Mathematical Metacognition Research Articles

Metacognition in mathematics education: From academic chronicle to future research scenario–A bibliometric analysis with the Scopus database

Originally introduced by psychologists, metacognition has attracted considerable interest within academic spheres and has transformed into a significant research focal point in the field of mathematics education, commonly denoted as ‘mathematical metacognition.’ This investigation constitutes the primary endeavor to comprehensively examine all publications within the Scopus database related to metacognition in mathematics education (MiME). The data encompasses a total of 288 documents, authored by 653 individuals hailing from 58 different countries and territories and disseminated across 162 diverse sources. Notably, this examination delineates two distinct developmental phases, with a particularly pronounced surge in publications emerging from the year 2016 onward. Although Asia has two representatives in the top-10 in terms of number of publications (China and Indonesia), authors from developed countries have made significant contributions to research on MiME, especially the United States, Germany, Turkey, and Belgium. Among the 15 most influential academic journals, merely two pertain to the domain of mathematics education, whereas the majority belong to the disciplines of psychology and social sciences (educational science). The main research directions that have been pointed out are adults’ metacognitive abilities, considering gender differences and problem-solving abilities; metacognition and the ability to learn mathematical concepts (more recently arithmetic concepts); control metacognitive processes and students’ academic achievement. Early-career researchers as well as interested scholars can find important scholars, documents, and research directions on this topic to refer to for their research activities.

INVESTIGATING THE METACOGNITION CALIBRATIONS AND MATHEMATICAL METACOGNITION AWARENESS OF 8TH GRADE STUDENTS; SKILL-BASED MATHEMATICS QUESTIONS

The purpose of this study is to examine the metacognitive awareness of eighth-grade students in mathematics and their metacognitive calibrations in skill-based mathematics questions from various variables, and to determine the relationship between these factors. A relational survey design is used in the study. The sample of the research consists of 303 female students, 217 male students, totaling 520 students who are in the eighth grade. Data were collected using the "Mathematical Metacognition Awareness Scale (MMAS)," the "Skill-Based Mathematics Questions Test (SMQT)," and the "Self-Evaluation Scale (SES)." In the research, the Cronbach's alpha reliability coefficient of MMAS is found to be .881. The discriminability indices of SMQT are above .34, and the item difficulty indices range from .28 to .88. Descriptive statistics, independent groups t-test, related and unrelated groups ANOVA, and multiple correlation techniques were used in the analysis of the data. In the results of the research, it was observed that students' genders significantly differentiated their mathematical metacognition awareness and biases, but did not differentiate their accuracy significantly. The socio-economic levels (SEL) of students were found to significantly affect their mathematical metacognition awareness but did not differentiate their metacognitive calibrations. The students' mathematics grades were found to significantly differentiate their mathematical metacognition awareness and metacognitive calibrations. There was no significant relationship between students' mathematical metacognition awareness and metacognitive calibrations. Another finding obtained from the study is that students tend to be better calibrated in medium and difficult mathematics questions compared to easy questions, and in difficult and easy questions, they tend to be excessively confident compared to medium difficulty questions.

Enhancing Mathematical Metacognition and Self-Efficacy in Third-Graders in Elementary School: Integrating Problem-Posing Activities within the Self-Regulated Learning Cycle

Enhancing Mathematical Metacognition and Self-Efficacy in Third-Graders in Elementary School: Integrating Problem-Posing Activities within the Self-Regulated Learning Cycle

The Development of Think Pair Share-Based Learning Tools to Improve Mathematical Metacognition and Communication Abilities

