Mathematical Critical Thinking Research Articles

Critical review: the effectiveness of student teams-achievement divisions vs numbered heads together cooperative learning in improving students' mathematical critical thinking abilities

Critical review: the effectiveness of student teams-achievement divisions vs numbered heads together cooperative learning in improving students' mathematical critical thinking abilities

Does Discovery Learning Enhance Secondary Students' Mathematical Critical Thinking Skills?

The implementation of the discovery learning (DL) model in Indonesia is believed to improve the mathematical critical thinking skills of the secondary students, so that it becomes the recommended learning model in the national curriculum. Several previous similar types of research have found that DL can enhance secondary students’ mathematical critical thinking skills. However, there were inconsistencies in the effect size of these primary studies. The meta-analysis was carried out to obtain a comprehensive analysis result and investigate the effect of study characteristics. Comprehensive meta-analysis (CMA) is a tool used to calculate hedge’s effect size (ES). An analysis of 25 relevant primary studies that met the inclusion criteria revealed that, based on the random-effects model, the implementation of the DL model had a high positive effect (ES = 0.981) on secondary students’ critical thinking skills compared to the conventional model. The duration of treatment and indexed publication are important factors that affect the effectiveness of implementing DL on students’ mathematical critical thinking skills. Based on the analysis, DL is recommended for use by secondary school teachers, taking into account the characteristics of the study. Keywords: iscovery learning, mathematical critical thinking skills, secondary students

The Impact of Mathematical Reasoning and Critical Thinking Skills on Mathematical Literacy Skills

For learning mathematics, mathematical skills are needed, some of which are mathematical reasoning skills, mathematical critical thinking skill, and mathematical literacy skills. This research aims to obtain information regarding the impact of mathematical reasoning and critical thinking skills on mathematical literacy skills. This research used a quantitative approach using an associative method with a correlational technique. The sample of this research was comprised 51 students who took integral calculus course in the Department of Mathematics and Mathematics Education, Faculty of Mathematics and Science in Universitas Negeri Jakarta, which were collected randomly using simple random sampling. The statistical analysis used in this research was multiple regression analysis. The results of this research showed that: 1) There was a positive impact of mathematical reasoning on mathematical literacy. 2) There was a positive impact of mathematical critical thinking skill on mathematical literacy. 3) There was an impact of both mathematical reasoning skill and mathematical critical thinking skill together on mathematical literacy. Further research is needed related to the impact of mathematical reasoning and critical thinking skills on mathematical literacy skills reviewed from the student’s initial mathematical skill. Keywords: critical thinking skills, mathematical literacy skills, mathematical reasoning

Development and validation of Mathematical Higher‐Order Thinking Scale for high school students

AbstractGlobally, significant attention is given to the cultivation and evaluation of Mathematical Higher‐Order Thinking Skills (MHOTS). This study aims to address the gap in developing and validating suitable MHOTS structures for high school students. In this study, 53 items were determined by experts in the field of mathematics education and scale development. The study group of this study consists of 654 students educated at the high school level. We decided to split the samples randomly in two by designating a random half as exploratory factor analysis (EFA) and the other half as confirmatory factor analysis (CFA). EFA was used to confirm a robust “four‐dimensional, nine‐factor” measurement structure, encompassing four key dimensions, namely mathematical critical thinking, mathematical creative thinking, mathematical problem‐solving, and mathematical metacognitive skills. The scale's quality was assessed through a retest using CFA and the structural validity was evaluated through CFA and correlation analysis. The criterion validity of the scale was also examined using math scores. The results from the double validity analysis showed that the scale had a reasonable and valid structure. The findings established the MHOTS for high school students as a reliable and valid instrument for measuring the level of MHOTS among high school students. This newly developed scale holds promise as an effective tool to assess and enhance mathematical higher‐order thinking in the student population.

