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.

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.

The main objective of this research was to study the effects of instructional management models and nominal variables on the development of students’ creative thinking. The researchers used the research synthesis of 400 studies on the development of students' creative thinking by a meta-analysis of research according to Cohen. The meta-analysis results revealed that the average effect size of the instructional management model (d = 3.43; [3.10, 3.17]) was positive and had a very high effect size with statistical significance. The most significant influence on the creative thinking development model was creative development theory (d = 4.217; [3.32, 5.11]). In addition, effect sizes varied with the attribute variables of the research, particularly the attribute variable of the research on instruction with the highest effect consisted of research with the focus on language, at the primary level, applied Torrance's creativity theory, designed between one to six lesson plans. Moreover, there was less than one hour per plan, the instructional period including the experiment conducted more than 31 hours and there were four weeks of instruction. In addition, there were six steps for instruction, there had quiz as an assessment tool, number of exams varied between 30 and 39 questions, and knowledge sheets were used as instructional materials. In the context of the meta-analysis, the findings indicated that the teachers should apply creative development theory in developing the students’ creative thinking for more effective instructional management.

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.

School placement plays a critical and complex role in student teacher development as well as in their professional dispositions and career attitudes. It is where theory and practice meet, teaching skills are developed, professional relationships formed and future careers envisioned. This mixed methods study explores student teachers’ experiences with and perspectives about new models of extended school placements developed in Ireland following significant policy and programme reform. Data was collected through interviews and questionnaires with one of the first cohorts to experience a reconceptualised initial teacher education programme, including extended school placement periods in a variety of school settings. This paper will explore student teachers’ perspectives regarding the value of the extended placement and factors influencing their professional learning, agency and sense of belonging. Overall, our findings confirm the pedagogical benefits of the extended placement in two different school settings for student teachers’ professional learning. However, they also highlight how a number of factors, including the existence (or absence) of school support structures, school culture, peer networks, paid or unpaid additional workload and financial pressures impacted on student teachers’ capabilities to develop their skills and professional agency, their sense of belonging and, in some cases, their physical and mental health.

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.

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

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

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.

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.

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.

Professional learning communities (PLCs) are important for improving student achievement and school development. According to PLC research, teachers' knowledge and practice in teaching are significantly improved by various PLC forms and favorable working environments. This qualitative research was conducted to find out what forms of PLCs were popular and what challenges were facing three primary schools in a province in Vietnam. The study utilizes a multiple-site case study design relating to PLCs in those schools with the data from interviews with the principals, group leaders and teachers, observations of PLC activities and related policy documents. The two forms of PLCs were identified in this research, including professional groups and groups of core teachers. Besides, four challenges facing PLCS implementation in those schools included the old habit of professional learning in PLCs, structural conditions of schedules and facilities, economic conditions of teachers and motivation for reforms. The study provides recommendations based on the findings for PLC research and practice within and beyond the Vietnamese context.

‘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.

This study presented the effect of interactive mathematics (IM) software assisted-teaching on primary three learners' conceptual understanding and performance. The cognitive theory of multimedia learning (CTML) supported the quasi-experimental design of this study drawing on IM software features that fit a multimedia tool for effective learning. This study used a sample of 138 lower primary learners. Learners’ test scores and examples of their work provided data to be analyzed. Learners' conceptual understanding was measured using the percentage of learners who performed a particular item and analyzed using sample learners' work while the overall performance was measured using the mean class scores. From the data analysis, IM-assisted teaching influenced conceptual understanding and performance based on a .05 p-value, the effect size of significance, and learning gains. The analysis of learners’ workings revealed different errors in addition, subtraction, division, and multiplication, which were remarkably reduced in the post-test by IM-supported teaching. This evidenced conceptual understanding development by IM-supported teaching. The study suggested the integration of IM in the Rwandan Competence-Based curriculum and its use as an instructional tool in teaching and learning mathematics at the primary level. Besides, it was recommended that Rwanda Education Board support teachers in developing basic computer skills to effectively create and monitor a multimedia learning environment for effective learning. Furthermore, further similar research would improve the literature about interactive technologies in supporting quality mathematics delivery and outcomes.

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.