Exploring the potential impact of reciprocal peer tutoring on higher education students’ metacognitive knowledge and regulation

It is widely recognized that metacognition is an important mediator for successful and high-level learning, especially in higher education. Nevertheless, a majority of higher education students possess insufficient metacognitive knowledge and regulation skills to self-regulate their learning adequately. This study explores the potential of reciprocal peer tutoring to promote both university students’ metacognitive knowledge and their metacognitive regulation skills. The study was conducted in a naturalistic higher education setting, involving 67 students tutoring each other during a complete semester. A multi-method pretest–posttest design was used combining a self-report questionnaire, assessing students’ metacognitive knowledge and their perceived metacognitive skilfulness, with the analysis of think-aloud protocols, revealing students’ actual use of metacognitive strategies. Results indicate no significant pretest to posttest differences in students’ metacognitive knowledge, nor in their perception of metacognitive skill use. In contrast, significant changes are observed in students’ actual metacognitive regulation. At posttest, students demonstrate significantly more frequent and more varied use of metacognitive regulation, especially during the orientation, monitoring, and evaluation phases. Furthermore, our findings point to an increase in more profound and higher-quality strategy use at posttest.     

Metacognitive learning strategies: differential development patterns in high school

The main objective of this study is to identify the development of students’ self-reported use of metacognitive learning strategies during high school. Therefore, the study analyses the differential development patterns of 1,432 students, between grade 10 and 12, in a longitudinal sample. The results suggest that, from a global perspective, there is no development of students’ self-reported use of metacognitive learning strategies during high school. The expected gender-specific differences in favour of female students are replicated in this sample. However, the self-reported use of monitoring and evaluation strategies tends to converge between genders during high school, whereas the differences in the self-reported use of planning strategies remain stable. The consequences for the understanding of metacognitive development are discussed.     

The Influence of Different Representations on Solving Concentration Problems at Elementary School

This study investigated the students’ learning process of the concept of concentration at the elementary school level in Taiwan. The influence of different representational types on the process of proportional reasoning was also explored. The participants included nineteen third-grade and eighteen fifth-grade students. Eye-tracking technology was used in conducting the experiment. The materials were adapted from Noelting’s (1980a) “orange juice test” experiment. All problems on concentration included three stages (the intuitive, the concrete operational, and the formal operational), and each problem was displayed in iconic and symbolic representations. The data were collected through eye-tracking technology and post-test interviews. The results showed that the representational types influenced students’ solving of concentration problems. Furthermore, the data on eye movement indicated that students used different strategies or rules to solve concentration problems at the different stages of the problems with different representational types. This study is intended to contribute to the understanding of elementary school students’ problem-solving strategies and the usability of eye-tracking technology in related studies.     

Approaches to learning and study orchestrations in high school students

In the framework of the SAL (Students’ approaches to learning) poosition, the learning experience (approaches to learning and study orchestrations) of 572 high school students was explored, examining its interrelationships with some personal and familial variables. Three major results emerged. First, links were found between family’s intellectual climate and students’ approaches to learning, in particular with Deep appraoch: The better the family’s intellectual climate the higher student’ scores on Deep approach. Second, along with general intelligence, these approaches predicted students’ academic achievement, higher grades being obtained by these students who scored lower in Surface learning approach and higher in Deep learning approach. Three, students from the four study orchestrations reported in previous research (two displaying conceptual consonance: Deep and Surface approaches, and the other two conceptual dissonance: high-high and low-low, in both Deep and Surface approaches) showed different profiles in some variables (e.g., metacognitive learning strategies, family’s intellectual climate, academic achievement), worse scores being obtained by those who orchestrated their study either in surface or in conceptually dissonant ways. These relationships shed more light on the nature of high school students ‘learning experience, and help to provide an integrated view of students’ webs of experience.     

