Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks

Calibration, or the correspondence between perceived performance and actual performance, is linked to students’ metacognitive and self-regulatory skills. Making students more aware of the quality of their performance is important in elementary school settings, and more so when math problems are involved. However, many students seem to be poorly calibrated, with a tendency towards over-confidence. The present study analyzes the relationship between post-performance calibration accuracy and the metacognitive process shown by 524 fifth- and sixth-grade students while solving two math problems. After calculating a calibration index and establishing the stability of students’ judgments and actual performance, differences in the metacognitive process exhibited by students with different calibration accuracy (Accurate vs. Inaccurate groups) were analyzed. The emergence of different calibration patterns and differences in the metacognitive process as a function of mathematics achievement and grade level were also examined. Results indicated that: (a) students in the overall sample were little calibrated and over-confident, showing high stability in their judgments and actual performance across problems; (b) inaccurate students reported using information representation sub-processes (drawing/summarizing) less frequently, but writing and reviewing (and also correcting mistakes) more frequently than their accurate peers; and (c) differences in calibration patterns and the metacognitive process were found when achievement level was considered, whereas grade level did not generate any important effect. These findings suggest the usefulness of process-based measures to examine the metacognitive processes involved in making post-performance judgments, considering achievement and its possible mediating role in this relationship.     

Effects of Metacognitive Skills and Nonverbal Ability on Academic Achievement of High School Pupils

Two experiments were conducted with senior high school pupils in the North‐West Province of South Africa to examine relationships of metacognitive strategies and nonverbal reasoning ability to their performance in tests of mathematics and English comprehension. The analyses of data revealed that both metacognitive ability and nonverbal reasoning ability have significant positive association with mathematics and English achievement scores. Significant sex differences in mathematics performance were also found. The findings of the two experiments suggested that some intervention programmes to teach metacognitive strategies to students, who lack such skills, may improve their academic attainment     

Confidence in performance judgment accuracy: the unskilled and unaware effect revisited

Since its introduction in the late 1990s, the unskilled and unaware effect motivated several further studies. As it stands, low-performing students are assumed to provide inaccurate and overconfident performance judgments. However, as research with second-order judgments (SOJs) indicates, they apparently have some metacognitive awareness of this. The current study with 266 undergraduate students aimed to provide in-depth insights into both the reasons for (in)accurate performance judgments and the appropriateness of SOJs. We implemented a general linear mixed model (GLMM) approach to study item-specific performance judgments in the domain of mathematics at the person and item level. The analyses replicated the well-known effects. However, the GLMM analyses revealed that low-performing students’ lower confidence apparently did not indicate subjective awareness, given that these students made inappropriate SOJs (lower confidence in accurate than in inaccurate judgments). In addition, students’ self-generated explanations for their judgements indicated that low-performing students have difficulties recognizing that they possess topic knowledge to solve an item, whereas high-performing students struggle with admitting that they do not know the answer to a question. In sum, our results indicate that students at all performance levels have some metacognitive weaknesses, which, however, occur subject to different judgment accuracy.     

The differential impact of academic self-regulatory methods on academic achievement among university students with and without learning disabilities

Although research on academic self-regulation has proliferated in recent years, no studies have investigated the question of whether the perceived usefulness and the use of standard self-regulated learning strategies and compensation strategies provide a differential prediction of academic achievement for university students with and without learning disabilities (LD). We developed and tested a model explaining interrelationships among self-regulatory variables and grade point average (GPA) using structural equation modeling and multiple group analysis for students with LD (n = 53) and without LD (n = 421). Data were gathered using a new instrument, the Learning Strategies and Study Skills survey. The results of this study indicate that students with LD differed significantly from students without LD in the relationships between their motivation for and use of standard self-regulated learning strategies and compensation strategies, which in turn provided a differential explanation of academic achievement for students with and without LD. These paths of influence and idiosyncrasies of academic self-regulation among students with LD were interpreted in terms of social cognitive theory, metacognitive theory, and research conducted in the LD field.     

Teacher Judgments of Student Reading and Math Skills: Associations With Child- and Classroom-Related Factors

The purpose of the study was to examine whether students’ linguistic skills and task-avoidant behavior (i.e., the child-related factors) and the mean level of academic skills (reading comprehension and math) of classmates (i.e., the class-related factor) are associated with teacher judgments of children’s reading comprehension and math skills. The participants were third-grade Estonian-speaking students (n?=?656; age 9?11 years) and their classroom teachers (n?=?51). The results of the structural equation modeling path analyses indicated that teachers tend to judge students showing higher academic and linguistic skills and lower avoidance behavior as higher on the reading comprehension and math skills. In contrast, the classmates’ higher academic skill level was related to lower judgments of individual children’s reading comprehension and math skills by teachers.     

