The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS). The explanatory method was used in this qualitative study. The participants were mathematics students at the Department of Mathematics, Universitas Negeri Semarang. The researchers collected the data with the cognitive style test using the Matching Familiar Figure Test (MFFT), used a valid problem-solving skill test, and the interview questions. The data analysis techniques used were processing and preparing the data for analysis, extensive reading of the data, coding all data, applying the coding process, describing the data, and interpreting the data. The results showed that (1) the problem-solving process of students with symbolic representation was characterized by the use of mathematical symbols to support the problem-solving process in the problem representation phase; (2) the problem-solving process of students with symbolic-visual representation was characterized by the use of symbols, notations, numbers, and visual representation in the form of diagrams in the problem representation phase.

This study aims to analyze the characteristics of social skills, digital literacy disposition, and mathematical literacy abilities of 49 students; to analyze the theoretical model of the direct and indirect influence of digital literacy skills and social skills on mathematical literacy skills. The number of samples is 49 of the 12th-grade students at state high school #1 Southern Konawe. The research instruments consisted of a mathematical literacy ability test, a social skills questionnaire, and a digital literacy disposition questionnaire. The data were analyzed by descriptive statistics and structural equational models (SEM) with a Smart PLS 3.0 application. The results showed that students' mathematical literacy skills tended to be better on content and context indicators but they are weak on competency and process indicators. Students' social skills tend to be better on indicators of peer-relationship skills and self-management skills, but are also weak on indicators of academic skills and compliance skills. Mastery of the digital literacy disposition tends to be better on the internet searching, content evaluation, and information sharing indicators but is still weak on knowledge assembly. Furthermore, it was found that (a) social skills have a direct effect on digital literacy disposition but do not directly affect mathematical literacy skills; (b) the digital literacy disposition has a direct effect on mathematical literacy skills.

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 aim of this work is to characterise the understanding that students in compulsory secondary education (14-16 years old) have of number sequences in graphical representations. The learning of numerical sequences is one of the first mathematical concepts to be developed in an infinite context. This study adopts the focus of semiotic representations as its theoretical framework. The participants consisted of 105 students and a qualitative methodology was used. The data collection instruments were a questionnaire and a semi-structured interview. The results allowed for three student profiles regarding number sequences in graphical representations to be identified. These profiles may facilitate a possible progression in the learning of number sequences for students in compulsory secondary education to be considered. Therefore, the results presented in this study can provide information about the learning hypotheses of mathematical tasks related to numerical sequences and can help in the design of such tasks.

Research is considered a vital component for propelling progress and development. This study aims to investigate the effects of problem-based learning (PBL) in the teaching of research methodology and statistics courses on improving research writing skills and enhancing course achievement. It also projects an action plan model for the effective implementation of PBL in the instructional aspect. The study utilised a positivist research paradigm based on action research design using the technique of content analysis. Employing a universal rubric, 45 proposals of graduate programme students enrolled in the College of Education at Minia University in North Upper Egypt were subjected to content analysis to rate students’ skills in writing research proposals before and after the delivery of the course. The students volunteered to participate in the study after they were given a synopsis of the aims and procedures. Students’ achievement was assessed through a test consisting of 90 items, developed primarily for this purpose at the end of the second semester in the academic year 2018–2019. The post-content analysis revealed a significant improvement in scientific research skills, with a considerable difference between the pre- and post-achievement scores. It is imperative to consider the feasibility of using the PBL approach in teaching research methodology and statistics courses for graduate students. The study recommended the adoption of PBL in undergraduate programmes as well as in high school education.

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.