Improving Students' Mathematical Critical Thinking Abilities Using Join Learning Groups Techniques

Joint Learning Groups (JLG) are groupings of students where one group of students works with activities that are interrelated with other groups, resulting in a set of interlinked activities. Task Planning Groups (TPG) are grouped based on the task plan that the teacher will give. This research aims to determine the increase in students' mathematical critical thinking skills after different treatments in the final test. The experimental research method aims to determine the increase in students' critical mathematical thinking skills using the Join Learning Groups technique and the results of students' critical mathematical thinking using the Task Planning Groups technique regarding Systems of Linear Equations in Two Variables. Research at SMPN 11 Jambi City, which was the sample for class VIII experimental group VIIIJ control group VIIIK. Experiments were treated with the JLG technique, and controls were treated with the TPG technique. From the results of this research hypothesis research using the t-test and SPSS.25, with tcount = 3.08 – 1.667, the JLG Technique further improves critical thinking skills with the TPG Technique in class VIII SMPN 11 Jambi City. The results of students' critical mathematical thinking using the JLG technique were 83.33, and the TPG technique was 75.03, better than the results of students' critical mathematical thinking using the TPG technique. In this research, it is recommended that teachers pay more attention to techniques that can improve student learning outcomes.

Analisis Proses Pemecahan Masalah Matematika Berdasarkan Kerangka Kerja Mason pada Siswa SMP dengan Kategori Kemampuan Berpikir Kritis Matematis yang Berbeda

Problem-solving ability is an ability that affects the success of learning mathematics. One that affects problem-solving ability is critical thinking ability. Teachers must know the problem-solving process that students have to improve the problem-solving-oriented learning process. The purpose of this qualitative descriptive study was to analyze the mathematical problem-solving process based on the Mason framework for junior high school students with different categories of mathematical critical thinking abilities. The subjects of this study were 4 grade VII E students of SMP Negeri 5 Tuban with high and low mathematical critical thinking skills categories. The instruments used are written test questions for comparison materials with FRISCO indicators, written test questions for comparative materials in the form of HOTS, and interview guidelines. The results of the study will be analyzed descriptively and qualitatively based on the Mason framework. From the results of the study, it can be concluded that: (1) subjects with the category of high critical thinking skills can solve HOTS questions with cognitive levels C4, C5, and C6 correctly and fulfill all Mason's framework, namely the entry, attack, and review stages; (2) subjects with low mathematical critical thinking skills were unable to solve all HOTS questions with cognitive levels of C4, C5, and C6 and only met Mason's framework, namely the entry stage with complete aspects.

PENERAPAN PEMBELAJARAN INKUIRI DALAM MENINGKATKAN KEMAMPUAN BERPIKIR KRITIS MATEMATIS SISWA SMK

The research aims to be able to find out the applications of inquiry learning using exponential material which can improve the mathematical critical thinking skills of vocational school level students in Bekasi Regency. This research approach uses descriptive methods of analysis in testing and observing the improvement of the ability to think critically mathematically of learners, test instruments are used in the form of questions on students' mathematical critical thinking skills on exponent material. The results showed a percentage score of 100% for six students classified as "very critical"; 80% percentage for six students who fall into the critical category; 60% percentage for six students who fall into the less critical category; and a 40% rate for four students who fall into the non-critical category. It can be concluded that the inquiry-based learning model used to improve students' critical thinking is successful.

The Effectiveness of Worksheet-Based Tri-N on Students' Mathematical Critical and Creative Thinking Abilities Material on Linear Equations in One Variable

