Problem-solving and mathematical communication are essential skills needed by students in learning mathematics. However, empirical evidence reports that students’ skills are less satisfying. Thus, this study aims to improve students’ problem-solving and mathematical communication skills using a Metacognitive-Based Contextual Learning (MBCL) model. A quasi-experimental non-equivalent control group design was used in this study. The participants were 204 fifth-grade students; consisting of experimental (n = 102) and control (n = 102) groups selected using convenience sampling. This study was conducted in four Indonesian elementary schools in the first semester of the academic year 2019/2020. The Problem-Solving Skills Test (PSST) and Mathematical Communication Skills Test (MCST) were used as pre- and post-tests. In order to analyze the data, one-way ANOVA was used at the 0.05 significance level. The results showed that students in the experimental group had higher post-test scores than the control group in terms of problem-solving and mathematical communication skills. It can be concluded that the MBCL effectively promotes fifth-grade students’ problem-solving and mathematical communication skills. Therefore, it is suggested that MBCL should be used more frequently in primary school mathematics to further improve students’ problem-solving and mathematical communication skills.

Self-efficacy and critical thinking represent two vital components for university graduates in the 21st century learning. However, several studies reported that these two important outcome predictors were unsatisfactory. This study aimed at investigating the effects of problem-based learning (PBL) on pre-service teachers’ self-efficacy and critical thinking. A quasi-experimental nonequivalent pretest-posttest control group design was utilized. A total of 44 pre-service elementary school teachers (aged 19-22) at a private university in Indonesia were assigned as experimental (n = 22) and control (n = 22) groups. The experimental group learning received PBL, while the control group learning with traditional college instruction. The Self-Efficacy Scale (SES) and the Critical Thinking Questionnaire (CTQ) were administered before and after the intervention in both groups. Independent and paired samples t-tests were employed to analyze the pretests and posttests data. The results indicated that PBL was more effective in increasing self-efficacy and critical thinking of pre-service elementary teachers than traditional teaching. It is suggested that PBL should be used more frequently in science learning to further enhance students’ self-efficacy and critical thinking skills in higher education.

Learning models that can improve critical thinking, skills collaborate, communicate, and creative thinking are needed in the 21st-century education era. Critical and creative thinking are the two essential competencies of the four skills required in the 21st century. However, both are still difficult to achieve well by students due to a lack of thinking skills during mathematics learning. This study was conducted to determine the model of learning that is appropriate to develop students' critical and creative thinking skills. The study used three-class samples from eighth grade. The first class is given the problem-posing lesson; the second class is given contextual learning and third class as a control class. The results of the study indicate that improving students' critical and creative thinking skills are included in the moderate category for types using contextual learning and problem-posing. Also, it is found that contextual learning is more effective for improving critical thinking skills when compared with learning problem posing and expository learning. Meanwhile, learning problem posing is more useful to enhance creative thinking skills compared with contextual and expository learning.

This research aims to test (1) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on written mathematical communication skills, (2) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills, (3) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on the written mathematical communication skills from each cognitive style, and (4) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills from each learning model. This quantitative research employed a quasi-experimental method. The research sample consisted of 240 fifth-grade elementary school students in Jebres District, Surakarta, Indonesia. Data collection techniques included tests of written mathematical communication skills and cognitive styles. The data were analyzed using prerequisite (normality, homogeneity, and balance), hypothesis, and multiple-comparison tests. The findings prove that (1) PP model with Indonesian realistic mathematical education approach is more effective than the PP and direct instruction models, (2) field-independent cognitive style is better than field dependent, (3) PP with Indonesian realistic mathematical education is as effective as the PP model, but more effective than the direct instruction model, and the PP model is more effective than the direct instruction model in each cognitive style, and (4) in the PP learning model with Indonesian realistic mathematical education approach, field-independent cognitive style is same skill as with field-dependent, but field-independent is better than field-dependent cognitive style in the PP and direct instruction learning models.

