Mathematical Critical Thinking Skills Research Articles

Analyzing Student’s Mathematical Critical Thinking Ability of Concept Newman’s Error Analysis Review from Habits of Mind

This study aims to analyze and describe the mistakes made by students in completing mathematical critical thinking skills in terms of habits of mind (HOM) with three categories, namely limited, developing, and proficient. The review was also analyzed from the factors that led to the occurrence of errors based on error analysis according to Newman. This research uses qualitative research methods. The data collection techniques used are questionnaires, tests, and interviews. The instruments used are HOM questionnaires and mathematical critical thinking ability tests. The selection of the study subject was carried out purposively with the consideration that the subject had a HOM category. A total of 25 students who filled out the HOM scale and mathematical critical thinking ability test, 3 students were selected to be interviewed based on the HOM category classification. The data analysis techniques used in this study are data reduction, data presentation, and drawing conclusions. Based on the results of the study, students with limited HOM were only able to solve questions up to indicator 1 because they made mistakes in reading and process skills. Students with HOM develop, only able to solve problems up to indicator 2 due to Comprehension and transpormation errors. Students with proficient HOM, are able to solve questions up to indicator 3 because they make mistakes in the skill and encoding process.

The Effectiveness of Differentiated Learning Strategies on Elementary Students' Mathematical Critical Thinking Ability

This study explores the effectiveness of differentiated learning strategies in improving elementary students' mathematical critical thinking skills. The independent variable is the application of differentiated learning strategies, while the dependent variable is the students' mathematical critical thinking ability. A quantitative approach was used, utilizing a quasi-experimental design with a non-equivalent control group. The sample included 30 fourth-grade students from Al-Falaah Islamic Elementary School and 30 from Jombang 01 Ciputat Elementary School, selected through purposive sampling. Data collection involved tests, questionnaires, observation sheets, and interview guides, and the analysis was conducted using independent sample t-tests and N-Gain tests with the help of SPSS IBM 22.0 software. The statistical analysis showed a significant effect of differentiated learning strategies on critical thinking skills, with a p-value of 0.000 and an N-Gain score of 74.56%. This indicates a notable improvement in students’ abilities in interpretation, analysis, evaluation, and inference. Differentiated learning strategies accounted for 58% of the variation in outcomes, with the remaining 42% influenced by other factors. In conclusion, differentiated learning strategies significantly enhance elementary students' mathematical critical thinking, and educators are encouraged to adopt these methods to foster deeper cognitive engagement.

Analysis of Mathematical Critical Thinking Ability based on Students' Ability Level

Analyzing and testing mathematical critical thinking skills based on the ability level of class VIII students of junior high school is the aim of this research. By understanding the level of students' abilities, educators can determine students' mathematical critical thinking abilities and develop appropriate teaching strategies to improve students' abilities. This study uses a qualitative descriptive research method. This research was conducted at one of the junior high schools in Cipatat, West Bandung Regency with heterogeneous abilities of 8 students. This research uses data collection techniques by providing mathematical critical thinking ability questions on SPLDV material which consists of 5 essay test questions based on the following indicators: (1) Checking the completeness of problem solving steps. (2) Look for alternative solutions to problems. (3) Identify spldv equations with certain characteristics. (4) Choose the best way to solve the problem from alternative ways of solving it. (5) Identifying the adequacy of data on a problem. In this study, the results of the analysis have shown that students at a high level of ability can check the completeness of problem solving steps, students with a medium level of ability have little difficulty in identifying spldv equations with certain characteristics, and students with a low level of ability have difficulty finding alternatives problem solution.

Analysing the Mathematical Critical and Creative Thinking Abilities in Problem Solving Introverted Students

This study aims to evaluate the critical and creative thinking abilities in the context of mathematics when solving problems related to arithmetic sequences and series among introverted students in the 11th grade at Xaverius 1 High School in Jambi City. This issue arises due to differences in thinking skills and cognitive processes among students based on personality types, where it was found that introverted students tend to have low mathematical critical and creative thinking abilities. The research method employed is a descriptive qualitative approach, collecting data through personality questionnaires, tests, and interviews. Research subjects were selected from introverted students based on personality questionnaire results and answer sheet analysis, with three students representing the various response groups. The results of this study indicate that introverted students demonstrate good mathematical critical thinking skills in understanding problems, planning, and implementing plans. However, they tend to overlook rechecking their solutions. The creative mathematical thinking abilities of introverted students mainly involve fluency and flexibility in understanding problems, planning, and implementing plans, although they lack in terms of originality and elaboration in problem-solving

