It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to analyze the multiplication and division of fractions problems posed by pre-service elementary mathematics teachers and to investigate how the problems posed change according to the year of study the pre-service teachers are in. The study employed developmental research methods. A total of 213 pre-service teachers enrolled in different years of the Elementary Mathematics Teaching program at a state university in Turkey took part in the study. The “Problem Posing Test” was used as the data collecting tool. In this test, there are 3 multiplication and 3 division operations. The data were analyzed using qualitative descriptive analysis. The findings suggest that, regardless of the year, pre-service teachers had more conceptual difficulties in problem posing about the division of fractions than in problem posing about the multiplication of fractions.

The development of the revolution era 4.0 which increasingly rapidly demands the wider community to have the ability to think creatively mathematically. One effort to improve the ability to think creatively is through quality education. Quality education can be improved through to train thinking using the right learning model. This study aims to see which results are more effective in improving students' thinking skills between the two learning models applied. The two models are Problem Based Learning (PBL) and Aptitude Treatment Interaction (ATI) models. This research method uses quasi experimental method with a posttest only control test design not control group. This study uses two group subjects with two experimental classes. The analysis of the data used the hypothesis testing of the non-correlated 2-sample t-test. Based on the research results obtained Aptitude Treatment Interaction (ATI) models have a better effect on students' creative thinking abilities compared to Problem Based Learning (PBL) models.

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.

This research is motivated by a linear equations system, which is the basis for studying necessary linear algebra materials, such as rank, range, linear independent/dependent, linear transformations, characteristic values and vectors. There are still prospective mathematics teachers who have difficulty solving linear equations system and understanding the form of row echelon and reduced row echelon forms. In this study, subjects were three prospective mathematics teachers from Swadaya Gunung Jati University Cirebon who were taking matrix algebra courses. This study aims to reveal the conceptual understanding of prospective mathematics teachers in determining the solution to systems of linear equations. The results show that there are still prospective mathematics teachers who only use memory about the properties and procedures in determining whether a matrix is said to be a row echelon form or a reduced row echelon form. Then, there is still weakness in building the algorithms' relationship due to the immature knowledge of the concepts. Researchers found that many prospective mathematics teachers were more comfortable solving problems that were performed procedurally. Further research is needed to determine how the mental construction process and mathematical conceptual knowledge of prospective mathematics teachers are through meaningful learning so that conceptual understanding is maximized.

Creative thinking is the highest level of the kind of high order thinking. In observations at the schools in Indonesia, teachers overly equate all levels of achievement of students' creative thinking to obtain higher order thinking skill improvements in mathematics learning. This condition results in an imbalance in learning practices. Therefore, this research fills the gap of this imbalance by describing the student’s creative thinking profile as a high order thinking skill in the improvement of mathematics learning. These results can contribute knowledge to educators to manage teaching strategies that can improve mathematics learning which refers to high order thinking skill for all levels of their creative thinking. This research is qualitative descriptive research. The subject were junior high school students in Malang, Indonesia. Data collection methods are tests, observations, and interviews. Data analysis is conducted by reducing data, present data, and conclusions. These research results are descriptions of student’s creative thinking profiles as a high order thinking in mathematics learning improvement, namely students have problems planning problem solving; students take a break to make plans; identify the essence of the problem, provide original ideas, provide alternative problem-solving plans, combine previous ideas with problem questions; operate and implement their plans by creating various original solutions.

Teaching mathematics in general and instructing mathematics at junior schools in particular not only create favorable conditions for students to develop essential and core competencies but also help students enhance mathematical competencies as a foundation for a good study of the subject and promote essential skills for society, in which mathematical communication skill is an important one. This study aimed to train students in mathematics communication by presenting them with topics in line with the structure's congruent triangles. An experimental sample of 40 students in grade 8 at a junior school in Vietnam, in which they were engaged in learning with activities oriented to increase mathematical communication. A research design employing a pre-test, an intervention, and a post-test was implemented to evaluate such a teaching methodology's effectiveness. For assessing how well the students had progressed in mathematical language activities, the gathered data were analyzed quantitatively and qualitatively. Empirical results showed that most students experienced a significant improvement in their mathematical communication skills associated with congruent triangles. Additionally, there were some significant implications and recommendations that were drawn from the research results.

Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on Action-Process-Object-Schema (APOS) theory. APOS theory is used to explore spatial thinking processes which consist of mental structures of action, process, object, and schema. This research is qualitative research with an exploratory method. It provided the students' opportunity to solve problems alternately until the method found the most appropriate subjects for the research objectives. The subjects were 2 students of Mathematics Education in the fourth semester of Universitas Muria Kudus Indonesia. The data collection techniques were started by distributing the validated and reliable spatial thinking questions, the cognitive style question, and the interview. The applied data analysis consisted of data reduction, presentation, and conclusion. The findings showed (1) spatial thinking process of holistic-external representation typed learners were indicated by the representative thinking element, abstract-illustrative figure expression to communicate and complete the tasks correctly, (2) spatial thinking process of the holistic-internal representation typed learners were indicated by the representative means, having ideas, connecting with the previous knowledge in the forms of symbols and numbers, and finding the final results correctly although incomplete.