QuickSmart: a basic academic skills intervention for middle school students with learning difficulties

QuickSmart is a basic academic skills intervention designed for persistently low-achieving students in the middle years of schooling that aims to improve the automaticity of basic skills to improve higher-order processes, such as problem solving and comprehension, as measured on standardized tests. The QuickSmart instructional program consists of three structured, teacher- or teacher aide-directed, 30-minute, small-group lessons each week for approximately 26 weeks. In this study, 42 middle school students experiencing learning difficulties (LD) completed the QuickSmart reading program, and a further 42 students with LD took part in the QuickSmart mathematics program. To investigate the effects of the intervention, comparisons were made between the reading and mathematics progress of the intervention group and a group of 10 high-achieving and 10 average-achieving peers. The results indicated that although the standardized reading comprehension and mathematics scores of QuickSmart students remained below those of comparison students, they improved significantly from pretest to posttest. In contrast, the standardized scores of comparison students were not significantly different from pretest to posttest. On measures of response speed and accuracy gathered using the Cognitive Aptitude Assessment System (CAAS), QuickSmart students were able to narrow the gap between their performance and that of their high- and average-achieving peers. Implications are drawn regarding the importance of interventions that emphasize the automaticity of basic academic skills for students with learning difficulties.     

高职生英语学习障碍与元认知策略培养

高职生在英语学习过程中,大多存在学习障碍问题。究其原因,除了基础差、个人心理方面因素外,主要是由于缺乏元认知策略所致。缺少策略意识,不懂得有效运用相关学习策略计划、指导、评价和调整学习过程,是当前高职生英语学习中的通病。因此教师有必要培养学生元认知策略意识,帮助学生运用元认知策略计划、评价、调整和改进学习。     

What do second-order judgments tell us about low-performing students’ metacognitive awareness?

According to the unskilled and unaware effect (Kruger and Dunning 1999), low-performing students tend to overestimate their performance. Differentiating the assessment of metacognitive judgments into performance judgments (PJs) and second-order judgments (SOJs), PJs of low-performing students tend to be inflated, while their SOJs are usually lower than those of high-performing students (Händel and Fritzsche 2016; Miller and Geraci 2011). This suggests some level of awareness. The present study investigated whether low-performers’ lower SOJs actually indicate metacognitive awareness. We studied SOJs after adequate and inadequate PJs, and investigated whether low-performers’ lower SOJs are made by default or whether their lower SOJs differ in a similar magnitude compared to those of high-performers (indicating metacognitive awareness). We address this issue by disentangling student and item effects via generalized linear mixed models. Reanalyzing the data of Händel and Fritzsche (2016) from N?=?116 students, we found that SOJs depended on the students who provided the SOJ and on the items on which the SOJ was made. Overall, SOJs depended on the PJs and on the interaction of performance and PJs, but not on the performance itself. Separate analyses for students of different performance levels revealed that low-performing students showed less awareness, indicated by a non-significant interaction effect of performance and PJs. Thus, it takes mixed models to tell the whole story of low-performing students’ lower SOJs.     

Positive and Negative Self‐Perceptions: Is There a Cyclical Relationship Between Teachers' and Students' Perceptions of Effort,Strategy Use,and Academic Performance?

This study was part of a larger research program designed to investigate how effort interacts with strategy use to mediate the academic performance of successful students with learning disabilities (LD) and how teachers' and students' perceptions influence these relationships. The sample consisted of 46 students with LD and 46 matched students without LD and their seven teachers from Grades 6–8. A self‐report survey was used to obtain an index of students' perceptions of their effort, strategy use, academic struggles, and academic competence. Our findings indicated that students with LD with positive academic self‐perceptions were more likely to work hard and to use strategies in their schoolwork than were students with LD who had negative academic self‐perceptions. Teachers viewed students with LD who had positive academic self‐perceptions as working equally hard and attaining similar levels of academic competence as their peers without LD. In marked contrast, students with LD who had negative academic self‐perceptions were judged by their teachers as making limited effort in school and achieving at a below‐average level in comparison with their peers. Findings suggested a cyclical relationship between students' self‐perceptions and their teachers' judgments and supported the notion of a reciprocal strategy‐effort interaction.     

Using Explicit and Strategic Instruction to Teach Division Skills to Students With Learning Disabilities

Students with mathematics learning disabilities (LD) exhibit difficulties with retrieval and cognitive skills that impede their ability to perform basic mathematical skills. Instruction in mathematical procedures (i.e., procedural knowledge) is necessary to help students learn and apply skills such as basic facts and whole-number computation. Division is a skill that is identified in curriculum across the grade levels; yet, it is a skill that is often taught last in instructional sequences because of its complexity and prerequisite knowledge. Reviews of research have revealed that students with LD benefit from a combined model of academic instruction that includes both explicit and strategic instructional procedures. This article presents an overview of division instruction and a sample of interventions for teaching division that include explicit and strategic instructional procedures, which are found in the combined model of teaching.     

