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.

This research is a developmental research aiming at developing a good mathematical test instrument using polytomous responses based on classical and modern theories. This research design uses the Plomp model, which consists of five stages, (1) preliminary investigation, (2) design, (3) realization/construction, (4) revision, and (5) implementation (testing). The study was conducted in three vocational schools in Lampung Province, Indonesia. The study involved 413 students, consisting of 191 male and 222 female students. The data were collected through questionnaire and test. The questionnaire was used to identify the assessment instruments currently employed by teachers and to be validated by the experts of mathematics and educational evaluation. The test used an open polytomous response test numbering of 40 items. The data were analyzed using both classical and modern theories. The results show that (1) the open polytomous response test has a good category according to classical and modern theory. However, the discrimination power of test items in classical theory needs several revisions, (2) the assessment instrument using the polytomous response of open multiple choice can guarantee information on the actual competence of students. This is proven by the fact that there is a harmony between the analysis result obtained from classical and modern theory from the students' arguments when giving reasons for their choices. Therefore, the open polytomous response test can be used as an alternative to learning assessment.

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.

The government has imposed social restrictions during the COVID-19 pandemic, affecting the education sector, including the early childhood school. Distance education offers different methods from the conventional methods, as the students are expected to gain the same skills, including critical thinking skills. Therefore, teachers must provide distance learning innovations using relevant learning media, such as multimedia-based learning. This research aims to assess the efficacy of multimedia learning in early childhood distance learning. This research is a quantitative model with a quasi-experimental pretest and posttest design. The data collection technique utilized questionnaires given to 30 samples of early childhood children. The data were statistically analyzed using SPSS software. The results confirmed that multimedia-based learning for distance learning could develop critical thinking skills in early childhood children during the COVID-19 pandemic. The results of this study offer exploration of learning strategies to improve children’s critical thinking.

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.

This investigation examined English as a foreign language (EFL) teachers’ perceptions of their self-efficacy in using instructional strategies in the context of the Mekong Delta of Vietnam. The research was designed as a descriptive research collecting quantitative and qualitative data from a questionnaire and semi-structured interviews. Forty-six Vietnamese EFL teachers were invited to partake in the study. The results indicated that participants were in general confident in using instructional strategies in their English classes. Specifically, the participants were highly confident in their abilities to use multimedia (M=4.41), assessment techniques (M=4.35), and classroom English (M=4.35). The study also indicated that participants were not confident in evaluating the level of task difficulty (M=3.37), dealing with unmotivated students (M=3.57), and meeting students’ particular needs for support (M=3.62). Pedagogical implications and recommendations were addressed to help manifold stakeholders at the end of this paper.

Systemic thinking skills are an increasingly important aspect of contemporary life for all students. Therefore, the first aim of the present study was to investigate the relationship between systemic thinking skills, epistemological beliefs, and mathematical beliefs in a sample of 120 secondary school students aged 16-18 years in Saudi Arabia. The second objective was to examine gender differences in these three variables. Participants answered scales measuring the Systemic Thinking Inventory (STI) and the Mathematical Beliefs Scale (MBS) created by the researcher. Additionally, participants answered the Epistemic Belief Inventory (EBI). Results showed a positive correlation between systemic thinking skills, epistemological beliefs, and mathematical beliefs. In addition, significant differences were found in favor of men on the systemic thinking skills on the holistic vision of the system and systemic synthesis skills subscales and females on the systemic analysis subscale. Significant differences were found in epistemological beliefs. A particular difference was innate knowledge and omniscient authority in favor of males, simple knowledge, certain knowledge, and rapid learning in favor of females. In addition, differences were found for mathematics teacher competence and self-efficacy beliefs in favor of males and the usefulness of learning mathematics, difficulty in mathematics, and enjoyment of mathematics in favor of females. The results are discussed in light of the relevant literature, and suggestions are made.

The decline in student character is the result of low student learning outcomes. The common student learning outcomes are influenced by several factors, and one of them is teacher-centered, monotonous learning model. For this reason, it is deemed necessary to conduct research that aims to determine the effect of project-based assessment on values clarification technique (VCT) learning on improving students’ learning outcomes by controlling the family environment. This study uses a 2x2 factorial experimental design. The sample was selected through multistage random sampling with 120 students. The two-way ANCOVA data analysis technique was used to analyze the data. The findings obtained after controlling the family environment are: 1) civics learning outcomes from the group of students who used value clarification techniques are higher than those using conventional learning models and 2) civics learning outcomes from the group of students who were given project-based assessments are higher than the group who are given conventional assessments. Thus, it can be recommended that civics education teachers used appropriate VCT and project-based assessments to improve learning outcomes.

