Mathematical Critical Thinking Skills Research Articles

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.

LEARNING STYLES AND MATHEMATICAL DISPOSITIONS AS PREDICTORS OF THE CRITICAL THINKING SKILLS OF JUNIOR HIGH SCHOOL STUDENTS

The primary purpose of this study is to determine whether learning styles and mathematical dispositions predict students critical thinking skills. This study employed a descriptive and correlational research approach. Using stratified random sampling, 271 grade 10 students were selected as respondents from six public secondary schools in Kapalong East District, Davao del Norte Division during the school year 2022-2023. Furthermore, this study employed two adapted survey questionnaires and one researcher-made questionnaire, all of which were validated to collect data and treated using mean, standard deviation, Spearmans Rank Correlation Coefficient, and regression analysis. The findings showed that the learning styles among the students are high, their mathematical dispositions are moderate, and their critical thinking skills are low. The findings also revealed that learning styles has a positive significant relationship and influence on students critical thinking skills in mathematics. However, students mathematical dispositions have an inverse relationship and influence to their critical thinking skills in mathematics. These findings underscore the importance of nurturing critical thinking skills among students. It is recommended that teachers and DepEd officials collaborate to create interventions aimed at enhancing students critical thinking skills. Furthermore, replication studies across diverse contexts are advised to validate the longevity of these relationships and further advance our comprehension of the subject matter. KEYWORDS: Learning styles, mathematical dispositions, critical thinking skills, grade 10 students, descriptive-correlational approach, regression analysis, Kapalong East District, Davao del Norte.

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.

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

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.

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.

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.

SYSTEMATIC LITERATURE REVIEW: MATHEMATICAL CRITICAL THINKING ABILITY IN THE STUDENT FACILITATOR AND EXPLAINING (SFE) LEARNING MODEL

The purpose of writing this article is to explain the relationship between the Student Facilitator and Developing (SFE) learning model in mathematics learning and students' critical thinking abilities. The method used in this study is Literary Study. The literature study is carried out by searching various written sources, in the form of books, archives, magazines, articles and journals, or documents that are relevant to the problem being studied. By using 10 articles that have met the inclusion criteria, namely research subjects of middle school - high school students, meeting synta 1-4 and in the years 2013-2023. These articles were searched using national and international journal databases, namely Google Scholar, Garuda, Researchgate, Scopus and Science Direct. The findings showed that junior high school students' abilities in mathematical critical thinking skills were influenced after using the Student Facilitator and Developing (SFE) learning model. For further research, we can examine more broadly the use of the SFE model and its influence in critical mathematical thinking at various levels of educational units.

PENINGKATAN KEMAMPUAN BERPIKIR KRITIS MATEMATIS SISWA DENGAN MENGGUNAKAN PENDEKATAN PROBLEM POSING

The purpose of the study was to determine how the problem posing approach in learning mathematics can improve mathematical critical thinking skills. This type of research is Quasi experimental with Post Test Only Control Group design. The population in this study were VIII grade students of SMP Negeri 12 Bandar Lampung. The cluster random sampling method was used to select sample members from the population without considering the students' ability level. The results showed that the problem posing approach with steps to create mathematical situations, formulate mathematical questions, solve mathematical problems, and apply mathematical concepts has a relationship with indicators of mathematical critical thinking skills. Indicators of critical thinking skills include interpretation, analysis, evaluation, inference, explanation, and self-regulation. So, it can be concluded, students' mathematical critical thinking skills can be improved using the problem posing approach.

STRUKTURAL EQUATION MODEL (SEM) MENGANALISIS JALUR PATH KOMPETENSI DAN KOMPENSASI TERHADAP PRODUKTIVITAS KARYAWAN DI CV. SEMARANG INDAH

The purpose of this study was to analyze and improve students' mathematical critical thinking skills in terms of learning styles in class X MIPA 1 students at SMAN 9 Depok. The research method used in this research is analytical method. The sampling technique used purposive sampling technique. Instruments for collecting data in this study were in the form of a learning style questionnaire and a test of critical thinking skills. All students of class X MIPA 1 were identified with the type of learning style by using learning styles and critical thinking skills tests taken by 6 students representing each type of learning style of 2 students. The test is carried out on the Absolute Value material. Furthermore, the analysis of all data is carried out with the following steps: data reduction stage, data presentation stage, and conclusions. The results showed that: 1) students with visual learning styles were able to overcome indicators at the stage of providing simple explanations and arranging tactics but were less able to meet indicators at the inference stage, 2) students with auditory learning styles were less able to reach the stage of providing simple explanations but were able to in arranging strategies-tactics and inference stages, 3) students with kinesthetic learning styles are able to fulfill all indicators at the stage of giving simple explanations, setting strategies-tactics, and inferences

Implementasi Model Realistic Mathematics Education (RME) Untuk Meningkatkan Kemampuan Critical Thinking Matematika Pada Siswa Kelas IV Sekolah Dasar

The purpose of the research was to increase students' critical thinking skills in mathematics by applying the Realistic Mathematics Education (RME) model. The type of research method is Classroom Action Research (PTK) which is carried out in 2 cycles. Each cycle consists of planning, implementation, observation, and reflection. The subjects of classroom action research were fourth grade students of SD Negeri 34 Lubuklinggau totaling 19 students consisting of 10 female students and 9 male students. Data collection techniques using observation and tests. The result from this reasearch showed that by applying the Realistic Mathematics Education (RME) model can increase the ability of critical thinking mathematics students in fourth grade SD Negeri 34 Lubuklinggau. It can be seen from the increasing students' critical thinking skills in mathematics from the pre-cycle condition of 54%, cycle I of applying the Realistic Mathematics Education (RME) model for critical thinking skills of 69%, based on deficiencies in cycle I then followed up in cycle II, the results of critical thinking skills at this stage increased to 80.5%. It is concluded that the application of the Realistic Mathematics Education (RME) model can increase students' mathematical critical thinking skills in fourth grade SD Negeri 34 Lubuklinggau.

