The Antecedents and Consequences of Metacognitive Knowledge in Mathematics Learning: A Self-Determination Perspective

Grounded in the self-determination theory and the metacognitive and affective model of self-regulated learning, this study investigated the longitudinal relationship of self-determined motivation as the antecedent and academic performance as the consequence of metacognitive knowledge (MK) in mathematics learning. Two waves of data were collected from senior high school students (N = 327) in the second semester in Grades 10 and 11. A longitudinal mediation model was analyzed using structural equation modeling. Results revealed that autonomous motivation was positively related to MK of competence-enhancing strategies and negatively related to MK of avoidance strategies. Furthermore, mathematics performance was positively predicted by MK of cognitive/metacognitive strategies and negatively predicted by MK of avoidance strategies. This study expands the understanding of MK and elaborates on the dynamics between MK, self-determined motivation, and mathematics performance. Especially, this study differentiates the MK of adaptive and maladaptive strategies and examines their motivational antecedents and academic effects. Our findings also suggest that autonomous motivation has longitudinal benefits on MK.

Exploring Students’ Learning of Integral Calculus using Revised Bloom’s Taxonomy

<p>Integral calculus is one of the topics involved in mathematical courses both at secondary and tertiary level with several applications in different disciplines. It is part of gateway mathematical courses at universities for many majors and important for the development of the science. Several studies had been undertaken for exploring students’ learning of integral calculus, both at the secondary and tertiary level, using a variety of frameworks (e.g., Action-Process-Object-Schema (APOS) theory (Dubinsky, 1991). However, students’ learning of integral calculus has not been explored in terms of metacognitive experiences and skills, and the number of studies which have explored metacognitive strategies in relation to the students’ learning of integral calculus is limited. Therefore, this study used Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001), Efklides’s metacognition framework (Efklides, 2008), and an adaptation of VisA (Visualization and Accuracy) instrument (Jacobse & Harskamp, 2012) for exploring students’ learning of integral calculus. A multiple case study approach was used to explore students’ learning of the integral-area relationships and the Fundamental Theorem of Calculus in relation to the RBT’s factual, conceptual, and procedural knowledge, and the facets of metacognition including metacognitive knowledge, experiences, and skills. The study sample comprised of nine first year university and eight Year 13 students who participated in individual semi-structured interviews answering nine integral calculus questions and 24 questions related to the RBT’s metacognitive knowledge. Integral calculus questions were designed to address different aspects of RBT’s knowledge dimension and activate RBT-related cognitive processes. A think aloud protocol and VisA instrument were also used during answering integral calculus questions for gathering information about students’ metacognitive experiences and skills. Ten undergraduate mathematics lecturers and five Year 13 mathematics teachers were also interviewed in relation to the teaching and learning of integral calculus to explore students’ difficulties in the topic. The entire teaching of integral calculus in a first year university course and a Year 13 classroom were video recorded and observed to obtain a better understanding of the teaching and learning of integral calculus in the context of the study. The study findings in terms of the RBT’s factual knowledge show several students had difficulty with notational aspects of the Fundamental Theorem of Calculus (FTC) (e.g., Thompson, 1994) whereas this issue was not dominant for the definite integral. In relation to the RBT’s conceptual and procedural knowledge for both topics, conceptual knowledge was less developed in students’ minds in comparison to procedural knowledge (e.g., students had not developed a geometric interpretation of the FTC, whereas they were able to solve integral questions using the FTC). The obtained results were consistent with previous studies for these three types of knowledge. The study contributes to the current literature by sharing students’ metacognitive knowledge, experiences and skills in relation to integral calculus. The findings highlight some student learning, monitoring, and problem-solving strategies in these topics. A comparison between University and Year 13 students’ results showed students across this transition had different factual, conceptual, procedural, and metacognitive knowledge in these topics. For instance, University students in the sample use online resources more often than Year 13 students, are more interested in justifications behind the formulas, and have more accurate pre and post-judgments of their ability to solve integral questions. The information obtained using questions based on RBT and the metacognition framework indicates that these two together may be very useful for exploring students’ mathematical learning in different topics.</p>