Pengaruh model pembelajaran 3CM (cool – critical - creative – meaningfull) terhadap kemampuan berpikir kritis siswa kelas VIII

This research aims to determine the differences in the mathematical critical thinking abilities of students who use the 3CM learning model and students who use the direct learning model with a scientific approach, the influence of the 3CM learning model on students' mathematical critical thinking abilities and student learning activities. The type and research design used is quantitative research with a Quasi Experimental design in the form of a Nonequivalent Posttest-Only Control Design. The sampling technique used was purposive sampling. The data collection instruments were posttest mathematical critical thinking skills and observation sheets of student learning activities. Data analysis techniques in this research are normality test, homogeneity test, independent two-sample t-test, and percentage of student learning activities. The results of the research show that the mathematical critical thinking abilities of students who use the 3CM learning model are higher than students who use the direct learning model with a scientific approach, the 3CM learning model has a big influence on students' mathematical critical thinking abilities, and student activities are classified as very active after implementing the 3CM learning model.

Mathematical Critical Thinking Skills through STEM/STEAM Approach: A Systematic Literature Review

The STEM/STEAM approach provides opportunities for students to develop critical thinking skills through the integration of different disciplines. This study aims to provide a comprehensive picture of the extent to which the STEM/STEAM approach develops critical thinking skills in mathematics teaching and learning. A systematic literature review (SLR) was conducted using guidelines from the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). We searched Springer Link, Eric, and Google Scholar for 21 articles on critical thinking published between 2018 and 2022. The results show that most of the lead authors studying critical thinking through STEM/STEAM are from Indonesia, with fewer contributions coming from the United States, Taiwan, Saudi Arabia, Turkey, Japan, and Malaysia. The most common research methods used are quantitative research and R & D. These methods correspond to the types of data collection tools used by researchers and critical thinking tests to identify critical thinking skills for the cognitive aspect and questionnaires for the affective aspect. The best practice for improving learner’s mathematical critical thinking skills in STEM/STEAM is Project-Based Learning (PBL). However, this practice is not used by many development researchers. The authors find distinctive features in the interventions used by researchers to improve the critical thinking of learners from each country. The most common intervention was an analysis of the implementation of the STEM/STEAM approach in Indonesia. Many Indonesian researchers also developed learning models and media. Other countries focused more on computer-based activities, developing community programs, and identifying participants' perceptions of critical thinking. These differences give each country its own characteristics in improving and identifying the critical thinking skills of its people. These differences in practices and interventions can also provide alternatives for researchers in their research on critical thinking through the STEM/STEAM approach.

MODEL DISCOVERY LEARNING BERBANTUAN GEOGEBRA UNTUK MENINGKATKAN KEMAMPUAN BERPIKIR KRITIS MATEMATIS DAN KEMANDIRIAN BELAJAR SISWA

Mathematics, as an important foundation in education, contributes to the advancement of science and technology and teaches students logical, analytical, and creative thinking. This is in accordance with the Merdeka Curriculum which emphasizes the development of 21st century skills and character development, including critical thinking and self-regulated learning. However, the low mathematical critical thinking skills and self-regulated learning in Indonesia is still a challenge. One of the factors that influence this is the use of inappropriate learning models. The Discovery Learning learning model supported by technology such as GeoGebra is a potential solution to improve both capabilities. The purpose of this study was to determine the increase in mathematical critical thinking skills and determine the increase in self-regulated learning of students who obtained the GeoGebra-assisted Discovery Learning model compared to students who obtained conventional learning models. This research method is a quasi-experiment with the nonequivalent pre-test post-test control group design. Sampling is done by purposive sampling technique. This research was carried out in one of the Junior High Schools in Serang City in the 2023/2024 school year, involving two classes of grade VII students as an experimental and control group. The instruments in this study consisted of tests of mathematical critical thinking skills and learning independence scales. The results showed that the improvement of mathematical critical thinking skills and increased self-regulated learning of students who applied the GeoGebra-assisted Discovery Learning model were better than students who applied conventional learning models