Several concerted movements toward mathematical modeling have been seen in the last decade, reflecting the growing global relationship between the role of mathematics in the context of modern science, technology and real life. The literature has mainly covered the theoretical basis of research questions in mathematical modeling and the use of effective research methods in the studies. Driven by the Realistic Mathematics Education (RME) theory and empirical evidence on metacognition and modeling competency, this research aimed at exploring the interrelationships between metacognition and mathematical modeling and academic year level as a moderator via the SEM approach. This study involved 538 students as participants. From this sample, 133 students (24.7%) were from the first academic year, 223 (41.4%) were from the second and 182 (33.8%) were from the third. A correlational research design was employed to answer the research question. Cluster random sampling was used to gather the sample. We employed structural equation modeling (SEM) to test the hypothesized moderation employing IBM SPSS Amos version 18. Our findings confirmed the direct correlation between metacognition and mathematical modeling was statistically significant. Academic year level as a partial moderator significantly moderates the interrelationships between the metacognitive strategies and mathematical modeling competency. The effect of metacognition on mathematical modeling competency was more pronounced in the year two group compared to the year one and three groups.

Numeracy is one of the essential competencies that the objectives of teaching math to primary students should be towards. However, many research findings show that the problem of “innumeracy” frequently exists at primary schools. That means children still do not feel at home in the world of numbers and operations. Therefore, the paper aims to apply the realistic mathematics education (RME) approach to tackling the problem of innumeracy, in the case of teaching the multiplication of two natural numbers to primary students. We conducted a pedagogical experiment with 46 grade 2 students who have not studied the multiplication yet. The pedagogical experiment lasted in six lessons, included seven activities and nine worksheets which are designed according to fundamental principles of RME by researchers. This is mainly a qualitative study. Based on data obtained from classroom observations and students’ response on worksheets, under the perspective of RME, the article pointed out how mathematization processes took place throughout students' activities, their attitudes towards math learning, and their learning outcomes. The study results found that students were more interested in math learning and understood the concepts of multiplication of two natural numbers.

Literacy ability is an individual's ability to reason, formulate, solve, and interpret mathematically to solve problems related to daily life. Executive function is a cognitive aspect that has a relation with mathematical literacy. One of some aspects that affects the low mathematical literacy ability is the aspect of executive function. This study aims to investigate the characteristics of mathematical literacy based on the executive function aspects of 15 years old students. A qualitative method with a descriptive approach is employed in this study. The present research applies interview guidelines, questionnaires, and students' mathematical literacy tests as the instruments. Research subjects are junior high school students in grade VIII from two different schools. The result shows that the students' executive function influences mathematical literacy ability. Students' mathematical literacy ability is not fully achieved by fulfilling all the indicators involved. Another aspect found in the research is the low critical thinking ability impacts the achievement of mathematical literacy ability indicators.

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.

Numerical thinking is needed to recognize, interpret, determine patterns, and solve problems that contain the context of life. Self-efficacy is one aspect that supports the numerical thinking process. This study aims to obtain a numerical thinking profile of Mathematics pre-service teachers based on self-efficacy. This study used descriptive qualitative method. The data obtained were based on the results of questionnaires, tests, and interviews. The results of the self-efficacy questionnaire were analyzed and categorized (high, moderate, and low). Two informants took each category. The results showed the following: informants in the high self-efficacy category tend to be able to interpret information, communicate information, and solve problems with systematic steps. Informants in the moderate self-efficacy category tend to be able to interpret and communicate information, but tend to be hesitant in choosing the sequence of problem-solving steps. Meanwhile, informants in the low self-efficacy category tend not to be able to fully interpret the information. As a result, the process of communicating information and solving problems goes wrong. Another aspect found in this study is the need for experience optimization, a good understanding of mathematical content, and reasoning in the numerical thinking process.

Despite receiving increasing attention from mathematics education scholars, there has not yet been any overall understanding of the current state of realistic mathematics education (RME). To address this gap, this study aims to provide a review of 288 studies on realistic mathematics education from the Scopus database between 1972 and 2019. Using descriptive and bibliometric analyses, this study addresses four research issues as follows: (i) the total volume, growth trajectory, and geographic distribution; (ii) the most influencing authors and research groups; (iii) the most influencing sources (i.e., journals, books, conferences); and (iv) the most important topics. Several implications for not only mathematics education scholars but also other stakeholders, including policymakers, school managers, mathematics teachers, may not be considered in this study.

This study was conducted following the initial stage of the transition to distance education necessitated by the onset of the COVID-19 pandemic and meeting the various challenges that came with it. At this point, countries and teachers have gained experience in preparing and delivering online education. Therefore, the study aimed to identify the beliefs of primary school mathematics teachers about teaching in synchronous virtual classrooms. It adopted a mixed methods approach, following a convergent parallel design. The overall study sample comprised 410 male and female teachers. A questionnaire was used to collect quantitative data across three dimensions (teaching efficiency, employing the philosophy of active learning, mathematical achievement). There were 31 items (verified for validity and reliability) comprising statements measured using a five-point Likert scale, together with open-ended options for further elaboration. In total, 130 teachers completed the questionnaire. Interviews were conducted with 10 teachers to collect qualitative data. The results show means in the range 3–5.75 for agreement with statements concerning the beliefs of mathematics teachers about teaching in virtual classrooms in the following order of importance: teaching competence; mathematical achievement; employing the philosophy of active learning. The study also found no statistically significant differences attributable to the variables of gender, qualification, or teaching experience, and also that many factors are considered to affect teaching in synchronous virtual classrooms related to the teacher, the family, and the student.