This study was to support the understanding of the set structure, binary operations, and their properties as a prerequisite of group theory material categorized as 9 structure senses. This study aimed at investigating the process of students’ structure sense in recognizing the structure of mathematical properties or objects as a prerequisite of group theory material. A task-based case study by exploring 9 categories of structure senses through three integrated process frameworks in the questionnaire was employed in this study. It involved 26 students who had obtained a prerequisite of group theory material and would take abstract algebra course. The choice of subjects was determined based on the results of the questionnaire, in which it identifies the type of structure sense processes. There were 6 out of 26 subjects were chosen. The 6 subjects consisted of 2 subjects from the first path process, 2 subjects from the second path process, and 2 subjects from the third path process. Then, the 6 subjects were interviewed. The choice of 2 subjects for each path process was because it used a fixed comparison theory. Then, the data were validated by using triangulation methods by comparing the students’ work on assignments and questionnaires as well as audio recordings of interviews. The results show the tendency of the process of structure sense was more dominated by students from the second type of path process, in which the subjects still depend on the well-known structure of the properties or mathematical objects in the form of sample questions. The subjects were unable to understand definitions in order to construct structures of properties or mathematical objects.

This study aims to analyze students’ creative thinking skills in answering the problem-solving questions. This study employs qualitative design, involving 110 fifth graders in Malang Municipality and Regency as the subjects. The obtained data were analyzed using the descriptive-explorative approach. The findings reveal that the high-achievers in Mathematics showed good skills in the aspects of fluency and flexibility, but were still struggling in the novelty aspect.  The average-achievers showed good skills in flexibility aspects but were lacking in the fluency and novelty aspects. They showed an understanding of Mathematics problems but found it difficult to decide the solving strategies, and thus their answers were lacking in structure and less systematic. When solving a problem, the calculation made seemed rushing, was less careful, and frequented with trial and error strategy. The low-achievers showed difficulties in understanding the problems. Their answers were not systematic, not well-structured, and not detailed. This indicates that the low-achievers had not shown creative thinking skills in fluency, flexibility, and novelty aspects.

This study aimed at analyzing the implementation of authentic assessments and constraints faced by junior high schools' teachers in mathematics teaching. A qualitative approach was applied in the study. The data on the implementation of authentic assessments and constraints were obtained from 50 mathematics teachers in several public junior high schools in Malang City, East Java Province-Indonesia, trained by the 2013 curriculum. Documentation, questionnaires, observations, and interviews were used to collect the data. The study results showed that most teachers implemented authentic assessments in mathematics teaching as designed in the learning plan. The obstacles faced by the teachers in the implementation of the authentic assessment included the time limit and accuracy. The efforts made by the teachers varied, but the teachers tried to administer the authentic assessment properly following the demands of the curriculum.

The aim of this study is to analyze and explain the mathematical connection process for students with a high mathematical ability to solve problems in terms of gender. Explorative descriptive research with a qualitative approach was used in this study. Data was collected through written tests and interviews conducted to a male and female student of class X Mathematics and Natural Sciences with high mathematical abilities. Data credibility is obtained through triangulation of methods and time. Furthermore, the data are analyzed with a flowchart which includes data reduction, data presentation, and conclusion drawing. The results showed that there were similarities and differences in the mathematical connection processes of male and female students. Similarities in the process of mathematical connections occur when making mathematical connections with other sciences and with everyday life in each of Polya's stages. In addition, the similarity of the connection process also occurs when connecting in mathematics during the re-checking stage. While the difference in the connection process in mathematics between male and female students is done at the stage of understanding the problem, solving strategies and implementing problem solving.