KEMAMPUAN BERPIKIR KRITIS MATEMATIS DENGAN BRAIN BASED LEARNING: SYSTEMATIC LITERATURE REVIEW

One of the abilities of the 21st century is the ability to think critically. Mathematical critical thinking is the ability used to solve mathematical problems using higher thinking skills, namely analyzing, synthesizing, concluding and evaluating. Brain Based Learning (BBL) is an approach that can be used to carry out learning based on brain function. The aim of this research is to describe critical mathematical thinking skills that can be improved with the BBL approach. The research was conducted using the Systematic Literature Review (SLR) method with stages: planning, implementation and reporting. The results of the study from 13 articles show that BBL can improve students' critical mathematical thinking skills.BBL is carried out in 7 stages, namely: pre-exposure; preparation; initiation and acquisition; elaboration; incubation and inserting memory; verification and confidence checking; as well as celebration and integration. Learning with the BBL approach is an alternative that can improve students' mathematical critical thinking skills, so it is recommended to use BBL on various mathematical topics and collaborate with other learning approaches or models.

Analysis of Students' Mathematical Critical Thinking Skills and Collaborative Collaboration Skills

This study will provide an overview of the relationship between student collaboration and the mathematical critical thinking skills of grade VIII-F students of SMP N 1 Yogyakarta. The correlational technique is a technique used to test the relationship between the two variables. Based on the findings, there is a linear relationship between the mathematical critical thinking capacity of learners and the willingness to work together. The conclusion that can be drawn is that there is a substantial relationship between collaboration skills and mathematical critical thinking skills of grade VIII-F students of SMP N 1 Yogyakarta because of r_hitung>r_tabel (0.467>0.29). so that the conclusion that can be obtained is that there is a significant relationship between the ability to think critically mathematically and the collaboration of students of VIII-F SMP N 1 Yogyakarta. In addition, the relationship between the two research variables was positive because r_hitung= 0.467. Overall, students' collaboration skills fall into the medium, high, and very high categories, while their mathematical critical thinking skills fall into the low, medium, and high categories. However, some of them have collaboration skills that fall into the medium category but have low mathematical critical thinking skills, and there are also students who have collaboration skills that fall into the high category but have medium mathematical critical thinking skills. Low mathematical critical thinking skills make students unable to express reasons and justifications accurately. Although learners with intermediate critical thinking skills can provide reasonable justifications for such questions, the arguments they provide may not be entirely valid.

Systematic Literature Review: Kemampuan Berpikir Kritis Matematis Siswa Ditinjau dari Adversity Quotient

Critical thinking skills are very important in 21st century mathematics learning. Critical thinking skills need to exist in every student in order to solve various kinds of problems, especially mathematical problems. According to Facione (2013) the indicators of critical thinking skills are: (1) interpretation, (2) analysis, (3) evaluation, (4) inference, (5) explanation, and (6) self-regulation. A student's response when encountering an obstacle is known as adversity quotient. Adversity quotient has three different types of levels namely: (1) climber, (2) camper, and (3) quitter. The purpose of the following research is to describe the type of research used, research trends related to students' mathematical critical thinking skills in terms of adversity quotient from 2018-2023, and the effect of adversity quotient on students' mathematical critical thinking skills. SLR is the method used by this research. The data collection technique was carried out by reviewing articles related to students' mathematical critical thinking skills in terms of adversity quotient in articles published around 2018-2023. There were 10 articles found through google schoolar and scopus. The results of this study show: (1) the type of research that is often used is qualitative; (2) most research is conducted at the junior high school level; (3) adversity quotient has a positive influence on the results of students' mathematical critical thinking skills.

Students’ mathematical critical thinking through the conceptual change approach

Critical thinking ability is one of the higher order thinking skills. Students who have high critical thinking skills are expected to have the ability to analyze problems properly and precisely. The purpose of the present study was to find out the differences in students' mathematical critical thinking skills who received learning using the conceptual change approach and those who received conventional learning, namely the scientific approach. This study was conducted at a junior high school in South Tangerang City, Banten Province. The research method used was a quasi-experimental research design with a post test only control design. The research sample consisted of 70 students consisting of 37 students in the experiment group and 33 students in the control group selected by a cluster random sampling technique. Results indicate that students' mathematical critical thinking skills who learned with the conceptual change approach are higher than those of students who learned by the scientific approach. The critical thinking skills of students who received learning by the conceptual change approach were 72.64%, on the indicator of analyzing arguments, 67.23%, on the indicator of making conclusions, 84.46%, on evaluating, and 61.85% on solving problems