Metacognitive monitoring and control in elementary ...

LEAIND-00722; No of Pages 9 Learning and Individual Differences xxx (2012) xxx–xxx

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Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance☆ Claudia M. Roebers ⁎, Saskia S. Krebs, Thomas Roderer Center for Cognition, Learning, and Memory, School of Psychology, University of Bern, Bern, Switzerland

a r t i c l e

i n f o

Article history: Received 1 May 2012 Received in revised form 1 November 2012 Accepted 11 December 2012 Available online xxxx Keywords: Metacognition Monitoring Control Mastery motivation Achievement Elementary school children

a b s t r a c t Contemporary models of self-regulated learning emphasize the role of distal motivational factors for student's achievement, on the one side, and the proximal role of metacognitive monitoring and control for learning and test outcomes, on the other side. In the present study, two larger samples of elementary school children (9- and 11-year-olds) were included and their mastery-oriented motivation, metacognitive monitoring and control skills were integrated into structural equation models testing and comparing the relative impact of these different constituents for self-regulated learning. For one, results indicate that the factorial structure of monitoring, control and mastery motivation was invariant across the two age groups. Of specific interest was the finding that there were age-dependent structural links between monitoring, control, and test performance (closer links in the older compared to the younger children), with high confidence yielding a direct and positive effect on test performance and a direct and negative effect on adequate control behavior in the achievement test. Mastery-oriented motivation was not found to be substantially associated with monitoring (confidence), control (detection and correction of errors), or test performance underlining the importance of proximal, metacognitive factors for test performance in elementary school children. © 2012 Elsevier Inc. All rights reserved.

1. Introduction Imagine a 4th grader trying to answer the questions in a science test: She or he has paid more or less attention when the topic was presented in class and has invested more or less time at home to prepare for the test by reading, memorizing, elaborating, and/or pre-testing her or his knowledge. In trying to achieve an optimal result, the student will — during the exam — put effort in retrieving targeted information, judge the confidence of the upcoming candidate answers, (hopefully!) re-read his or her answers searching for errors, and then possibly correct (or only cross-out) answers that he or she believes to be incorrect. From these descriptions, it is obvious that different metacognitive monitoring (i.e., confidence judgments) and control processes (e.g., detecting and correcting errors) are involved in student's test taking behavior and the resulting test

☆ The present study is part of a larger research project partially financed by the Swiss National Science Foundation (SNF — grant no. 100014-126559/1) to the first author. We wish to thank the participating students, their teachers, and the responsive school authorities for their cooperation. We also gratefully acknowledge Uli Orths' help with the structural equation models and Balz Aklin's precise arthroscopy of Claudia's hip joint, allowing her to get back to work quickly and get this paper finalized in due time. ⁎ Corresponding author at: University of Bern, Center for Cognition, Learning and Memory, Muesmattstr. 45, CH-3000 Bern, Switzerland. E-mail address: [email protected] (C.M. Roebers).

performance. But also motivational factors, especially a student's mastery motivation for school work in general will influence the test taking behavior and the test result. With the present study, we aim to build a bridge between basic experimental research on metacognitive development between 9 and 12 years and educational research aiming at documenting factors predictive for student's achievement. An experimental approach that allows quantifying students' metacognitive monitoring and control will be combined with an individual differences perspective in order to investigate the role of task-bounded metacognitive processes and motivation for student's test outcomes. Special emphasis will thereby be put on the questions of (a) factorial invariance of the included motivational and metacognitive constructs across age groups and (b) age-related differences in the structural links between mastery-oriented motivation, monitoring, and controlling against the background of recent models of self-regulated learning.

1.1. Theoretical background Starting with metacognitive processes, these have traditionally been defined as “pure” cognitive processes taking the ongoing cognitive operations as their objects (Flavell & Wellman, 1977). Metacognitive processes differ as a function of the learning phase (acquisition, retention, retrieval), and typically, metacognitive

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Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

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monitoring is to be distinguished from control (Nelson & Narens, 1990). In that tradition, metacognitive monitoring mirrors an individual's ability to judge one's cognitive performance “on-line”, for example, judging the learning progress made during study (performance predictions), or estimating the correctness of a response just given (i.e., confidence judgments). In other words, monitoring processes inform the learner about her or his learning progress, thereby building the foundation for self-initiated learning behavior or adaptation thereof. From that cognitive perspective, metacognitive control processes are defined as the individual's executive activities enabling the use and adaptation of different cognitive operations with the aim to increase learning behavior or test performance. Thus, metacognitive control is based on the individual's subjective monitoring of current learning, thereby strongly relying on their accuracy, with monitoring accuracy being defined as an individual's ability to reliably distinguish in their metacognitive judgments between, for example, already learned vs. not-yet-learned, or, correct vs. incorrect answers. In different theoretical frameworks of self-regulated learning, metacognitive processes hold an intermediate position, located between a learner's long-term achievement goals and her or his more general mastery motivation (Wigfield & Eccles, 2002), on the one side, and the task-specific cognitive operations leading to learning progress, on the other side. The degree to which metacognitive processes are emphasized and the precise level on which metacognitive processes are assumed to operate differs across models (Boekaerts, 1999; Efklides, 2011; Pintrich, 2004; Winne, 2001; Zimmerman, 1990): In the traditional conceptualizations of self-regulated learning metacognitive processes are considered as relatively “pure” cognitive constructs that either operate on a general level in the form of declarative metacognitive knowledge and/or during learning in the form of “online” procedural metacognitions (Boekaerts, 1999; Nelson & Narens, 1990; Pressley, Borkwski, & Schneider, 1989). In more recent models of self-regulated learning, metacognitive monitoring and control processes are assumed to also include an affective, motivational aspect: Task mastery is thought to additionally produce metacognitive experiences (with different degrees of consciousness) and give rise to metacognitive feelings which in turn will affect (a) task-specific metacognitive control processes but also (b) an individual's more general self-perceptions and motivation (Efklides, 2011). Furthermore, it is assumed that the more distal and stable person characteristics (e.g., motivation, self-confidence) interact with motivational and affective states while learning (e.g. enjoyment, boredom), this way impacting on metacognitive experiences, control processes (e.g., investing more effort in retrieving information, termination of memory search, revising answers), but also on learning or test outcomes (Efklides, 2006, 2008; Kleitman & Stankov, 2001; Zimmerman & Moylan, 2009). Taken together, while traditional conceptualizations of selfregulated learning exclusively defined metacognitive processes as a “cool”, task-specific “pure” cognitive information processes (Flavell & Wellman, 1977; Nelson & Narens, 1990; Pressley et al., 1989), more recent models propose a broader conceptualization and integrate a “hot”, affective-motivational, task-independent, trait-like aspect to metacognitive monitoring and control (Efklides, 2011; Kleitman & Stankov, 2001). As these complex, multi-layered models of selfregulated learning are relatively recent, empirical tests on the veracity of the entire models are still rare and being called for. Moreover, self-regulated learning is an issue relevant not only for adults, but also for children and adolescents. Thereby, the models seem to make implicit assumptions of age-invariance of the included constituents and their interplay. As the developmental literature provides ample evidence that monitoring and control processes undergo not only quantitative but also qualitative changes in ontogeny (see below), empirical tests of age-invariance are needed; the present study makes a contribution into this direction by including 3rd and 5th grade students and testing for factorial and structural invariance across age groups.