Penelitian ini menguji validitas, kelayakan, dan keefektifan metode pembelajaran Think Pair Share untuk meningkatkan metakognisi dan komunikasi matematis siswa. Penelitian ini merupakan penelitian pengembangan 4-D. Penelitian ini melibatkan siswa SMP Negeri di Panyabungan kelas VIIIA dan VIII-B. Penelitian ini menemukan bahwa: perangkat pembelajaran Think Pair Share Buku Siswa, Lembar Kerja Peserta Didik, Tes Kemampuan Metakognisi Matematis, dan Tes Kemampuan Komunikasi Matematis valid; perangkat pembelajaran berbasis Think Pair Share praktis; perangkat dapat digunakan dengan sedikit revisi dan hasil observasi perangkat pembelajaran di kelas menunjukkan rata-rata nilai kepraktisan Trial II siswa mempunyai pre-test sebesar 20,83% dan post-test sebesar 87,50%, serta lebih dari 80% siswa menyukai perangkat pembelajaran dan 85% setiap komponen keterlibatan siswa membuktikan siswa belajar; kemampuan metakognisi dan komunikasi matematis siswa menggunakan perangkat pembelajaran berbasis Think Pair Share yang dikembangkan meningkat dengan skor N-gain 0,54 untuk kemampuan metakognisi matematis dan 0,52 untuk kemampuan komunikasi matematis. This research tested the validity, feasibility and effectiveness of the Think Pair Share learning method to improve students' metacognition and mathematical communication. This research is 4-D development research. This research involved State Middle School students in Panyabungan classes VIIIA and VIII-B. This research found that: the Think Pair Share learning tools: Student Books, Student Worksheets, Mathematical Metacognition Ability Tests, and Mathematical Communication Ability Tests were valid; think Pair Share based learning tools are practical; the tools can be used with a little revision and the results of observations of learning tools in class show that the average practicality score for Trial II students has a pre-test of 20.83% and a post-test of 20.83%. 87.50%, as well as more than 80% of students like learning tools and 85% of each component of student engagement proves students are learning; students' mathematical metacognition and communication abilities using the developed Think Pair Share-based learning tool increased with an N-gain score of 0.54 for mathematical metacognition abilities and 0.52 for mathematical communication abilities.

A Survey and Research on Mathematical Metacognition among Mathematics Normal Students in Local Universities

A Survey and Research on Mathematical Metacognition among Mathematics Normal Students in Local Universities

INTERPLAY BETWEEN CONSTRUCTIVISM AND METACOGNITIVE REGULATION: AN EXPERIMENTAL STUDY ON MATHEMATICS STUDENTS

This study was to examine the effect of constructivist approach on mathematical metacognition. Instructional intervention package was planned to implement through true-experimental design. Initially sixty students from ninth-grade were selected through randomly and assigned into two groups; experimental and control groups. These two groups; experimental and control groups were formed on the basis of Raven’s Progressive Matrix test scores through matched by randomization. Finally, forty-four students in which twenty-two in each group were included for interventions as a sample for this study. Inventory of metacognitive regulation as the form of pretest and posttest were administered before and after the implementing the instructional intervention. After analyzing data by using analysis of co-variance techniques, revealed that metacognitive regulation in terms of planning and monitoring skills were not improved by constructivist approach among the secondary level students.

Öğrencilerin Matematiksel Üstbiliş ve Problem Kurma Öz-Yeterliklerinin Bazı Değişkenlere Göre İncelenmesi

