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.

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

This review explores research into the effects of collaborative learning interventions on critical thinking, creative thinking, and metacognitive skill ability on biological learning. The search was conducted from 2000 to 2021. We found 36 critical thinking studies, 18 creative thinking studies, and 14 metacognitive skill studies that met the criteria. The results showed that collaborative learning influences large categories (ES=4.23) on critical thinking, influences large categories (ES= 7.84) on creative thinking, and influences large categories (ES= 8.70) on metacognitive skill. The study's findings show that collaborative learning interventions have the highest impact on metacognitive abilities. Based on these findings, we provide insights for education research and practitioners on collaborative learning interventions that seem to benefit the empowerment of high levels of thinking at various levels of education to be combined with various other interventions in the future. The type of intervention, level of education, materials used, and study quality criteria were included in the study.

High school teachers are mentors and facilitators that must be concerned about their students' formal thinking abilities. Students may not take a conservation task seriously because they perform operations without consulting. This necessitates modifying the learning process to increase student motivation. Therefore, this study aimed to examine students' mathematical spatial literacy through project-based blended learning with the cognitive conflict strategy. The study sample comprised 129 students, including 66 and 63 in the experimental and control classes, respectively, divided into the low, medium, and high levels. The findings showed that the experimental class students using project-based blended learning with the cognitive conflict strategy had higher mathematical spatial literacy than those in the control class using problem-based learning. Project-based blended learning with the cognitive conflict strategy and problem-based learning students at the high and moderate levels differed in their ability to increase their mathematical spatial literacy. However, low-level students are comparable in their ability to increase their mathematical spatial literacy.

Development research demands a improvement in the implementation of learning by developing products based on learning needs. The products of this development are teacher book and student book based on the realistic mathematic education (RME) approach for package A in statistics material. Validity testing in this study includes instrument validation, self-evaluation, expert validation, one-to-one evaluation. Aiken's V and Intraclass Correlation Coefficient (ICC) are used to determine the validity and reliability of the product. The result of research shows that the instruments and prototype are valid and feasible. Then, the ICC obtained moderate stability, it also categorize reliable. In terms of context and hypothetical learning trajectory (HLT) developed, the products should be revised to achieve meaningful learning.

Metacognitive, critical thinking and opinion expression are in high demand. This study aimed to investigate the effects of the blended project- based literacy that integrates school literacy movement strengthening character education (literasi berbasis proyek terintegrasi GLS dan PPK: Li-Pro-GP) learning model on students' metacognitive skills, critical thinking, and opinion expression. A post-test experimental design was used to answer the research question. The study was conducted from August to October 2021 at Government Junior High School 23 Malang. Seventh-grade students were selected as research participants. The participants included 30 students from class VII-2. The research instrument was five essay questions to measure critical thinking skills. Material and assessment experts validated the essay questions developed by the researcher. The items that were declared valid were tested for validity. The result showed five valid items with high reliability of .670. Metacognitive skills were measured using the Metacognition Awareness Instrument (MAI), which consists of 40 items. The questions declared valid were tested for validity with a very high reliability of .953 for 37 items, and only three items were invalid. The ability to express an opinion was measured with an observation questionnaire validated by experts with a valid instrument score. Data analysis was performed by path analysis using the SmartPLS software. The results showed that the Li-Pro-GP blended learning model significantly strengthened students' metacognitive skills, critical thinking, and opinion formation.

The aim of this work is to characterise the understanding that students in compulsory secondary education (14-16 years old) have of number sequences in graphical representations. The learning of numerical sequences is one of the first mathematical concepts to be developed in an infinite context. This study adopts the focus of semiotic representations as its theoretical framework. The participants consisted of 105 students and a qualitative methodology was used. The data collection instruments were a questionnaire and a semi-structured interview. The results allowed for three student profiles regarding number sequences in graphical representations to be identified. These profiles may facilitate a possible progression in the learning of number sequences for students in compulsory secondary education to be considered. Therefore, the results presented in this study can provide information about the learning hypotheses of mathematical tasks related to numerical sequences and can help in the design of such tasks.

