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.

In all years of the Program for International Student Assessment (PISA) in primary mathematics education, Finland ranked in the lower places (44-61) in the dispersion index (the difference in scores between the 95th percentile and the 5th percentile), while Israel ranked in the upper places (1-3) in the same index. In the last PISA test, Israel ranked first (among the 78 participating countries) in grade differences, while Finland ranked 61st. The score for dispersion in Israel is 356 points, the highest among the countries and economic entities of the Organization for Economic Cooperation and Development (OECD). Based on these results, this comparative study between Israel and Finland was conducted to investigate the most important sociological factor in the Pisa test that influences most student achievements in mathematics in Finland and Israel, as well as the reasons for the differences in achievement between mathematics scores. The results of this study show that the differences in achievement in Israel are due to students' socio-economic status and the sector. In contrast, Finland's first sociological factor influencing student performance is socio-economic status. Nevertheless, it has a more negligible influence than in Israel. The second factor is student motivation.

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.

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

This 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.

The greatest impact of the COVID-19 pandemic on Indonesian education was the decline in teacher performance. In light of this information, this study analyzes the role of supervision, salary and benefits, school climate, training and development, and perceived organizational support in moderating the impact of competence on teacher performance during the COVID-19 pandemic. This study also compares the relationships between employed government and private teachers. Data were collected through questionnaires to teachers with a sample of 166 government teachers and 175 private teachers in primary and secondary schools through a Google form and analyzed using moderated Structural Equation Modeling-Partial Least Square (SEM-PLS), multigroup, and multilevel analysis. The results showed that salary and benefits, training, and development did not affect the performance of public school teachers. In contrast, only salary and benefits did not affect teacher performance for private teachers. Moreover, only supervision significantly moderated the effect of competence on the performance of public school teachers. However, supervision, salary, benefits, school climate, training and development, and perceived organizational support did not affect private teachers' performance. The Ministry of Education or the Foundation needs to review and improve the mechanisms of training and development, supervision, and school organizational climate to promote optimal teacher performance during the pandemic.

This experimental research aimed to examine the effectiveness of the transformative learning program (TLP) on the active global citizenship (AGC) of 60 undergraduate students who had joined student affairs engaging in community development, working with a volunteer spirit, and community service. The participants were randomly assigned into experimental and control groups (n=30 for each group). The data were collected using the AGC Scale with a reliability of .968. Assessments were conducted three times: before, after the experiment, and follow-up. The TLP consisted of five steps: (a) Review social issues and crises contributing to disorientation; (b) Reflect critically to reach solutions; (c) Reformulate the meaning of perspectives to plan a course of action based on new perspectives; (e) Accept and improve new practices; and (f) Evaluate. MANOVA was performed to analyze the data. The results showed that students in the experimental group had a higher mean score of AGC than the control group, both after treatment and at follow-up (p < .05); the mean scores of the AGC of the experimental group after treatment and at follow-up were higher than the mean score before treatment (p < .05); and the mean score of AGC of the experimental group at follow up was higher than the score after treatment with no statistical significance. In conclusion, educational personnel could use this TLP to promote AGC for university students.

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.

Mathematical confidence and critical thinking are essential in preparing preservice teachers. Thus, this study explored the perceived confidence and critical thinking levels in mathematics of elementary and secondary preservice teachers. A descriptive-correlational-comparative research design was employed, with a sample of 107 randomly selected preservice teachers enrolled in the Bachelor in Elementary and Secondary Education programs of a state university in West Philippines. The study used arithmetic mean, standard deviation, Spearman’s rank-order correlation, and independent samples t-test to analyze and draw conclusions from the data. The findings revealed that the preservice teachers have high confidence and critical thinking skills. Their program significantly correlates with their perceived critical thinking and confidence level. Besides, the preservice teachers’ confidence levels and perceived critical thinking skills significantly correlate. Further analysis found significant confidence and critical thinking differences favoring the secondary over the elementary preservice teachers. These findings provide insights that would benefit mathematics educators in providing priority programs to enhance the preparation of future math teachers.

In this article, we present the results of empirical research using a combination of quantitative and qualitative methodology, in which we examined the achievements and difficulties of sixth-grade Slovenian primary school students in decimal numbers at the conceptual and procedural knowledge level. The achievements of the students (N = 100) showed that they statistically significantly (z = -7,53, p < .001) better mastered procedural knowledge (M = 0.60, SD = 0.22) than conceptual knowledge (M = 0.37, SD = 0.17) of decimal numbers. Difficulties are related to both procedural and conceptual knowledge, but significantly more students have difficulties at the level of conceptual knowledge. At the level of procedural knowledge, or in the execution of arithmetic operations with decimal numbers, we observed difficulties in transforming text notation into numerical expressions, difficulties in placing the decimal point in multiplication and division, and insufficient automation of mathematical operations with decimal numbers. At the level of conceptual knowledge of decimal numbers, the results indicate difficulties for students in understanding the place values of decimal numbers, in estimating the sum, product and quotient of decimals with reflection and in mathematical justification. In relation to difficulties in justification, we observed an insufficient understanding of the size relationship between decimal numbers and difficulties in expressing them in mathematical language. The results indicate that to overcome such difficulties in the learning and teaching of mathematics, more balance between procedural and conceptual knowledge is needed.