Bu araştırmanın amacı, ortaokul öğrencilerinin matematiksel üstbiliş farkındalıkları ve problem kurma öz-yeterlik düzeylerini belirlemek, ayrıca üstbiliş farkındalık ve öz-yeterliklerini cinsiyet, sınıf düzeyi, sosyo-ekonomik durum ve matematik başarı düzeyi değişkenlerine göre karşılaştırmaktır. Araştırma ilişkisel tarama modellerinden nedensel karşılaştırma yaklaşımında tasarlanmıştır. Araştırma 5., 6., 7. ve 8. sınıflarda öğrenim gören 462 ortaokul öğrencisi üzerinde yürütülmüştür. Veri toplama aracı olarak “Kişisel Bilgi Formu”, “Problem Kurma Öz-yeterlik Ölçeği” ve “Matematiksel Üstbiliş Farkındalık Ölçeği” kullanılmıştır. Verilerin analizinde Bağımsız Örneklem t-Testi, Tek Yönlü Varyans Analizi ve Pearson Momentler Çarpımı Korelasyon Katsayısı kullanılmıştır. Araştırma sonucunda, öğrencilerin matematiksel üstbiliş farkındalıkları ve problem kurma öz-yeterlikleri yüksek düzeyde bulunmuştur. Öğrencilerin matematiksel üstbiliş farkındalıkları ve problem kurma öz-yeterlikleri arasında sınıf düzeyi ve ailenin sosyo-ekonomik durumuna göre anlamlı farkın olmadığı, cinsiyet ve matematik başarısı açısından ise anlamlı bir farkın olduğu belirlenmiştir. Ayrıca matematiksel üstbiliş ve problem kurma öz-yeterliği arasında anlamlı bir ilişki bulunmuştur. Öğrencilerin matematiksel üstbiliş farkındalıkları ve problem kurma öz-yeterliklerini geliştirmeye yönelik etkinlikler cinsiyet ve matematik başarısı farklılıkları dikkate alınarak hazırlanmalıdır.

COGNITIVE AND METACOGNITIVE ACTIVITIES IN THE PROCESS OF DEVELOPING MATHEMATICAL COMPETENCE FOR SECONDARY SCHOOL STUDENTS

In an effort to innovate teaching and learning methods to prepare a new generation for the demands of a new era, many educators have discovered the value of metacognition. In this paper, the author presents these main issues: (i) cognitive activities and metacognitive activities; (ii) manifestations of cognition and metacognition in the 5 core components of mathematical competence for secondary school students; (iii) the influence and role of metacognition in learning Mathematics and developing mathematical competence for students.

Matematik Başarısının Yordanması: Matematiksel Üstbiliş ve Problem Kurma Öz-Yeterliğinin Rolü

Üstbiliş, öğrencilerin kendi düşünme süreçleri ve bilişleri hakkında bilgi sahibi olmaları ve bu yapıyı düzenleyebilmelerine ilişkin becerileridir. Üstbiliş problem çözme sürecinde belirli bir zihinsel süreci keşfetme veya seçme yöntemi olduğundan matematik problemi kurmada ve başarı üzerinde de önemli etkileri bulunmaktadır. Çalışmada ortaokul öğrencilerinin matematiksel üstbiliş farkındalıkları ve matematik problemi kurma öz-yeterlik düzeyleri belirlenmiş, ayrıca matematik başarıları ile arasındaki ilişki incelenmiştir. İlişkisel tarama modelinde tasarlanan çalışma 462 ortaokul öğrencisi üzerinde yürütülmüştür. Çalışmanın verileri “Problem Kurma Öz-yeterlik Ölçeği” ve “Matematiksel Üstbiliş Farkındalık Ölçeği” yoluyla toplanmıştır. Verilerin analizinde Pearson Momentler Çarpımı Korelasyon Katsayısı ve Çoklu Doğrusal Regresyon Analizi kullanılmıştır. Araştırma sonucunda, öğrencilerin matematiksel üstbiliş farkındalıkları ve matematik problemi kurma öz-yeterlikleri ile matematik başarıları arasında orta düzeyde anlamlı bir ilişki bulunmuştur. Ayrıca öğrencilerin matematiksel üstbilişsel farkındalıkları ve problem kurma öz-yeterliklerinin matematik başarısını %35 düzeyinde yordadığı tespit edilmiştir. Bu çalışmanın sonuçları, öğrencilerin matematik başarısı üzerinde önemli bir unsur olarak üstbiliş ve problem kurmanın önemini keşfetme ihtiyacına işaret etmektedir.