1.2. Empirical findings on the interplay of factors involved in self-regulated learning Generally spoken, metacognitive processes have repeatedly been shown to impact a learner's performance: Both declarative metacognitive knowledge assessed with questionnaires (for example, included in some of the large international studies such as PISA; OECD, 2005), as well as procedural (online) monitoring and control processes explain substantial amounts of individual differences in test performance (Dunlosky & Metcalfe, 2009; Koriat & Goldsmith, 1996; Schneider & Artelt, 2010; Schneider, Schlagmüller, & Visé, 1998). This general pattern holds true even when psychometric intelligence is being controlled for (van der Stel & Veenman, 2008; Veenman & Spaans, 2005), suggesting a specific and positive impact of metacognitive processes on test performance. With regard to the specific influence of monitoring in self-regulated learning situations and for students' achievement, the existing empirical evidence is inconsistent, at least at first sight. This is because on the one side, there are numerous studies documenting how “pure cognitive” monitoring influences subsequent control behavior in self-regulated learning: For example, hard-to-learn item pairs (low ease-of-learning judgments prior to learning or low feeling-of-knowing-judgments after an initial learning phase) are typically associated with increased study time allocation (Son & Metcalfe, 2000). Lower judgments of comprehension are positively associated with more effective self-regulation while learning with texts (Thiede, Anderson, & Therriault, 2003). And, of importance for the present approach, confidence judgments are predictive for learners' control behavior, that is, answers receiving lower confidence judgments have a significantly higher probability of being withdrawn (crossed-out answers in the test; “I don't know” answer in a verbal interview; Koriat & Goldsmith, 1998; Roebers & Schneider, 2005). In terms of individual differences in “cool” monitoring, high confidence judgments are thus negatively related to efficient control operations. When direct effects of monitoring, especially of predictions and confidence, on performance are considered, a positive association has been found: High confidence is typically positively related to performance, for example, in terms of achievement test performance in individual differences approaches (i.e., self-confidence; Kleitman & Gibson, 2011; Kleitman & Mascrop, 2010; Kleitman & Stankov, 2001, 2007), or in terms of learning outcomes assessed in multi-trials experiments (e.g., Shin, Bjorklund, & Beck, 2007). Against the theoretical background of broader conceptualizations of self-regulated learning, these positive relations between optimistic performance predictions or high confidence and performance seem to confirm the benefits of students' motivational states for learning outcomes (Efklides, 2011). From this perspective, confidence seems to additionally mirror “hot”, motivation-related individual differences and may this way also yield to positive direct effects on performance. Together, a picture of interrelations of “hot” and “cool” aspects of self-regulated learning activities emerges in which stable person characteristics such as mastery-oriented motivation (operating on a macro level) are related to task-bounded, micro-level metacognitive experiences and judgments that give rise to learning behavior. However, in these empirical studies, the effects of confidence on task-specific control behavior and on performance were not simultaneously taken into account as either an experimental set-up (i.e., confidence judgments → control: detection and correction of errors) or an individual differences approach was chosen (i.e., confidence as a trait → performance). Thus, the question arises whether high confidence may potentially yield a positive direct effect on performance via motivational processes (high confidence leading to increased effort and persistence) and, at the same time, yield a negative effect on control behavior (high confidence impeding detection and correction of errors). It may also be the case that high confidence stems from a pronounced mastery-oriented motivation (McInerney &

Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

C.M. Roebers et al. / Learning and Individual Differences xxx (2012) xxx–xxx

Sinclair, 1991), and thus individuals' mastery-oriented motivation should also be included. This approach was realized in the present study.

