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.

The purposes of the current study were to develop students' spatial orientation skills using Virtual Mathematics Kits (VMK) and to evaluate VMK as a form of digital media in terms of spatial orientation. This study involved 42 lower-class and 47 higher-class elementary school students as the intervention group and 36 lower-class and 41 higher-class students as the control group. The intervention group was administered spatial orientation activities for 10 weeks. These activities were performed using a VMK to facilitate solving spatial problems. In the end of activities, spatial orientation instruments administered to compare spatial orientation ability on each group. The findings of this study, spatial orientation activities using a VMK improved students' spatial orientation skills. More specific, VMK provides more significant effect on higher-class students. Finally, VMK allows students to explore many ideas and perspectives to solve various spatial problems. VMK can be used as a digital media that helps students to develop spatial reasoning.

Industrial revolution 4.0 is currently present in various countries, including Indonesia. Indonesia responded quickly through technological developments, especially education. The actions of the Indonesian government to deal with industrial 4.0 are contained in the 4C principle, one of which is Critical Thinking. The Science, Technology, Engineering, and Mathematics (STEM) learning approach has become an alternative in building critical thinking skills, especially in science learning. The purpose of this study is to quantitatively measure the impact of the STEM-inquiry model based on the K-13 Indonesian Curriculum towards critical thinking skills of 15-16 years old students. This study employed quasi-experimental with non-equivalent control group design at SMAN 1 (State Senior High School) Padang Cermin, Lampung, Indonesia. The research subjects consisted of 50 students. The critical thinking skill was measured through 10 items of an essay question on the momentum and impulse material. Based on the results of the non-parametric statistical hypothesis test Mann Whitney, the significance level of 0.004 was obtained (sig <0.05). The results of the hypothetical test showed that the student's critical thinking skills before and after using the STEM-based inquiry model were different. It can be concluded that the application of the STEM-based inquiry model was effective in increasing students' critical thinking skills.

Realistic Mathematics Education (RME) has gained popularity worldwide to teach mathematics using real-world problems. This study investigates the effectiveness of elliptic topics taught to 10th graders in a Vietnamese high school and students' attitudes toward learning. The RME model was used to guide 45 students in an experimental class, while the conventional model was applied to instruct 42 students in the control class. Data collection methods included observation, pre-test, post-test, and a student opinion survey. The experimental results confirm the test results, and the experimental class's learning outcomes were significantly higher than that of the control class's students. Besides, student participation in learning activities and attitudes toward learning were significantly higher in the RME model class than in the control class. Students will construct their mathematical knowledge based on real-life situations. The organization of teaching according to RME is not only a new method of teaching but innovation in thinking about teaching mathematics.

Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students’ common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students’ understanding of the wrong concepts to the correct ones. A research design was used to achieve this goal. It identified and solved the errors in the definition of angle and triangle among first-year students in the Department of Mathematics Education at an excellent private college in Mataram, Indonesia. The steps were as follows: A test instrument with open-ended questions and in-depth interviews were used to identify the errors, causes, and reasons for the students’ misconceptions. Then, the MDWI approach was used to identify a way to correct these errors. It was found that students generally failed in interpreting the concept images, reasoning, and knowledge connection needed to define angles and triangles. The MDWI approach eliminated the misconceptions in generalization, errors in concept images, and incompetence in linking geometry features.

High school teachers are mentors and facilitators that must be concerned about their students' formal thinking abilities. Students may not take a conservation task seriously because they perform operations without consulting. This necessitates modifying the learning process to increase student motivation. Therefore, this study aimed to examine students' mathematical spatial literacy through project-based blended learning with the cognitive conflict strategy. The study sample comprised 129 students, including 66 and 63 in the experimental and control classes, respectively, divided into the low, medium, and high levels. The findings showed that the experimental class students using project-based blended learning with the cognitive conflict strategy had higher mathematical spatial literacy than those in the control class using problem-based learning. Project-based blended learning with the cognitive conflict strategy and problem-based learning students at the high and moderate levels differed in their ability to increase their mathematical spatial literacy. However, low-level students are comparable in their ability to increase their mathematical spatial literacy.

