Improving students’ mathematical critical thinking through rigorous teaching and learning model with informal argument

This intervention study focused on: (1) analyzing whether there is a significant effect of guided inquiry learning model based on Deli Malay culture context towards student’s mathematical critical thinking ability or not and (2) analyzing whether there is a significant interaction between learning model and prior mathematical ability towards student’s mathematical critical thinking ability or not. This study is a quasi experimental research that used mathematical critical thinking ability test. Population in this study are all students in SMPN 1 Tebing Tinggi Academic Year 2017/2018 and the samples are 32 students in class VIII-A taught by using guided inquiry learning model based on Deli Malay culture context and 32 students in class VIII-C taught by using expository learning. The data was analyzed by using Two Way Anova and found that: (1) there is a significant effect of guided inquiry learning model based on Deli Malay culture context towards student’s mathematical critical thinking ability and (2) there is no a significant interaction between learning model and prior mathematical ability towards student’s mathematical critical thinking ability.

This research is a quantitative research that aims to (1) examine the differences of students 'mathematical critical thinking ability in terms of self regulated learning which gain learning with metacognitive approach and students who only get ordinary learning (2) examine the influence of self regulated learning on students' mathematical critical thinking ability and (3) to describe students' mathematical critical thinking skills in terms of self regulated learning. Subjects in this research were students of class XI in MAN 1 Cimahi with the subject amounted to 64 students consisting of the control class and experimental class. Subjects were divided into three groups based on self-regulated learning level, specifically high level, medium level, and low level. Based on the results of the research, it’s found that (1) the ability of mathematical critical thinking in the experimental class is better than the mathematical critical thinking ability of the control class (2) the students' self-regulated learning of the experimental group positively influences the critical thinking skills of mathematics (3) The students of high level already able the indicators of critical thinking ability. The students of medium level are still experiencing errors in the algorithm resulting in incorrect results and conclusions. The Students of low level have not been able to meet the indicators of critical mathematical 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.

This study examined the university students’ mathematically critical thinking ability through Concept Attainment Model learning. The Kolmogorov-Smirnov test, Levene test, t test, ANOVA one and two ways were used to analyse the data. The results of this study showed that (1) there is no difference grade on the student’s mathematical critical thinking ability between experimental group and conventional group as a whole, (2) there is no difference on the students’ mathematical critical thinking ability of experimental classes based on their mathematical early ability (3) there is no interaction between the learning that is used with the students’ mathematical early ability on the students’ mathematical critical thinking ability.

Students' mathematical critical thinking ability is one of the skills that need to be developed so that students can overcome future challenges. In addition, critical reasoning is one aspect of the Pancasila Student Profile that needs to be developed in the Independent Curriculum. In relation to efforts to improve these abilities, this study aims to determine the activities of educators and students in learning that applies the Problem-Based Learning (PBL) learning model with the Culturally Responsive Teaching (CRT) and Teaching at the Right Level (TaRL) approaches and to determine the increase in students' mathematical critical thinking abilities after carrying out the learning. The method used in this study is Classroom Action Research with two cycles, namely Cycle 1, consisting of 2 meetings, and Cycle 2, consisting of 3 meetings. The subjects of this study were students of class VIII A of SMP Negeri 13 Bandung. The conclusion obtained in this study is that the application of the PBL learning model with the CRT and TaRL approaches can improve junior high school students' mathematical critical thinking abilities.

The ability to think critically mathematically is one of the important abilities required in learning mathematics at the senior high school level in the independent curriculum. This ability is also one of the abilities demanded by the 21st century educational revolution. The importance of this ability is not in line with the mathematical critical thinking abilities of high school students, as was the problem of research in class X MIA at SMA Negeri 1 Natar Lampung Selatan. Given the importance of critical thinking skills, the purpose of this study was to determine the effect of using Everyone is a Teacher Here strategy on students' mathematical critical thinking abilities. This research is a quasi-experimental study with a population of all students of class X MIA even semester of SMA Negeri 1 Natar Lampung Selatan consisting of 8 classes with a total of 228 students, while 2 classes were taken, namely class X MIA 8 as the experimental class totaling 36, and class X MIA 7 as the control class, totaling 36. The sample was taken using a random sampling technique. Students' mathematical critical thinking ability is measured by a test in the form of a description of 5 questions which have previously been tested for validity and reliability. Testing the hypothesis in this study using the t test. From the results of hypothesis testing, it can be concluded that the use of the Everyone is a Teacher Here strategy can influence the mathematical critical thinking skills of class X MIA students at SMA Negeri 1 Natar Lampung.