<p>This research is motivated by the fact that most junior high school students have low critical and creative thinking abilities when facing mathematical problems. Even though these two abilities can be used as a basis for solving a mathematical problem, this research aims to determine the effectiveness of Tri-N based LKPD on students' critical thinking and creative thinking skills in One Variable Linear Equations material. The research method used is an experimental method with a Posttest-Only Control Design. The sample size was 39 students in a private junior high school in Piyungan, Bantul. This sample was taken using a cluster random sampling technique. The instrument used in this research is a mathematical problem test, which aims to measure critical and creative thinking abilities in dealing with mathematical problems. The data analysis technique used is the MANOVA test. The research results show that learning mathematics on equations and linear inequalities in one variable using Tri-N based worksheets does not significantly affect students' ability to think critically and creatively. In connection with the results of this research, Tri-N based LKPD on equations and inequalities in one variable can be used as an alternative teaching material for mathematics learning in equations and inequalities in one variable.</p><p><strong><br /></strong></p><p>Penelitian ini dilatarbelakangi bahwa sebagian besar siswa SMP memiliki kemamppuan berpikir kritis dan kreatif masih rendah saat menghadapi masalah matematis. Padahal dua kemampuan ini dapat digunakan sebagai dasar untuk menyelesaikan suatu permasalahan matematika. Penelitian ini bertujuan untuk mengetahui efektivitas LKPD berbasis Tri-N terhadap kemampuan berpikir kritis dan berpikir kreatif siswa pada materi Persamaan Linier Satu Variabel. Metode penelitian yang digunakan adalah metode eksperimen dengan desain <em>Posttest-Only Control Design</em>. Ukuran sampel sebesar 39 siswa SMP swasta di Piyungan, Bantul. Sampel ini diambil dengan teknik cluster random sampling. Instrumen yang digunakan dalam penelitian ini adalah tes masalah matematis yang bertujuan untuk mengukur kemampuan berpikir kritis dan kreatif dalam mengahdapi masalah matematis. Teknik analisis data yang digunakan adalah uji MANOVA. Hasil penelitian menunjukkan bahwa pembelajaran matematika pada materi persamaan dan pertidaksamaan linier satu variabel menggunakan LKS berbasis Tri-N tidak berpengaruh signifikan terhadap kemampuan siswa dalam berpikir kritis dan kreatif. Berkaitan dengan hasil penelitian ini, LKPD berbasis Tri-N pada materi persamaan dan pertidaksamaan satu variabel dapat digunakan sebagai alternatif bahan ajar pembelajaran matematika pada materi persamaan dan pertidaksamaan satu variabel.</p>

Model Pembelajaran Learning Cycle 5E Terhadap Keterampilan Critical Thinking Matematis Materi Fungsi Ditinjau dari Kemampuan Awal Siswa

This research aims to improve students' critical thinking or critical thinking skills which are divided into three levels, namely students who have high level, medium level, and low-level critical thinking through the application of the Learning Cycle 5E learning model in class X. This research is quasi-experimental research namely the development of true experimental design with Nonequievalent control group design research design through Posttest-Only Control Design carried out at Sukake 1 Public High School. The sample selected used Cluster random sampling, namely class X MIA 1 which was used as the experimental class. Data collection was carried out by trial at SMA Negeri 2 Menyuke followed by research school at SMA Negeri 1 Menyuke using the Learning Cycle 5E learning model and post-test final test to determine students' mathematical critical thinking skills at high, medium, and low levels, interviews to find out student responses regarding the results of the answers. The t-test results for both normal and homogeneous distributions obtained a significance value (2-tailed) = 0.031 < 0.05 with the decision H_1 being accepted. It was proven that there was a significant difference between the learning outcomes in the control class and the learning outcomes of students in the experimental class. Descriptively, students show improvement. Students also experienced quite good improvement. So, it can be concluded that the Learning Cycle 5E learning model provides an increase in critical thinking skills

Fostering critical thinking and self-efficacy in mathematics students

This research addresses the low critical mathematical thinking abilities of students when facing mathematical problem-solving challenges. The study aims to evaluate the impact of implementing various teaching approaches, including Contextual Teaching and Learning (CTL), Problem-Based Learning (PBL), and Direct Instruction (DI) models, on students' critical mathematical thinking abilities. Participants included 276 eighth-grade students from SMP La Tansa Mashiro 1, 2, and 3 in Lebak Banten during the academic year 2022/2023, divided into three classes. Samples were selected using simple random sampling, resulting in 94 students for CTL, 92 students for PBL, and 90 students for DI instructional models. Data collection involved self-efficacy questionnaires and critical mathematical thinking ability tests, analyzed using a two-way ANOVA. The findings suggest that implementing CTL and PBL models positively influences students' critical mathematical thinking abilities. Additionally, students' self-efficacy levels contribute significantly to their critical mathematical thinking abilities. Furthermore, a significant interaction was observed between the implementation of CTL, PBL, and DI models and students' efficacy levels, collectively influencing students' critical mathematical thinking abilities. These results emphasize the importance of employing active approaches, such as contextual, problem-based, and direct instructional methods, while also enhancing students' self-confidence to improve their critical mathematical thinking abilities. It is hoped that implementing these recommendations will enhance the effectiveness of mathematics learning and foster the development of students' critical thinking skills.