Digital puzzle worksheet (DPW) is innovative teaching material designed using open-source software such as Canva and Liveworksheets. Subsequently, puzzle games in the form of questions can improve problem-solving skills by engaging in metacognitive processes. This research used a case study method to describe the impact of applying the DPW to identify the metacognition levels of students through the assignment of contextual maths problems. The source of informants was third-grade elementary school students in West Java, Indonesia. Test instruments, observation sheets, and interviews were used, while data analysis adopted an iterative model. Furthermore, the method and time triangulation increased confidence in the resulting conclusions. The results showed that male students were at the metacognitive level of ‘strategic use’ and ‘aware use’ for females, based on the characteristics of the observed metacognitive level. The most prominent feature was identifying and determining problem-solving strategies with metacognitive awareness. The reaction of students to the DPW improved problem-solving abilities, expanded conceptual understanding, and enhanced digital technology competence. Therefore, this experience was applied when solving contextual mathematical problem assignments.

Many students have misconceptions about mathematics, so preservice teachers should be developing the skills to notice mathematical misconceptions. This qualitative study analyzed preservice teachers' skills in noticing student misconceptions about algebra, according to three aspects of noticing found in the literature: attending, interpreting and responding. Participants in this study were seven preservice teachers from one university in the capital of Aceh province, Indonesia, who were in their eighth semester and had participated in teaching practicums. Data was collected through questionnaires and interviews, which were analyzed descriptively. The results revealed the preservice teachers had varying levels of skill for the three aspects of noticing. Overall, the seven preservice teachers' noticing skills were fair, but many needed further development of their skills in interpreting and responding in particular. This university’s mathematics teacher education program should design appropriate assessment for preservice teachers’ noticing skills, as well as design and implement learning activities targeted at the varying needs of individual preservice teachers regarding noticing student misconceptions, in order to improve their overall teaching skills.

Logical-mathematical intelligence is highly needed to ease students’ understanding of mathematics concepts. Therefore, it is necessary to delivery an innovative teaching approach to enhance students’ logical-mathematical intelligence. This study aims to investigate the use of mathematics comics to increase the logical-mathematical intelligence of junior high school students in urban and rural schools. This study employed a quantitative approach with a pretest-posttest control group design. The population of this study were seventh-grade students from a junior high school in Banda Aceh (urban areas) and a junior high school in Aceh Besar (rural areas), Indonesia. The samples of this study were two classes (experimental and control) from each school which were selected randomly. To collect data, we used a logical-mathematical intelligence test and analyzed it by using t-test. This study shows that the use of mathematical comics in urban schools can improve mathematical logical intelligence. However, there was no improvement in students' mathematical logical intelligence in rural schools. Therefore, this study showed that using mathematics comics in different school conditions yield different results in logical-mathematical intelligence. The findings suggest that other learning innovations are required to improve students' logical-mathematical intelligence in rural areas.

This study aimed to compare and examine the effectiveness of interactive STEM learning and paper-and-pencil STEM learning in terms of mathematical literacy skills of elementary school students. This research is of a quasi-experimental type with a non-equivalent pretest-posttest control group design. Sampling was carried out on the elementary school populations in Bengkulu and South Sumatra Provinces in two stages. In the first stage, schools in rural and urban areas were selected, and in the second, classes in each school were randomly selected. The selected sample consisted of fifth-grade students of the Public Elementary School of Terawas, Musi Rawas, with an experimental class A (n = 20) and an experimental class B (n = 19), as well as fifth-grade students of the Public Elementary School of Bengkulu City, with an experimental class A (n = 25) and an experimental class B (n = 22). Data collection was conducted using mathematical literacy skills tests in reference to the PISA and Minimum Competency Assessment (level 1–3). Data analysis was performed using descriptive and inferential statistics; it employed an independent t-test for the comparative testing and an N-gain test for testing the effectiveness of STEM learning. The results showed that there were differences in math literacy skills between interactive STEM and paper-and-pencil STEM for students in urban schools, but not significantly different for students in rural schools. General STEM learning was effective in increasing the literacy of elementary school students, and interactive STEM in particular demonstrated the highest level of effectiveness in the urban school.