Enhancing Mathematical Critical Thinking Skills using Lectora Inspire Interactive Learning Media in the Discovery Learning

Critical thinking skills are one of the abilities that everyone must have to face the challenges of the 21st century. The use of interactive learning media lectora inspire in discovery learning can facilitate to develop students' mathematical critical thinking skills. Therefore, a study was conducted that aims to see the improvement of critical thinking skills using lectora inspire interactive learning media in the discovery learning model. This research is included in the pre-experimental design with the research design used is a single group one-group pretest-posttest design. The samples used in this study were 26 eighth-grade students in Pekanbaru, Riau. Data analysis techniques using Normality - Gain (N-Gain) test and t-test. The N-gain value obtained was 0.59 with moderate criteria. Based on the T-test results, there is a significant difference in the average pretest score and posttest score. The level of effectiveness occurs in the posttest after using lectora inspire interactive learning media, so the use of lectora inspire interactive learning media in the discovery learning model can improve students' mathematical critical thinking skills. This research makes a significant contribution to the innovation of mathematics learning in Indonesia, by offering a more effective and fun approach. The findings are expected to be a reference for educators, researchers, and educational policy makers in an effort to enhance the quality of mathematics learning.

Efektivitas Model Pembelajaran Kooperatif Tipe Numbered Head Together (NHT) Berbantuan Alat Peraga dalam Meningkatkan Kemampuan Berpikir Kritis Siswa pada Pembelajaran Matematika

The study aims to test the effectiveness of a Numbered Head Together (NHT) cooperative learning model with a tool in improving students' ability to think critically about learning mathematics. The research method used is quantitative with the type of Quasi-experimental research. The study population was class X students of SMA Negeri 1 Cigugur in the 2023-2024 school year, with samples taken using purposive sampling technique, namely classes X1 and X2 with a total of 64 students and the statistical test used was t-test. The instruments used included testing students' critical thinking skills and elevating students' responses. Data analyzed using test instruments and analysis of mathematical critical thinking abilities. The results of the study showed that there was a difference in average mathematical critical thinking skills between students who obtained cooperative NHT-type learning with a tool compared to students who gained conventional learning. Normality tests and homogenity tests show that the N-Gain Score data are distributed normally and the data variance is homogeneous. The results of the hypothesis test showed a significant improvement in students' ability to think critically in the experimental group. Students' response to the NHT learning model was also positive

TEAM GAMES TOURNAMENT AND MEANS-ENDS ANALYSIS: LEARNING TYPES IN IMPROVING MATHEMATICAL CRITICAL THINKING

The purpose of this research was to determine the effectiveness of Teams Games Tournament (TGT) and Means-Ends Analysis (MEA) learning types in improving mathematical critical thinking skills and to compare the effectiveness of the two learning types. This research used a quantitative approach with a purposive sampling technique. Two classes were selected from all XI classes at MA Ma'ahid Kudus: experimental class 1, which applied the TGT learning type, and experimental class 2, which applied the MEA learning type. Both experimental classes were chosen based on the pretest homogeneity test, and the two classes were homogeneous. The results obtained from this research are as follows: 1) There is an increase in students' mathematical critical thinking skills after being given the TGT learning type, 2) There is an increase in students' mathematical critical thinking skills after being given the MEA learning type, and 3) There is a difference in effectiveness between the TGT and MEA cooperative learning models.

Penerapan Model Problem Based Learning Untuk Meningkatkan Kemampuan Berpikir Kritis Matematis Siswa Di SMA Negeri 2 Medan

Mathematics is a discipline that focuses on developing thinking skills. Learning mathematics can hone critical thinking skills, which form the foundation for understanding mathematical concepts and effectively solving problems. This Classroom Action Research (PTK) study was conducted to improve students' critical mathematical thinking skills through a PBL approach. Medical School Negeri 2 Medan was the site of the research. A total of 36 students from the 2023/2024 academic year at SMA Negeri 2 Medan's class XI MIPA 9 served as the study subjects. There were two cycles to this research, and each one included the following steps: preparation, action, observation, and reflection. The data was analyzed using quantitative descriptive analysis, and the methods for data gathering included both tests and non-tests. The results showed that the PBL model has improved the critical mathematical thinking skills of students in class XI MIPA 9 at SMA Negeri 2 Medan. In the first cycle, students' critical mathematical thinking skills reached 75.52% with a high qualification, and in the second cycle, they increased to 87.27% with a very high qualification.