Scaffolding cognitive and metacognitive strategy instruction in regular class lessons

The quality of teachers’ knowledge about how people learn influences students’ learning outcomes. Similarly, the quality of students’ knowledge about how they learn influences their engagement in self-regulated learning and consequently, their learning achievement. There is a gap between research findings that support these two premises and teaching–learning practices in classrooms. In this paper we describe attempts to reduce this gap. In Study 1 we surveyed early adolescent students’ cognitive and metacognitive strategy use and demonstrated that students’ cognitive and metacognitive strategy knowledge has substantial room for improvement. In Studies 2 and 3 we collaborated with teachers to embed explicit cognitive and metacognitive strategy instruction, using learning protocols, into regular class lessons. Studies 2 and 3 showed that the learning protocols slipped readily into teachers’ typical lesson designs, scaffolded teachers’ delivery of strategy instruction, and scaffolded some students’ acquisition of strategy knowledge, although progress was sometimes slow. Recommendations are presented for supporting teachers and students to engage with cognitive and metacognitive strategy instruction.     

Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof

In this study, we explored the structural relationship between the students’ perceived use of cognitive and metacognitive reading strategies (CMRS) and their reading comprehension of geometry proof (RCGP), and we also examined the differences in students’ perceived use of reading strategies among the poor, moderate and good comprehenders. A sample of ninth graders (N = 533) completed a RCGP test and then the CMRS questionnaire. In the exploratory factor analysis with one subsample (n = 150), principal component analysis was used to extract factors of CMRS use for improving the CMRS instrument. Another subsample of students (n = 370) participated in the study on the confirmatory factor analysis with structural equation modelling method. Results revealed that the use of metacognitive reading strategies exerts an executive function over that of cognitive reading strategies, which directly influenced students’ RCGP. Our interesting findings were that good comprehenders tended to employ more metacognitive reading strategies for planning and monitoring comprehension and more cognitive reading strategies for elaborating proof compared with the moderate comprehenders, who in turn employed these strategies more often compared with the poor comprehenders.     

Metacognitive calibration—an extended conceptualization and potential applications

In this theoretical paper, I present a short critical review of research on calibration. Based on this conceptual analysis I argue for two extensions of this construct: In addition to traditional applications, the methodology should be transferred to also measure calibration between students’ metacognitive control processes (traditionally, only students’ metacognitive judgments were considered) and important external criteria (traditionally, judgments were only compared to students’ own performance). As an illustrative example, one application context will be highlighted where these proposed extensions would alleviate potential problems with the traditional conceptualization: While students’ idiosyncratic task definitions constitute unwanted error variance in the traditional account it would be possible to investigate them as a primary research question within this extended notion. More specifically, it would be possible to investigate how well students’ learning processes match objective task demands. I will put forward theoretical and empirical arguments in favor of these suggestions.     

Examining trace data to explore self-regulated learning

This exploratory case study examined in depth the studying activities of eight students across two studying episodes, and compared traces of actual studying activities to self-reports of self-regulated learning. Students participated in a 2-hour activity using our gStudy software to complete a course assignment. We used log file data to construct profiles of self-regulated learning activity in four ways: (a) frequency of studying events, (b) patterns of studying activity, (c) timing and sequencing of events, and (d) content analyses of students’ notes and summaries. Findings indicate that students’ self-reports may not calibrate to actual studying activity. Analyses of log file traces of studying activities provide important information for defining strategies and sequences of fine-grained studying actions. We contrast these analytic methods and illustrate how trace-based profiles of students’ self-regulated studying inform models of metacognitive monitoring, evaluation, and self-regulated adaptation.     

Promotion of self-regulated learning in classrooms: investigating frequency, quality, and consequences for student performance

An implication of the current research on self-regulation is to implement the promotion of self-regulated learning in schools. Teachers can promote self-regulated learning either directly by teaching learning strategies or indirectly by arranging a learning environment that enables students to practise self-regulation. This study investigates teachers’ direct and indirect promotion of self-regulated learning and its relation to the development of students’ performance. Twenty German mathematics teachers with their overall 538 students (grade 9) were videotaped for a three-lesson unit on the Pythagorean Theorem. Students’ mathematics performance was tested several times before and after the observed lessons. A low-inferent coding system was applied to assess the teachers’ implicit or explicit instruction of cognitive strategies (e.g., organisation), metacognitive strategies (e.g., planning), and motivational strategies (e.g., resource management). High-inferent ratings were used to assess features of the learning environment that foster self-regulation. Results reveal that a great amount of strategy teaching takes place in an implicit way, whereas explicit strategy teaching and supportive learning environment are rare. The instruction of organisation strategies and some features of the learning environment (constructivism, transfer) relate positively to students’ performance development. In contrast to implicit strategy instruction, explicit strategy instruction was associated with a gain in performance. These results reveal a discrepancy between the usefulness of explicit strategy instruction and its rare occurrence in classrooms.     