Exploring Students’ Learning of Integral Calculus using Revised Bloom’s Taxonomy

<p>Integral calculus is one of the topics involved in mathematical courses both at secondary and tertiary level with several applications in different disciplines. It is part of gateway mathematical courses at universities for many majors and important for the development of the science. Several studies had been undertaken for exploring students’ learning of integral calculus, both at the secondary and tertiary level, using a variety of frameworks (e.g., Action-Process-Object-Schema (APOS) theory (Dubinsky, 1991). However, students’ learning of integral calculus has not been explored in terms of metacognitive experiences and skills, and the number of studies which have explored metacognitive strategies in relation to the students’ learning of integral calculus is limited. Therefore, this study used Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001), Efklides’s metacognition framework (Efklides, 2008), and an adaptation of VisA (Visualization and Accuracy) instrument (Jacobse & Harskamp, 2012) for exploring students’ learning of integral calculus. A multiple case study approach was used to explore students’ learning of the integral-area relationships and the Fundamental Theorem of Calculus in relation to the RBT’s factual, conceptual, and procedural knowledge, and the facets of metacognition including metacognitive knowledge, experiences, and skills. The study sample comprised of nine first year university and eight Year 13 students who participated in individual semi-structured interviews answering nine integral calculus questions and 24 questions related to the RBT’s metacognitive knowledge. Integral calculus questions were designed to address different aspects of RBT’s knowledge dimension and activate RBT-related cognitive processes. A think aloud protocol and VisA instrument were also used during answering integral calculus questions for gathering information about students’ metacognitive experiences and skills. Ten undergraduate mathematics lecturers and five Year 13 mathematics teachers were also interviewed in relation to the teaching and learning of integral calculus to explore students’ difficulties in the topic. The entire teaching of integral calculus in a first year university course and a Year 13 classroom were video recorded and observed to obtain a better understanding of the teaching and learning of integral calculus in the context of the study. The study findings in terms of the RBT’s factual knowledge show several students had difficulty with notational aspects of the Fundamental Theorem of Calculus (FTC) (e.g., Thompson, 1994) whereas this issue was not dominant for the definite integral. In relation to the RBT’s conceptual and procedural knowledge for both topics, conceptual knowledge was less developed in students’ minds in comparison to procedural knowledge (e.g., students had not developed a geometric interpretation of the FTC, whereas they were able to solve integral questions using the FTC). The obtained results were consistent with previous studies for these three types of knowledge. The study contributes to the current literature by sharing students’ metacognitive knowledge, experiences and skills in relation to integral calculus. The findings highlight some student learning, monitoring, and problem-solving strategies in these topics. A comparison between University and Year 13 students’ results showed students across this transition had different factual, conceptual, procedural, and metacognitive knowledge in these topics. For instance, University students in the sample use online resources more often than Year 13 students, are more interested in justifications behind the formulas, and have more accurate pre and post-judgments of their ability to solve integral questions. The information obtained using questions based on RBT and the metacognition framework indicates that these two together may be very useful for exploring students’ mathematical learning in different topics.</p>

The Student Self-Accommodation Strategy for Students with Visual Impairments

Introduction Accommodations are essential for the successful participation of individuals with visual impairments in post-secondary education and employment. Passive experiences with accommodations in school, plus a complex advocacy process warrant the need to support students to engage in the accommodations process. Methods Four high school students with visual impairments were taught the Student Self-Accommodation Strategy. A parallel multiple-case design was used to determine how and how well the participants learned and used the strategy and to investigate their development of metacognitive knowledge and self-regulated learning (SRL) skills. Results The participants all learned the strategy to varying extents. The cross-case analysis revealed that recall and understanding the purpose of the strategy supported strategy performance but were not associated with in-class use of the strategy. Additionally, participants did not experience changes with metacognition or SRL; however, they did demonstrate metacognitive knowledge on multiple data sources, with few demonstrations of SRL. Discussion Findings indicate that the Student Self-Accommodation Strategy is accessible to students with visual impairments. Three factors seemed to be associated with the learning and use of the strategy: verbal and reasoning skills, achievement, and emotional-behavioral regulation. Metacognition and SRL can positively affect students with visual impairments. Implications Future work with the Student Self-Accommodation Strategy should incorporate in-class strategy coaching and an explicit investigation of the factors that seemed to influence strategy learning and performance. Research and practice should give greater attention to metacognition and SRL for students with visual impairments.

