This research is motivated by a linear equations system, which is the basis for studying necessary linear algebra materials, such as rank, range, linear independent/dependent, linear transformations, characteristic values and vectors. There are still prospective mathematics teachers who have difficulty solving linear equations system and understanding the form of row echelon and reduced row echelon forms. In this study, subjects were three prospective mathematics teachers from Swadaya Gunung Jati University Cirebon who were taking matrix algebra courses. This study aims to reveal the conceptual understanding of prospective mathematics teachers in determining the solution to systems of linear equations. The results show that there are still prospective mathematics teachers who only use memory about the properties and procedures in determining whether a matrix is said to be a row echelon form or a reduced row echelon form. Then, there is still weakness in building the algorithms' relationship due to the immature knowledge of the concepts. Researchers found that many prospective mathematics teachers were more comfortable solving problems that were performed procedurally. Further research is needed to determine how the mental construction process and mathematical conceptual knowledge of prospective mathematics teachers are through meaningful learning so that conceptual understanding is maximized.

Many problems in real life are full of uncertainty. Probabilistic thinking is one way to solve this uncertainty problem. The personality abilities that are interesting to examine include how independent the students are in facing probabilistic solutions. For this reason, it is necessary to study the probabilistic thinking profile of prospective mathematics teachers in solving probabilistic problems in terms of learning the self-regulation. The research method used in this research is qualitative research. In this study, the researcher conducted an analysis of students' probabilistic thinking with the scope of the probability material related to the sample space, the probability of events, and the probability of the random variable space. The profile of the level of probabilistic thinking is influenced by cognitive factors in the form of probabilistic knowledge obtained by students and personality in the form of self-regulated learning. Student learning self-regulated influences the mental activity in decision making. By studying the profile of probabilistic thinking, students are better prepare to face uncertainty with various aspects that influence it.

Absenteeism is of great concern for K–12 school students in the United States. The aim of this study is to evaluate effects of parental participation types in absenteeism of Elementary and Secondary Education (K-12) students in the United States. We analyze the data of the U.S. Department of Education (Hanson et al., 2019), in relation to students, schools and parents’ characteristics, along with various parental involvement activities, for exploring how these factors influence K-12 students’ absenteeism in the United States. We employ Chi-square tests for the significance of relationships between parental involvement types and absenteeism of K-12 students. We also undertake multiple logistic regression analyses to evaluate the significance and odds of K-12 students’ absenteeism due to parental involvement activities and other underlying factors. The results of bivariate analyses suggest that parental involvement types are significantly associated with K-12 absenteeism (chi-squared p-value<0.05). Multiple logistic regression analysis reveals that only a subset of underlying parental activities is significantly related to higher odds of absenteeism as measured by estimates of odds ratios (OR) and 95% confidence interval estimates. It also suggests that parental education, ethnicity and poverty adjusted for other factors also significantly affect absenteeism.

Creative thinking is the highest level of the kind of high order thinking. In observations at the schools in Indonesia, teachers overly equate all levels of achievement of students' creative thinking to obtain higher order thinking skill improvements in mathematics learning. This condition results in an imbalance in learning practices. Therefore, this research fills the gap of this imbalance by describing the student’s creative thinking profile as a high order thinking skill in the improvement of mathematics learning. These results can contribute knowledge to educators to manage teaching strategies that can improve mathematics learning which refers to high order thinking skill for all levels of their creative thinking. This research is qualitative descriptive research. The subject were junior high school students in Malang, Indonesia. Data collection methods are tests, observations, and interviews. Data analysis is conducted by reducing data, present data, and conclusions. These research results are descriptions of student’s creative thinking profiles as a high order thinking in mathematics learning improvement, namely students have problems planning problem solving; students take a break to make plans; identify the essence of the problem, provide original ideas, provide alternative problem-solving plans, combine previous ideas with problem questions; operate and implement their plans by creating various original solutions.

Teaching mathematics in general and instructing mathematics at junior schools in particular not only create favorable conditions for students to develop essential and core competencies but also help students enhance mathematical competencies as a foundation for a good study of the subject and promote essential skills for society, in which mathematical communication skill is an important one. This study aimed to train students in mathematics communication by presenting them with topics in line with the structure's congruent triangles. An experimental sample of 40 students in grade 8 at a junior school in Vietnam, in which they were engaged in learning with activities oriented to increase mathematical communication. A research design employing a pre-test, an intervention, and a post-test was implemented to evaluate such a teaching methodology's effectiveness. For assessing how well the students had progressed in mathematical language activities, the gathered data were analyzed quantitatively and qualitatively. Empirical results showed that most students experienced a significant improvement in their mathematical communication skills associated with congruent triangles. Additionally, there were some significant implications and recommendations that were drawn from the research results.