1.3. A developmental perspective of self-regulated learning The majority of theoretical accounts on self-regulated learning and studies on its constituents focus on adults. Whether and to what extent these models and the related empirical findings generate to children and adolescents is an issue that is underrepresented in the literature. A developmental perspective on interrelations between motivation, metacognition, and cognitive performance thereby necessarily embraces (a) the question of factorial equivalence across different ages and (b) the question of age-dependent patterns of the interplay of the involved constructs. These issues will briefly be addressed in the following paragraphs. Confidence judgments mirroring an individual's stable person characteristic of self-confidence has been shown to be comparable to adults' self-confidence from an age of 11 years on (Kleitman & Mascrop, 2010). Confidence judgments mirroring a child's metacognitive ability to differentiate between correct and incorrect responses (estimations of correctness) appear to be quantifiable from the age of 8 to 9 years on (Roebers, 2002; Von der Linden & Roebers, 2006). Nevertheless, accuracy of these “cool” monitoring processes (reliably giving higher confidence judgments to correct than to incorrect answers) appears to depend more strongly on favorable task conditions and memory properties in younger compared to older elementary school children (Roebers, von der Linden, & Howie, 2007), and to undergo changes in terms of consistency of judgments across different tasks and measures in the late elementary school years (Roebers, von der Linden, Schneider et al., 2007; van der Stel & Veenman, 2008). Children below the age of 8 years are consistently found to strongly overestimate their performance (e.g., Schneider, 1998; Shin et al., 2007; Yussen & Berman, 1981). A young child's persistent overconfidence despite practice, feedback, and experiences (e.g., Lipko, Dunlosky, & Merriman, 2009) may in fact — at least to a certain extent — mirror self-confidence in the sense of a person characteristic (and thus to a certain extent a self-serving bias), that is typically interpreted as a protective factor in ontogeny (e.g., Bjorklund & Bering, 2002; Dunlosky & Rawson, in press). In line with the expected positive effects of high confidence for effort investment, individual differences in children's overconfidence have been found to be associated with smaller decreases in learning outcomes in a multi-trial experimental approach (i.e., under repeated testing conditions; Shin et al., 2007; for a recent review of early and emerging metacognitive skills and their development see Roebers, in press). Thus, it is questionable whether confidence judgments measure the same construct when children of different ages are included in one study, with the expectation that the younger the participants, the more strongly confidence judgments reflect a person characteristic and yield a direct and positive effect on performance (Kleitman & Stankov, 2007; Shin et al., 2007). Moreover, this self-serving confidence factor is expected to be more closely related to masteryoriented motivation (Kleitman & Gibson, 2011), compared to a metacognitive confidence factor that should be directly and negatively associated with control behavior in a test situation (lower confidence yielding to superior control). In fact, previous studies on the relation between metacognitive monitoring and subsequent control behavior suggest age-dependent differences in the link between monitoring and control, with this relation being direct and closer in older compared to younger elementary school children (de Bruin, Thiede, Camp, & Redford, 2011; Krebs & Roebers, 2010, 2012; Schneider, Körkel, & Weinert, 1987; van der Stel, Veenman, Deelen, & Haenen, 2010).

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1.4. The present study Based on more recent and broader theoretical frameworks of self-regulated learning, the interrelations between students' masteryoriented motivation, metacognitive monitoring, and control processes, as well as their relations to test performance were investigated in the present study. By these means, an integration of one distal factor (students' mastery-oriented motivation) and proximal factors (monitoring and control) into the prediction of academic performance is achieved. Because existing findings have produced mixed and sometimes contradictory results depending on the chosen age groups, the measures used (e.g., confidence for correct vs. incorrect answers vs. self-confidence), and the assumed structural links (monitoring impacts control vs. monitoring impacts performance; control impacts performance), younger (3rd graders) and older (5th graders) elementary school children were included in the present study testing the factorial and structural invariance of the included factors across age. As Dunlosky and Rawson (in press) have recently outlined, self-regulated learning activities are not equivalent to test taking behavior, especially when the effects of motivation and monitoring are considered. Because there is a predominance of studies addressing self-regulated learning processes in the context of learning situations (de Bruin & van Gog, 2012; Rhodes & Tauber, 2011), the current study focuses on test taking behavior. With regard to the targeted question of age-invariance of the factors included, we expected that monitoring and control would differ across age groups: Precisely, we anticipated that the correction and detection of errors as indicator of effective control and confidence judgments as indicator of monitoring were more accurate representations in older compared to younger children, as younger children's metacognitive skills are more prone to contextual biases, task specifics, and general self-serving biases (Roebers, in press). As to the assumed structural links between motivation, monitoring, and control, we expected to find closer interrelations between monitoring, control, and performance in older compared to younger children, as substantial developmental progression in these skills is still on its way in this age range (Krebs & Roebers, 2010, 2012; Roebers, Schmid, & Roderer, 2009; Schneider & Lockl, 2008). That is, better monitoring skills (here, lower confidence for incorrect answers) will be more closely linked to efficient control, and more developed control skills will yield a stronger positive effect on test performance in older compared to younger students. Moreover, we aimed to explore the effects of monitoring on both, performance and controlling, that may possibly point to a double-edged sword: high confidence may impede efficient controlling (detection and correction of errors; e.g., Krebs & Roebers, 2010, 2012) but, at the same time, yield a positive effect on performance through self-confidence (Kleitman & Gibson, 2011). Students' general masteryoriented motivation was expected to yield positive effects on confidence (high motivation linked to high confidence), adequate control behavior and on performance (for a recent review, see Wigfield & Cambria, 2010). 2. Method 2.1. Sample A total sample of N = 305 children (47% female, 53% male) completed the study. There were N = 158 children in 3rd grade with a mean age of 9 years and 1 month (SD = 5.7 months) and N = 147 participants in 5th grade with a mean age of 11 years and 2 months (SD = 4.9 months). Children were recruited through different public schools in the vicinity of Bern, Switzerland, and came from lower to upper-middle class families, with 86% being native Swiss/German speakers. The remaining 14% children came from immigrant families but had sufficient language skills in German to attend regular classes and to participate in the study. Written parental consent was

Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

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obtained prior to the study; children gave oral approval for participating. 2.2. Material Relying on data and experiences from previous studies (see Krebs & Roebers, 2010, 2012; Roderer & Roebers, 2009; Roebers et al., 2009, a multi-phased experimental approach was chosen for the present study: In the first phase of the experiment, an educational film (7 minutes) from the German children's educational TV program ‘Die Sendung mit der Maus’ about the production of sugar from sugar beets was presented. For assessing recall and metacognitive monitoring and control skills in the second phase, a written cloze test including 18 items was applied. Test items were of different degrees of difficulty: 6 items were easy (item difficulty: proportion correct = .83), 7 items were difficult (.28), and 4 items were of medium difficulty (.66). To each answer, children gave confidence judgments of correctness (= monitoring) on 7-point Likert scales (Roebers, 2002; 1 = absolutely unconfident; 4 = indecisive; 7 = very confident). In the last phase, children were allowed to cross-out previously given answers (= metacognitive control). In order to explore the influence of mastery-oriented motivation on children's metacognitive processes and test performance, the 11 items of the mastery motivation subscale from the Inventory of School Motivation (ISM; McInerney & Ali, 2006; McInerney & Sinclair, 1991) assessing children's mastery orientation were utilized. The statements of this paper-and-pencil test were answered on a 5-point Likert scales with higher values indicating a higher level of motivation (1= strongly disagree; 3 = not sure; 5 = strongly agree). Examples of items are “I like to see that I am improving with my school work”, “I like being given the chance to do something again to improve my school outcomes”, “I try harder at school because I am interested in my work”, “I don't mind working a long time at schoolwork that I find interesting”. 2.3. Procedure Two experimenters visited each class on three afternoons separated by one week. On the first visit, children's mastery-oriented motivation in school was assessed through the corresponding subscale from the Inventory of School Motivation (e.g., McInerney & Sinclair, 1991). The questionnaires were distributed in the classroom and participants individually responded to the items. On the second visit, the experimenters presented the educational movie in smaller groups of 5 to 12 children. Children were told to pay close attention as we were interested to find out what children — in general — can learn from watching television. The movie was shown a second time one week later on the third visit in order to ensure sufficient knowledge acquisition (Michel, Roebers, & Schneider, 2007). This time, children were explained that there was an upcoming test on the film content and that they may have already forgotten some details. Following the second film presentation, the experimenters distributed the cloze test on the educational film. The cloze test consisted of written statements about the contents of the film with one keyword missing in the sentence that children had to fill in (e.g., “The sugar beets have a _____________ color.”). In order to explore the influence of metacognitive monitoring on subsequent controlling, the above-mentioned multi-phased approach was realized at this stage: In the first test-taking phase, children filled out every blank of the cloze test (forced report) leading to confidence judgments to every answer. Then, in the second phase (i.e., monitoring), children were instructed to give confidence judgments to every answer on a 7-point-Likert scale using a differently colored pen. The rationale of the confidence scale was illustrated by one experimenter, and examples for low, medium, and high confidence were given. Without exception, the use of the scale was easily understood by the children. In the following last phase (i.e., control), participants were given the option to cross-out answers (again with a differently colored pen allowing

to clearly separate the different phases of the experiment for the later analyses) that they believed to be incorrect and asked to work as accurately as possible; no further instructions were given. At the end of the experiment, all participants received positive feedback and were allowed to choose a small gift. 2.4. Dependent measures Test accuracy, metacognitive monitoring and control were quantified through the cloze test that consisted of 22 items, with 18 items and confidence judgments used for the analyses. Four additional items were very easy (over 98% of the participants answered them correctly) and therefore served as filler items. To examine monitoring, confidence judgments were averaged as a function of correctness of the respective given answer. Confidence judgments for answers that had turned out to be incorrect were used as indicator of the latent variable “metacognitive monitoring” (see below) as in this measure the confound with performance is avoided and as developmental progression in monitoring has mostly been documented with respect to the confidence in incorrect responses (Roebers, von der Linden, & Howie, 2007; Roebers, von der Linden, Schneider et al., 2007; Von der Linden & Roebers, 2006). Therefore, the mean level of confidence judgments for items that had been answered incorrectly was computed. As to the measure of metacognitive control, the number of answers correctly maintained or adequately crossed-out (to the benefit of test accuracy) in the control phase was calculated. Test performance was mapped as “test accuracy,” calculated with the number of correct answers divided by the overall number of answers (correct and incorrect answers) in the final phase of the experiment. Concerning mastery-oriented motivation, answers of the used questionnaire were averaged. All latent variables used for the structural equation models were built using item parcels (Little, Cunningham, Shahar, & Widaman, 2002): the latent variables of metacognitive monitoring, control, and test accuracy were indexed by item parcels including 6 items each with varying degrees of difficulty (with the identical items as basis for the parcels of monitoring, control, and test performance); the items assessing mastery-oriented motivation were randomly allocated to the three parcels, with parcels containing 3 or 4 items, respectively. 3. Results The following section is divided into several parts: first, descriptive statistics and results on developmental progression concerning metacognitive monitoring and control in the participating children is provided. Then, as major part of the results, structural equation models will be presented testing first the factorial invariance and then the structural relations between children's monitoring, control, mastery-oriented motivation, and test performance. 3.1. Test performance As monitoring and control processes are based on recall, the percentages of correct answers in the first, forced report phase of the experiment shall be reported: Overall, the younger children recalled M = 52% (SD= 15%) of the 18 items that were used for the analyses correctly, while the recall of the older children was significantly higher, F (1, 303)= 43.77, p b .001, η 2 = .13, with M= 64% (SD= 16%) correctly recalled items. 3.2. Metacognitive monitoring and control In order to explore whether children monitored their confidence for the answers adequately, confidence judgments for correct and incorrect answers were compared. An ANOVA with age as between-subjects factor and correctness of answer as within-subject factor revealed a

Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

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main effect of correctness of answer, F (1, 303) = 894.59, p b .001, η 2 = .74, and an interaction between correctness of answer and age, F (1, 303) = 11.15, p b .01, η 2 = .04. In line with many previous studies (e.g., Krebs & Roebers, 2010, 2012; Roebers, 2002; Schneider & Lockl, 2008), these results indicate that although a majority of the children metacognitively differentiated between correct and incorrect answers in a relative satisfactory manner, the older compared to the younger children showed superior metacognitive monitoring performance. Inspection of Table 1 reveals that there were no age-related differences in the level of confidence regarding correct answers. However and as expected, older compared to younger children gave lower confidence judgments for incorrect answers. Hence, older children's more accurate monitoring was mainly due to lower confidence in incorrect answers. Therefore and because monitoring of incorrect answers is more important for control behavior than monitoring of correct answers, confidence judgments of incorrect answers were used as indicator for the latent variable “metacognitive monitoring” in the structural equation models below. Metacognitive control was assessed in the last phase of the experimental approach when participants were given the option to cross-out previously given answers, for example, because they were unsure about their correctness. Overall, about 76% (see Table 2: incorrectly+correctly maintained) of the initial answers of the 9-year-olds were maintained while approximately 24% (correctly+incorrectly crossed-out) were crossed-out. In the 11-year-olds, about 80% of the initial answers were maintained and approximately 20% were crossed-out. In an ANOVA, percentages of answers that were crossed-out and percentages of answers that participants maintained (i.e., correcting behavior) were compared as a function of correctness of the corresponding answer and age. Main effects of correcting behavior (crossing-out or maintaining answers), F (1, 303) = 547.18, p b .001, η 2 = .95, and correctness of answer, F (1, 303) = 4.17, p b .05, η 2 = .01, were observed. These main effects were qualified through a significant three-way interaction between correcting behavior, correctness of answer, and age, F (1, 303) = 43.17, p b .001, η 2 = .13. As was found in previous studies (Krebs & Roebers, 2010, 2012) and as depicted in Table 2, these findings indicate that overall and in relation to all 18 items considered, more correct than incorrect answers were maintained and more incorrect compared to correct answers were crossed-out. These differences in correcting behavior were more pronounced in older as opposed to younger children. Moreover, the systematic differences between correct and incorrect answers were more accentuated considering maintained compared to the crossed-out answers: Inspection of Table 2 reveals that metacognitive control indexed as “crossed-out answers” was appropriate and comparable across both age groups. In contrast, older children adequately maintained more correct and also maintained less incorrect answers than younger children. This result is also mirrored in a higher proportion of correct vs. incorrect items that were maintained in this age group, while the participating 9-year-olds maintained about the same number of correct and incorrect answers. Based on these results, adequate metacognitive control (percentages of correct answers maintained plus percentages incorrect answers crossed-out) was used as a latent variable in the following structural equation models. 3.3. Structural equation modeling To investigate the links between metacognitive processes, school motivation, and test performance, structural equation modelling was realized using AMOS 18 software (Arbuckle, 2009). In order to handle missing data, the full information likelihood approach was administered which is considered as producing the least biased and most efficient estimates (Peugh & Enders, 2004). The Chi 2-value (χ 2), the Tucker–Lewis index (TLI), the comparative fit index (CFI), and the root-mean-square error of approximation (RMSEA) were used to assess the model's fit. Thereby, a good model fit is indicated

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Table 1 Monitoring: mean confidence judgments for correct and incorrect answers as a function of age (min = 1; max = 7; higher values indicate higher confidence; standard deviations appear in parenthesis). Confidence judgments

9-year-olds 11-year-olds

Correct answer

Incorrect answer

5.7 (.07) 5.9 (.07)

4.1 (.09) 3.8 (.09)

by TLI- and CFI-values greater than .95, a RMSEA-value smaller or equal than .06, and a χ 2-value that is ideally not significant, however, that tends to be significant in larger samples as the present one (see Byrne, 2001; Hu & Bentler, 1998). Figs. 1 and 2 illustrate the structural equation model that was used for testing the hypothesis that there are substantial and direct associations between metacognitive processes, mastery-oriented motivation, and test performance among 9- (Fig. 1) and 11-year-olds (Fig. 2). Due to the specifics of the experimental multi-phased paradigm in the current study, it was further tested if monitoring has a direct effect on students' subsequent control (but not vice versa). In the model, monitoring was indexed by confidence judgments given to incorrect answers, controlling by adequate controlling, and motivation by mastery-oriented motivation. Factor loadings and path coefficients were estimated separately for the 9- and 11-year-olds and are depicted in Table 3. The model was drawn fully recurrent, that is, any path between any two variables was allowed and estimated. Covariances between the residuals of all indicators derived from the cloze test were allowed as these parcels contained the identical items from the cloze test, and were thus all linked to initial recall.

3.4. Testing for factorial invariance of the constructs across age-groups One major issue to be addressed with the present data concerned the age-dependent or age-invariant measurement of metacognitive monitoring and control, or the question if an age-invariant weighting of the indicators onto their latent variables is acceptable. Therefore, a model was tested in which the factor loadings of the indicators onto their latent variables were held constant in both age groups. The fit of such an age-invariant factorial model was compared with a factorial model allowing varying factor loadings of the indicators for the two age groups. Thus, in a first step of the structural equation modelling, our model's fit to the data with equal factor loadings for 9- and 11-year-olds was compared with a model's fit without assuming equal factor loadings between the two age groups. The model including unequal factor loadings had a good fit to the data, χ2 (78, 305) =90.86, p = .15, TLI = .970, CFI= .985, and RMSEA= .023. However, when comparing this model with the model assuming age-invariant factor loadings, there was no deterioration in the model's fit, χ2 (86, 305)= 93.50, p = .27, TLI= .984, CFI = .991, and RMSEA = .017. Table 3 depicts the final factor loadings of the parcels onto their latent variables, for the

Table 2 Control: mean number of answers crossed-out and maintained in percentages (of all 18 items) as a function of age and correctness of answer (standard deviations appear in parenthesis). % Crossed-out

9-year-olds 11-year-olds

% Maintained

Correct answers

Incorrect answers

Correct answers

Incorrect answers

4.7 (6.4) 4.6 (5.6)

18.9 (15.8) 15.1 (13.3)

47.6 (17.3) 59.5 (17.2)

28.3 (16.3) 20.3 (12.9)

Note: Although testing was realized in small group setting, and although children were urged to fill in a keyword in every blank of the cloze test, a very small proportion of keyterms in the cloze test were missing (0.5% altogether). This is why the values do not perfectly add up to 100% in Table 2.

Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

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9-year-olds

Table 3 Factor loadings of the indicators on the latent variables in 9- and 11-year-olds as shown in Figs. 1 and 2.

Metacognitive Monitoring

Latent variable

Standardized factor loadings

.76**

.08

55% -.23

Motivation

Metacognitive monitoring

Test Performance

-.01

Metacognitive control

.13 -.08 Metacognitive Control

Motivation

Fig. 1. Resulting structural equation model for the 9-year-olds (standardized factor loadings onto the latent variables are presented in Table 3).

Test performance

Parcel Parcel Parcel Parcel Parcel Parcel Parcel Parcel Parcel Parcel Parcel Parcel

1 2 3 1 2 3 1 2 3 1 2 3

9-year-olds

11-year-olds

.63⁎⁎⁎ .63⁎⁎⁎ .62⁎⁎⁎ .57⁎⁎⁎ .74⁎⁎⁎ .36⁎⁎⁎ .63⁎⁎⁎ .78⁎⁎⁎ .69⁎⁎⁎ .67⁎⁎⁎ .71⁎⁎⁎ .79⁎⁎⁎

.59⁎⁎⁎ .67⁎⁎⁎ .61⁎⁎⁎ .62⁎⁎⁎ .76⁎⁎⁎ .39⁎⁎⁎ .75⁎⁎⁎ .82⁎⁎⁎ .72⁎⁎⁎ .73⁎⁎⁎ .72⁎⁎⁎ .73⁎⁎⁎

⁎⁎⁎ p b .001.

two age groups separately. All standardized factor loadings were significant at p b .001. Despite the small differences in factor loadings, for the subsequent analyses, age-invariance of the factorial structure of the constructs, that is, the relative weighting of the single indicators were held constant as these differences were found to be non-significant. 3.5. Age-invariant structural links between motivation, metacognitive processes, and test performance In a next step of the analyses, it was tested whether motivation (indexed by mastery-oriented motivation) had the same influence on monitoring, control, and test performance in 9- compared to 11-year-olds. In other words, in this step of the analyses only the structural paths involving mastery-oriented motivation were held constant by setting the path coefficients from motivation to the other latent variables as equal in both age groups. This resulted in a very good model's fit, χ2 (89, 305)= 95.49, p = .30, TLI = .987, CFI =.993, and RMSEA= .016. This model did not differ significantly in terms of fit from a model assuming age-dependent path coefficients for the two age groups, with the change in the model's fit being χ2 (3, 305)= 1.99, p = .57, n.s. Thus, age-invariance of the structural links involving mastery-orientation was assumed. In a last step, this structural model was contrasted with a structural model that now assumed age-independent structural relations between all exogenous and endogenous variables. In this model, all path coefficients involving mastery-oriented motivation, metacognitive monitoring, and control were held constant across the two age groups. Results revealed a significant decline in the model's fit when age-invariance of the structural links involving metacognitive monitoring, control, and performance were additionally assumed. Although this overall model's fit was still acceptable, χ2 (92, 305)= 104.83, p = .17, TLI = .975, CFI =.985, and RMSEA = .021, the structural model with only the path coefficients involving mastery-oriented motivation as

11-year-olds Metacognitive Monitoring .52***

.08

26%

-.30** Motivation

Test Performance

-.01

-.09

.28** Metacognitive Control

being age-invariant was chosen to optimally represent the our data. This is because there was a significant decrease of the model's fit when all paths were assumed to be age-invariant compared to the model with only age-invariant paths from mastery-oriented motivation onto the other variables, χ2 (3, 305)= 9.34, p = .03. This is the final model presented in Figs. 1 and 2 for the 9- and for the 11-year-olds, respectively, with the corresponding factor loadings of the parcels as a function of age group for these models being shown in Table 3. The overall model's fit of this final model for both age groups was very good, with χ2 (89, 305) = 95.49, p = .30, TLI = .987, CFI = .993, and RMSEA= .016 (see above). Starting with the younger sample, inspection of Fig. 1 reveals that there were neither significant links between mastery-oriented motivation and metacognitive processes, nor between mastery-oriented motivation and test performance. Individual differences in metacognitive monitoring were found to have a strong and positive effect on test performance. The link between monitoring and subsequent metacognitive control missed significance (p = 0.68). Importantly, 9-year-olds' control behavior had no substantial effect on test performance. Thus, for the younger children a picture of structural links between the included variables emerged suggesting that individual differences in test performance are substantially influenced by children's ability to monitor incorrect answers adequately (indicate low confidence), but not by motivation or their metacognitive control skills. Together, 55% of the variance in test performance was explained by the included variables. Turning to the older sample, Fig. 2 presents the structural links between the included variables in 11-year-olds. As can be seen and as has been found for the 9-year-olds, mastery-oriented motivation was not related to metacognitive processes and test performance. Metacognitive monitoring was significantly related to both, test performance and metacognitive control. Thereby, monitoring yielded a positive direct effect on test performance and a negative direct effect on control. Moreover, individual differences in metacognitive control had a substantial, direct and positive impact on test performance in the 11-year-olds. That is, in the sample of 11-year-olds, lower confidence ratings concerning incorrect answers were associated with more sophisticated control behavior and subsequent superior test performance. In other words, in addition to the direct effect of monitoring on test performance, there was also an indirect effect of monitoring via metacognitive control. Noteworthy, although the structural links were closer in the older compared to the younger age group, less variance in test performance was explained with the included variables (26%). 4. Discussion

Fig. 2. Resulting structural equation model for 11-year-olds (standardized factor loadings onto the latent variables are presented in Table 3).

