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The current research trend of metacognitive regulation has shifted from an individual to a social context. One such social context is collaborative problem-solving. Interaction between group members is an essential factor in completing collaborative problems. Metacognitive regulation is divided into four forms based on the interaction in collaborative problem-solving. This study aims to analyze the emergence and form of metacognitive regulation in groups that are more and less successful at solving geometric problems collaboratively. Each group consists of two undergraduate students who have taken geometry courses. The group tries to solve geometry problems in the form of proof problems. This study examines how metacognitive regulation emerges in group discussion activities. The emergence of metacognitive regulations was identified through student utterances when discussing in groups. In addition, interview data support researchers in exploring metacognitive regulation carried out by groups. This study also identifies forms of metacognitive regulation that occur when groups interact. The study results showed differences in the metacognitive regulation activity in four aspects: orientation, planning, monitoring, and evaluation. The more successful group has a form of co-constructed social metacognitive regulation. In contrast, the less successful group has a form of ignored social metacognitive regulation.

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.

The purpose of this quantitative research with correlational design is to determine whether there is independent learning with learning motivation in online-based mathematics learning. So, it can support the success of learning process. This study was conducted in the odd semester of the 2021/2022 Academic Year. All seventh-grade students of SMP Santo Yoseph Medan were used as the research population. While the samples of this study were all students of class VII-A who collected 30 people and all students of class VII-B who collected 31 people. In mathematics learning, all students are taught online through the Zoom cloud meeting platform, WhatsApp, and Google Classroom. Sampling was done by purposive sampling technique. The study instruments is a learning independence questionnaire and student learning motivation questionnaire. The results of the questionnaire were analyzed based on product moment correlation data. Data analysis of the research results showed sig. (2-tailed) < 0.05 so that there is a significant relationship between learning independence and students' learning motivation in online-based mathematics learning with a value of 0.433 including the category of moderate correlation.

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.

The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof.

This paper reports a two-year research project studying Indonesian primary and secondary teachers' mathematics-related beliefs (MrB) and mathematical problem-solving knowledge for teaching (MPSKT). In the first year, a quantitative study involving 80 primary teachers, 70 lower secondary school, and 55 upper secondary schools from four districts in East Java province, Indonesia was carried out to examine whether there is a difference between the MrB and the MPSKT among them. In the second year, a multiple case study involving ten primary teachers and 13 lower secondary teachers was conducted to understand their MrB and MPSKT through some particular issues related to three domains of MrB: nature of mathematics, mathematics teaching, mathematics learning. Results indicate that there is no significant difference of MrB between primary and secondary teachers, while there is a significant difference between the MPSKT of primary teachers and secondary teacher. Findings also suggest that inconsistencies not only occur between the three domains of MrB but also occurs between particular issues discussed within one domain. Also, this study highlights that teacher beliefs about nature of mathematics were mainly influenced by teachers' experience when learning mathematics during their schooling experience while teacher beliefs about teaching and learning were mainly influenced by the demand of current reform of mathematics curriculum.

Beliefs and pedagogical content knowledge (PCK) are two factors influencing teaching practice in the classroom. This research aims to describe the beliefs and PCK of the prospective mathematics teachers and the relationship between the two factors on the teaching practices in the mathematics classroom. Participant in this research includes a prospective teacher who has taken a micro teaching subject and has good communication skill. Data were collected through interview and video analysis on the teaching practice in the classroom. The data obtained were coded, simplified, presented, and triangulated for the credibility and concluded. The result of the research shows that the prospective teachers who hold a constructivist belief view mathematics as a dynamic knowledge which evolves and is regarded as the space of creation for humans. Their beliefs on the nature of mathematics support the belief in the teaching-learning process in mathematics classrooms. Furthermore, a good understanding of the prospective teachers have on the components of the PCK has been sufficient, which can be identified in every step of practical activities in the classroom. More elaboration on the relationship between the belief and PCK is presented in this research.

Purpose: This study aimed at investigating the effectiveness of implementing Project Based Learning (PBL) on the topic of statistics at a lower secondary school in Surabaya city, Indonesia, indicated by examining student learning outcomes, student responses, and student activity. Research Methods: A quasi experimental method was conducted over two months involving two classes of seventh grade students, consisting an experiment class (PBL) and a control class (conventional learning). Data were collected through student activity observation sheets, student responses, and pretest-posttests. Data were analyzed by employing covariance analysis (ANCOVA). Findings: Based on ANCOVA, student learning outcomes in PBL are higher than those in conventional learning. In addition, based on the results of a descriptive analysis, results of the student learning outcomes in PBL obtained more than the minimum standard score (MSC), the students' responses in learning were positive, and the students were active in the class activities. Thus, PBL is effective in statistical learning. Implications for Research and Practice: Based on the results of the research, it can be concluded that PBL was effective in statistical learning. These findings suggest that the students were enthusiastic in working the given project and actively discussed with other students in the class. We suggest teachers apply PBL on other mathematics topics so students can be enthusiastic in mathematics learning in the class. Alternatively, teachers can use PBL with technology-assisted learning to make learning more interesting for students.