This study aims to present the potential of Participatory Action Research (PAR) to bring together the experiences of teachers and researchers with the intention of improving teaching practices and students’ learning outcomes. Participants in the study were 7 teachers, their 160 fifths grade students, and researchers (authors). Teachers and researchers participated as partners in all collaborative activities during the period of 12 weeks.  All teachers assisted by the researcher (first author) who serves as a teacher at the same school, were involved in implementing the reciprocal teaching method (RTM) in math classes. They examined each step of the implementation of this method in order to investigate whether it has an impact on student achievement in solving mathematical word problems. Teachers observed the work of students in their classes, whereas in the joint meetings they discussed occasional ambiguities as well as issues that were most challenging for them and their students. The results showed that there was a significant improvement of the students’ results in the post-test of the mathematical word problems. The analysis of teachers' reflections highlights the benefits of collaboration within the PAR project, both for students and teachers. The study suggests that the PAR model can be used effectively within school settings as a research model, and as a pedagogical practice.

Learning in high schools has used a lot of smartphone assistance to make it easier for students to understand the material explained by the teacher. However, with the many uses of smartphones in learning, of course, it must provide positive benefits to the ability of students, especially the science literacy ability. In this study, the objectives to be achieved are to examine how much the smartphone's usability in physics learning, examine students' science literacy and examine the effect of the smartphone’s usability on students' science literacy in physics learning. The method used in this study is a quantitative method with a research design used is a one-shot case study. The data on smartphone usability is obtained using a questionnaire, and science literacy of students is obtained through on physics science literacy test. The results of this study indicate that the smartphones usability and students' science literacy in physics learning are respectively in the high and medium categories with a respective percentage of 57.20% and 36.36%. The students' science literacy is influenced by the smartphone's usability in physics learning by 34.30%. These results indicate that smartphone usability by most students is very high, but has not been able to contribute optimally to students' science literacy. Therefore, special treatment is needed in utilizing the use of smartphones in physics learning so that students' science literacy can be optimized.

The primary purpose of this article is to analyze how the origin of the Cold War is represented in Turkish history textbooks for general secondary school education for the twelfth grade. The author examined three history textbooks, which are only approved by the Ministry of National Education (MoNE) for teaching the course of Contemporary Turkish and World History. This research applied content analysis, including narratives and visual interpretation of the origins of the Cold War, and also the events regarding the emergence of Soviet Bloc and Western Bloc in high school history textbooks in Turkey. Findings indicate that treatments of the origin of the Cold War in Turkish history textbooks are remarkably similar in many ways. The traditional approach of the origin of the Cold War, which depicts the Soviet Union as an aggressive power whose primary purpose was to expand Communism to the world, constitutes the dominant narrative in Turkish history textbooks. The representation of the United States is very positive. All textbooks underline that the United States played a crucial role in solving many problems in many different parts of the world to prevent the expansion of Communism.

This article presents the findings of an action research study that evaluated the effectiveness of differentiated instruction in the subject of Information and Communications Technology (ICT) in primary education in Greek primary schools. Effective teaching poses a challenge to all educators in all educational levels. The subject of ICT poses multiple challenges to educators due to its applied nature, the limited allocated time and the diverse needs of the students. A differentiated teaching intervention was designed and applied from January to March 2020 to 113 upper elementary students from two elementary schools in Athens. The findings of the research highlight the improvement of the quality of the students’ assessment and the level of students’ active participation due to differentiated instruction. Furthermore, the strategy of flexible grouping, the technique of “thumb it up” cards and the applied differentiated working routine proved to be highly effective. Lastly, the implementation of asynchronous working combined with hierarchical learning activities proved to be challenging to the educator due to its complexity. Based on these findings, the article discusses the importance of further research in the systematic implementation of differentiated instruction in mixed ability classrooms and in multiple subjects.

