Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on Action-Process-Object-Schema (APOS) theory. APOS theory is used to explore spatial thinking processes which consist of mental structures of action, process, object, and schema. This research is qualitative research with an exploratory method. It provided the students' opportunity to solve problems alternately until the method found the most appropriate subjects for the research objectives. The subjects were 2 students of Mathematics Education in the fourth semester of Universitas Muria Kudus Indonesia. The data collection techniques were started by distributing the validated and reliable spatial thinking questions, the cognitive style question, and the interview. The applied data analysis consisted of data reduction, presentation, and conclusion. The findings showed (1) spatial thinking process of holistic-external representation typed learners were indicated by the representative thinking element, abstract-illustrative figure expression to communicate and complete the tasks correctly, (2) spatial thinking process of the holistic-internal representation typed learners were indicated by the representative means, having ideas, connecting with the previous knowledge in the forms of symbols and numbers, and finding the final results correctly although incomplete.

Several concerted movements toward mathematical modeling have been seen in the last decade, reflecting the growing global relationship between the role of mathematics in the context of modern science, technology and real life. The literature has mainly covered the theoretical basis of research questions in mathematical modeling and the use of effective research methods in the studies. Driven by the Realistic Mathematics Education (RME) theory and empirical evidence on metacognition and modeling competency, this research aimed at exploring the interrelationships between metacognition and mathematical modeling and academic year level as a moderator via the SEM approach. This study involved 538 students as participants. From this sample, 133 students (24.7%) were from the first academic year, 223 (41.4%) were from the second and 182 (33.8%) were from the third. A correlational research design was employed to answer the research question. Cluster random sampling was used to gather the sample. We employed structural equation modeling (SEM) to test the hypothesized moderation employing IBM SPSS Amos version 18. Our findings confirmed the direct correlation between metacognition and mathematical modeling was statistically significant. Academic year level as a partial moderator significantly moderates the interrelationships between the metacognitive strategies and mathematical modeling competency. The effect of metacognition on mathematical modeling competency was more pronounced in the year two group compared to the year one and three groups.

The research delved into the assessment of integrating Learning Management System as an aid in teaching. Data were collected from 26 students at Rizal Technological University-College of Education, Philippines, through pretest-posttest quasi-experimental and normative survey design of research. Data were statistically tested using the frequency, percentage, mean, standard deviation, t-test for dependent and independent samples, and paired t-test. Results of the research indicate that the respondents have optimistic attitudes towards the integration of learning management system in teaching. The respondents performed poorly in the pretest examination but performed very satisfactorily in the posttest examination. Furthermore, the research found out that there is no significant difference between the performances of the experimental group and control group in pretest and posttest, moreover, there is a significant difference between the pretest and posttest scores of the experimental group and the pretest and posttest scores of the control group.

Critical thinking skills are one of the thinking skills needed to live in the 21st century and the era of the Industrial Revolution 4.0. This study aims to develop a Virtual Classroom Critical Thinking (VC2T) Model, which is valid, practical, and effective to improve students' critical thinking skills. VC2T model has six steps: problem orientation, formulation, group discussion, analysis, result discussion, and reflection. This study is a Research & Development (R & D) involving 33 high school students in Surabaya, Indonesia. Before being tested, the VC2T Model was designed based on the theory of Plomp and Nieveen and then validated by 3 (three) experts in physics education. Data were analyzed using validity by experts, implementation of teaching with the VC2T Model, paired t-test, calculation of n-gain, effect size and percentage of student responses. The results showed that the VC2T Model is: (1) valid with an average validity score of 4.14 in the high validity category; (2) practical with an average score of implementations teaching of VC2T Model 4.26 in the outstanding category; and (3) effective as indicated by increasing of students' critical thinking skills scores which are statistically significant at alpha .05, the average n-gain is .38 in the medium category, the effect size of 6.93 is in a strong category and the average students' response is 87.59 % with outstanding category.

In recent years, integrating technology into education continues to attract more attention along with the rapid growth of information and communication technology. In the literature, teachers’ technological pedagogical content knowledge (TPACK) plays an essential role in successfully integrating technology into teaching and learning contexts. This study aims to provide a comprehensive view of prior literature and some possible directions for researchers and educators for further TPACK studies. A total of 106 papers were chosen from the Springer database and synthesized. Frequency of annual publications, number of documents with and without TPACK in the title, research methods, number of authors, major contributed countries, most cited papers, and most productive journals in TPACK research were reviewed. The results showed that TPACK has continued to receive attention from researchers in the past decade. Among the reviewed publications, each of the 53 documents included the term TPACK in the title and abstract. To date, qualitative methods were more frequently adopted in TPACK research than quantitative, mixed, and non-empirical methods. Most papers published in TPACK research have two authors. When ranked by country, the US has the highest contribution compared to other countries in this field, followed by Turkey, Australia, Singapore, and Taiwan. The authors with the most cited papers were Min-Hsien Lee and Chin-Chung Tsai with 210 citations. Based on the number of articles published in TPACK, The Asia-Pacific Education Researcher and TechTrends seemed to be the most contributing journal in this field.