The aim of this study was to investigate how the use of the technologized model of critical thinking development affected the self-study process of students of higher educational institutions (HEIs). The research methodology was based on a combination of qualitative and quantitative empirical methods, as well as a descriptive approach to data analysis. The study involved a quasi-experimental model supposed to influence the variables under study. The technology-based educational model of autonomous learning with a focus on the critical thinking development in students of HEIs consisted of the following processes, such as: communication, analysis, synthesis, problem-solving, evaluation, and reflection. The Watson Glaser Test was adapted to monitor the level of students’ critical thinking. The average score on the final control of students’ knowledge was used to monitor the experimental group students’ performance. By monitoring the development of students’ critical thinking and the dynamics of their performance in the course of training, where 90% of the time students studied independently, it was established that the use of a technological educational model had a positive effect on the critical thinking of students of HEIs, and as a result, the effectiveness of their self-study.

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.

This study aims to investigate lecturers' needs for academic writing learning materials and determine their prototypes. This study is qualitative research in the form of an exploratory case study. The research instruments were semi-open-ended questionnaires and unstructured and open-ended interview guides. The data were analyzed using content analysis. The results show that the developed learning material for academic writing skills contains seven needs for lecturers in the Department of Indonesian Language and Literature. Four of them have not been found by previous researchers. The results from this study provide new knowledge and contribution to the literature about the need to prototype the learning materials. The lecturers or other researchers can use these seven needs in prototyping learning materials for academic writing skills, such as the needs of learning materials, their forms, presentation system, language use, evaluation form, main menu design, and the way of creating learning materials.

The actions, processes, objects, and schemas (APOS) theory is a constructivist learning theory created by Dubinsky based on Piaget's epistemology and used to teach math worldwide. Especially the application of APOS theory to the curriculum of a mathematics class helps students better understand the concepts being taught, which in turn contributes to the formation and development of mathematical competencies. With the aid of the APOS theory and the activity, classroom discussion, and exercise (ACE) learning cycle, this study sought to ascertain the effect of teaching derivatives in Vietnamese high schools. In this quasi-experimental study at a high school in Vietnam, there were 78 grade 11 students (40 in the experimental and 38 in the control classes). As opposed to the control class, which received traditional instruction, the experimental class's students were taught using the ACE learning cycle based on the APOS theory. The data was collected based on the pre-test, the post-test results and a survey of students' opinions. Also, the data that was gathered, both qualitatively and quantitatively, was examined using IBM SPSS Statistics (Version 26) predictive analytics software. The results showed that students in the experimental class who participated in learning activities based on the APOS theory improved their academic performance and attitudes. Additionally, it promoted the students' abilities to find solutions to problems about derivatives.

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.

Lesson study, observation and analysis are relevant to professional development and initial teacher education. As a strategy, it helps to bridge the gap between theory and practice. The health conditions brought on by the COVID-19 pandemic forced the restriction of the tutors’ direct observation of preservice teachers at school. This study analyses preservice teachers’ performance through video observations to evaluate their professional activity at school during the COVID-19 pandemic. The Fifteen Items Revised Tsang-Hester Observation Rubric (FIR-THOR) was administered to a sample of 166 preservice teachers in their internship schools and their video recordings each one of 45-minute teaching lessons were analysed. The results show that the FIR-THOR appears as a robust instrument, which allows us to conclude that the instrument works well in the three five-items dimensions that compose it - Instruction, Management, and Assessment - proving to be reliable for assessing teacher intervention in the classroom. Among the three dimensions, the preservice teachers’ performance stands out in the Management of the classroom, as well as in the classroom Instruction. This contribution is relevant considering the potential of lesson analysis in learning and professional development during initial teacher training.

Many students have misconceptions about mathematics, so preservice teachers should be developing the skills to notice mathematical misconceptions. This qualitative study analyzed preservice teachers' skills in noticing student misconceptions about algebra, according to three aspects of noticing found in the literature: attending, interpreting and responding. Participants in this study were seven preservice teachers from one university in the capital of Aceh province, Indonesia, who were in their eighth semester and had participated in teaching practicums. Data was collected through questionnaires and interviews, which were analyzed descriptively. The results revealed the preservice teachers had varying levels of skill for the three aspects of noticing. Overall, the seven preservice teachers' noticing skills were fair, but many needed further development of their skills in interpreting and responding in particular. This university’s mathematics teacher education program should design appropriate assessment for preservice teachers’ noticing skills, as well as design and implement learning activities targeted at the varying needs of individual preservice teachers regarding noticing student misconceptions, in order to improve their overall teaching skills.