The equal symbol has been used in diverse mathematical frameworks, such as arithmetic, algebra, trigonometry, set theory, and so on. In mathematical terms, the equal sign has been used in fixed command of standings. The study reports on the students meaning and interpretations of the equal sign. The study involved Grade 6, 7, and 8 students in a secondary school in Alain, United Arab Emirates (UAE). Much of the earlier research done on the equal sign has focused on the primary school level, but this one focuses on middle school students. The study shows that the maximum foremost understanding of the equal sign amongst Grade 6, 7, and 8 students is a do-something, unidirectional symbol. Students realize the equal sign as an instrument for marking the response moderately than as an interpersonal symbol to associate extents.

The Coronavirus disease (COVID-19) pandemic impacted various lines in the international world, including Indonesia. Pandemic COVID-19 in Indonesia has also changed multiple performances in multiple sectors, one of which is education. The concept of learning from home changes lecturers' paradigm as educators in tertiary institutions applying online learning. This study aims to identify students' perceptions of the implementation of online learning during the COVID-19 pandemic. This study uses a qualitative research approach with the type of phenomenology. The subject of this study was 22 students in Indonesia who experienced the impact of the COVID-19 pandemic. This research instrument uses semi-structured interview guidelines. Students perceive online learning during the COVID-19 pandemic as (1) ineffective learning activities; (2) unpleasant learning activities; (3) limit self-actualization in education; (4) helping to become an independent person in learning; and (5) fun learning activities. Higher Education should create innovative and creative online learning strategies. Thus, students have a high enthusiasm for online learning.

While previous studies on assessments focused on measurement of principles and constructs, existing attention is given to content validation involving vocational education and skills. The emphasis on content validation has prompted a holistic perspective of teaching and learning to demand alternative research approaches. Using evidence of content validity based on expert judgment and assessment items, this paper argues that vocational knowledge and skills could be determined via constructs and construct functions. Content validity analysis was studied in two major phases, namely, through an assessment of an electrical technology course at a Malaysian higher education institution and expert panels’ examination of items. It was found that to increase confidence in providing reliable instruments for future empirical studies, a careful process in item development and content validity analysis was considered important. Therefore, applying these findings on item analysis and expert panels to reflect content validity can enhance the validity of assessment items.

Many studies have pointed out a proportionate relation between metacognition and reading strategies. This study advances such an understanding by arguing that this relation is comprised of several sub-relations. Metacognitive Awareness Inventory and Reading Strategies Inventory were conducted among 92 English as Foreign Language students at a Vietnamese university. This study highlights 3 major findings. First, metacognition processes do not merely mean “cognition about cognition”. Second, while previous studies tended to portray metacognition as a whole, it is argued in this study that it is constituted by two main clusters (knowledge of cognition and regulation of cognition) which can be further specified into eight sub-components. Third, there seem to be some sub-linearities that underpin students’ metacognition and that influence their uses of reading strategies. These findings are hoped to shed light on preserving spaces and autonomy in curriculum/syllabus development for students to exercise their own metacognition.

The discussion about the loss of nationalism values in the Indonesian migrant workers’ (IMW’s) children in border areas, has become an important issue in the world of Indonesian education. The purpose of this study is to describe the role of Community Learning Center (CLC) in fostering nationalism values in IMW’s children, as well as to reveal the teaching experience and meaning of nationalism from the perspective of teachers at CLC Sarawak, Malaysia. The research uses qualitative method with case study approach that focuses on factors that can foster nationalism of IMW’s children. Data collection obtained through observation techniques, in-depth interviews, and documentation. The results showed meaningful findings according to the conditions in the education system in CLC, as well as socio-cultural conditions that affect every activity in the border area. The first finding indicates that CLC has an important (central) role in fostering the nationalism of IMW’s children in border areas. The second finding shows the fact that teachers are still experiencing some problems in the field, such as; limited access to information and communication, teacher education background, school conditions, limited educational units, learning facilities, and family and social environments. The third finding emphasizes the importance of nationalism for teachers who devote themselves to teaching in border areas, because teachers have a crucial role in transferring knowledge, providing meaningful learning experiences, and fostering the nationalism of IMW’s children.