Metacognition inventory supports increased awareness and self-control to improve student’s academic success, including physics. However, there are limitations to revealing the Physics Metacognition Inventory (PMI), especially in Indonesia. This study aims to explore and evaluate the psychometric properties of PMI. This survey research has involved 479 students from three high schools in Indonesia. The psychometric properties of the I-PMI were evaluated using a Confirmatory Factor Analysis and Rasch Model approach. The results show that the Indonesian Physics Metacognition Inventory (I-PMI) is collected in 6 constructs from 26 items. The validity, reliability, and compatibility tests have also been analyzed with good results. The five rating scales used have adequate functionality. This research has also presented more comprehensive information about the Physics Metacognition Inventory in the context of Indonesian culture. This study has implications for using I-PMI to assess students’ metacognition at the high school level in Indonesia and recommendations for future research.

Numeracy is one of the essential competencies that the objectives of teaching math to primary students should be towards. However, many research findings show that the problem of “innumeracy” frequently exists at primary schools. That means children still do not feel at home in the world of numbers and operations. Therefore, the paper aims to apply the realistic mathematics education (RME) approach to tackling the problem of innumeracy, in the case of teaching the multiplication of two natural numbers to primary students. We conducted a pedagogical experiment with 46 grade 2 students who have not studied the multiplication yet. The pedagogical experiment lasted in six lessons, included seven activities and nine worksheets which are designed according to fundamental principles of RME by researchers. This is mainly a qualitative study. Based on data obtained from classroom observations and students’ response on worksheets, under the perspective of RME, the article pointed out how mathematization processes took place throughout students' activities, their attitudes towards math learning, and their learning outcomes. The study results found that students were more interested in math learning and understood the concepts of multiplication of two natural numbers.

The response of most universities to the Coronavirus disease (COVID-19) pandemic was Online Distance Teaching (ODT), which was a new experience for many educators and students. The aim of the study was to investigate the response of university teachers to ODT. A questionnaire was sent to all university teachers (N = 914). We received 290 usable responses. To create a Continuance Intention Model of Forced Online Distance Teaching (CIMoFODT), Confirmatory Factorial Analysis (CFA) and Structural Equation Modelling (SEM) were used in addition to descriptive and inferential statistics. The main findings were as follows: (i) during the closure, use of the videoconferencing system MS Teams was the only item that increased significantly, owing to mandatory use; (ii) the increase in the use of other applications (e.g., Moodle, email) was minimal; (iii) after the reopening of the university, email, Moodle, and supplementary online materials will be used for ODT; MS Teams will be used for small group teaching and individual consultations; (iv) CIMoFODT can be applied to explain the intention to continue ODT. The main conclusion is that teachers will return to traditional teaching when classrooms reopen.

Realistic Mathematics Education (RME) has gained popularity worldwide to teach mathematics using real-world problems. This study investigates the effectiveness of elliptic topics taught to 10th graders in a Vietnamese high school and students' attitudes toward learning. The RME model was used to guide 45 students in an experimental class, while the conventional model was applied to instruct 42 students in the control class. Data collection methods included observation, pre-test, post-test, and a student opinion survey. The experimental results confirm the test results, and the experimental class's learning outcomes were significantly higher than that of the control class's students. Besides, student participation in learning activities and attitudes toward learning were significantly higher in the RME model class than in the control class. Students will construct their mathematical knowledge based on real-life situations. The organization of teaching according to RME is not only a new method of teaching but innovation in thinking about teaching mathematics.

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

In this research, the influence of the Coronavirus disease (COVID-19) pandemic on 9th grade students’ mathematics achievement is analyzed through quantitative and qualitative methods. A posttest only with control group design was used to compare the mathematics marks of 9th grade students from the previous school year (before the pandemic, control group) and the current school year (during the pandemic, experimental group). Seventy-three students from a public high school in Spain attending class on alternate days participated in the study. Three focus group sessions were held with students, and five semi-structured interviews were conducted—two with teachers and three with students’ families. Results show statistically significant differences in students’ mathematics achievement, with students enrolled in 9th grade the previous (pre-pandemic) year outscoring their peers currently enrolled in 9th grade (during the pandemic) by 22.17%. An overall negative effect size of Hedge’s g = -1.11 was reported. Although significant statistical differences between groups were reported for both male and female students, the effect was 42.31% larger for male students (Hedge’s g = -1.11) than for females (Hedge’s g = -0.78). The qualitative information supported the quantitative results. Changes in educational settings, students’ lack of motivation, monotony, and students’ level of responsibility were qualitatively reported as factors that may explain this phenomenon. The main conclusion of this study is that the COVID-19 pandemic may be significantly and negatively affecting 9th grade students’ mathematics achievement.