The delivery of science, technology, engineering and mathematics (STEM) learning to improve an individual’s competence and future career interests has become a critical scientific undertaking for teachers and researchers alike. A plethora of research has proposed various hands-on robotics activities built on constructivist theories, thereby facilitating the development of knowledge based on reality for scientific and non-scientific stakeholders. Robotics may become an essential focus point within technology provision, which is an essential underlying characteristic for the seminal development of computational thinking (CT). However, despite the potential benefit of CT in developing an individual’s problem-solving skills, strategies for improving this ability through hands-on robotics activities largely remain underexplored. This paper highlights the constructs drawn from hands-on robotics activities in a STEM workshop designed for pre-service teacher students. The qualitative research design involved eight participants to investigate the responses of pre-service teachers to a hands-on robotics activity intended to provide STEM material. The research findings emphasise the correlations between the CT principles and STEM learning phases and underscore the roles played by educational robotics to enhance previous literature on learning experience.

Mathematics teachers’ instructional strategies lack in-depth knowledge of algebraic systems and hold misconceptions about solving two algebraic equations simultaneously. This study aimed to gain an in-depth analysis of teachers’ knowledge and perceptions about the promotion of conceptual learning and effective teaching of algebraic equations. The main question was, ‘How do junior secondary school mathematics teachers manifest their pedagogical practices when teaching algebraic equations? This article reports on a qualitative, underpinned by the knowledge quartet model study, that sought to explore how junior secondary school teachers’ pedagogical practices manifested in the teaching of algebraic equations. Data were collected from observations, semi-structured interviews, and document analysis of two mathematics teachers purposely selected from two schools. The collected data were analysed using a statistical analysis software called Atlas-ti. (Version 8) and triangulated through thematic analysis. The study revealed that teachers’ choices of representations, examples, and tasks used did not expose learners to hands-on activities that promote understanding and making connections from the underlying algebraic equation concepts. The study proposed Penta-Knowledge Collaborative Planning and Reflective Teaching and Learning Models to enable teachers to collaborate with their peers from the planning stage to lesson delivery reflecting on good practices and strategies for teaching algebraic equations.

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.

Learning activities are conducted to help students achieve optimal academic achievement. This research aims to optimize student academic achievement through a learning process that integrates comprehensive formative assessments, including formative tests, self-assessment, peer assessment, and the initiator of creating summaries or concept maps that are given to students in a structured manner at the end of every lesson. The research method used was a quasi-experimental method with a 2x2 factorial design. Students enrolled in the biology education program of the basic physics course for the 1st semester of the 2019 academic year participated in this study. The participants were 66 undergraduate students divided into two classes. Thirty-four students in the experimental group were in class A, while 32 students in the control group were in class B. Data were collected using a learning outcome test instrument to measure academic achievement, which was tested at the end of the semester. Data were analyzed using a two-way ANOVA. This study concluded that a learning process that includes comprehensive formative assessment significantly affects students' academic achievement. These findings support the theory that formative assessment provides feedback, correction, and improvement in student learning.

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.

Scientific literacy is a critical competency for people to take an essential role in science, technology, and social advancement. It is important to note that this competence is still a problem for most students worldwide. Therefore, this study analysed students' scientific literacy differences between a project-based learning flipped classroom (PjBL-FC) and a project-based learning (PjBL) class assisted by learning resources in wetlands environments. This quasi-experimental study used a non-equivalent control group design involving Class X Senior High School as the sample. The data were inferentially analysed by t-test. The results showed that the scientific literacy of students in the class that applied the PjBL-FC was better than those who applied only PjBL. Furthermore, all the indicators reach the high to very high category except the ability to propose a hypothesis, which is in the medium category. It was concluded that flipped classroom makes the PjBL take place more efficiently and effectively. Further studies can be carried out to determine how students use the learning materials, how teachers design the PjBL strategy in an online platform, their effect on scientific literacy, and how to combine PjBL with other approaches.

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.

This study explored the effects of collaborative writing strategies on students' writing skills and self-efficacy. The study used a mixed methods design combining quantitative and qualitative approaches. Several instruments were used in data collection, including questionnaires, writing tests, writing assessment rubrics, and semi-structured interviews. The participants were randomly divided into two groups: the experimental group and the control group, which comprised 62 students. Data from the questionnaire and writing tests were analyzed using one-way MANOVA and MANCOVA tests, while interview data were explored using thematic analysis techniques. Participants were randomly divided into two groups: the experimental group and the control group. The results showed that collaborative writing strategies could improve students' writing skills and self-efficacy. Moreover, the qualitative results showed that most students responded positively to using these strategies to improve their writing skills and self-efficacy.