Development of HOTS-Based Student Activity Sheet with an Open Ended Approach to Improve Mathematical Metacognition Ability and Self Confidence of Students of 20 Medan Junior High School

This study aims to describe: 1) how the quality of HOTS-based student activity sheet with an Open Ended approach is quality; 2) increasing students' mathematical metacognition skills through HOTS-based worksheets with an Open Ended approach; and 3) increasing students' self confidence through HOTS-based worksheets with an Open Ended approach. This research is a development research. This research was conducted in two stages, namely the first stage of developing HOTS-based worksheets with an Open Ended approach using a formative evaluation type Tessmer development model, and the second stage testing HOTS-based worksheets with an Open Ended approach which was developed in class VIII-1 and VIII-3 SMP. State 20 Medan. From the results of trial I and trial II, it was obtained: 1) HOTS-based worksheets with an Open Ended approach to improve students' mathematical metacognition and self confidence skills that have been developed have met the valid, practical and effective criteria; 2) Increasing the ability of mathematical metacognition using HOTS-based worksheets with the Open Ended approach which has been developed as seen from the N-gain value in the first trial of 0.43 which increased to 0.47 in the second trial, meaning that it is in the "moderate" category; and 3) The increase in students' self confidence with the Open Ended approach which has been developed as seen from the N-gain value in the first trial of 0.46 increased to 0.51 in the second trial, meaning that it is in the "medium" category. Keywords: development LKPD, Tessmer model, Open Ended Approach, HOTS, Mathematical Metacognition, Self Confidence . DOI: 10.7176/JEP/13-16-06 Publication date: June 30 th 2022

Development and Application of Intelligent Assessment System for Metacognition in Learning Mathematics among Junior High School Students

Metacognition is one of the key factors that determine students’ mathematics learning and affects students’ sustainable development. Metacognition assessment has attracted more and more attention from researchers, but how to effectively assess and improve students’ metacognition is still unknown. Based on the theoretical basis and practical verification, a mathematics metacognitive intelligence assessment and strategy implementation system for middle school students was developed from both qualitative and quantitative perspectives. This system features the mix of an assessment structural model, assessment scales, a set of norms, improvement strategies and the intelligent assessment and strategy implementation program, which can intelligently output students’ mathematical metacognition level and propose targeted improvement strategies. Through the application of the system to 2100 students in Tianjin, China, the results show that the subjects have advantages in mathematical metacognitive knowledge and mathematical metacognitive management. The mathematical metacognitive experience needs to be improved. After intervening with the subjects, according to the improvement strategy provided by the system, it was found that their mathematical metacognition was improved, indicating that the system has a good effect.

ICTs for the Development of the Cognitive and Metacognitive abilities of the students with Specific Learning Disorder in Mathematics

This article is a literature review that analyses the cognitive and metacognitive abilities of the students with Specific Learning Disorder in Mathematics (SLDM). It aims to present the cognitive and metacognitive deficits of these students along with the ways and methods that can improve the corresponding cognitive and metacognitive abilities and analyze the role of metacognition in mathematics education. It also aims to present ICT tools that are used worldwide in order to develop and enhance these abilities. These tools are designed for the development of either the cognitive or the metacognitive abilities of the students with SLDM and include computer based and mobile applications, serious games, educational software and robotics. The results of the study indicate that the existed ICT tools for the development of the cognitive and metacognitive abilities of the students with SLDM can have a crucial impact on the improvement of the symptoms of this Specific Learning Disorder. They can enhance the cognitive abilities of the attention, the working memory and the visuospatial ability along with the mathematical ability and also improve the metacognitive abilities such as reflection, self-regulation, the problem solving ability and the mathematical metacognition.