Research trends in critical thinking skills in mathematics: a bibliometric study

<span lang="EN-US">This study systematically reviews and analyzes previous studies’ literature to identify the research gaps and the steps that must be taken for research on critical thinking in further mathematics education. Two methods, namely bibliometric analysis and descriptive content analysis, were used to achieve this goal. Data for the bibliometric analysis was obtained from the Scopus database, with the keywords “critical thinking” and “mathematics” Documents accessed are limited to the publication range of 2012-2022. The results show that the number of critical thinking research in mathematics has increased significantly, with a peak in 2021 of 65 articles; the United States has the most research and citations. The source that received the most citations was the journal Educational Studies in Mathematics. The evolution of the theme of critical thinking in mathematics began to link critical thinking with collaboration learning, mathematics education, teacher education, engineering, education, and collaborative learning. The quantitative approach with a student sample, tests as data collection instruments, and the analysis of variance (ANOVA) method is the methodology most often used by researchers. The results of this study are likely helpful for other researchers who will examine critical thinking skills in mathematics, namely as a research guide that they will develop. In addition, the existence of several research gaps can motivate other researchers to fill these gaps to contribute to improving the quality of critical thinking in mathematics.</span>

Analisis Kemampuan Berpikir Kritis Matematis Siswa Berdasarkan Soal Berbasis TIMSS

This research aims to determine the analysis of students' mathematical critical thinking abilities based on questions based on TIMSS VIII SMP Negeri 29 Medan. This research is descriptive qualitative research. The subjects in this research were 33 students in class VIII-7 of SMP Negeri 29 Medan. The results of the research show that: (1) The average value of students' interpreting abilities is 76.01, which indicates that students' interpretation indicators are in the high category. (2) The average student score in analyzing the mathematical critical thinking ability test is 64.39, which shows that the students' analysis indicators are in the medium category. (3) The average score of students' abilities in the evaluation indicators on the mathematical critical thinking ability test is 41.48, which shows that the students' evaluation indicators are in the low category. So it is concluded that students with high abilities are only able to fulfill 2 critical thinking indicators, namely interpreting and analyzing indicators, 2 students with moderate mathematical abilities are only able to fulfill 2 critical thinking indicators and students with low mathematical abilities, there is 1 student only fulfilling 1 critical thinking indicator in One of the question numbers is the evaluating indicator in question number 3.

Implementation of Differentiated Learning on Mathematical Critical Thinking Ability

This research focuses on the differences in mathematical critical thinking skills between students who use differentiated learning strategies and those who use undifferentiated learning strategies. The methodology used in this research is experimental research using the nonequivalent posttest-only control group design. The participants of this study consisted of X-1 and X-3 students at SMA Negeri 1 Mantup with 30 students in each class. Each class was divided into 5 groups with the number of each group of 6 students. The data used in this study came from instruments in the form of a questionnaire that assessed students' learning styles in the experimental class, as well as a post-test that measured mathematical critical thinking skills. The posttest used consists of three essay questions covering 4 critical thinking indicators, namely interpreting, analyzing, evaluating, and inferring. The scores obtained by students will be assessed using the T test or independent samples T test. Based on the research findings, 3 learning style groups were obtained with 14 students of visual learning style, 8 students of auditorial learning style, and 8 students of kinesthetic learning style, respectively. For the post-test results of each class showed that there were differences in mathematical critical thinking skills between students who received differentiated learning and students who received undifferentiated learning with a t value of 2.781 exceeding the t table value of 2.001 which means there is an influence between differentiated learning on mathematical critical thinking skills.