This study is qualitative with descriptive and aims to determine the process of generalizing the pattern image of high performance students based on the action, process, object, and schema (APOS) theory. The participants in this study were high performance eighth-grade Indonesian junior high school. Assignments and examinations to gauge mathematical aptitude and interviews were used to collect data for the study. The stages of qualitative analysis include data reduction, data presentation, and generating conclusions. This study showed that when given a sequence using a pattern drawing, the subjects used a number sequence pattern to calculate the value of the next term. Students in the action stage interiorize and coordinate by collecting prints from each sequence of numbers in the process stage. After that, they do a reversal so that at the object stage, students do encapsulation, then decapsulate by evaluating the patterns observed and validating the number series patterns they find. Students explain the generalization quality of number sequence patterns at the schema stage by connecting activities, processes, and objects from one concept to actions, processes, and things from other ideas. In addition, students carry out thematization at the schematic stage by connecting existing pattern drawing concepts with general sequences. From these results, it is recommended to improve the problem-solving skill in mathematical pattern problems based on problem-solving by high performance students', such as worksheets for students.

Digital puzzle worksheet (DPW) is innovative teaching material designed using open-source software such as Canva and Liveworksheets. Subsequently, puzzle games in the form of questions can improve problem-solving skills by engaging in metacognitive processes. This research used a case study method to describe the impact of applying the DPW to identify the metacognition levels of students through the assignment of contextual maths problems. The source of informants was third-grade elementary school students in West Java, Indonesia. Test instruments, observation sheets, and interviews were used, while data analysis adopted an iterative model. Furthermore, the method and time triangulation increased confidence in the resulting conclusions. The results showed that male students were at the metacognitive level of ‘strategic use’ and ‘aware use’ for females, based on the characteristics of the observed metacognitive level. The most prominent feature was identifying and determining problem-solving strategies with metacognitive awareness. The reaction of students to the DPW improved problem-solving abilities, expanded conceptual understanding, and enhanced digital technology competence. Therefore, this experience was applied when solving contextual mathematical problem assignments.

Creativity and information literacy are skills necessary for students for task completion in the learning process. One of the tasks assigned to students in learning is to write drafts of scientific articles. Furthermore, teachers must pay attention to cognitive styles in the learning process. This study aimed to describe students' creativity in writing drafts of scientific papers based on information literacy concerning reflective and impulsive cognitive styles. This research was exploratory qualitative research to explain the creativity of reflective and impulsive students in writing scientific article drafts based on information literacy. The research subjects comprised two students for each reflective and impulsive cognitive style. The cognitive style was measured using the Matching Familiar Figure Test instrument. Students' creativity was measured using a test with fluency, flexibility, originality, and elaboration indicators. The results indicated that reflective students were highly creative in writing drafts of scientific articles. Meanwhile, impulsive students were relatively creative in the same activity. In conclusion, students possessing the reflective cognitive style are more creative than students following the impulsive cognitive style in writing drafts of scientific articles based on information literacy. We recommend that writing articles based on information literacy is required to increase HOTs (Higher Order Thinking Skills).

Understanding graphs in the dynamics of market (DM) is a challenge to learners; its teaching demands a specific kind of teacher’s knowledge. This study aims to examine the topic-specific pedagogical content knowledge (TSPCK) of experienced economics teachers in teaching graphs in DM to enhance learners’ understanding of the topic. It reports using a qualitative approach underpinned by the TSPCK framework for teaching specific topics developed by Mavhunga. Data were collected through classroom observations and analyzed thematically using a case study of two economics teachers. The study revealed that adopting a step-by-step approach and the use of worked graphical examples promote an understanding of graphs in DM. It also established that active learning is preferable to the predominant chalk-and-talk (lecture) method of teaching graphs in DM. The study proposed a Dynamics of Market Graphical Framework (DMG-Framework) to enable teachers, particularly pre-service teachers in lesson delivery, to enhance learners’ understanding of graphs in DM. The result of this study will broaden the international view in the teaching of graphs in DM.