This research aims to describe secondary school students' functional thinking in generating patterns in learning algebra, particularly in solving mathematical word problems. In addressing this aim, a phenomenological approach was conducted to investigate the meaning of functional relationships provided by students. The data were collected from 39 ninth graders (13-14 years old) through a written test about generating patterns in linear functions. The following steps were conducting interviews with ten representative students to get detailed information about their answers to the written test. All students' responses were then analyzed using the thematic analysis software ATLAS.ti. The findings illustrate that students employed two types of approaches in solving the problem: recursive patterns and correspondence. Students favored the recursive patterns approach in identifying the pattern. They provided arithmetic computation by counting term-to-term but could not represent generalities with algebraic symbols. Meanwhile, students evidenced for correspondence managed to observe the relation between two variables and create the symbolic representation to express the generality. The study concludes that these differences exist due to their focus on identifying patterns: the recursive pattern students tend to see the changes in one variable, whereas the correspondence ones relate to the corresponding pair of variables.

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.

A virtual-based disaster learning model was created to enhance understanding of COVID-19 disaster mitigation following the characteristics of elementary school students because the high number of child deaths brought on by the COVID-19 pandemic served as the driving force behind this research. The virtual-based disaster learning model had been deemed valid, but more study is required to ascertain its impact on primary school pupils' comprehension of COVID-19 disaster mitigation. This study sought to determine how the virtual disaster learning model affected elementary school pupils' understanding of COVID-19 disaster mitigation. This study was a quasi-experimental investigation. Non-equivalent control group design was the type of experimental design employed. The t-test showed that students who studied using virtual-based disaster learning models and those who used conventional learning had different average levels of understanding of COVID-19 disaster mitigation. According to the findings, primary school children who learned using virtual disaster learning models had higher scores than students who used conventional methods. This finding revealed that virtual disaster learning models could improve understanding of COVID-19 disaster mitigation. The results of this study's implications can be applied as a different approach to enhancing elementary school kids' comprehension of emergency planning for COVID-19.

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.

Motivation is essential in shaping how much a student is interested in learning and also affects how much students will learn from a learning activity or how much students' ability to capture the information presented by the teacher. Well-motivated students will produce a vibrant learning atmosphere and a better success rate. This research aims to determine whether the motivating active learning in physical education (MALP) model can help kids in elementary school develop their capacity for critical thinking. The design used is experimental. The research subjects were grade 6 elementary school students representing five sub-districts in the Tasikmalaya district. One elementary school was taken from each sub-district through a probability sampling technique using the cluster random sampling approach. The total sample taken was 137 people. The results of the study prove that applying the MALP model can greatly influence improving the critical thinking skills of elementary school students. The result of the study is proven by the significance test using the paired sample t-test; the results obtained from sig. (2-tailed) of .001< .05. So applying motivating active learning in the physical education model influences increasing elementary school students’ critical thinking skills.

Although the central role of classical mechanics in physics teacher education is undisputed, divergent interests and perspectives from different disciplinary cultures might exist when thinking about how to best support pre-service teachers' professional development. In this article, we report the results of an exploratory mind map study to investigate which classical mechanics topics are regarded essential for physics teacher education according to N = 29 experts from different physics disciplines. The participants’ mind maps were analyzed using a category system and frequency analysis was applied. The results hint at similarities and differences in terms of key topics to be addressed in physics teacher education on classical mechanics according to experts from different physics disciplines, e.g., in terms of the depth of mathematics considered relevant for physics teacher education.