Efektivitas Model Pembelajaran Flipped Classroom (FC) Terhadap Kemampuan Berpikir Kritis Matematis Siswa pada Materi Peluang

The purpose of the study is to determine the achievement of student learning completeness on opportunity material after applying the Flipped Classroom (FC) learning model, knowing whether the mathematical critical thinking skills of students who get learning with the Flipped Classroom (FC) learning model are better than students who get learning with the direct learning model and to find out student learning activities during the application of the Flipped Classroom (FC) learning model. This study used a Quasi-Experimental design with the form of The Nonequivalent Posttest-Only Control Design. The population in this study was all grade VIII students of SMP Negeri 6 Singkawang totaling 115 students and the sample in this study consisted of 2 classes selected from 5 classes. Sampling using purposive sampling technique and selected class VIII E as experimental class and class VIII B as control class. The consideration of choosing the two classes is because there are still many students who have difficulty in learning and the average completeness of students has not reached KKM. Data collection is carried out by providing posttest questions on opportunity material and observation of student learning activities. Hypothesis testing using one sample t-test, two sample t-test. The results showed that: 1) Students achieved individual and classical completeness in classes applied to the Flipped Classroom (FC) learning model; 2) The mathematical critical thinking ability of students applied the Flipped Classroom (FC) model is better than students who applied the direct learning model; 3) Student activities are classified as active during the implementation of the Flipped Classroom (FC) learning model.

Analisis Kemampuan Berpikir Kritis Matematis Siswa ditinjau dari Gender

Mathematical critical thinking is the ability to solve problems using knowledge, reasoning, and mathematical proof. This research aims to test students' mathematically necessary thinking abilities based on gender. The subjects of this research were students of class X TKJ SMKN 2 Soe. This research method is descriptive-qualitative, where data collection uses observation techniques, tests in the form of story questions, and semi-structured interviews. Data analysis in this research uses the Miles and Huberman technique in data reduction, data presentation, and concluding/verification. Data validity testing uses technical triangulation. The results of the research show that there is no significant difference in students' mathematical critical thinking abilities based on gender. Most male and female students can fulfil all indicators of mathematical critical thinking, namely providing simple explanations, building basic skills, drawing conclusions and further explanations, and determining problem-solving strategies and tactics. Female students are more detailed in the problem-solving process based on stages, while male students are less detailed

KEMAMPUAN BERPIKIR KRITIS MATEMATIS SISWA PADA MATERI RELASI DAN FUNGSI

The purpose of this study was to describe the extent of mathematical critical thinking skills of junior high school students on the material of relations and functions. The research method used is a descriptive qualitative approach involving 3 students from 39 students of class VIII SMPN 3 Cihampelas as research subjects. Data was collected through giving test questions related to relation and function material and interviews to gain in-depth understanding. Based on the results of this study, it can be concluded that students' mathematical critical thinking skills in relation and function material can be classified as quite good. This can be seen from the number of students who are in the medium category. While some others are in the high and low categories. Students who have high mathematical critical thinking skills can fulfill all five indicators of mathematical critical thinking, namely elementery clarification, basic support, advance clarification, strategy and tactic, inference. Students in the medium category were only unable to fulfill the inference indicator, while students in the low category were only able to fulfill the elementary clarification indicator.

Mathematical Critical Thinking Profile Of Students On Pisa Framework Space And Shape Content Questions Reviewed From Self-Efficacy

The critical thinking skills of students in Indonesia are still low. This is attributed to teachers emphasizing solving mathematical problems with given formulas. Therefore, the PISA framework's space and shape content was used in this study to test students' abilities to identify similarities and differences in different objects, analyze the components of objects, and recognize different dimensions and representations. This research aims to describe and obtain students' cognitive knowledge at each stage of the mathematical critical thinking ability in working on PISA's space and shape content framework problems. The five indicators of mathematical critical thinking skills used are demonstrating problem understanding, explaining arguments according to mathematical concepts, using appropriate problem-solving methods, providing systematic modeling or explanations, and using alternative solutions in problem-solving. This qualitative research employed a grounded theory approach. Data were obtained through self-efficacy questionnaires, critical thinking ability tests on spatial geometry, and interviews. The self-efficacy questionnaire results were analyzed and categorized (high, medium, and low), with two students selected from each category as subjects. The research finding show that the indicator of using alternative solutions in mathematical problem-solving is not fulfilled in all three subject categories, which have high, medium, and low self-efficacy. Another aspect found in this study is the need for optimalization of reflective thinking for critical inquiry (contemplating) with effective communication among students or groups. This is necessary for identifying problems, detecting the correctness and errors of answers, and correcting them to draw accurate conclusions.

