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 mixed method case study examined potential influences of social agents or immediate environments on individuals’ metacognition. Via quantitative methodologies, 122 pre-service teachers’ metacognition was measured by the Turkish Metacognitive Awareness Inventory, and metacognitive components did not show any variations across majors, locations of previous studies, the highest degree of education in the family, frequently communicated friends, and regions. Regression analyses revealed that friends were a significant predictor for metacognition. Also, focus group interviews were analyzed thematically via deductive codes regarding the theory of metacognition. Findings confirmed that friends may support individual metacognition at all levels, metacognitive knowledge, regulation, and experiences through cooperation, modeling, reflections, discussions, feedback, and peer evaluation. Pre-service teachers’ engagement on the social media may also support their regulatory strategies due to models’ task performances or by their reflecting upon those performances. Teachers and family may support metacognitive knowledge, specifically career goals via expectations, anecdotes, and experiences. On the other hand, schools and the Turkish culture may impose some limitations on the youth, and they may engage in reflection and self-questioning to manoeuvre negative experiences or conflicts. Thereby, cross-national and longitudinal studies are highly suggested to explicate the social foundations of metacognition.

Successful teaching requires teachers' reflections and metacognitive awareness. However, few studies have investigated the impacts of reflections on teachers' metacognitive awareness in teaching. This study aimed to examine whether or not reflections can empower Indonesian pre-service English teachers' metacognitive awareness in teaching. Mixed-methods research was conducted to collect quantitative and qualitative data from 36 pre-service English teachers (PSETs) in two micro-teaching classes at the Undergraduate Program, Sanata Dharma University, Yogyakarta, Indonesia. Quantitative data from the pre-semester and post-semester were analyzed descriptively and statistically. Qualitative data from reflections and focus group discussions (FGD) focused on determining key issues related to PSETs' metacognitive awareness in teaching. Data analyses revealed that Indonesian PSETs' perceived metacognitive awareness in teaching increased post-semester. They also admitted the positive contributions of reflections in enhancing their metacognitive awareness in teaching. The increase was primarily attributable to the implementation of explicit reflections of the elements of metacognitive awareness in teaching. This research provides recommendations for teachers, lecturers, and future researchers.

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.

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 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 qualitative study is part of a feasibility study conducted by State University of Malang (SUM), Indonesia, to determine stakeholder needs for a study program specializing in managing bilingual education. The study participants included one SUM lecturer who held a managerial position in the division of SUM laboratory schools and twelve teachers/leaders of bilingual schools in some cities in East Java and South Sulawesi. Data were collected using an online questionnaire and in-depth interviews with two selected participants. The results indicate issues related to teachers' English competencies, materials development, and integrating an internationally-oriented curriculum into the national curriculum. Teachers' low English competencies prevented them from conducting teaching and learning bilingually and developing instructional materials in appropriate English. In addition, the combination of national and international curricula was identified as the biggest challenge for bilingual schools. The teachers/leaders were never trained to manage the bilingual program. They learned based on their experiences, and it took years to figure out how to manage bilingual programs successfully. Therefore, the establishment of a new program of study is needed.

In today's World, data-driven methods are behind the determination of potential action plans in every area of life. These data-driven methods help individuals or policymakers to figure out the strengths and weaknesses on the subject that are worked on and to make a comparison to the best practices. Thus, actions can be taken immediately on the specific factors that have a huge impact on the topic investigated. In the educational area, countries are using the same approach to measure, monitor, and improve the quality of education by attending international studies. In this study, for both Turkish and Singaporean students, Artificial Neural Network (ANN) model is performed to predict the students' mathematics achievement and to identify factors that have a high impact on achievement using Trends in International Mathematics and Science Study (TIMSS) in 2019 with the data of 3,586 Turkish and 4,750 Singaporean students. The reason behind comparing the results of Turkey to Singapore is that Singapore is the best-performing country in terms of mathematics achievement in the TIMSS in 2019. The model results show that the top two crucial factors in both countries are the frequency of absenteeism from school, and students’ confidence in mathematics with the accuracy of 75%. In addition, relevant policy implications are given based on the importance level of significant factors.

‘Panic-gogy’ is a term that describes the educational situation during the pandemic due to the transformation phenomenon from face-to-face learning to distance learning. Various types of research are used to uncover the constraints of this phenomenon, but not many researchers use phenomenological studies with parents as participants. Therefore, we used a phenomenological study to describe parents’ views on the constraints, expectations, and approvals regarding the preparation of distance learning modules at the junior high school level (aged 13-15 years). Data collection was carried out using semi-structured interviews. Data were analyzed using NVivo-12-assisted thematic analysis. The main findings are that most parents experience problems. Namely, children do not understand mathematics material, incomplete explanations of material from teachers, internet disturbances, and quota limitations, and children cannot learn mathematics optimally during the distance learning period. Most parents want face-to-face learning to be carried out immediately, teachers to provide detailed explanations, and use digital learning platforms. In addition, 85% of parents agree that mathematics teachers should develop distance learning modules. However, because the pandemic is still not over, this study recommends using blended learning to maintain the quality of mathematics learning.