Consistent results with the consistency hypothesis? The effects of epistemic beliefs on metacognitive processing

We explored relations between students’ epistemic beliefs, metacognitive monitoring and recall performance in the context of learning physics through metaphor. Eighty-three university undergraduate students completed questionnaires designed to measure their epistemic beliefs and prior knowledge about Newtonian physics. Students were epistemically profiled as rational, empirical, or metaphorical in their approaches to knowing. Using a think-aloud protocol, students read a text on Newton’s First and Third Laws. The text included metaphors as examples of the various laws described. Results revealed that students profiled as metaphorical engaged in more metacognitive processing compared to students profiled as rational or empirical. Moreover, path analyses revealed that metacognitive monitoring positively predicted recall performance. Results challenge Muis’ (2008) consistency hypothesis; the ways in which knowledge is represented in text may be the linking factor for relations between metacognitive monitoring and epistemic beliefs rather than the underlying epistemology of the domain.     

Impact of authenticity on sense making in word problem solving

The study presented in this paper seeks to investigate the impact of authenticity on the students’ disposition to make necessary real world considerations in their word problem solving. The aim is also to gather information about the extent to which different reasons for the students’ behaviors are responsible for not providing solutions that are consistent with the ‘real’ situations described in the word problems. The study includes both written solutions to word problems and interview data from 161 5th graders. The results show an impact of authenticity on both the presence of ‘real life’ considerations in the solution process and on the proportion of written solutions that were really affected by these considerations. The students’ frequent use of superficial solution strategies and their beliefs about mathematical word problem solving were found to be the main reasons for providing solutions that are inconsistent with the situations described in the word problems.     

Facilitating Students’ Problem Solving in a Technological Context: Prospective Teachers’ Learning Trajectory

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working with two different groups of students. Case study methods were used to identify and analyze critical events that occurred throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies; (3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent with the nature of their interactions and perceived role with students. The implications inform the development of an expanded learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics in technology-rich environments.     

Motivational beliefs and cognitive processes in mathematics achievement, analyzed in the context of cultural differences: a Korean elementary school example

The relations among students’ motivational beliefs, cognitive processes, and academic achievement were investigated. A 51-item questionnaire together with a mathematics achievement test was administered to 459 fifth graders in Korean elementary school mathematics classrooms. Results indicated that, in general, students’ cognitive processes related closely to competence beliefs, task values, and achievement goals, and more importantly their success or failure in mathematics achievement was closely linked to competence beliefs, performance-avoidance goals, and persistence strategies. Positive evidence of performance-approach goals was observed in math learning relative to task goals. As expected, performance-avoidance goals turned out to be detrimental to students’ math learning. These findings are generally congruent with the motivational theories and support the position that students should be encouraged to adopt task goals and actively involve themselves in math class activities. However, it also behooves us to recognize the potential benefits of performance-approach goals in different cultural contexts, such as the Korean elementary school math classrooms.     

Approach to mathematical problem solving and students’ belief systems: two case studies

The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12–13 years old. In this study we identified different types of approaches to problems that determine the behavior of students in the problem-solving process. The research found two aspects that explain the students’ approaches to problem solving: (1) the presence of a dualistic belief system originating in the student’s school experience; and (2) motivation linked to beliefs regarding the difficulty of the task. Our results indicate that there is a complex relationship between students’ belief systems and approaches to problem solving, if we consider a wide variety of beliefs about the nature of mathematics and problem solving and motivational beliefs, but that it is not possible to establish relationships of causality between specific beliefs and problem-solving activity (or vice versa).     