The relation between intellectual and metacognitive skills in early adolescence.

The first objective of this study was establishing to what extent metacognitive skill is associated with intelligence. As a second objective, the impact of hints on the execution of metacognitive skills was investigated. Both issues have major implications for the training and transferability of metacognitive skills during performance on a representative school task. First, a standardized intelligence-test was administered to a group of first-year secondary-school students. Next, these students solved six math word problems, three without metacognitive hints and three including these hints. Metacognitive skilfullness was assessed through systematical observation, while learning performance consisted of performance on a math task and grade point average (GPA). Results show that without hints metacognitive skilfulness is the main predictor of initial learning, while intelligence additionally enters the regression equation after the presentation of metacognitive hints. GPA also appears to be predicted by a combination of intellectual and metacognitive skills. Consequences for the early acquisition of metacognitive skills are discussed.     

Self‐Regulation and Mathematics Instruction

Abstract The purpose of this article is to provide an overview of research‐based interventions that incorporate self‐regulation strategies to improve mathematics performance of students with learning disabilities (LD). Self‐regulation is a metacognitive function essential to academic success. Students with LD are notoriously poor at self‐regulation and must be taught explicitly to monitor and control their cognitive activities as they engage in academic tasks such as mathematical problem solving. This article describes intervention studies that use self‐regulation strategies to improve mathematics performance of students with LD at the elementary, middle, and secondary school levels. Several techniques to facilitate effective implementation of self‐regulation instruction in the classroom are presented.     

元认知对中学生运动技能学习的影响研究

本文首先对元认知及元认知在体育领域的发展现状进行了阐述,并采用调查法对长春市初中生使用元认知的情况及制定实验方案对体育课上学生运用元认知学习运动技能的成绩情况进行分析,从而得出它对体育运动技能学习的重要性。     

Enhanced monitoring accuracy and test performance: Incremental effects of judgment training over and above repeated testing

From a self-regulated learning perspective, adequate monitoring of own learning processes and outcomes is crucial to regulate one's own learning effectively. Research on metacognitive judgments, however, clearly indicates that students frequently overestimate their actual performance. Therefore, the present study with N = 209 undergraduate students aimed to support students in developing accurate judgments in order to improve learning processes and, eventually, performance. A quasi-experimental design with three conditions (metacognitive training, testing, and control) and five testing sessions was implemented. In addition to repeated testing plus individual feedback in the testing group, students in the metacognitive training group received psychoeducation, made item-specific judgments, and were given feedback. Over and above the positive effects of repeated testing, metacognitive training positively influenced several monitoring accuracy scores (bias, absolute accuracy, and specificity) and students' performance. Moreover, the metacognitive training group exhibited a nonlinear interindividual decrease in overconfidence. Overall, the study provided considerable evidence that monitoring accuracy and performance can be improved by means of judgment training.     

Developing Student Metacognition through Reflective Writing in an Upper Level Undergraduate Anatomy Course

Incorporating metacognitive strategies in the classroom helps students monitor and adjust their learning strategies throughout the semester, and helps students progress from novice to expert learners in a subject. Journaling (i.e., reflective writing) is one metacognitive task that allows students to contemplate and articulate their skill development as they learn a new subject. The research reported here examines the use of ‘blogs’ (i.e., online journals) in an upper level undergraduate human anatomy course. The blogs both facilitated development of students' metacognitive skills and provided researchers insight into student metacognitive process. Data were examined from 92 students from three successive semesters (spring 2010, 2012 and 2014). Each student reviewed 10 radiology online cases throughout the semester and then reflected on their understanding of anatomy and radiology in an online blog for each case. A total of 927 blogs were examined for this research. The researchers used a grounded theory approach to analyze the blog narratives and develop a codebook based on common themes. The 927 blogs yielded 11,082 statements that were coded with the codebook. As the semester progressed, the blog entries showed that students demonstrated greater self-confidence in their abilities to understand the subject matter, expressed greater enthusiasm for anatomy in general, and they improved their metacognitive skills. This research illustrates that reflective writing in an undergraduate anatomy course not only facilitates improvement in student metacognitive skills, but also provides the instructor with evidence how a student progresses from novice to more experienced learner in anatomy.     

