The purpose of this study was to investigate how mental rotation strategies affect the identification of chemical structural formulas. This study conducted event-related potentials (ERPs) experiments. In addition to the data collected in the ERPs, a Chemical Structure Conceptual Questionnaire and interviews were also administered for data collection. Eighteen university students majoring in chemistry were recruited. In the ERP experiments, the participants were required to identify 2D figures, 2D chemical structural formulas, 3D objects and 3D chemical structural formulas. The contours of 2D figures are similar to those of 2D chemical structural formulas, but they contain no content knowledge. Likewise, the contours of 3D objects are similar to 3D chemical structural formulas without content knowledge. The results showed that all students used similar strategies of mental rotation in identifying 2D figures, 3D objects and 3D chemical structural formulas. However, the high-achieving students used different strategies in identifying 2D figures and chemical structural formulas, while the low-achieving students tended to use similar strategies of mental rotation in identifying both 2D figures and chemical structural formulas. The results indicate that some of the difficulties in identifying 2D chemical structural formulas that students encounter are due to their inappropriate strategies of mental rotation.

This study attempts to reveal pre-service teachers’ conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews were conducted with them. The factors influential on pre-service teachers’ definitions of parallelograms and conceptions regarding internal relationships between quadrilaterals were analyzed. The strongest result involved definitions based on prototype figures and partially seeing internal relationships between quadrilaterals via these definitions. As a different result from what is reported in the literature, it was found that the fact that rectangle remains as a special case of parallelogram in pre-service teachers’ figural concepts leads them not to adopt the hierarchical relationship. The findings suggested that learners were likely to recognize quadrilaterals by a special case of them and prototypical figures, even though they knew the formal definition in general. This led learners to have difficulty in understanding the inclusion relations of quadrilaterals.

Learning models that can improve critical thinking, skills collaborate, communicate, and creative thinking are needed in the 21st-century education era. Critical and creative thinking are the two essential competencies of the four skills required in the 21st century. However, both are still difficult to achieve well by students due to a lack of thinking skills during mathematics learning. This study was conducted to determine the model of learning that is appropriate to develop students' critical and creative thinking skills. The study used three-class samples from eighth grade. The first class is given the problem-posing lesson; the second class is given contextual learning and third class as a control class. The results of the study indicate that improving students' critical and creative thinking skills are included in the moderate category for types using contextual learning and problem-posing. Also, it is found that contextual learning is more effective for improving critical thinking skills when compared with learning problem posing and expository learning. Meanwhile, learning problem posing is more useful to enhance creative thinking skills compared with contextual and expository learning.

This research aims to test (1) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on written mathematical communication skills, (2) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills, (3) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on the written mathematical communication skills from each cognitive style, and (4) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills from each learning model. This quantitative research employed a quasi-experimental method. The research sample consisted of 240 fifth-grade elementary school students in Jebres District, Surakarta, Indonesia. Data collection techniques included tests of written mathematical communication skills and cognitive styles. The data were analyzed using prerequisite (normality, homogeneity, and balance), hypothesis, and multiple-comparison tests. The findings prove that (1) PP model with Indonesian realistic mathematical education approach is more effective than the PP and direct instruction models, (2) field-independent cognitive style is better than field dependent, (3) PP with Indonesian realistic mathematical education is as effective as the PP model, but more effective than the direct instruction model, and the PP model is more effective than the direct instruction model in each cognitive style, and (4) in the PP learning model with Indonesian realistic mathematical education approach, field-independent cognitive style is same skill as with field-dependent, but field-independent is better than field-dependent cognitive style in the PP and direct instruction learning models.

The purposes of the current study were to develop students' spatial orientation skills using Virtual Mathematics Kits (VMK) and to evaluate VMK as a form of digital media in terms of spatial orientation. This study involved 42 lower-class and 47 higher-class elementary school students as the intervention group and 36 lower-class and 41 higher-class students as the control group. The intervention group was administered spatial orientation activities for 10 weeks. These activities were performed using a VMK to facilitate solving spatial problems. In the end of activities, spatial orientation instruments administered to compare spatial orientation ability on each group. The findings of this study, spatial orientation activities using a VMK improved students' spatial orientation skills. More specific, VMK provides more significant effect on higher-class students. Finally, VMK allows students to explore many ideas and perspectives to solve various spatial problems. VMK can be used as a digital media that helps students to develop spatial reasoning.