Analysis of Mathematical Critical Thinking Skills using Problem-Based Learning Models in Junior High School Students

Analysis of Mathematical Critical Thinking Skills using Problem-Based Learning Models in Junior High School Students

Enhancing self-regulated learning and critical thinking in STEM through flipped classroom models

One of the causes of low proficiency among high school students in mathematical critical thinking is their lack of willingness to learn independently. This study investigated the mathematical critical thinking skills and self-regulated learning of high school students through the Flipped Classroom STEM approach. The research employed a sequential explanatory design, beginning with quasi-experimental pre-tests and post-tests for quantitative assessment of the learning process, followed by qualitative methods such as questionnaires, interviews, and observations for deeper analysis. Data analysis utilized quantitative techniques, including normality and homogeneity tests and hypothesis testing in SPSS, alongside qualitative methods for data reduction, data presentation, and conclusion. The findings revealed that flipped classroom learning significantly improved students' abilities in critical mathematical thinking, particularly highlighting the importance of self-regulated learning. There was a notable difference in post-test scores compared to those from traditional learning methods. Moreover, the study found that students with higher self-regulated learning skills were more effective in critical thinking, underscoring the effectiveness of the flipped classroom approach in fostering independent learning and enhancing essential thinking abilities in mathematics education.

Implementasi Model Pembelajaran Kooperatif Tipe Team Game Tournament (TGT) Dalam Melatih Berfikir Kritis Peserta Didik

Critical thinking skills in mathematics are very important to develop, for this reason it is necessary to have a mathematics learning process that involves students actively, especially in the learning process in the classroom. The aim of this research is to determine the level of students' critical thinking abilities in learning using the Teams Games Tournament (TGT) model, as well as to determine the factors that inhibit and support learning using the Teams Games Tournament (TGT) learning model. The type of research used is qualitative research. Data collection techniques use observation. Meanwhile, the data analysis technique used is descriptive interpretative. The results of the research show that the Teams Games Tournament (TGT) learning model really helps students understand the learning material. One of the things that supports learning using the Teams Games Tournament (TGT) model is the supporting media used, while the inhibiting factor in learning using the Teams Games Tournament (TGT) model is the lack of time in carrying out the learning process.

Development of E-Worksheets Using Contextual Teaching and Learning to Increase Students' Critical Mathematical Thinking

This study aims to develop e-worksheets using contextual teaching and learning to improve students' critical mathematical thinking. The method used in developing e-worksheets was design research. The research data were obtained through validation questionnaires, student responses, and critical mathematical thinking skills tests. The research subjects used were 36 Year 10 students in one of the public high schools in West Bandung Regency. Based on the results of data analysis, the validation results obtained were 3.6 with valid criteria, and student responses about practicality obtained 'very practical' criteria with an average percentage of 86%. The product's effectiveness is said to be 'Very Good' with an average score of 80.75 from the students' post-test. The increased students' critical thinking resulted in the ‘Moderate’ criteria with an N-Gain of 0.66. E-worksheets with contextual teaching and learning are feasible and can improve students' critical mathematical thinking skills on the comparison of trigonometric function.

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

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.

The Improvement of Students' Mathematical Critical Thinking Skills and Learning Motivation Through Contextual Teaching and Learning

This research aims to investigate the improvement of students' critical thinking skills and learning motivation using a problem-solving approach through Contextual Teaching and Learning (CTL) in the topic of statistics with the assistance of GeoGebra. This study employs a pre-experimental research design with a one-group pretest-posttest approach. The sample consists of one eighth-grade class in a public junior high school in Yogyakarta. Data collection techniques include pretests and posttests to measure students' critical thinking skills and a questionnaire to assess students' learning motivation. The paired sample t-test is utilized for data analysis. The results reveal an improvement in critical thinking skills, with an average pretest score of 49.33 and a posttest score of 85.00. Students' learning motivation also increased, with an average pretest score of 73.60 and a posttest score of 88.87. The t-test result shows a significance value of 0.000 < 0.05, indicating the rejection of the null hypothesis. This implies that there is a significant influence on students' critical thinking skills using a problem-solving approach through Contextual Teaching and Learning in the statistics subject, resulting in an enhancement of students' critical thinking skills