The aim of this study was to identify and classify the student’s concept image and its influence on the reasoning of the problem-solving of the derivative. The research used a qualitative description approach and used eight research subjects. From the answers collected upon the given problems, we obtained several variations of students’ concept images, thus it showed how students’ concept image influenced the reasoning. In order to clarify and classify the characteristic of the obtained answers, we summarized there were three categories of the concept image of the derivative, namely symbolically related to a basic formula of the derivative of a function, limit of the ratio of difference value of the functions, and the properties of the derivative of the functions. Furthermore, our study suggested that each student’s concept image affecting the reasoning of the derivative. In addition, we found some misperceptions in answering the problem and misconception in the use of the basic formula of the derivative of the functions among the students’ answers.

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.

This research aims to investigate the effect of socio-scientific issues (SSI) based instruction on preservice science teachers’ soft skills and environmental awareness. By applying cluster random sampling, 83 preservice science teachers (PSTs) were selected from the Department of Science Education at a university in Indonesia. The participants were divided into two groups which comprised the experimental group who were taught using SSI-based instruction, while the control group received direct instruction. The quasi-experimental study was carried out through a pre- and posttest control group design. Data was gathered quantitatively using soft skills and environmental awareness questionnaires. The soft skills questionnaire comprised six sub-skills questions: communication, collaboration, problem-solving, creativity, teamwork, and social interaction. The environmental awareness questionnaire contained questions about the PSTs’ attitudes, behavior, and willingness to act. These sub-skills were developed based on literature studies and reviews of previous studies. Face validity was conducted by the experts, and Cronbach’s alpha coefficients of 0.84 (for soft skills) and 0.86 (for environmental awareness) were obtained. The data were analyzed using the Wilcoxon signed-rank test. The result showed that SSI-based instruction had a significant effect on improving preservice science teachers’ soft skills and environmental awareness. After being taught using SSI-based instruction, all the sub-skills of the soft skills of the experimental group had increased compared to before. A similar trend was also found in their scores for environmental awareness. All the components of environmental awareness, after lecturing using SSI-based instruction, showed a significant increase compared to before. These results support the claim that SSI-based instruction fosters soft skills and promotes environmental awareness.

This study aims to determine the effectiveness of the IPA KIT teaching aids for earthquakes science KIT in improving students' collaboration skills and creative thinking. The design of this research is a quasi-experimental research with a stratified random sampling technique. This study involved two classes, namely the experimental class (n = 32) and the control class (n = 33) with a pretest-posttest control group design. This research was conducted at SMP Negeri 5 Depok. The statistical analysis used to test the research hypothesis based on the pretest and posttest scores is the normality test, linearity test, homogeneity test, correlation test, effect size, and MANOVA test. The results showed that the use of IPA KIT teaching aids for earthquakes was more effective in improving students' creative thinking skills and collaboration. Therefore, teachers are advised to use the earthquake science KIT teaching aids for earthquakes to improve the creative thinking skills and collaboration of junior high school students.

The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we were interested in how sixth-grade primary school students solve non-contextual and contextual problems involving the same mathematical content (in the contextual problems this content still needs to be recognised, whereas in the non-contextual problems it is obvious). The main guideline in the research was to discover the relationship between mathematical knowledge, which is the starting point for solving problems from mathematical literacy (contextual problems), and mathematical literacy. The empirical study was based on the descriptive, causal and non-experimental methods of pedagogical research. We used both quantitative and qualitative research based on the grounded theory method to process the data gathered from how the participants solved the problems. The results were quantitatively analysed in order to compare the success at solving problems from different perspectives. Analysis of the students’ success in solving the contextual and non-contextual tasks, as well as the strategies used, showed that the relationship between mathematical knowledge and mathematical literacy is complex: in most cases, students solve non-contextual tasks more successfully; in solving contextual tasks, students can use completely different strategies from those used in solving non-contextual tasks; and students who recognise the mathematical content in contextual tasks and apply mathematical knowledge and procedures are more successful in solving such tasks. Our research opens up new issues that need to be considered when developing mathematical literacy competencies: which contexts to choose, how to empower students to identify mathematical content in contextual problems, and how to systematically ensure – including through projects such as NA-MA POTI – that changes to the mathematics curriculum are introduced thoughtfully, with regard to which appropriate teacher training is crucial.