This study is experimental research that aims to know about the influence Adversity Quotient (AQ) of the achievement students’ mathematical critical thinking ability. The population of this study is the students of Junior High School in Cimahi City, West Java, Indonesia; while the sample is 79 students selected purposively. The instruments of this study are tests and non-tests. They are based on the assessment of good characteristics towards students' mathematical critical thinking abilities, while the non-test instrument is based on the assessment of good characteristics towards AQ. The results show that: (1) AQ gives positive influence to the achievement students’ mathematical critical thinking ability with the influence of 61%, while the rest of it (39%) is influenced by other factors outside AQ; (2) there are differences in achievement in the students’ mathematical critical thinking ability based on AQ level (climber, camper, quitter).

Students' mathematical critical thinking ability (MCTA) in Indonesia is still low, and one contributing factor is that students are not accustomed to solving non-routine problems, including ill-structured problems. This research aimed to explore the mathematical critical thinking ability (MTCA) in solving ill-structured using a qualitative approach with a case study method. This research involved 24 grade IX students from a junior high school in Bandung City, Jawa Barat Province, who had learned quadratic equations. Data were collected through a written test on MCTA and follow-up interviews. The results reveal that students fail to meet the MCTA indicators due to their lack of practice in solving contextual problems on quadratic equations and ill-structured problems. In addition, to gain a deeper understanding of mathematical critical thinking ability and the ability to solve ill-structured problems, future researchers could use two separate instruments, as these abilities involve distinct cognitive processes: convergent thinking and divergent thinking.

This study aims to determine whether there is the influence of ARIAS model based on Two Stay Two Stray model to critical thinking ability mathematically. This research is Quasi-Experimental Design research. Hypothesis testing using variance analysis of two different cell roads Based on the test of cell variance analysis is not the same obtained that there is influence of ARIAS model based on Two Stay Two Stray to critical mathematical thinking ability and there is influence of cognitive style to critical thinking skill mathematically, where student with treatment of learning using integrated learning model ARIAS TSTS learning model on the ability of critical thinking is better than students with learning treatment using lecture methods in terms of each student's cognitive style. The students' mathematical critical thinking ability with independent field cognitive style is better than students with cognitive field dependent style. There is no interaction between learning and cognitive styles to critical mathematical thinking skills.

This study aims to determine the mathematical critical thinking ability of junior high school students in Rancabali District with indicators of the mathematical critical thinking ability of students used to understand the problem, provide arguments, induce and the ability to make decisions or actions. The ability of mathematical critical thinking is the ability to think that aims to make decisions or actions that make sense through what is believed to be truth and can be done correctly. This research was conducted on 10 students in one junior high school in Rancabali District by using a qualitative descriptive method. The instrument used in the form of 4 items about students' mathematical critical thinking skills on the material to build flat side spaces accompanied by interviews with students. The conclusion of this study is the mathematical critical thinking ability of junior high school students in Rancabali District is still very low.

The purpose of this study is to analyze the role of mathematics realistic education (RME) approach on students’ mathematical critical thinking and resiliency. This study is an experiment with pre test-post test control group design and involves 62 eleventh grade students, a mathematical critical thinking test, a mathematical resiliency scale, and a perception on RME approach scale. The study found, on mathematical critical thinking ability (MCTA), its N Gain, and mathematical resiliency (MR) students getting treatment with RME approach attained better grades than the grades of students taught by conventional teaching. The first group students attained at medium grade level on MCTA and fairly good grade level on MR, while the second group students obtained at low grade level on MCTA, medium grade level on MR, and they realized difficulties in some items of mathematical critical thinking tasks. The other findings, there was no association between MCTA and MR, and students learned actively, thought critically and creatively, were unafraid to pose their opinion and performed to be self confident during RME approach.

