This study aimed to describe the creative thinking process of students with active learning styles in proposing and solving problems on geometry material. The research instruments were Honey and Mumford's Learning Style Questionnaire (LSQ), problem-solving and submission test sheets, and interview guidelines. The LSQ questionnaire was distributed to students majoring in mathematics education at a university in Malang, Indonesia, with a total of 200 students. Students who have an active learning style and meet the specified criteria will be selected as research subjects. Based on research on creative thinking processes in proposing and solving problems in students with active learning styles, it was found that there were differences in behaviour between subject 1 and subject 2 at each stage of creative thinking. However, based on the researcher's observations of the behaviour of the two subjects at each stage of their thinking, there are similarities in behaviour, namely, they tend to be in a hurry to do something, prefer trial and error, and get ideas based on daily experience.

This study was conducted to corroborate in understanding the teachers’ beliefs about assessment practices. The prior studies related to teachers’ assessment beliefs in mathematics have been done to assess teachers’ beliefs in the general context of mathematics teaching. This study developed an instrument to assess teachers’ assessment beliefs of mathematical thinking. The research aimed to develop and validate a scale of assessment beliefs of mathematical thinking by using the confirmatory factor analysis. The first draft of the scale contained 25 items. The sample of the study consisted of 537 mathematics teachers from public schools in Oman. The instrument was a questionnaire with a 5-point Likert scale. The scale was validated by asking a number of experts in mathematics educational measurement and evaluation. Exploratory and confirmatory factor analysis was applied to test the model of assessment beliefs of mathematical thinking scale using AMOS 25.0. All constructs had acceptable reliability. The model had a good model fit for the assessment beliefs of mathematical thinking scale which obtainable from the fit indices tests. The findings revealed that all fit criteria indices were realized. The results also showed acceptable validity and construct reliability for the scale.

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.

The study objectives were (1) developing a valid and reliable Affective Self-assessment Instrument of Chemistry for High School Student and (2) discovering the chemistry affective domain ability trend of high school students based on gender. The current development study utilized 10 non-test instrument development procedures from Mardapi. The study population was all high school students in Yogyakarta Special Region. The sample size was 405 students categorized into two stages and sampling techniques, i.e., the trial stage using cluster random sampling and the measurement stage using simple random sampling. The data analysis techniques were validity test using the Aiken index and construct validity and reliability using the second-order Confirmatory Factor Analysis model. The study findings were (1) the Affective Self-assessment Instrument of Chemistry for High School Student had 15 valid and reliable items and 15 available items to be utilized by teachers to measure students’ affective in the learning process and (2) the chemistry affective domain ability trend of male high school students was dominated by the “good” category and “very good” category for female students.

The positive effect of peer assessment and self-assessment strategies on learners' performance has been widely confirmed in experimental or quasi-experimental studies. However, whether peer and self-assessment within everyday mathematics teaching affect student learning and achievement, has rarely been studied. This study aimed to determine with what quality peer and self-assessment occur in everyday mathematics instruction and whether and which students benefit from it in terms of achievement and the learning process. Two lessons on division were video-recorded and rated to determine the quality of peer and self-assessment. Six hundred thirty-four students of fourth-grade primary school classes in German-speaking Switzerland participated in the study and completed a performance test on division. Multilevel analyses showed no general effect of the quality of peer or self-assessment on performance. However, high-quality self-assessment was beneficial for lower-performing students, who used a larger repertoire of calculation strategies, which helped them perform better. In conclusion, peer and self-assessment in real-life settings only have a small effect on the student performance in this Swiss study.

Cognitive processes are procedures for using existing knowledge to combine it with new knowledge and make decisions based on that knowledge. This study aims to identify the cognitive structure of students during information processing based on the level of algebraic reasoning ability. This type of research is qualitative with exploratory methods. The data collection technique used began by providing a valid and reliable test instrument for algebraic reasoning abilities for six mathematics education student programs at the Islamic University of Sultan Agung Indonesia. Subjects were selected based on the level of upper, middle, and lower algebraic reasoning abilities. The results showed that (1) students with the highest level of algebraic reasoning ability meet the logical structure of Logical Reasoning which shows that students at the upper level can find patterns and can generalize; (2) Students at the intermediate level understand the cognitive structure of Symbolic Representations, where students can make connections between knowledge and experience and look for patterns and relationships but have difficulty making rules and generalizations; (3) students at lower levels understand the cognitive structure of Comparative Thinking, where students are only able to make connections between prior knowledge and experience.