The objective of this research is to analyze the twelfth graders' mathematics critical thinking skills using a mathematics learning model to stimulate fundamental critical thinking abilities of science courses in SMA Negeri, Pacitan Regency, East Java Province, Indonesia. This quasi-experimental research design was used in this study with one group posttest only design using multiple substantive posttests. The sample of 141 students from the total population of six public schools involving the twelfth graders of the natural sciences was selected through purposive sampling technique, data were taken through tests of students' critical thinking skills and interviews. The data analysis consists of five stages, namely an analysis of one sample t-test, an analysis of students' grades, an analysis of problem-solving stages, an analysis of critical thinking abilities indicators, and an analysis of mathematics critical thinking abilities indicators. The results showed (1) The results of the one sample t-test show that the mathematics learning model is effective to stimulate critical thinking, which means that the application of the mathematics learning model is effective to stimulate critical thinking; (2) the overall grades of students that met the minimum mastery criteria; (3) the data analysis of eleven problem-solving stages proves that the criteria for critical thinking abilities are categorized as good and very good. The highest score indicator considers the principle and definition of transformation, while the lowest grade indicator is mainly concerned with the questions on right and coherent steps; (4) the critical thinking skills have seven indicators that highlight the criteria of students' critical thinking abilities categorized as good and very good. The indicators that get the highest score determine the definitions of terms, while the indicators of the lowest score determine the action; (5) the results of the analysis show indicators of mathematics critical thinking skills that have eight indicators. The criteria of students' critical thinking abilities met good and very good categories along with indicators with the highest value score by considering the definitions of terms, while the indicators of the lowest score deal with the habit of caution.

The teaching and learning in Indonesian elementary schools focus both on students’ concept mastery and character development.  Teachers are encouraged to implement a learning model that integrates character values and yet promote learning interest.  This study was aimed at investigating the mathematics learning interest of grade three elementary school students through the integration of thematic learning with character education, referred to as the character-integrated thematic learning model. Using a quasi-experimental pretest-posttest control group design, this study involved 70 students and employed a questionnaire to obtain data, which were analyzed using descriptive and inferential statistical techniques. Descriptively, the average scores of students' learning interest before and after the implementation of the character-integrated thematic learning model are respectively 117.54 and 140.69 with the gain index of 0.44 in the fair category. While score obtained for thematic learning model are 116.11 and 120.23 with the gain index of 0.07 in the low category. The results of the statistical inference analysis using the independent sample t-test were obtained t-count of 4.98 > t-table of 1,667. This indicates that there has been a significant increase in students’ learning interest scores with the implementation of character-integrated thematic learning model. Thus, this learning model can be applied to pay attention to the development of student’s character which has an impact on increasing student’s learning interest.

Considering the low achievement of Indonesian students in international studies (PISA), which measures Higher-Order Thinking Skill (HOTS) in solving the problem, improving the quality of mathematics learning in Indonesia is very important. The purpose of this research was conducted to explore the variations in students’ learning strategies and students’ Self–Regulated Learning (SRL) in solving mathematical HOT problems. The study employed a mixed-method, namely quantitative and qualitative methods were applied through five tests and seven interviews for over eight weeks. Two types of instruments were employed in this study, and they include tests and interviews. At the initial stage, we randomly selected 30 students from all those in grade 10 (Senior High School ), after which 12 were chosen purposively after the pre-test for an interview, having satisfied all complete group, middle group, and lower group. All of them were treated using metacognitive questions. Data analysis techniques used were percentage, data reduction, presentation, and conclusion. The quantitative results showed the students could generally use orientation, organization, and elaboration learning strategies as observed with 68.3%, 60%, and 56.7% for complete, middle, and lower groups. Moreover, the students were also observed to have conducted three cognitive processes in selecting the rules for solving the mathematical HOT problem, namely using models and drawing, written texts, and combining both. Furthermore, their final solution failures were affected by their misconceptions and errors in creating the mathematical model. The interview results on designing the learning procedures, monitoring the progress, and evaluating the outcomes, show that the students’ SRL level is good for complete (89.3%), middle (75%), and lower groups (60.7%).