Problem-solving is considered one of the thinking skills that must be possessed in 21^st-century education because problem-solving skills are required to solve all problems that arise. The problem-solving stages that can be used are Polya's four steps, namely, understanding the problem, devising a plan, carrying out the plan, and looking back. Problem-solving skills are essential for solving word problems. Word problems based on arithmetic operations are divided into three types: one-step, two-step, and multistep. This qualitative research aimed to see problem-solving skills viewed from the type of word questions and elementary school students’ third, fourth, and fifth grades. A purposive sampling technique with 22 third-grade students, 28 fourth-grade students, and 21 fifth-grade students was used. The data were collected using documentation, testing, and interview methods. The findings of the study showed that fourth-grade students’ problem-solving skills are better than those of third-grade students, and the problem-solving skills of fifth-grade students are better than those of fourth-grade students. The percentage of Polya's steps always decreases because not all students master problem-solving. Based on the types of questions, the percentage of the one-step word problem is better than that of the two-step while the percentage of the two-step word problems is higher than that of the multistep.

This study aims to measure the effectiveness of “multiplex teaching method” in mastering vocabulary for deaf students. Multiplex teaching method consists of picture language, sign language, printed-word language, written language, and spoken language. The research was designed as a single subject research (SSR) with baseline, intervention, and maintenance phase (A-B-A’ design). The research subjects consisted of two deaf students in special school of SLB Bhakti Luhur Malang, Indonesia. In addition, a special education teacher and an observer were involved in this study. The intervention instrument comprised five lesson plans (LP), each containing a vocabulary of four words. The data were analyzed using intra-condition and inter-condition graphical inspection with a focus on data stability, trends, and score changes. The effectiveness was determined by the Percentage of Non-Overlapping data (PND). The change of score from A'/A achieved by Subject-1 was 7.86 points, while Subject-2 obtained 7.68 points. Subject-1 obtained an average PND B/A of 100% and average PND A'/B of 82.5%. Subject-2 achieved an average PND B/A of 99% and PND A’/B of 90%. Thus, multiplex teaching method is very effective in helping deaf students master vocabulary.

The quality of the educational process within the humanistic concept and holistic-developmental approach is interpreted as the optimal adaptation to the individual needs and abilities of children, while inclusiveness presupposes equal inclusion and participation of all children. This article explores the opinions of teachers as bearers of pedagogical-educational process. The aim of this research was to determine how much importance teachers attach to certain dimensions of the educational process, and the procedures of inclusive practice. Empirical research included teachers in 5 preschool institutions (N=146). The research instrument was constructed based on relevant literature. Teachers in this sample recognize the importance: of individualized support to all children; of respecting the diversity; of collaboration with parents, and personal professional development. At the same time, the level of formal education and in-service teacher training is positively correlated with the assessment of importance towards child-oriented practice, and respect for diversity. Teachers with a higher level of education significantly value the importance of additional vocational training in the field of developmental and social risks, the use of community resources, and involvement of parents in planning individual support for children.

Academic optimism has an essential role in the adjustment of students in school. This study aimed to examine a model of academic optimism formed from democratic parenting, school climate, internal locus of control, and students’ self-concept. This a cross-sectional non-experimental design research design involved 335 Junior High School students in Kediri. The data collection tool was a scale while the data analysis technique was Structural Equation Modeling (SEM) analysis. The results showed that the theoretical model for developing academic optimism in Junior High School students was in line with the research data and obtained empirical support (X2 = 246.056 < 255.6018; p = 0.110 > 0.05), so this model is feasible and can be used in samples that have been studied. In general, this study adds knowledge about positive psychology studies and supports democratic parenting, school climate, self-concept, and internal locus of control as ultimate factors for creating students’ academic optimism.

The research aims to develop an instructional tool based on Discovery Learning (DL) combined with a Metacognitive Knowledge Strategy (MKS) to enhance students’ Critical Thinking Skills (CTSs). In doing so, the study employed a Research and Development (R&D) method to develop such a tool. The developed instructional tool was tested for its validity by experts and practitioners’ evaluation. Further, the empirical data were collected from the results of implementation in learning and the student's responses, while the data of tools effectiveness were acquired from the critical thinking tests given to students (analyzed by related t-test). The developed instructional tools were implemented in a limited-scale trial of 32 students and a large-scale trial of 59 students. The results show that: firstly, the DL and MKS-integrated instructional tools are stated as valid in terms of the lesson plan, student worksheet, and critical thinking test. Secondly, the practicality criteria have been successfully met; the learning implementation, students’ activity, and students' responses were regarded as in accordance with the feasibility standard. Thirdly, the instructional tool was deemed effective in enhancing students’ CTSs (p = 0.05).

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.