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.

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.

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.

Science, technology, engineering and mathematics (STEM) education is regarded as one of the formulas to embracing many of our imminent challenges. STEM education benefits the learners by encouraging interest in STEM disciplines. This daunting task needs everyone’s concerted efforts in creating and innovating mathematics teachers’ classroom practices Therefore, a systematic review was conducted to identify best practices for STEM education following the guidelines of the Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) by Moher et al. (2015). The reviewed articles were published from 2016 to 2020 and accessed using the Scopus and Web of Science (WoS) databases. Three themes for best practices were identified namely (a) core competencies encompassing 21st-century teaching skills; (b) instructional designs; and (c) requisite STEM execution. Results of PRISMA determined the dominant STEM practices were critical thinking, communication, collaboration, problem-solving, research-based pedagogy, problem-based learning and project-based learning, technological integration, accessibility, professional development and learning support, evidence of effectiveness, access to materials and practitioner support, and scalability. Mathematics teachers should determine the best STEM practices to employ even though there is a lack of studies on integrated STEM domains. When more students are interested in venturing and exploring into the field of STEM, the high demand for STEM related careers could be met by the younger generation.

The present study aimed to investigate the relationship between students’ academic motivation, implicit beliefs about intelligence and learning strategies among undergraduate healthcare students. First-year students of healthcare degree courses from a university in Southern Italy were surveyed. The study measured psychological constructs by means of Academic Motivation Scale, Motivated Strategies for Learning Questionnaire, and Dweck’s implicit questions about beliefs of intelligence. Two regression models were computed to assess the association between students’ beliefs about intelligence, motivations for studying, and learning strategies. In the first regression model, predicting students’ use of cognitive strategies from implicit intelligence beliefs and motivations for studying, stronger autonomous motivations were significant predictors of cognitive strategies. The second regression model, predicting students’ use of metacognitive strategies from implicit intelligence beliefs and motivations for studying, was not significant. These findings can be useful to plan tailored educational interventions to promote students’ motivation, incremental beliefs about intelligence and their use of learning strategies positively related with academic performance.

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.

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.

Understanding phylogenetic trees representing evolutionary relationships of living organisms is essential in school biology. Traditional instructions based on lectures and textbooks with pictorial presentations have been proven ineffective to promote students’ understanding of the concept. This study, therefore, developed a game-based learning activity called the VERT card game to enhance students’ learning of the phylogenetic taxonomy of chordates. The VERT card game was designed to lay the foundation for different characteristics of chordate classes, as well as to allow students to construct and interpret their evolutionary relationships based on the phylogenetic tree. The effectiveness of the VERT card game was verified by a pre-test and post-test design with 109 middle school students in Thailand. The statistical result revealed that students’ mean scores increased significantly in the post-test, compared to the pre-test, indicating their improved understanding. In addition, after participating in the learning activity, the student participants were found to increase their self-efficacy to learn evolutionary biology statistically. Also, it showed positive views towards the usefulness of the developed card game as a large number of them expressed that they would like to use it for their lesson reviews and wished to have this form of learning activity in other topics in biology.

Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students’ commognition of routine aspects in understanding derivative tasks for heterogeneous groups of cognitive styles-field dependent and independent. This qualitative study involved six third-semester mathematics education students in the city of Palu, Indonesia. We divided the subjects into two groups with field-independent (FI) and field-dependent (FD) cognitive styles. The first group consisted of two FI students and one FD student, and the second group consisted of two FD students and one FI student. Moreover, the subjects also have relatively the same mathematical ability and feminine gender. Data was collected through task-based observations, focused group discussions, and interviews. We conducted data analysis in 3 stages, namely data condensation, data display, and conclusion drawing-verification. The results showed that the subjects were more likely to use routine ritual discourse, namely flexibility on the exemplifying category, by whom the routine is performed on classifying and summarizing categories, applicability on inferring category, and closing conditional on explaining category. The result of ritual routine is a process-oriented routine through individualizing. This result implies that solving the questions is not only oriented towards the correct answers or only being able to answer, but also students need to explain it well.

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.

This study aims to develop a mathematics learning application, namely Android-based mobile learning to increase students' High Order Thinking Skills (HOTs). The result of mathematics learning media is a valid and practical mobile learning application product. "Mastering Math" is the name of a mathematics e-learning application designed as a mobile or smartphone application, with specifications for the OS Android. The procedure for the development of virtual mathematical media used the development of the 4D model of Thiagarajan: (1) define; (2) design; (3) develop, and (4) disseminate. The trials conducted included five expert judgments and a small group. The research instruments used were a validation sheet, a practical assessment sheet by the teacher, a practical assessment sheet by students, and a media effectiveness test instrument. Data analysis was performed using Cochran's Q test for similarity of expert validation and qualitative analysis. The teaching materials used are junior high school teaching materials with validity and practicality in the good category to increase students' HOTs. This research implies that the learning of mathematics is more effective and efficient, students' divergent thinking develops, and their learning motivation for mathematics increases.