Metacognitive skills in Belgian third grade children (age 8 to 9) with and without mathematical learning disabilities

This paper presents a study on mathematical problem solving in third-grade pupils. The relationship between mathematics, metacognition and intelligence was investigated in children with (n = 191) and without mathematical learning disabilities (n = 268). A significant relationship was found between prediction, evaluation, intelligence, procedural and mathematical fact retrieval skills in children without mathematical learning disabilities. In the children with mathematical learning disabilities a relationship was found between metacognitive and procedural skills. No such relationship was found between intelligence and metacognition or between metacognition and mathematical fact retrieval skills. In addition it was investigated if children with mathematical learning disabilities had less adequate metacognitive skills than peers without learning problems. At group level significant differences were found between both groups. However on analyzing these results further, it was found that four out of five children with combined mathematical learning disabilities, half of the children with procedural disabilities and only 5% of the children with a retrieval deficiency had low metacognitive skills. Furthermore, metacognitive problems were found in one out of five children without learning disabilities. Moreover, a majority of the children with mathematical learning disabilities and inadequate metacognitive skills had problems with prediction and evaluation skills. Most third graders with low metacognitive skills only appeared to have problems predicting the level of difficulty of tasks. Inaccurate evaluations were found on a more regular basis in children with mathematical learning disabilities and inadequate metacognitive skills as opposed to the sample of children with inadequate metacognitive skills but without learning difficulties, where their occurrence was rather a one off. The implications of this study for diagnosis and treatment will be discussed later in this paper.     

The expertise reversal effect and worked examples in tutored problem solving

Prior research has shown that tutored problem solving with intelligent software tutors is an effective instructional method, and that worked examples are an effective complement to this kind of tutored problem solving. The work on the expertise reversal effect suggests that it is desirable to tailor the fading of worked examples to individual students’ growing expertise levels. One lab and one classroom experiment were conducted to investigate whether adaptively fading worked examples in a tutored problem-solving environment can lead to higher learning gains. Both studies compared a standard Cognitive Tutor with two example-enhanced versions, in which the fading of worked examples occurred either in a fixed manner or in a manner adaptive to individual students’ understanding of the examples. Both experiments provide evidence of improved learning results from adaptive fading over fixed fading over problem solving. We discuss how to further optimize the fading procedure matching each individual student’s changing knowledge level.     

“Accepting Emotional Complexity”: A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom

A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students’ learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and motivational processes in a specific context. Understanding the role of emotions in the mathematics classroom then implies understanding the nature of these situated processes and the way they relate to students’ problem-solving behaviour. We will present data from a multiple-case study of 16 students out of 4 different junior high classes that aimed to investigate students’ emotional processes when solving a mathematical problem in their classrooms. After identifying the different emotions and analyzing their relations to motivational and cognitive processes, the relation with students’ mathematics-related beliefs will be examined. We will specifically use Frank’s case to illustrate how the use of a thoughtful combination of a variety of different research instruments enabled us to gather insightful data on the role of emotions in mathematical problem solving.     

Assessment of metacognitive skills by means of instruction to think aloud and reflect when prompted. Does the verbalisation method affect learning?

Recent research on metacognition points out the crucial role of on-line methods when endeavouring to conduct valid assessments of metacognitive skills. Presently, different on-line methods are used, however, it is still a question of research whether and how they affect students’ learning behaviour and learning outcome. Thus, the aim of this study is to quasi-experimentally analyse the effects of two on-line verbalisation methods on learning performance. By means of the thinking-aloud method, students in one experimental group (n = 24) were instructed to read and think aloud during learning. With the reflection when prompted method, students of another experimental group (n = 24) were prompted at each navigational step to reflect on the reasons why they chose specific information. Students in the control group (n = 22) learned without being instructed to verbalise. All three groups were treated identically except for the different use of verbalisation assessment methods. The students’ task was to learn the concepts and principles of operant conditioning presented in a hypermedium within 30 min. The students’ learning sessions were videotaped and learning performance was obtained immediately afterwards. Based on Ericsson and Simon’s (Protocol analysis: Verbal reports as data, MIT, Cambridge, 1993) model, no performance differences between the thinking aloud and the control group were hypothesised. However, prompting students for metacognitive reflection should affect learning performance positively, which is confirmed by the results only in tendency for transfer performance. Implications for on-line assessment methods of metacognitive skill will be discussed.     

A working memory model applied to mathematical word problem solving

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.