The aim of this study is to find out the influence of online project collaborative learning and achievement motivation on problem-solving ability in the area of citizenship. This study uses a quasi-experimental design. The total of study subjects is 71 students of higher education; consist of 36 students as the experimental group and 35 students as the control group. Data of problem-solving ability is obtained by using an essay test, while data of achievement motivation is obtained by using a questionnaire. Data analysis is done with ANOVA (Analysis of Variance). The study results show that online based-project collaborative learning strategy has a positive influence on civic problem-solving ability. There is a difference in civic problem-solving ability between students with high achievement motivation and students with low achievement motivation. Online project collaborative learning strategy and achievement motivation interact in influencing the civic problem-solving ability of students. It is recommended that further study corroborate this finding by testing again the effectiveness of using online-based project collaborative strategy in the aspect of problem-solving in a similar field of study.

As a part of learning process, project-based assessment (PBA) is determined to be a potential approach in higher education evaluation that focuses on developing the important objectives related to critical thinking, team working and problems solving skills. The aim of the paper is to find out students’ reflection and teachers’ beliefs towards using this project-based assessment method in teaching Intercultural Communication Competence (ICC). To collect the data, a project-based assessment design was applied for 124 English major students at B University in the 9 weeks ICC course. This project was implemented from the beginning of the course, and at the end of the course, learners’ products were performed with specific activities regarding culture knowledge competition, online cultural community activities, talent performance, situational judgment ability, and eloquence skills. In addition, a set of questionnaires were delivered to the participants, plus the interviews with 36 teachers who have taught culture-related subjects from the universities in Vietnam, Thailand and Malaysia. The findings revealed that although there were certain challenges, using project-based assessment in teaching culture had satisfactory effects on students’ intercultural competence, problem- solving skills, critical thinking, and learning motivation.

This study aimed to analyze the critical thinking skills of students in learning of environmental change material using e-learning madrasah. This study used explanatory sequential design by mixed-methods experiment. The data were collected by interviewing, observing, and essay testing that have indicators modified from critical thinking skills by Watson-Glaser, Facione, and Ennis. There were 67 participants in this study as 7th grade student at a junior high school in Sleman district. Quantitative data analyzed by determining average score and standard deviations and, qualitative data analyzed from interviews and observation. Quantitative analysis showed that there were 3 levels of student’s critical thinking skills which were 14 students (20.90%) in the high category, 38 students (56.72%) in the middle category, and 15 students (22.38%) in the low category. Qualitative analysis indicated learning model made students to learn actively, independently, and enthusiastically looking for several sources. This study provided information about student critical thinking skills in junior high school, especially in the environmental change matter which are still low. Thus, the alternative learning strategies to improve students critical thinking skills are very needed. Besides, information on the application of the discovery learning model with e-learning Islamic school was obtained in the COVID-19 pandemic.

Many problems in real life are full of uncertainty. Probabilistic thinking is one way to solve this uncertainty problem. The personality abilities that are interesting to examine include how independent the students are in facing probabilistic solutions. For this reason, it is necessary to study the probabilistic thinking profile of prospective mathematics teachers in solving probabilistic problems in terms of learning the self-regulation. The research method used in this research is qualitative research. In this study, the researcher conducted an analysis of students' probabilistic thinking with the scope of the probability material related to the sample space, the probability of events, and the probability of the random variable space. The profile of the level of probabilistic thinking is influenced by cognitive factors in the form of probabilistic knowledge obtained by students and personality in the form of self-regulated learning. Student learning self-regulated influences the mental activity in decision making. By studying the profile of probabilistic thinking, students are better prepare to face uncertainty with various aspects that influence it.