The fact that there is no much study on reversibility is one of reason this study was conducted. Others, the importance of reversibility is also being researcher's motivation for focusing pupils' reversibility. On the other hand, the concern on pupils' reversibility is a major concern. The objective of this research is to identify errors done by the pupils in solving arithmetic problems related to reversibility concept. The result of this study can inspire teachers to consider the problem-solving in minimizing errors which must be done by the pupils in solving other arithmetic errors. The result of this study can be used as a reference in designing further learning and tasks for student's reversibility development. This research is qualitative with descriptive approach. The subjects of this research are fifth grade pupils of three Elementary Schools in Jombang, Indonesia. Researcher gave arithmetic task related to reversibility concept to the research subject. The pupils' worksheet was analyzed by calculating a number of pupils who did error for each arithmetic item. Then, it was classified to groups which were based on the error types done by the pupils. Furthermore, the researcher described error types done by the pupils related to Roberts, namely wrong operation, obvious computation error, defective algorithm, and random response. This case proved that there are some elementary school pupils who are still having difficulty in solving arithmetic problems related to reversibility concept.

Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking is focused on flexibility, fluency, and novelty in mathematical problem solving and problem posing. As students have various backgrounds and different abilities, they possess different potential in thinking patterns, imagination, fantasy and performance; therefore, students have different levels of creative thinking. A research study was conducted in order to develop a framework for students' levels of creative thinking in mathematics. This research used a qualitative approach to describe the characteristics of the levels of creative thinking. Task-based interviews were conducted to collect data with ten 8th grade junior secondary school students. The results distinguished five levels of creative thinking, namely level 0 to level 4 with different characteristics in each level. These differences are based on fluency, flexibility, and novelty in mathematical problem solving and problem posing.

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Pictorial representation skills are crucial for blind individuals to understand and interpret visual information. This study aimed to develop and validate a reliable and informative instrument that can measure these skills in blind junior high school students. Grounded in cognitive theory and existing research on spatial reasoning, visualisation, and communication in blind individuals, the study developed four description-type geometric concept tasks involving interpreting and describing geometric shapes, spatial relationships, and data visualisations. These tasks were specifically chosen to encompass diverse aspects of pictorial representation, allowing for a comprehensive assessment of students' abilities. Content validity was established using the Aiken formula, which demonstrated strong alignment between the tasks and the targeted constructs, specifically by exceeding the recommended cut-off score for item-to-total correlations. Internal consistency, assessed using Cronbach's Alpha, was acceptable at 0.823. Item difficulty and discrimination analyses revealed a moderate level of difficulty for all tasks, indicating an appropriate challenge while ensuring differentiation among students. Furthermore, all tasks showed good discrimination power, effectively distinguishing between students with different levels of pictorial representation skills. This validated instrument provides a valuable tool for educators and researchers working with blind students. It can be used to (i) assess individual strengths and support the development of pictorial representation skills in blind students, and (ii) design and adapt instructional materials to cater to diverse needs. However, it is important to acknowledge the limitations of this pilot study, including the small sample size. Future research with a larger and more representative sample is necessary to fully validate the psychometric properties of the instrument and confirm its generalisability across different settings and populations. [ABSTRACT FROM AUTHOR]

It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking is focused on flexibility, fluency, and novelty in the mathematical problem solving and problem posing (Silver, 1997). Students have various backgrounds and different abilities. They possess different potential in thinking pattern, imagination, fantasy and performance. Therefore, students have a different level of creative thinking. This research used qualitative approach which aims to describe the characteristic of the level of student's creative thinking in mathematics. The task-based interview was conducted to collect data from the 8th grade students of junior secondary school. Snowball method was used to determine subject research. Finally, there were nine students from junior secondary school of "SMP Negeri 6 Sidoarjo" and one student from "SMP Al Hikmah" Surabaya. The result of this research pointed out the five levels of creative thinking that are of level 0 to level 4 which has a different characteristic. This difference is based on fluency, flexibility, and novelty in mathematical problem solving and problem posing. (Contains 1 table and 1 figure.)