Environmental learning in the 21st century requires a high level of thinking ability, especially to solve environmental problems when COVID-19 pandemic. This was to develop a new level of thinking, namely Higher Order Thinking Skills of Environmental Problem (HOTSEP) which is a revision of Anderson's Taxonomy. The purpose of this study was to measure students HOTSEP in the context of environmental problems related to COVID-19. The research method used in this research was descriptive. The sample used 277 university students from several cities in Indonesia. The instrument used HOTSEP which has 3 categories of thinking level start from develop innovation about environment (C6), solve environmental problem (C5), criticize environmental problem (C4). The results showed that students HOTSEP were still in the very low category (33.64). This study concludes that the HOTSEP of students was still low and needs to be improved to the understanding of COVID-19 concept in environmental learning. Suggestion for further research was HOTSEP need to implement in school or university for several environmental learning topics in many subjects/courses start from Natural Science, Social Science, Engineering, and others relevant subject. HOTSEP can be measured not only in school or university, HOTSEP can be implement in community and public.

The purpose of this study was to find the determinants of effective diffusion of educational robotics in rural areas. The study analysed the key components, difficulties, and major lessons of the successful case of the remote northern region of Russia – Sakha Republic. The study used a mixed-method approach consisting of interviews, survey, literature analysis, and participants’ observation.  In the survey participated 57 robotics teachers and 113 elementary, middle, and high school students of the Sakha Republic. From survey participants were randomly chosen 30 robotics teachers and 18 middle and high school students for the interview. The literature analysis explored reports and articles on the educational robotics activities in the Sakha Republic for the period of 2011-2018. Based on the findings, the study developed a process model with five principles and ten components that influenced educational robotics diffusion in the Sakha Republic. One of the main determinants of the model was a support system of public-private partnerships and a local community of educators. Another was the need to consider the local area’s constraints, possibilities, and culture when implementing any technology in the rural region's education. In the researched case two major determinants would not be possible and sustainable without strong leadership. The findings showed that strong local leadership could use knowledge of the local area to provide more appropriate solutions and could build the active support of the local community and public-private partnerships that would accelerate the diffusion of technology in the rural region's education.

Cognitive is an essential developmental aspect for children. The cognitive barrier is one of the learning barriers experienced by children with autism. From educational perspective, teacher language input can appropriately develop cognitive abilities of autistic students. This study aims to describe (1) teacher’s language input for recognizing the cognitive abilities of autistic students in classroom interactions and (2) cognitive abilities of autistic students based on teacher language input in classroom interactions. The approach of the study was conducted qualitatively with case study, while source of data was oral texts from the teacher language input toward autistic students in classroom. The results shows that the cognitive abilities of autistic students can be recognized through teacher's language input in classroom learning by engaging interrogative speech acts, such as representative, directive, expressive, and commissive. The cognitive level is used to see the variants of the teacher's language input. Meanwhile, the acquisition of students' cognitive abilities based on teacher language’s input is developed through memorizing, understanding, applying, and analyzing skills with criteria student A and B in the medium category, and G in low category.

Industrial revolution 4.0 is currently present in various countries, including Indonesia. Indonesia responded quickly through technological developments, especially education. The actions of the Indonesian government to deal with industrial 4.0 are contained in the 4C principle, one of which is Critical Thinking. The Science, Technology, Engineering, and Mathematics (STEM) learning approach has become an alternative in building critical thinking skills, especially in science learning. The purpose of this study is to quantitatively measure the impact of the STEM-inquiry model based on the K-13 Indonesian Curriculum towards critical thinking skills of 15-16 years old students. This study employed quasi-experimental with non-equivalent control group design at SMAN 1 (State Senior High School) Padang Cermin, Lampung, Indonesia. The research subjects consisted of 50 students. The critical thinking skill was measured through 10 items of an essay question on the momentum and impulse material. Based on the results of the non-parametric statistical hypothesis test Mann Whitney, the significance level of 0.004 was obtained (sig <0.05). The results of the hypothetical test showed that the student's critical thinking skills before and after using the STEM-based inquiry model were different. It can be concluded that the application of the STEM-based inquiry model was effective in increasing students' critical thinking skills.