Teacher leadership theory has underlined the essence of teacher collaboration (TC) in helping students learn better. Also, many studies and theories have argued that TC can be an effective way to provide learning feedback. Thus, this mixed-method study aimed to experimentally examine the effect of teacher collaborative metacognitive feedback (TCMF) on educational management (EM) students’ metacognition, to see the different effects on EM students’ metacognition as affected by TCMF and by individual teaching metacognitive feedback (ITMF), and to qualitatively probe into students’ perceptions of teacher collaboration. The quantitative study conducted a quasi-experimental method by involving 44 EM students. A valid and reliable scale of metacognition adopted from a previous study was utilized as the instrument of data collection. The qualitative study conducted interviews with 8 students selected purposively, and the data were analyzed interactively to reach credible information. This study revealed that TCMF positively and significantly affected EM students’ metacognition. TCMF contributed to EM students’ metacognition better than ITMF did. The students perceived that TC developed their collaborative skills, continuously supporting their critical thinking skills, intercultural communicative competence, and problem-solving skills. Limitations, implications, and recommendations for further research are discussed.

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.

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.

This study aimed to determine the effect of cognitive and affective factors on the performance of prospective mathematics teachers. Cognitive factors include cognitive independence level and working memory capacity, while affective factor include math anxiety. Mathematical performance was then assessed as basic math skills, advanced math skills and problem-solving ability. This research combined quantitative and qualitative research methods. In order to determine the effects of cognitive independence, working memory capacity, and math anxiety on math performance, multiple regression tests were used. To then see the effects of these three factors on problem-solving ability, a qualitative approach was used. Eighty-seven prospective math teachers participated in this study. Based on the results of the multiple regression, it was found that the level of cognitive independence affects basic math skills but has no effect on advanced math skills. Working memory capacity was seen to positively affect math performance (basic and advanced math skills, problem-solving skills), while mathematics anxiety demonstrated negative effects on advanced math skills and problem-solving skills.

Visual representations and the process of visualisation have an important role in geometry learning. The optimal use of visual representations in complex multimedia environments has been an important research topic since the end of the last century. For the purpose of the study presented in this paper, we designed a model of learning geometry with the use of digital learning resources like dynamic geometry programmes and applets, which foster visualisation. Students explore geometric concepts through the manipulation of interactive virtual representations. This study aims to explore whether learning of geometry with digital resources is reflected in higher student achievements in solving geometric problems. This study also aims to explore the role of graphical representations (GRs) in solving geometric problems. The results of the survey show a positive impact of the model of teaching on student achievement. In the post-test, students in the experimental group (EG) performed significantly better than students in the control group (CG) in the overall number of points, in solving tasks without GR, in calculating the area and the perimeter of triangles and quadrilaterals than the CG students, in all cases with small size effect. The authors therefore argue for the use of digital technologies and resources in geometry learning, because interactive manipulatives support the transition between representations at the concrete, pictorial and symbolic (abstract) levels and are therefore important for understanding mathematical concepts, as well as for exploring relationships, making precise graphical representations (GRs), formulating and proving assumptions, and applying different problem-solving strategies.

Problem-solving process requires information processing, and the information processing is related to working memory capacity (WMC). This study aims to determine the effect of WMC on students' mathematical abilities and to describe the ability of the students with high and low WMC in solving mathematical problems. This research used mixed method with Sequential Explanatory Design. The quantitative data were collected through the provision of OSPAN tasks and math tests to 58 students aged 15-17 years, while the qualitative data were collected through interviews based on mathematical problem-solving tasks. The results showed that WMC had a significant effect on students' mathematical abilities (R=0.536; p=0.000). Researchers found differences in students' mathematical problem-solving abilities with high and low WMC. Students with high WMC can remember and manage information well which supports the determination of more advanced problem-solving strategies and have better attention control so that they find varied appropriate solutions. Students with low WMC experienced decreased attention control as the complexity of the tasks increased, missed important information in problem solving strategies, and did not recheck their work, leading to wrong solution/answer. The mathematical performance of students with high WMC outperformed the mathematical performance of students with low WMC.

Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathematics also require the concept of computational thinking (CT). However, many still find it challenging to solve this problem. The subjects in this study were twenty-one prospective mathematics teachers who took number theory courses, and then two research samples were selected using the purposive sampling technique. This study uses a qualitative descriptive method to describe the thinking process of prospective teachers in solving Diophantine linear equation problems. The results showed that the first subject's thought process was started by turning the problem into a mathematical symbol, looking for the Largest Common Factor (LCF) with the Euclidean algorithm, decomposition process, and evaluation. The second subject does not turn the problem into symbols and does not step back in the algorithm. The researcher found that teacher candidates who found solutions correctly in their thinking process solved mathematical problem used CT components, including reflective abstraction thinking, algorithmic thinking, decomposition, and evaluation. Further research is needed to develop the CT components from the findings of this study on other materials through learning with a CT approach.