A major issue of the present study concerned the question of age-invariance of the included constituents of self-regulated learning

Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

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in two age groups of elementary school children. Results revealed a factorial invariance that embraced mastery-oriented motivation, metacognitive monitoring, control, and test performance. It seems therefore reasonable conclude that we were able to measure these constructs in a way that was comparable across the two age groups. Item number, item difficulty and variation in item difficulty of the included variables were good, allowing a well-balanced mapping of item parcels onto their latent variables. Finding factorial invariance across age-groups is not trivial as the literature offers ample evidence that the nature of psychological constructs and measures changes significantly over the course of development (for a review, see Roebers, in press). For example, the fact that mastery-oriented motivation and monitoring judgments could be mapped onto their latent variables and still produce a very good fit to the data suggests that even in 9-year-old children these factor mirror distinguishable and separable psychological factors. We are aware that we focused on a relatively narrow age window as a first step and therefore suggest that future studies should explore whether the factorial invariance holds true for even younger children who are more prone for a general self-serving overoptimistic bias of their achievements (Shin et al., 2007). In a similar vein, mastery-oriented motivation was empirically distinct from control behavior executed in a test situation, again in both age groups. This is interesting as previous studies on children's control behavior in a test taking situation were not able to unambiguously separate motivational factors (Krebs & Roebers, 2010, 2012; Roebers et al., 2009). Thus, the present structural equation modelling approach for studying motivation, monitoring, and control supports the notion that these constructs can be operationalized similarly in 9- to 11-year-olds and thereby mirror comparable contents. In contrast to the documented age-invariance of the included factors, structural equation modelling techniques revealed that there was no structural invariance among the included variables between 9- and 11-year-olds. As inspection of Figs. 1 and 2 reveals, it is especially the interplay between monitoring, control, and test performance that underlies a developmental change. Although the direction of the paths was comparable across both age groups, a closer and more sophisticated interplay between monitoring and control on resulting test performance was found in the older compared to the younger participants. This is an important finding as in many developmental studies the adequacy of monitoring and/or control is addressed (Schneider, 2010), but individual differences in their interplay is less often targeted directly. We not only documented developmental progression in both, monitoring and control (see Tables 1 and 2), but also developmental change towards a substantial influence of prior monitoring on control, as well as of control on resulting test performance. Thus, fifth graders who are better able to metacognitively distinguish between correct and incorrect answers by experiencing lower confidence for incorrect answers will initiate more adequate control behavior by more often maintaining the correct answers and by more reliably crossing-out answers that would in fact have been incorrect. The individual differences approach thereby confirms the experimental cognitive development literature but also extends our knowledge on this interplay by estimating the magnitude of the effects. It is important to consider that these interrelations were far from perfect. Detailed knowledge of the interplay among the involved cognitive processes may nevertheless provide a starting point for effective interventions aiming to improve students' test taking cognitions and behavior. Thus, the structural links between metacognitive processes and test performance were closer in 11-year-olds than in 9-year-olds. At the same time, there were differences in the amounts of explained variance in test performance between the two age groups, with more variance of test performance being explained in the younger compared to the older children. As the model was found to have a very good fit to the data, it seems safe to conclude that it mirrors adequately the interplay between the included variables. The smaller

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amount of explained variance may then point to the fact that other variables (not included in the present study) become more important with increasing age. One such candidate factor may be general and prior knowledge as domain-specific knowledge has repeatedly been found to be the strongest predictor for academic outcomes and as domain-specific knowledge was undoubtedly important for the science test used in the present study (e.g., Watkins, Lei, & Canivez, 2007). This constitutes a limitation of the current approach and studies including additional indicators of test performance are warranted. Fluid and crystallized intelligence are additional candidate factors that may explain individual differences in test performance, probably independent of participants' age (e.g., Jensen, 1998; Watkins et al., 2007). Thus, the present findings may stimulate future studies including and determining factors yielding substantial impacts on students' test performance, over and above metacognitive processes. From a theoretical perspective, the impact of students' masteryoriented motivation is clear by assuming direct effects on learning (see Wigfield & Cambria, 2010). Our study failed to confirm these links (see also Kleitman & Mascrop, 2010), although mastery-oriented motivation was assessed with a classical instrument. One reason for why we did not find a direct effect of motivation on test taking may lie in the fact that by the nature of our study academic achievement was operationalized with one single test. Mastery-oriented motivation as assessed in the present study taps generalized, long-term achievement goals and learning behavior but this may not be directly involved in making situation-specific decisions on effort investment, persistence, employment of control strategies in one specific test situation. Alternatively, a distinction between distal (learning motivation) and proximal (procedural metacognitions but also test motivation) factors may provide an explanation for the unexpected non-significant link. Another reason may be found in the specific age groups included: A student's general, trait-like mastery-oriented motivation may possibly only exert its influence later in development through continuous learning and test experiences in school. Following-up on this interpretation, theoretical models of self-regulated learning may possibly need to be conceptualized differently depending on the age of the targeted population. Although further evidence is clearly needed, the present findings seem to suggest that the influence of a distal factor such as motivation on academic outcomes may be difficult to empirically confirm when (a) children instead of adults are included, and (b) proximal powerful online (meta-)cognitive processes are simultaneously taken into account. As outlined in Introduction, different bodies of literature suggest diverging links between monitoring and test performance. When monitoring in the form of overall self-confidence is considered, there is theoretical and empirical evidence (stemming from both adults and children) that higher confidence is associated with better test performance (Kleitman & Gibson, 2011; Kleitman & Stankov, 2007; Shin et al., 2007). When monitoring is operationalized and used in cognitive psychology, both theoretical and empirical perspectives assume a negative relation with a learner's control strategies, with high confidence hindering effective control such as the detection and correction of errors in a test situation (Krebs & Roebers, 2010, 2012; Roebers et al., 2009). Intriguingly, the present study revealed both, a positive link between monitoring and test performance (high confidence being linked to better test scores) and a negative link to control (high confidence being associated with inefficient control). As monitoring was indexed by confidence in answers that all turned out to be incorrect, we can rule out the possibility that confidence and overall capabilities are confounded. To our knowledge, this is the first study to reveal both a positive effect of high confidence on performance and a negative effect of high confidence on adequate control simultaneously that definitely deserve further research attention. Future studies would need to include personality characteristics (e.g., self-concept; extraversion), and more and other measures of metacognitive monitoring with the aim to better disentangle these different effects. In other words,

Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003

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the underlying mechanisms contributing to these effects between monitoring and performance should be addressed in future investigations. There are widely acknowledged advantages of structural equation modelling techniques, such as error-free estimation of the variables and testing multiple links among variables simultaneously. At the same time, as measures of monitoring, control, and test performance were derived from the same tasks by the nature of the present approach, it is possible that the estimation of the structural links became somewhat inflated due to shared variance linked to the task itself. But, online metacognitive processes as the ones quantified in this study are always task-specific and task-bound; that is the very nature of such metacognitive processes. In a recent study on 8-year-olds' metacognitive monitoring and control skills in the context of a spelling task, even stronger structural links between confidence, control, and test performance were found compared to the present study (Roebers, Cimeli, Röthlisberger, & Neuenschwander, 2012), thereby somewhat attenuating an interpretation of inflated paths between confidence judgments, control, and test performance in the present study. Taken together, the present study aimed at integrating a distal, motivational factor and proximal, metacognitive information processes in one study on individual differences in elementary school children's achievement test performance. Results thereby revealed a growing interplay between metacognitive monitoring, control, and test performance, with individual differences in monitoring apparently yielding to direct and positive effects on performance and direct negative effects on control (i.e., indirect positive effects on performance). Against the background of theoretical models of self-regulated learning, the present approach underlines the necessity to include various factors operating at different stages of task mastery for increasing our understanding concerning the mechanisms operating on the micro- and macro-level of self-regulated learning and test taking behavior. References Arbuckle, J. (2009). AMOS 18™ User's Guide. Crawfordville, FL: Amos Development Corporation. Bjorklund, D. F., & Bering, J. M. (2002). The evolved child applying evolutionary devlopmental psychology to modern schooling. Learning and Individual Differences, 12, 1–27, http://dx.doi.org/10.1016/S1041-6080(02)00047-X. Boekaerts, M. (1999). Self-regulated learning: Where we are today. International Journal of Educational Research, 31, 445–457, http://dx.doi.org/10.1016/S0883-0355(99)00014-2. Byrne, B. M. (2001). Structural equation modeling with AMOS. New Jersey, NJ: Lawrence Erlbaum. de Bruin, A. B. H., Thiede, K. W., Camp, G., & Redford, J. (2011). Generating keywords improves metacomprehension and self-regulation in elementary and middle school children. Journal of Experimental Child Psychology, 109, 294–310, http://dx.doi.org/ 10.1016/j.jecp. 2011.02.005. de Bruin, & van Gog (2012). Improving self-monitoring and self-regulation: From cognitive psychology to the classroom. Learning and Instruction, 22, 245–252, http://dx.doi.org/10.1016/j.learninstruc.2012.01.003. Dunlosky, J., & Metcalfe, J. (2009). Metacognition. Thousand Oaks, CA: Sage Publications. Dunlosky, J., & Rawson, K. A. (in press). Overconfidence produces underachievement: Inaccurate self-evaluations undermine students' learning and retention. Learning and Instruction, 22(4), 271–280. http://dx.doi.org/10.1016/j.learninstruc.2011.08.003. Efklides, A. (2006). Metacognitive experiences: The missing link in the self-regulated learning process. Educational Psychology Review, 18, 287–291, http://dx.doi.org/ 10.1007/s10648-006-9021-4. Efklides, A. (2008). Metacognition: Defining its facets and levels of functioning in relation to self-regulation and co-regulation. European Psychologist, 13, 277–287, http://dx.doi.org/10.1027/1016-9040.13.4.277. Efklides, A. (2011). Interactions of metacognition with motivation and affect in self-regulated learning: The MASRL model. Educational Psychologist, 46, 6–25, http://dx.doi.org/10.1080/00461520.2011.538645. Flavell, J. H., & Wellman, H. M. (1977). Metamemory. In R. V. Kail, & J. W. Hagen (Eds.), Perspectives on the development of memory and cognition (pp. 3–33). Hillsdale, NJ: Erlbaum. Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424–453, http://dx.doi.org/10.1037//1082-989X.3.4.424. Jensen, A. R. (1998). The g factor: The science of mental ability. Westport, CT: Praeger. Kleitman, S., & Gibson, J. (2011). Metacognitive beliefs, self-confidence and primary learning environment of sixth grade students. Learning and Individual Differences, 21, 728–735, http://dx.doi.org/10.1016/j.lindif.2011.08.003.

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Please cite this article as: Roebers, C.M., et al., Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance, Learning and Individual Differences (2012), http://dx.doi.org/10.1016/j.lindif.2012.12.003