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.

Assessment is a topic that continues to be developed in science education research. Assessment evaluates not only students' cognitive abilities but also their thinking skills. Therefore, in this study, an assessment that could measure students' chemical literacy was developed. Chemical literacy is a thinking skill that students must develop as part of their chemistry learning. The goal of this study was to assess item' quality, as well as student’ chemical literacy on the concept of chemical rate. The Rasch model was employed to analyze the data in this study. The results of this study depict that the developed assessment had sufficient reliability and validity to be used to assess students' chemical literacy. Furthermore, the analysis of the students’ responses to the items revealed that many students did not understand or were unaware of the context presented. These findings suggest that students' chemical literacy in the material for the reaction rate is still lacking and needs to be improved. As a result, the teacher's role in assisting students in improving their chemical literacy through chemistry learning is critical.

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.

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.

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.

In contemporary school systems, the concept of a teacher is defined as a socially and emotionally intelligent, pedagogically, and psychologically competent school leader. This would mean that not only the teacher's subject knowledge is sufficient, but also good knowledge of general pedagogical-psychological skills, knowledge, and management of the didactic approach, etc. Social and emotional skills/intelligence (SEI) restore the value of teachers as creators of learning and connect education to the larger social world in which SEI plays the most important role. This paper highlights the importance of social and Emotional Intelligence (SEI) in teacher education, examining the current state of research and the most important role of SEI in students' personal, social, and academic achievement, as well as teacher effectiveness and personal growth. By presenting the scientific evidence of SEI in teaching and teacher education, this study assesses the SEI level of student teachers at the University of Primorska, Faculty of Education, Slovenia. SEI is examined, through its main components: Self-awareness, Self-management, Social Awareness and Social Skills. In conclusion, this paper aims to show the need to develop SEI in future teacher education in Slovenia.

This study investigated the effectiveness of visual mind mapping as a reading strategy for improving English language learners' critical thinking skills. Students from two general English courses were randomly assigned to experimental and control groups. California Critical Thinking Test was used to assess participants' critical thinking skills. The findings revealed a statistically significant difference at (p < .005) in the mean scores of the experiment and control groups in the post-test due to visual mind mapping strategy in favor of the experimental group with a positive and significant impact on participants' critical thinking skills. The findings also showed that the experimental group’s scores were significantly improved in all indicators of critical thinking. The study results showed that visual mind mapping strategy affected the increased of critical thinking skills and reading comprehension ability. The study's findings revealed that using a visual mind mapping strategy had a significant improvement impact on English language learners critical thinking skills and reading ability.

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.

This paper investigates the quantitative literacy and reasoning (QLR) of freshmen students pursuing a Science, Technology, Engineering, and Mathematics (STEM)–related degree but do not necessarily have a Senior High School (SHS) STEM background. QLR is described as a multi-faceted skill focused on the application of Mathematics and Statistics rather than just a mere mastery of the content domains of these fields. This article compares the QLR performance between STEM and non-STEM SHS graduates. Further, this quantitative-correlational study involves 255 freshman students, of which 115 have non-STEM academic background from the SHS. Results reveal that students with a SHS STEM background had significantly higher QLR performance. Nevertheless, this difference does not cloud the fact that their overall QLR performance marks the lowest when compared to results of similar studies. This paper also shows whether achievement in SHS courses such as General Mathematics, and Statistics and Probability are significant predictors of QLR. Multivariate regression analysis discloses that achievement in the latter significantly relates to QLR. However, the low coefficient of determination (10.30%) suggests that achievement in these courses alone does not account to the students’ QLR. As supported by a deeper investigation of the students’ answers, it is concluded that QLR indeed involves complex processes and is more than just being proficient in Mathematics and Statistics.

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.

For biology students, the diversity, complexity, and abundance of content in this field yield a heavy study load. Hence, appropriate learning strategies are key in supporting learners’ academic success. In biology, the factors gender and interest hold a unique position within the natural sciences, as there is an academic imbalance to the disadvantage of male students. In the present study, we examined the influence of gender and interest as well as its interdependences on the students’ use of learning strategies for biology learning. A total of 180 seventh through tenth grade students (Mage=14.47; SD=1.35; 60% female) from four general-track secondary schools located in Germany participated in this study. Data on the students’ level of interest and the use of learning strategies in biology lessons were collected. We used multivariate analysis of covariance with the students’ age as the covariate to analyse our data. Results revealed a significant effect of gender on the students’ use of the learning strategies rehearsal, organisation, effort, and time management. With regard to elaboration and effort, the effects of interest were found to be significant. The gender gap regarding learning strategy use was narrower for students with high levels of interest. These findings might have implications for beneficial teacher behaviour in biology.