Ursula von der Leyen identifies diverse classrooms have different knowledges and ‘epistemologies’. A typology of epistemologies for democratising knowledge ‘A Blueprint for Character Development for Evolution’ (ABCDE) is offered to mainstream policy benefits for all by Higher Education as hubs i) credentialing educational leaders by doctoral-study and ii) propelling networks of Professional Educators and Administrators Committees for Empowerment (PEACE) across professions credentialed by Higher Education and chaired by educational leaders. PEACE builds robust evidence bases to inform redesigning curriculums and culturally responsive pedagogies as policy benefits that empower students to use ABCDE with Assessment for Personal and Social Learning (APSL) to problem solve across the quadruple-helix. Education Outcomes include students’ self-management of personal and social understanding and wellbeing for resilience within sustainable circular, entrepreneurial, green and digitised economies with products and means of production regulated by professions credentialed by Higher Education. Impacts include communities developing responsible historical social consciousness to reinvigorate democratic governance, accountability, transparency, effectiveness and trustworthiness of rule-of-law based institutions and policies to expand active and inclusive citizenship empowered by safeguarding human rights. Further research, building on the powerful European Commission funded platform ‘DocEnhance’ is recommended to inform effective and efficient investment into high quality education and training.

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.

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.

School quality has become a guiding concept that increasingly shapes educational planning and school development. For many decades, it has been a topic of significant interest, resulting in a wide-ranging and diverse research field. However, it is far from clear how school quality should be defined, what it should encompass, and how it influences student performance. The goal of this scoping review is to examine the existing evidence of the relationship between characteristics of school quality and student cognitive output/ student performance in secondary school. More precisely, it aims to (a) identify, (b) categorize, and (c) examine and evaluate the effects of characteristics of school quality affecting student performance and teaching characteristics in secondary school. In order to achieve these aims, we selected, clustered, and analyses 37 articles. The process was conducted by the research group through regular meetings, discussions, and consensus decisions. Our findings contribute to the comprehensive body of literature by identifying the following dimensions: aims and strategies for quality development, leadership and management, professionalism, school culture, and resources. Furthermore, the review revealed that although the field of school quality has been extensively researched, it lacks consistency, with many different operationalisations and definitions, making comparisons and syntheses challenging or even impossible. We believe that clear operationalisations and definitions are crucial to achieving comparability. Additionally, to achieve a standardized understanding of school quality and establish the categories internationally, uniform, theoretically sound, and content-related definitions of each category are necessary.

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.

Education delivers systematic instruction so effective learning acquisition may take place. It molds students into holistic well-being to contribute to various industries; hence, relevant competencies are developed. Strengthening education significantly encompasses the production of formfitting and distinct instructional materials to invite a sequential way of presenting quality instruction. This research is focused on knowing the effectiveness of the modules developed in Human Resource Management for Filipino business students. Specifically, it is developmental research and utilizes a pretest and post-test control group design. Numerical data were supported by phenomenological interviews, strengthening the study's results. It involved 80 college students classified as the experimental and control group. Moreover, the interview includes 10 participants. Findings reveal that utilizing the modules realized the increase in performance of the experimental group due to their exposure to the materials. However, one of the pitfalls has been revealed in utilizing self-directed learning material; thus, academic performance will only improve if students are organized to set their own goals and learning pace. Using outcomes-based instructional materials leads to substantiating learning, effectively enticing learners' interest. It maximizes students' motivation and participation since topics are well-planned and designed comprehensively. The materials are an essential tool in inviting the enthusiasm of business students to engage in learning. These are valuable means to encourage independent learning without sacrificing the competencies to be learned and applied by the learners.

The accuracy of assessing the capabilities of the process and product in chemical practice activities requires appropriate measurement procedures to be followed. It is crucial to identify the components that can introduce bias while measuring student abilities during the measurement process. This study aims to identify the components or criteria used by teachers to assess student performance in practicum activities and analyze the quality of the rubrics developed. The study was conducted with the participation of three raters, 27 high school students, and nine assessment criteria. A quantitative descriptive approach was employed using the many-facet Rasch model (MFRM) analysis for measurement. The results of the MFRM analysis show no significant measurement bias, with data measurement facets fitting the MFRM model. The reliability of all the facets meets the criteria, and the scale predictor functions appropriately. While all students can easily pass four out of nine items, five items can only be partially passed by students. The assessment criteria that require special attention include communication skills, tools and assembly, interpretation, cleanliness, and accuracy when performing practicums. These criteria provide feedback for teachers and students to ensure successful practicum activities. The Discussion section of this study delves into the findings and their implications.

The peer tutoring approach is a student-cantered teaching method in which students learn in pairs with teacher supervision. The study discussed in this paper is a systematic literature review related to the effectiveness of peer tutoring approaches which has been published within the last 5 years. A complete text analysis was conducted using 20 research papers stating the impact of the peer mentoring approach for this writing. Among the things obtained from previous studies are the variety of ways to implement peer tutoring approach, the impact on 3 aspects in students which are mathematical achievement, social skills and cognitive skills and the teaching theories used. The findings of the study indicate that most past studies used quantitative research methods with the concept of age peer approach. Then, constructivism theory was the most frequently applied with a sample of high school students. In conclusion, this systematic literature review shows that the peer tutoring approach in mathematics education has many benefits in various aspects and needs to be extended to improve the quality of education.