Geometric thinking affects success in learning geometry. Geometry is studied from elementary school to university level. Therefore, in higher education and basic education, it is necessary to carry out a systematic review in order to obtain tips for improving geometric thinking skills. A systematic review of geometric thinking was done in this study. In this study from 2017 to 2021, geometric thinking was investigated in the form of a synthesis review of the effect size of the given treatment. This is a comprehensive discussion of theories, models, and frameworks on the topic of geometric thinking from 36 articles. The research findings revealed that the interventions used were predominantly effective, with effect sizes ranging from "small" to "very large," with the "very large" effect obtained in the intervention of van Hiele's learning phase and various technology-based-media and concrete manipulative media. The research trend was reflected through twelve clusters of interrelated keywords. The results of this literature review suggested that it is necessary to carry out a specific study on how to achieve the highest level of geometric thinking, a more detailed form of scaffolding, and concrete manipulative media and technology that can be explored for a certain level of the participants’ geometric thinking.

This review explores research into the effects of collaborative learning interventions on critical thinking, creative thinking, and metacognitive skill ability on biological learning. The search was conducted from 2000 to 2021. We found 36 critical thinking studies, 18 creative thinking studies, and 14 metacognitive skill studies that met the criteria. The results showed that collaborative learning influences large categories (ES=4.23) on critical thinking, influences large categories (ES= 7.84) on creative thinking, and influences large categories (ES= 8.70) on metacognitive skill. The study's findings show that collaborative learning interventions have the highest impact on metacognitive abilities. Based on these findings, we provide insights for education research and practitioners on collaborative learning interventions that seem to benefit the empowerment of high levels of thinking at various levels of education to be combined with various other interventions in the future. The type of intervention, level of education, materials used, and study quality criteria were included in the study.

Mathematics anxiety has always been an interesting topic to study and discuss in the world of education. This study aimed to (1) investigate the impact of teacher roles, mathematics content, and mathematics anxiety on learning motivation, and (2) explore how students manage mathematics anxiety as a stimulus in learning motivation. This research used mixed methods with embedded concurrent design. The research sample was 100 respondents. The questionnaire instrument was arranged based on a Likert scale with 5 answer choices. This study used a structural equation model and confirmatory factor analysis as data analysis methods. The research findings indicated that: (1) a significant direct impact emerged between mathematics anxiety and students' learning motivation, and there was an indirect impact between the teacher's role and mathematics content on learning motivation; (2) students could manage mathematics anxiety when they were in optimal anxiety or positive anxiety so that they could overcome mathematics anxiety as a stimulus for achievement and deconstruct anxiety into motivation according to experience and personal resources. Results of this study confirmed that the statements about mathematics anxiety which always has a negative impact on motivation and learning achievement is not universal, because mathematics anxiety does not always have a negative impact on motivation and learning achievement if this anxiety is managed effectively.

This research aims to determine second-year university students’ understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of 112 student teachers of primary teacher education program at two private universities in Indonesia were involved in this research. A qualitative method with a holistic type case study design was used in this research. The results indicate that a significant percentage of the participants could not correctly interpret and represent fractions. In terms of interpretation, it is found how language could obscure the misunderstanding of fractions. Then, the idea of a fraction as part of a whole is the most widely used in giving meaning to a fraction compared to the other four interpretations, but with limited understanding. Regarding data representation, many participants failed to provide a meaningful illustration showing the improper fraction and mix number compared to the proper fraction. Improvement of fraction teaching at universities - particularly in primary teacher education programs - is needed so that students get the opportunity to develop and improve their knowledge profoundly. We discuss implications for teaching fractions.

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.

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts using common procedural similarities. This quasi-experimental study investigates the influence of algebraic knowledge in solving problems in a chemistry context by using analogical transformations. The impact of structured steps that students need to take during the process of solving stoichiometric problems was explicitly analyzed. A total of 108 eighth-grade students participated in the study. Of the overall number of students, half of them were included in the experimental classes, whereas the other half were part of the control classes. Before and after the intervention, contextual problems were administered twice to all the student participants. The study results indicate that the students of the experimental classes exposed to structured steps in solving algebraic problems and the procedural transformations scored better results in solving problems in mathematics for chemistry compared to their peers who did not receive such instruction. Nevertheless, the result shows that although the intervention was carried out in mathematics classes, its effect was more significant on students' achievements in chemistry. The findings and their practical implications are discussed at the end of the study.