The Coronavirus disease (COVID-19) pandemic has caused an inevitable shift from face-to-face to distance learning, a phenomenon known as panic-gogy. Parents are the main students’ companions while studying at home. Although various studies show the constraints in this condition, few employ phenomenology that accurately describes people’s experience regarding a situation. Therefore, this study aimed to describe parents’ experience during distance learning mathematics using a phenomenology approach. The participants comprised 71 35-50-year-old parents of junior high school students. A Google form with open-ended questions was used as the main instrument in data collection. Data were analyzed using NVivo-12-assisted thematic analysis in coding, while source triangulation was used to strengthen the data trustworthiness. The results showed that students did not learn the content well due to poor explanations by the teacher. Furthermore, they did not study well at home due to signal constraints and quota limitations. This study recommends blended learning by combining limited face-to-face and online learning.

Evolution is one of the most difficult and controversial topics. Scientific knowledge of evolution should belong to general knowledge of people, it should be the part of their natural science knowledge or biological education because it is the basis for accepting or refusing of other important topics such as genetical modification, global climatic change and others. Our aim was to analyse the inclusion of evolution in the teaching process in Slovakia in the subjects of history and biology and the associated potential threats to the formation of misconceptions. We measured the level of knowledge and understanding of evolution and evolutionary processes among high school graduates (N = 200). In doing so, we hypothesized that graduating high school students who have received evolutionary education achieve higher levels of both knowledge and understanding of evolutionary processes compared to those who have not received such education. We hypothesized that interest in science and acceptance of evolution would also positively influence levels of knowledge about evolutionary phenomena and understanding of evolutionary processes. Having used research, we claimed the impact of interest in natural science. We suggest to include the evolution as a main topic of biology into education through exploration- oriented teaching.

Lesson planning is considered to be an important and efficient tool for effective teaching and learning process. Preparations of effective lesson plan requires teachers to be competent in the pedagogical content knowledge (PCK). This study investigated how the mathematics teachers’ PCK impact their competences on designing effective lesson plans. Twelve in-service mathematics teachers from public secondary schools in Unguja-Island (Zanzibar) of Tanzania were involved. The data were collected using the reviewing of the teachers’ mathematics lesson plan documents and teachers’ interview. The data were analyzed in both quantitative and qualitative mode based on the lesson plan framework guideline (LPFG) and the criteria for better planning of the sections jointly with PCK abilities indicators. The percentage average of occurrence of the sections in the teachers’ designed lesson plan (DLP) and the percentage of occurrence of different category within the sections of the DLP in relation to the criteria were determined. Also, the challenges faced by the teachers in their DLP were identified. The result of the analysis revealed that the PCK competences of mathematics teachers are not good enough to impact their DLP, as some of their designing lesson plan sections were occurred inconsistently. Also, the implementation of PCK competences for effective mathematics teaching found to be at developing stage, as some criteria related to it were not clearly observed in their DLP. The study recommends the demand of in-service training for mathematics teachers on the implementation of teachers’ competences particularly PCK in the lesson plan designing for effective classroom practices.

The increase of English language learners (ELLs) in the United States of America (USA) public school classrooms and the diversification of the global education landscape urges initial teacher preparation programs to equip mainstream teachers with appropriate skills, knowledge, and dispositions to teach ELLs. This paper reports findings from a focus group study on elementary teacher candidates' (TCs') field experiences with ELLs. Based on interviews with four groups of TCs who completed their two practicums with ELLs, the study illustrates how mainstream TCs perceive their field experiences as future teachers of ELLs. The findings suggest that TCs recognize dissonances and develop care toward ELLs through their engagements in ELL-specific field experiences. The study also demonstrates how the recognition of dissonances led to changes in TCs' beliefs and values, which was observed through their imagination. Informed by their field experiences with ELLs, TCs began forming professional agency as future teachers by imagining specific teaching strategies, methods, and approaches they would like to implement with ELLs. Implications and future directions of teacher education programs are also discussed.

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

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 study investigates the contribution of teachers’ willingness to their professional competence in adapting to digital learning transformation during the Coronavirus disease (COVID-19) pandemic and its relationship to instructional leadership and self-efficacy. Data were collected by distributing online questionnaires consisting of 4 constructs, namely instructional leadership, self-efficacy, teacher’s willingness to change, and professional competence, and distributed to 221 Indonesian High School teachers. Structural Equation Model (SEM) was used for analysis using Analysis of Moment Structure (AMOS) version 23.0 to examine the hypotheses. The results showed that instructional leadership significantly influences teachers’ willingness to change with a positive impact on their professional competence. Furthermore, there is a significant effect on teachers’ willingness to change their professional competence, insignificant on self-efficacy with substantial impacts on their willingness to change. The analysis results through the Sobel test showed that the teachers’ willingness to change is an excellent mediating variable for self-efficacy in influencing professional competence. Conversely, it is not an excellent mediating variable for instructional leadership towards professional competence. The importance of teachers’ willingness to improve their professional competence is a new finding that significantly contributes to their professional development.

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

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