Teachers' learning styles are a crucial part of the learning process as they determine how teachers' brains capture and integrate information linked with the senses. Kurnia, identified as an auditory teacher, was expected to capture written information in a provided numeracy problem. Nevertheless, she prefers to capture visual information, like tables or figures, and utilize them to develop thought-provoking questions. Thus, this study intends to investigate her reasons and the factors affecting Kurnia's decision to utilize visual information as a reference in developing questions. This research adopts a qualitative design covering a case study. Kurnia was selected from 32 teachers from 28 schools; roughly 43% were from public schools, and 57% from private schools. Kurnia placed more emphasis on pictorial information before proposing questions, which was caused by situational factors: the subject matter, the grade level, the student's engagement in the class, the teacher's experience, the teaching experience, and the diversity of students' learning styles. This article recommends that teachers recognize their learning styles to know their strengths and weaknesses in teaching mathematics, and that they convey understandable information utilizing effective instructional methods that represent each learning style of students in the classroom.

Momentum-impulse requires critical thinking skills, and teaching should be encouraging for students. Critical thinking skills can be fostered through inquiry-based learning. During the COVID-19 pandemic, familiar learning media were used for students. Therefore, it is necessary to develop creative learning media. This developmental research aimed to create a momentum-impulse e-book based on inquiry supported by infographics (MIB -In-graph) to enhance students' critical thinking skills. The developmental model was a 4D model with field testing, i.e., a pretest-posttest control group design with three classes. Descriptive analysis showed that MIB-In-graph, an Android application, received a good average rating in content, worksheets, and forms. Students’ responses were very positive. Mixed design ANOVA showed that the mean score of students’ critical thinking skills increased significantly from the pretest to the posttest in each class and students’ critical thinking skills in the experimental class was more salient than control class 1 and control class 2. The highest difference in mean scores was in the experimental class. The differences were influenced by various factors such as learning approaches, media use, pictures, and collaboration.

This study aims to analyze the effects of working memory capacity and learning styles of prospective mathematics teachers on their ability to solve higher-order thinking problems. In the present study, learning style was considered students' tendency to learn visually or verbally. In addition, the types of higher-order thinking skills (HOTS) problems are complex and non-complex. Multiple regression tests were used to analyze the effects of learning style and working memory capacity. An ANOVA test was also conducted to analyze the ability of each group to solve each HOTS problem. In addition, one hundred twenty-six prospective mathematics teachers voluntarily participated in this study. The study found that learning styles only affected visual problems while working memory capacity (WMC) only affected the ability to solve complex problem-solving skills. Furthermore, WMC affected the ability to solve complex HOTS problems, not non-complex ones. The ability of visual students to solve HOTS problems will greatly increase when the problems are presented in visual form. On the other hand, the obstacle for visual students in solving verbal problems was to present the problem appropriately in visual form. The obstacle for students with low WMC in solving complex HOTS problems was to find a solution that met all the requirements set in the problem.

Understanding graphs in the dynamics of market (DM) is a challenge to learners; its teaching demands a specific kind of teacher’s knowledge. This study aims to examine the topic-specific pedagogical content knowledge (TSPCK) of experienced economics teachers in teaching graphs in DM to enhance learners’ understanding of the topic. It reports using a qualitative approach underpinned by the TSPCK framework for teaching specific topics developed by Mavhunga. Data were collected through classroom observations and analyzed thematically using a case study of two economics teachers. The study revealed that adopting a step-by-step approach and the use of worked graphical examples promote an understanding of graphs in DM. It also established that active learning is preferable to the predominant chalk-and-talk (lecture) method of teaching graphs in DM. The study proposed a Dynamics of Market Graphical Framework (DMG-Framework) to enable teachers, particularly pre-service teachers in lesson delivery, to enhance learners’ understanding of graphs in DM. The result of this study will broaden the international view in the teaching of graphs in DM.