Development research demands a improvement in the implementation of learning by developing products based on learning needs. The products of this development are teacher book and student book based on the realistic mathematic education (RME) approach for package A in statistics material. Validity testing in this study includes instrument validation, self-evaluation, expert validation, one-to-one evaluation. Aiken's V and Intraclass Correlation Coefficient (ICC) are used to determine the validity and reliability of the product. The result of research shows that the instruments and prototype are valid and feasible. Then, the ICC obtained moderate stability, it also categorize reliable. In terms of context and hypothetical learning trajectory (HLT) developed, the products should be revised to achieve meaningful learning.

Metacognitive, critical thinking and opinion expression are in high demand. This study aimed to investigate the effects of the blended project- based literacy that integrates school literacy movement strengthening character education (literasi berbasis proyek terintegrasi GLS dan PPK: Li-Pro-GP) learning model on students' metacognitive skills, critical thinking, and opinion expression. A post-test experimental design was used to answer the research question. The study was conducted from August to October 2021 at Government Junior High School 23 Malang. Seventh-grade students were selected as research participants. The participants included 30 students from class VII-2. The research instrument was five essay questions to measure critical thinking skills. Material and assessment experts validated the essay questions developed by the researcher. The items that were declared valid were tested for validity. The result showed five valid items with high reliability of .670. Metacognitive skills were measured using the Metacognition Awareness Instrument (MAI), which consists of 40 items. The questions declared valid were tested for validity with a very high reliability of .953 for 37 items, and only three items were invalid. The ability to express an opinion was measured with an observation questionnaire validated by experts with a valid instrument score. Data analysis was performed by path analysis using the SmartPLS software. The results showed that the Li-Pro-GP blended learning model significantly strengthened students' metacognitive skills, critical thinking, and opinion formation.

The purpose of this study was to explore the factor structure of a measurement and to evaluate its internal reliability. Overall, 525 math-majoring elementary school teachers volunteered to participate in this study by answering online survey questions via Google Form. These samples were randomly partitioned into 262 participants for exploratory factor analysis (EFA) and 263 observations for confirmatory factor analysis (CFA). The EFA tended to largely prefer a four-factor solution, which was proven to explain over 68% of the variation in the data. Awareness, effectiveness, engagement, and opportunity were the provisional labels for these hidden variables. The CFA results verified and validated the four-factor model, with all test measures exceeding the specified thresholds, suggesting an acceptable and excellent fit. The results of this study, on the one hand, provide four key areas for realistic math teachers, educators, and policymakers to discuss as opposed to examining individual indicators, and on the other hand, they serve as a foundation for interested researchers to conduct additional analyses, such as multivariate linear regression or complement for cluster analysis.

Logical-mathematical intelligence is highly needed to ease students’ understanding of mathematics concepts. Therefore, it is necessary to delivery an innovative teaching approach to enhance students’ logical-mathematical intelligence. This study aims to investigate the use of mathematics comics to increase the logical-mathematical intelligence of junior high school students in urban and rural schools. This study employed a quantitative approach with a pretest-posttest control group design. The population of this study were seventh-grade students from a junior high school in Banda Aceh (urban areas) and a junior high school in Aceh Besar (rural areas), Indonesia. The samples of this study were two classes (experimental and control) from each school which were selected randomly. To collect data, we used a logical-mathematical intelligence test and analyzed it by using t-test. This study shows that the use of mathematical comics in urban schools can improve mathematical logical intelligence. However, there was no improvement in students' mathematical logical intelligence in rural schools. Therefore, this study showed that using mathematics comics in different school conditions yield different results in logical-mathematical intelligence. The findings suggest that other learning innovations are required to improve students' logical-mathematical intelligence in rural areas.

The Think-Pair-Share (TPS) strategy makes the learning environment interactive, lively, collaborative and democratic. It allows students to interact; accept information; develop collaborative discussion skills; refine their thinking; and participate effectively in the classroom. In this study, the researchers investigated the effect of the collaborative discussion strategy (think-pair-share) on developing students' skills in solving engineering mathematical problems. Once we had confirmed the validity and reliability of the tools, we used the quasi-experimental approach. The study sample consisted of 66 students divided into two groups: Namely, an experimental group, which comprised 33 students who studied mathematics using the (think-pair-share) strategy; and a control group, which comprised 33 students who studied in the traditional way. Both groups sat for a pretest and post-test in mathematics. The test results showed that the use of the TPS strategy had a positive effect on developing problem-solving skills compared to the traditional method. In light of these results, the study recommended the use of TPS strategy to improve the skills of students in solving engineering mathematical problems.