Transcript Based Lesson Analysis (TBLA) is a transcript-based learning analysis method developed at Nagoya University, Japan. This new method is believed to justify the success of instructional design planned by the teacher. So far, the success of learning design has been reflected in student learning outcomes, even though the learning outcome data are not sufficient to provide an overview of the actual classroom conditions. This study aims to analyse the communication patterns in learning Chemistry using the TBLA method. This research is a descriptive qualitative study that analysed the lesson of Chemical Bonds and Carbon Atoms Characteristics, which were conducted in two Senior High Schools in South Kalimantan, Indonesia. The data were collected using observation and documentation study. The lessons recorded using cameras and camcorders devices were transcribed and analysed using the Excel program based on the number of words spoken by teachers and students and the frequency of keywords in learning chemistry. The data were transformed into graphs. The results showed that analysis using TBLA provided integrated information about communication patterns and classroom quality. In these two classes, communication pattern occurs in Chemistry learning was teacher-student interaction only. The multi-ways transactions pattern has not occurred. The low quality of teacher questions and the incomplete deep learning phase in learning chemistry caused the expected multi-directional transaction communication has not been conducted. The result implies that TBLA is an effective tool to reflect on teacher practices and improve their teaching process for better instructional practices.

Creative thinking skills are 21st century learning needs that can be applied through the Scientific Reading Based Project (SRBP) model. The purpose of this study is to empower creative thinking skills through SRBP models in science learning in elementary school teachers’ education students. This research is mixed research with qualitative and quantitative approaches. Qualitative research is used to explore students' creative thinking abilities. Quantitative research uses a quasi-experimental approach carried out for six months on the candidates of elementary school teachers’ education. Participants in this study were the candidate of elementary school teachers’ education of 75 people who took the Basic Concept of Science subject. Data collection in this study was through observation, documentation, pre-test, and post-test with essay questions to measure creative thinking skills. The final result of the project is the final product to measure creativity. The data analysis used was an ANOVA test to measure every aspect of creative thinking skill. Qualitative analysis was used to describe the learning process and the final project of creativity. The results showed that there was an increase in creative thinking skills from aspects of flexibility, elaboration, fluency and originality. The SRBP model has a positive effect on improving the ability to think creatively.

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.

The aims of the recent study were; analyzing the effect of creative and online learning using Instagram on the ability to create new products in the technology and learning media course, and determining the level of users’ experience in processing visual media through the Canva application on android. Quantitative approach with this research was carried out through a quasi-experimental research model because it measured the post-test was applied to 58 students as the respondents in two experimental and control classes. This study used two instruments; the cognitive learning outcome questionnaire according to the subject to get the students’ ability to create new products, and the second instrument was taken from ueq-online.org in the Indonesian version to know the users' experience in processing visual media. The data were analyzed using one-way ANOVA, mean and standard deviation assisted by IBM SPSS Statistics 24.0. The results demonstrated that the effect of creative and online learning using Instagram on the ability to create new products in The Technology and Learning Media course was found significant at 0.028 <0.05 which meant it could be applied well. Meanwhile, the level of users' experience in processing the visual media application Canva on Android had the highest score on the Stimulation scale at 1.59, categorized "Very Good" and the lowest score was on the Novelty scale at 0.93, categorized "Above Average". With the strong creative encouragement to create new products, the students were able to process their own visual media which were tailored to the agreed digital visual designs and were published on Instagram.

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.

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.

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.

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.

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.

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.