Comparison of student marks obtained by an assessment panel reveals generic problem-solving skills and academic ability as distinct skill sets

Generic problem-solving skills have been identified as one of the key competencies valued by professional programmes, university students and their future employers. A lack of widely available and simple testing tools prevents assessment of the development of student problem-solving skills. As part of a research study, a generic problem-solving test was administered to 130 third-year science students during three consecutive years. A comparison between the scores students achieved in this test with their six academic marks obtained in this course showed no significant correlation. Lack of correlation between the problem-solving skill test scores and academic marks of students was confirmed in a larger population of students participating in a campus-wide study of generic problem-solving skills (n = 830). Problem solving and academic performance may represent two independent skill sets of students; testing problem-solving skills of students could be introduced to achieve a more comprehensive evaluation of undergraduate student progress and achievement.     

Development of metacognitive skillfulness: A longitudinal study

This study shows the results of a two-year longitudinal study where the same participants were followed for two consecutive years as they enter secondary school (aged 12–14 years). The main issue was to investigate the development of both the quantity and the quality of metacognitive skills. Another issue was to establish whether the development of metacognitive skillfulness is intelligence-related or relatively intelligence-independent. Finally, the generality vs. domain-specificity of developing metacognitive skillfulness was investigated. Thirty-two secondary school students participated in this study. While thinking aloud they performed two different tasks representing two different domains: A text-studying task for history and a problem-solving task for math. Participants' intellectual ability, metacognitive skillfulness and learning performance were assessed. Results show a quantitative as well as a qualitative growth in metacognitive skillfulness. Furthermore, results of both years show that metacognitive skillfulness contributed to learning performance (partly) independent of intellectual ability. A parallel development of metacognitive and intellectual ability was found. Finally, metacognitive skills predominantly appear to be general. Domain-specific metacognitive skills, however, played a substantial, but minor role as well in both years. Instructional implications are being discussed.     

Improving metacognition in the classroom through instruction,training, and feedback

Accurately judging one’s performance in the classroom can be challenging considering most students tend to be overconfident and overestimate their actual performance. The current work draws upon the metacognition and decision making literatures to examine improving metacognition in the classroom. Using historical data from several semesters of an upper-level undergraduate course (N?=?127), we analyzed students’ judgments of their performance and their actual performance for two exams. Students were instructed on the concepts of overconfidence, received feedback on exams, and were given incentives for accurate calibration. We found results consistent with the “unskilled and unaware” effect Kruger & Dunning (Journal of Personality and Social Psychology, 77(6), 1121–1134, 1999) where lower performing students initially displayed overconfidence and the highest performing students initially displayed underconfidence. Importantly, students were able to change both judgments and performance such that metacognitive accuracy improved significantly from the first to the second exam. In a second study, two additional semesters for the same course used in Study 1 were examined (N?=?90). For one of the semesters feedback was not provided, allowing us to determine whether feedback can improve both metacognitive judgments and performance. Our findings revealed significant improvements in performance paired with decreases in overconfidence on Exam 2, but only for students who received feedback about their performance and judgments. We postulate that feedback may be an important component in improvement metacognitive judgments.     

Predicting performance on academic and non-academic tasks: A comparison of adolescents with and without learning disabilities

Previous research suggests that adolescents with learning disabilities (LD) are less accurate in predicting academic performance than normally achieving (NA) adolescents and display a tendency to overestimate their level of performance (e.g., Klassen, 2007). However, no studies have been conducted investigating whether this overestimation is specific to academic contexts or a phenomenon that extends across domains. Ninety-four adolescents (46 LD, 48 NA) predicted their performance on a spelling task and on a ball-throwing task. Results revealed group differences in performance calibration across domains with adolescents with LD showing an overestimation of ability on the spelling and ball-throwing tasks, and NA adolescents demonstrating more precise self-appraisals. Additionally, the accuracy of non-academic performance predictions remained stable with increasing difficulty in the NA group whereas the adolescents with LD demonstrated a decrease in accurate performance prediction as the difficulty level increased.     

Differences in Metacognitive Regulation in Introductory Biology Students: When Prompts Are Not Enough

Strong metacognition skills are associated with learning outcomes and student performance. Metacognition includes metacognitive knowledge—our awareness of our thinking—and metacognitive regulation—how we control our thinking to facilitate learning. In this study, we targeted metacognitive regulation by guiding students through self-evaluation assignments following the first and second exams in a large introductory biology course (n = 245). We coded these assignments for evidence of three key metacognitive-regulation skills: monitoring, evaluating, and planning. We found that nearly all students were willing to take a different approach to studying but showed varying abilities to monitor, evaluate, and plan their learning strategies. Although many students were able to outline a study plan for the second exam that could effectively address issues they identified in preparing for the first exam, only half reported that they followed their plans. Our data suggest that prompting students to use metacognitive-regulation skills is effective for some students, but others need help with metacognitive knowledge to execute the learning strategies they select. Using these results, we propose a continuum of metacognitive regulation in introductory biology students. By refining this model through further study, we aim to more effectively target metacognitive development in undergraduate biology students.