STUDENT’S MATHEMATICAL PROBLEM-SOLVING ABILITY WITH MATHEMATICAL RESILIENCE AND METACOGNITION SKILLS: A QUANTITATIVE ANALYSIS

One of the main goals in learning mathematics, both at the primary and secondary education levels, is to equip students with mathematical problem solving skills. This is important because there are so many problems in life that need to be solved by mathematics. However, several studies show that students' problem solving abilities are still low, so teacher efforts are needed to improve them. This research has a focus on improving students' mathematical problem solving abilities based on factors within the students themselves, namely Mathematical Resilience and metacognition abilities. This study uses a quantitative approach, with the type of expost facto research. The population in this study were elementary school students in Majalengka Regency with a sample of fifth grade students at SDN Jatipamor I, Panyingkiran District. The results showed that the problem solving abilities of students who had high Mathematical Resilience and metacognition skills were better than other students. Thus it can be concluded that Mathematical Resilience and metacognition skills have a very large influence on students' ability to solve mathematical problems.

Examining the Relationship between Academic Motivations and Mathematical Metacognition Awareness of Middle School Students

Bu araştırmanın amacı, ortaokul öğrencilerinin akademik motivasyonları ile matematiksel üstbiliş farkındalıkları arasındaki ilişkiyi incelemektir. Bu çalışmada, nicel araştırma yöntemlerinden betimsel tarama modeli tercih edilmiştir. Araştırmanın örneklemini, 2019-2020 öğretim yılı ikinci döneminde basit seçkisiz örnekleme yöntemiyle seçilen ve Sivas ilindeki 6 devlet ortaokulunda öğrenim gören toplam 1318 öğrenci oluşturmuştur. Vallerand, Blais, Brière, ve Pelletier’in (1989) geliştirdiği Türkçeye uyarlamasını ise Yurt ve Bozer’in (2015) yaptığı “Akademik Motivasyon Ölçeği” ve Kaplan ve Duran’ın (2000) geliştirdiği “Matematiksel Üstbiliş Farkındalık Ölçeği” uygulanarak elde edilmiştir. Araştırma verilerinin analizinde bağımsız gruplar t testi, ANOVA, Tukey testi, Pearson korelasyon testi ve Basit Doğrusal Regresyon kullanılmıştır. Araştırmanın sonuçlarına göre; akademik motivasyon ile matematiksel üstbiliş farkındalık arasında orta düzeyde, pozitif yönlü ve anlamlı bir ilişki vardır. Öğrencilerin akademik motivasyonları matematiksel bilişüstü farkındalıklarının %20’lik bir kısmını açıklamaktadır.

The association between mathematical attitudes, academic procrastination and mathematical achievement among primary school students: the moderating effect of mathematical metacognition

The association between mathematical attitudes, academic procrastination and mathematical achievement among primary school students: the moderating effect of mathematical metacognition

ORTAOKUL ÖĞRENCİLERİNİN MATEMATİK ODAKLI AKADEMİK RİSK ALMA DAVRANIŞLARINI ETKİLEYEN FAKTÖRLERİN YAPISAL EŞİTLİK MODELLEMESİYLE İNCELENMESİ

Bu araştırmanın amacı, ortaokul öğrencilerinin cinsiyetleri, sınıf düzeyleri, matematiğe karşı tutum düzeyi ve matematiksel üstbilişsel farkındalık düzeylerinin birbiri üzerindeki ve matematik odaklı akademik risk alma davranışları üzerindeki etkilerini belirlemektir. Araştırma ilişkisel araştırma modeli kullanılarak gerçekleştirilmiştir. Araştırmanın örneklemini uygun örnekleme yöntemi kullanılarak seçilen 895 ortaokul (6, 7 ve 8. sınıf) öğrencisi oluşturmaktadır. Araştırmada veri toplama aracı olarak Matematiksel Üstbiliş Farkındalık Ölçeği, Matematiğe Yönelik Tutum Ölçeği ve Matematik Odaklı Akademik Risk Alma Ölçeği kullanılmıştır. Araştırmada toplanan veriler yapısal eşitlik modellemesi (YEM) ile analiz edilmiştir. YEM analizi sonucunda araştırma kapsamında kuramsal bilgilere dayalı olarak geliştirilen 9 hipotezden 4’ü kabul edilmiş, 5’i ise reddedilmiştir. Araştırma bulgularına göre, matematiğe karşı tutum, matematiksel üstbilişsel farkındalık değişkenlerinin akademik risk alma değişkenine ilişkin varyansın %68’ini açıkladığı belirlenmiştir. Ayrıca araştırmada cinsiyet ve matematiğe karşı tutum değişkenlerinin matematiksel üstbilişsel farkındalık değişkenine ilişkin varyansın %49’unu açıkladığı tespit edilmiştir.