This study aimed to describe the creative thinking process of students with active learning styles in proposing and solving problems on geometry material. The research instruments were Honey and Mumford's Learning Style Questionnaire (LSQ), problem-solving and submission test sheets, and interview guidelines. The LSQ questionnaire was distributed to students majoring in mathematics education at a university in Malang, Indonesia, with a total of 200 students. Students who have an active learning style and meet the specified criteria will be selected as research subjects. Based on research on creative thinking processes in proposing and solving problems in students with active learning styles, it was found that there were differences in behaviour between subject 1 and subject 2 at each stage of creative thinking. However, based on the researcher's observations of the behaviour of the two subjects at each stage of their thinking, there are similarities in behaviour, namely, they tend to be in a hurry to do something, prefer trial and error, and get ideas based on daily experience.

This study was conducted to corroborate in understanding the teachers’ beliefs about assessment practices. The prior studies related to teachers’ assessment beliefs in mathematics have been done to assess teachers’ beliefs in the general context of mathematics teaching. This study developed an instrument to assess teachers’ assessment beliefs of mathematical thinking. The research aimed to develop and validate a scale of assessment beliefs of mathematical thinking by using the confirmatory factor analysis. The first draft of the scale contained 25 items. The sample of the study consisted of 537 mathematics teachers from public schools in Oman. The instrument was a questionnaire with a 5-point Likert scale. The scale was validated by asking a number of experts in mathematics educational measurement and evaluation. Exploratory and confirmatory factor analysis was applied to test the model of assessment beliefs of mathematical thinking scale using AMOS 25.0. All constructs had acceptable reliability. The model had a good model fit for the assessment beliefs of mathematical thinking scale which obtainable from the fit indices tests. The findings revealed that all fit criteria indices were realized. The results also showed acceptable validity and construct reliability for the scale.

Literacy ability is an individual's ability to reason, formulate, solve, and interpret mathematically to solve problems related to daily life. Executive function is a cognitive aspect that has a relation with mathematical literacy. One of some aspects that affects the low mathematical literacy ability is the aspect of executive function. This study aims to investigate the characteristics of mathematical literacy based on the executive function aspects of 15 years old students. A qualitative method with a descriptive approach is employed in this study. The present research applies interview guidelines, questionnaires, and students' mathematical literacy tests as the instruments. Research subjects are junior high school students in grade VIII from two different schools. The result shows that the students' executive function influences mathematical literacy ability. Students' mathematical literacy ability is not fully achieved by fulfilling all the indicators involved. Another aspect found in the research is the low critical thinking ability impacts the achievement of mathematical literacy ability indicators.

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 study objectives were (1) developing a valid and reliable Affective Self-assessment Instrument of Chemistry for High School Student and (2) discovering the chemistry affective domain ability trend of high school students based on gender. The current development study utilized 10 non-test instrument development procedures from Mardapi. The study population was all high school students in Yogyakarta Special Region. The sample size was 405 students categorized into two stages and sampling techniques, i.e., the trial stage using cluster random sampling and the measurement stage using simple random sampling. The data analysis techniques were validity test using the Aiken index and construct validity and reliability using the second-order Confirmatory Factor Analysis model. The study findings were (1) the Affective Self-assessment Instrument of Chemistry for High School Student had 15 valid and reliable items and 15 available items to be utilized by teachers to measure students’ affective in the learning process and (2) the chemistry affective domain ability trend of male high school students was dominated by the “good” category and “very good” category for female students.

The study aims to find out the influence of Mistake-Handling Activities to determine mathematical definitions knowledge, which can be regarded as a component of mathematics content knowledge, of teachers on the development of teachers in providing mathematical definitions. Within this framework, Mistake-Handling Activities were carried out with five volunteer mathematics teachers. Written opinions and semi-structured face-to-face interviews were used as data collection tools. During the application, focus group interviews were carried out, and the application was enhanced with discussions. The data were analyzed using the document review method, and codes, categories, and themes were also determined. The results revealed that Mistake-Handling Activities yielded certain emotional advantages such as increasing teachers’ interest and curiosity, critical thinking, self-confidence, awareness, and offering different viewpoints as well as yielding cognitive advantages such as recognizing their shortcomings, acknowledging the importance of knowing the definition of a concept, and using the definition.

Cognitive processes are procedures for using existing knowledge to combine it with new knowledge and make decisions based on that knowledge. This study aims to identify the cognitive structure of students during information processing based on the level of algebraic reasoning ability. This type of research is qualitative with exploratory methods. The data collection technique used began by providing a valid and reliable test instrument for algebraic reasoning abilities for six mathematics education student programs at the Islamic University of Sultan Agung Indonesia. Subjects were selected based on the level of upper, middle, and lower algebraic reasoning abilities. The results showed that (1) students with the highest level of algebraic reasoning ability meet the logical structure of Logical Reasoning which shows that students at the upper level can find patterns and can generalize; (2) Students at the intermediate level understand the cognitive structure of Symbolic Representations, where students can make connections between knowledge and experience and look for patterns and relationships but have difficulty making rules and generalizations; (3) students at lower levels understand the cognitive structure of Comparative Thinking, where students are only able to make connections between prior knowledge and experience.