granted by Finnish Academy GrantNo.324381, No: 308809 and No. 297686.Data collection was carried out with the support of LeaF Research Infrastructure (https:// www.oulu.fi/ leaf-eng/), University of Oulu, Finland.

Table 1
Time points at which participants completed situated self-reports in the Tailorshop simulation

Table 4
Metacognitive Awareness Inventory (MAI) used in the study.Please put a tick in the box [✓] which seems most appropriate for you.There are no right or wrong answers

Table 5
Descriptive Statistics of the Datasets