Delphi method looking for factors of collaborative problem solving competencies and collaborative metacognition in Mathematics

Delphi method looking for factors of collaborative problem solving competencies and collaborative metacognition in Mathematics

수학 학습에서 정의적 특성, 메타정의, 메타인지의 구조적 관계 분석

In this study, the structural relationships between students' affect, meta-affect, and meta-cognition in mathematics learning were analyzed using structural equations. Affect in mathematics is defined by cognizing value, interest, and confidence, whereas meta-affect involves affective awareness, evaluation, regulation and using. Meta-cognition is characterized by critical thinking, rehearsal, self-regulation, elaboration and organization. The model was secured by verifying the model fit, the convergent and discriminant validity, and the final model was established. The study revealed that affect in mathematics learning had a direct effect on meta-affect and meta-cognition. In other words, the more positive the students' interest, confidence, and recognition of value in mathematics learning, the higher was the meta-affect associated with affect.
 Affect had a tremendous indirect effect on meta-cognition via meta-affect, and thus the total effect of the affect on meta-cognition in mathematics learning was very large. Finally, the meta-affect had a direct effect on meta-cognition. In this study, affect, meta-affect, and meta-cognition were investigated as student characteristics; however, we have not investigated the formation of these variables. Therefore, further experimental studies are proposed to improve the meta-affect via teaching and learning strategies, investigation into the educational role of meta-affect as a learning goal and the impact of research into the role of affect in meta-cognitive strategy, and a closer analysis of similarity between meta-affect and meta-cognition.

The implementation of research based learning and the effect to the student metacognition thinking skills in solving H-irregularity problem

This study aims to develop learning tools based on Learning Based Research and produce learning tools in the form of student worksheets (LKM), learning outcomes tests (THB) and monographs and describe the profile of students’ metacognitive skills. The procedure of this study refers to Thiagarajan’s 4D development model which consists of 4 stages, namely defining, designing, developing, and disseminating. This research is a type of mixed research method which is a multimethod approach. Data collection techniques using test methods, interviews, observation and documentation. Educational research data analysis techniques using quantitative research approaches, data collection techniques are usually carried out with test techniques. While data collection techniques in qualitative research generally use observation techniques, in-depth interviews and documentation. The results showed, after the application of research-based learning, 14% of students were categorized in low-level mathematical metacognition thinking skills, and 34% were categorized as medium-level mathematical metacognition thinking skills and 52% were categorized in high-level mathematical metacognitive thinking skills. The results revealed that the implementation of research-based learning can improve the ability of students’ metacognitive thinking skills in solving H-Irregularity problems.

Metacognition, self-efficacy, and mathematics learning achievement: A study based on gender differences

This research was conducted in 2018 in the 4th semester students of the mathematics education study program at the Catholic University of Widya Mandira Kupang. The aim was to determine the effect of metacognition and self-efficacy on mathematics learning achievement in terms of gender differences. The method used was multiple regression analysis. The results of this study indicated that both partially and simultaneously in male and female student groups all had a significant effect on mathematics learning achievement. The effect of metacognition and self-efficacy on mathematics learning achievement in female students was greater than that of male students. Of the two independent variables, self-efficacy had more influence on mathematics learning achievement than metacognition in both male students and female students. The results of this study indicated that male students' metacognition and self-efficacy need to be further improved. Self-efficacy needs to be given the most attention compared to metacognition in mathematics learning so that student mathematics learning achievements can be improved.