Gamification of Mathematics Teaching Materials to Improve Problem Solving and Critical Thinking Ability: The Experts’ Assessment

Gamification is a learning approach in which moving games or visualizations are specifically designed to teach certain skills to students so that the learning process motivates students to think and solve problems. The purpose of this study was to develop gamification-based junior high school mathematics teaching materials in the form of GEMAS games to improve problem-solving skills and mathematical critical thinking. This study uses the ADDIE model of research and development but is limited to only 3 stages, namely analysis, design, and development, as well as an assessment by a team of experts using the Delphi technique. The research instruments used were the validation sheet for the critical thinking ability test using FRISCO theory, the validation sheet for the problem-solving ability test instrument with the Krulik and Rudnick indicators, and the game validation sheet. Data were analyzed descriptively. Based on the results of content validity data analysis related to the GEMAS game that has been developed, it is found that the criteria in the context of problem-solving skills and critical thinking skills used are 90.20% fulfilled, and the fulfillment of game content criteria reaches 94%. Based on these data overall 92% of the GEMAS game feasibility assessment criteria have been met. Thus, the gamification-based teaching material in the form of the GEMAS game has been developed as an assessment in a very valid category and is suitable for use in learning

Computational thinking ability becomes a predictor of mathematical critical thinking ability

This research aims to determine the relationship between computational thinking ability and mathematical critical thinking ability of seventh-grade students at SMPN 49 Jakarta. Computational thinking ability is skills or processes in solving problems effectively, while mathematical critical thinking ability is a process of analyzing problems to make an accurate decision. This research used correlation research with research subjects consisting of 14 female students and 16 male students. The instrument in this study is a test in the form of a description, which is measured using indicators. This study used decomposition, pattern recognition, abstraction, and algorithm thinking as indicators of computational thinking ability. This study uses elementary clarification, essential support, inference, advanced clarification, strategy, and tactics as indicators of mathematical critical thinking. The outcome of this research showed a positive correlation between computational thinking ability and students’ mathematical critical thinking ability. The relationship analysis shows a simultaneous and significant relationship between computational thinking and essential mathematical thinking abilities. The correlation test results using Pearson Product Moment obtained a result of 0.897 with a coefficient of determination of 80.5%. The magnitude of the correlation indicates that the two abilities have a solid relationship. If computational thinking ability is high, then mathematical critical thinking ability is also high, and if computational thinking ability is low, then mathematical critical thinking ability is also low.

Analisis kemampuan berpikir kritis peserta didik ditinjau dari self-confidence

Students' critical thinking abilities which are still low need to be developed and one of the abilities that must be instilled in students is self-confidence. This research aims to describe students' mathematical critical thinking abilities in terms of self-confidence. The type of research used in this research is qualitative research with a case study method. The research subjects were 9th-grade students at one of the junior high schools in Siak Hulu and numbered 33 people. The data collection technique in this research is a test technique using mathematical critical thinking ability test instruments and non-test techniques in the form of student self-confidence questionnaires and interviews. The data analysis technique is carried out through several stages, including reducing data, presenting data, and drawing conclusions. Based on the research results, it was found that; (1) overall students' mathematical critical thinking abilities are classified as less critical and need to be improved; (2) self-confidence is in line with mathematical critical thinking skills where students with high self-confidence have sufficient critical thinking skills which are indicated by students being able to master two indicators of critical thinking. Students with moderate self-confidence have sufficient critical thinking skills, which is indicated by students being able to master two critical thinking indicators. In contrast, students with low self-confidence have sufficient critical thinking skills, which is indicated by students being able to master two critical thinking indicators.