Dampak Pembelajaran Process Oriented Guided Inquiry Learning Terhadap Pengetahuan Metakognitif Siswa Pada Topik Kesetimbangan Kelarutan

<p><strong>Abstract:</strong> The aim of this study is to investigate the difference of XI grade science students’ metacognitive knowledge as the impact of POGIL and verification learning on solubility equilibrium topic. The study used quasy experiment design. Analysis is done using Mann-Whitney U test at 5% significance. The result showed that there is difference on students’ metacognitive knowledge who are taught by POGIL and verification learning. The students who are taught by POGIL have higer metacognitive knowledge than that of are taught by verification learning.</p><strong>Abstrak:</strong><em> </em>Penelitian ini bertujuan untuk mengetahui perbedaan pengetahuan metakognitif siswa kelas XI IPA sebagai dampak dari pembelajaran POGIL dan verifikasi pada topik kesetimbangan kelarutan. Desain penelitian yang digunakan adalalah <em>quasy experiment</em>. Analisis dilakukan dengan menggunakan uji <em>Mann-Whitney U </em>pada taraf signifikansi 5%. Hasil penelitian menunjukkan terdapat perbedaan pengetahuan metakognitif antara siswa yang dibelajarkan dengan menggunakan pembelajaran POGIL dan verifikasi. Siswa yang dibelajarkan dengan POGIL memiliki pengetahuan metakognitif lebih tinggi dibandingkan siswa yang dibelajarkan dengan pembelajaran verifikasi.

Combination of Discovery Learning and Metacognitive Knowledge Strategy to Enhance Students’ Critical Thinking Skills

<p style="text-align: justify;">The research aims to develop an instructional tool based on Discovery Learning (DL) combined with a Metacognitive Knowledge Strategy (MKS) to enhance students’ Critical Thinking Skills (CTSs). In doing so, the study employed a Research and Development (R&D) method to develop such a tool. The developed instructional tool was tested for its validity by experts and practitioners’ evaluation. Further, the empirical data were collected from the results of implementation in learning and the student's responses, while the data of tools effectiveness were acquired from the critical thinking tests given to students (analyzed by related t-test). The developed instructional tools were implemented in a limited-scale trial of 32 students and a large-scale trial of 59 students. The results show that: firstly, the DL and MKS-integrated instructional tools are stated as valid in terms of the lesson plan, student worksheet, and critical thinking test. Secondly, the practicality criteria have been successfully met; the learning implementation, students’ activity, and students' responses were regarded as in accordance with the feasibility standard. Thirdly, the instructional tool was deemed effective in enhancing students’ CTSs (p = 0.05).</p>

Comparison of indicators of metacognitive awareness of doctors at different stages of education

Introduction. Metacognition is essential for developing clinical thinking skills. Metacognitive skills are widely regarded as important for doctors, but they are rarely formed and evaluated in higher medical school. To solve this problem, it is required to determine how the cognitive, regulatory and reflexive indicators of metacognitive awareness in doctors change throughout their professional life. This work aims to study the metacognitive awareness of doctors at different stages of professional education. Methods. The study involved 1st-year students of the Department of General Medicine (N=48), medical residents (N=44), and doctors enrolled in advanced training cycles (N=34) of the Yaroslavl State Medical University. To study the cognitive, regulatory and reflexive indicators of metacognitive awareness, the following methods were used: "Metacognitive Awareness Inventory" (G. Schraw, R. Dennison, adaptation by E.Yu. Savin, A.E. Fomin), "Assessment of metacognitive knowledge and metacognitive activity" (Yu.V. Poshekhonova, M.M. Kashapov), "Methodology of the level of expression and direction of reflection" (M. Grant). Research results. Significant differences were revealed in metacognitive awareness indicators at the initial and final stages of higher education (U=800.0, p≤0.05). According to the results of the study, it was found that the higher the stage of higher professional education is, the higher is the ability to manage information (U=783.0, p≤0.05), choose the main ideas (U=800.0, p≤0.05) and control errors (U=790.0, p≤0.05). Moreover, indicators of socio-reflection are more pronounced (U=702.5, p≤0.01). The doctors enrolled in further education courses have a high level of metacognition. The significant differences were found in terms of the following indicators: metacognitive knowledge (U=309.5, p≤0.001), metacognitive activity (U=295.5, p≤0.001), concentration (U=417.5, p≤0.001), acquisition of information (U=275.5, p≤0.001), choice of main ideas (U=528.5, p≤0.05), and time management (U=338.0, p≤0.001). There are no significant differences in the reflexive component of the metacognitive awareness of doctors at the stage of additional professional education and the final stage of higher education. Conclusion. All indicators of metacognitive awareness among doctors are formed at the stage of higher education. The reflexive component of metacognitive awareness helps to adapt to the changing conditions of obtaining additional professional education. Metacognitive awareness, with the help of which doctors are aware of their own thoughts and use the best ways to solve problematic situations, allows them to cope with difficulties in the learning process and in professional activity.