Mathematical critical thinking ability is the capacity to investigate, discover, connect, and assess every aspect of a problem carefully and thoughtfully to arrive at the best solution. This study aims to describe students' mathematical critical thinking abilities regarding circles in Grade VIII at SMP Negeri 09 Lebong. This research is a qualitative descriptive study with 20 student participants. Three students were interviewed: one with high ability, one with medium ability, and one with low ability. Data collection methods included tests, interviews, and documentation. The research instruments consisted of test items and interview guidelines. The data analysis technique involved data collection, data reduction, data presentation, and conclusion. The results of the study show that high-ability students met all indicators of mathematical critical thinking: Interpretation, Analysis, Evaluation, and Conclusion. Medium-ability students met two indicators: Interpretation and Analysis. Low-ability students were unable to meet the indicators of mathematical critical thinking: Interpretation, Analysis, Evaluation, and Conclusion.

Abstract: Math is able to train logical, analytical, systematic, critical, and creative thinking of students. Mathematical critical thinking ability is a capability that supports a variety of other mathematical thinking abilities. The students' critical thinking ability is also closely related to the personality or character of the student. Personality can affect how a person behaves, thinks, or interacts with around. The personality types discussed in this study are examined from four types of temperaments by the theories of Hippocrates and Galenus. This research includes the type of qualitative research that uses descriptive qualitative research methodology. This research will be conducted on the students of class XI MIA SMA Negeri 2 Kota Jambi. The thing described in this research is the students' mathematical critical thinking based on the dominant personality type on linear program solution. The results of personality tests of the instrument adapted from the patterns of personality by Lana Bateman found 40 dominant students that is the type of phlegmatic personality. Furthermore, based on sampling technique that is purposive sampling technique, 2 students are taken as research subjects ie phlegmatic students with the highest level of critical thinking ability called first phlegmatic students and phlegmatic students with the lowest level of critical thinking ability is called second phlegmatic student. From the results obtained can be concluded that the first phlegmatic students have the level of critical thinking skills are very critical and the second phlegmatic students have a critical level of critical thinking is not critical. This is inversely between the ability to think critically and the type of phlegmatic personality. The first phlegmatic student with enough phlegmatic category has critical critical mathematical thinking and the second phlegmatic student with very high / dominant phlegmatic category, critical critical thinking ability is not critical.Keywords: Mathematical Critical Thinking Ability, Four Temperament Types

This study aims to determine the comparison between students' mathematical critical thinking skills taught with macromedia flash interactive learning media compared to PowerPoint media. This type of research is an experimental research. This research was conducted at SD Negeri 101788 Marindal I. The population in this study was students of SD Negeri 101788 Marindal I. While the samples in this study were 27 students in class IV/a and 27 students in class IV/b. The data collection in this study used a mathematical critical thinking ability test. The research hypotheses were tested using independent sample t-test data analysis techniques. The results showed that: (1) There was a significant difference between students' mathematical critical thinking skills taught with interactive learning media macromedia flash compared to powerpoint media (Fcount = 4.005; sig. = 0.004); and (2) The average mathematical critical thinking ability of students who are taught with interactive learning media macromedia flash is higher than the powerpoint media with a Mean Difference value of 7.40. In other words, it can be said that there is a significant effect of the application of interactive learning media macromedia flash on students' mathematical critical thinking skills.

The purpose of this study was to determine the mathematical critical thinking ability of students who were taught using the Auditory Intellectually Repetition learning model was better than the mathematical critical thinking skills of students who were taught through a scientific learning approach. This study uses a quantitative approach and the type of research used is quasi-experimental research. The population in this study were 11th grade students of SMA Negeri 5 Simeulue Barat, the samples in this study were two classes selected using a nonprobability sampling technique of purposive sampling type, namely class 11 IPA-1 as an experimental class using the Auditory Intellectually Repetition model and class 11 IPA-2 as a control class using a scientific approach. The data processing technique uses SPSS version 25 with the results of the study showing that: the value of Sig (p-value) > 0.05), it is accepted that it is 0.629 in the experimental class and 0.273 in the control class so that the data has a normal distribution. The t-test analysis of students' mathematical critical thinking skills was obtained 0.001 < 0.05, then Ho was rejected and Ha was accepted. This means that the mathematical critical thinking ability of students who are taught with the Auditory Intellectually Repetition learning model is better than the mathematical critical thinking skills of students who are taught with a scientific learning approach.