This research aimed to develop a historical thinking assessment for students' skills in analyzing the causality of historical events. The development process of Gall and colleagues and Rasch analysis models were used to develop an assessment instrument consisting of two processes, including the analysis of the framework of cause and consequence, the validity, reliability, and difficultness test. This research involved 150 senior high school students, with data collected using the validation sheet, tests, and scoring rubric. The results were in the form of an essay test consisting of six indicators of analyzing cause and consequence. The instruments were valid, reliable, and suitable for assessing students’ skills in analyzing the causality of historical events. The developed instruments were paired with a historical thinking skills assessment to improve the accuracy of the information about students' level of historical thinking skills in the learning history.

This study aims to explore the pattern of external representation of suspending objects in a static fluid. The study used a qualitative descriptive method involving 57 elementary, junior, senior school, and university students. Data collection implemented a 30-item test covering the dominant context of suspending and partially floating and sinking.  Some of phenomenographic steps were adapted in data analysis. Based on the data analysis, it can be concluded that there is a dominant external representation pattern, where there is a simplification of the depiction of suspending objects. Suspending position tends to be locked in a limited area, namely in the middle of the depth of the liquid. In the context of suspending objects' cuts, the cuts were generally represented by an upward shifting pattern. Factors that influence the pattern of representation are the involvement of intuition in conceptualizing the phenomena presented, and the conceptual aspect of density has not been integrated into the reasoning process for compiling external representations, both diagrams, and texts. Research limitation is presented in this article.

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.

Numerical thinking is needed to recognize, interpret, determine patterns, and solve problems that contain the context of life. Self-efficacy is one aspect that supports the numerical thinking process. This study aims to obtain a numerical thinking profile of Mathematics pre-service teachers based on self-efficacy. This study used descriptive qualitative method. The data obtained were based on the results of questionnaires, tests, and interviews. The results of the self-efficacy questionnaire were analyzed and categorized (high, moderate, and low). Two informants took each category. The results showed the following: informants in the high self-efficacy category tend to be able to interpret information, communicate information, and solve problems with systematic steps. Informants in the moderate self-efficacy category tend to be able to interpret and communicate information, but tend to be hesitant in choosing the sequence of problem-solving steps. Meanwhile, informants in the low self-efficacy category tend not to be able to fully interpret the information. As a result, the process of communicating information and solving problems goes wrong. Another aspect found in this study is the need for experience optimization, a good understanding of mathematical content, and reasoning in the numerical thinking process.

Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students’ common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students’ understanding of the wrong concepts to the correct ones. A research design was used to achieve this goal. It identified and solved the errors in the definition of angle and triangle among first-year students in the Department of Mathematics Education at an excellent private college in Mataram, Indonesia. The steps were as follows: A test instrument with open-ended questions and in-depth interviews were used to identify the errors, causes, and reasons for the students’ misconceptions. Then, the MDWI approach was used to identify a way to correct these errors. It was found that students generally failed in interpreting the concept images, reasoning, and knowledge connection needed to define angles and triangles. The MDWI approach eliminated the misconceptions in generalization, errors in concept images, and incompetence in linking geometry features.

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.

Visual representations and the process of visualisation have an important role in geometry learning. The optimal use of visual representations in complex multimedia environments has been an important research topic since the end of the last century. For the purpose of the study presented in this paper, we designed a model of learning geometry with the use of digital learning resources like dynamic geometry programmes and applets, which foster visualisation. Students explore geometric concepts through the manipulation of interactive virtual representations. This study aims to explore whether learning of geometry with digital resources is reflected in higher student achievements in solving geometric problems. This study also aims to explore the role of graphical representations (GRs) in solving geometric problems. The results of the survey show a positive impact of the model of teaching on student achievement. In the post-test, students in the experimental group (EG) performed significantly better than students in the control group (CG) in the overall number of points, in solving tasks without GR, in calculating the area and the perimeter of triangles and quadrilaterals than the CG students, in all cases with small size effect. The authors therefore argue for the use of digital technologies and resources in geometry learning, because interactive manipulatives support the transition between representations at the concrete, pictorial and symbolic (abstract) levels and are therefore important for understanding mathematical concepts, as well as for exploring relationships, making precise graphical representations (GRs), formulating and proving assumptions, and applying different problem-solving strategies.

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 research is a developmental research aiming at developing a good mathematical test instrument using polytomous responses based on classical and modern theories. This research design uses the Plomp model, which consists of five stages, (1) preliminary investigation, (2) design, (3) realization/construction, (4) revision, and (5) implementation (testing). The study was conducted in three vocational schools in Lampung Province, Indonesia. The study involved 413 students, consisting of 191 male and 222 female students. The data were collected through questionnaire and test. The questionnaire was used to identify the assessment instruments currently employed by teachers and to be validated by the experts of mathematics and educational evaluation. The test used an open polytomous response test numbering of 40 items. The data were analyzed using both classical and modern theories. The results show that (1) the open polytomous response test has a good category according to classical and modern theory. However, the discrimination power of test items in classical theory needs several revisions, (2) the assessment instrument using the polytomous response of open multiple choice can guarantee information on the actual competence of students. This is proven by the fact that there is a harmony between the analysis result obtained from classical and modern theory from the students' arguments when giving reasons for their choices. Therefore, the open polytomous response test can be used as an alternative to learning assessment.