The Role of Dispositions and Metacognitive Experiences in the Process of Solving Mathematical Problems

The main problem of this study was the lack of ability in problem solving of junior high school (SMP) students about Comparison. To improve this ability, it was used the cooperative learning model of Number Head Together (NHT) type with approaching of problem based learning. The problem formulations would be studied in this study namely: Whether the cooperative learning model of NHT type with approaching of problem based learning influenced the students' skills in problem solving of comparison lesson. For the purposes of this study were to: (1) describe the implementation of cooperative learning model of NHT type with approaching of problem based learning; (2) describe an improvement in problem solving ability of students in comparison taught by using cooperative learning model of NHT type and approaching of problem based learning. Design of this study was two-group pretest-posttest design. The population was all students of class VII SUMBUL. Ability of mathematical problem solving of students was measured by using test of ability of problem solving. But looking for quality of the improvement obtained from two groups was conducted by testing on the index gain. The result of study showed that the ability of mathematical problem solving between students who were taught by using cooperative learning model of NHT type with approaching of problem based learning was higher than students who were taught just by problem based learning. It showed that there was the influence of cooperative learning model of NHT type with approaching of problem based learning to ability of mathematical problem solving. Based on the result of this study, it was suggested that teachers taught the mathematical problem solving by using cooperative learning model of NHT type with approaching of problem based learning. Key Words: Cooperative Learning Model of NHT Type; Approaching of Problem Based Learning; Ability of Problem Solving.

In recent years, research has increasingly focused on developing engaging, developmentally appropriate coding tools, including unplugged coding activities, which have been recommended as an effective starting point for teaching programming and helping children learn coding concepts through practical applications. This experimental study was conducted to reveal the effect of unplugged coding activities on the problem-solving skills and attitudes towards coding education of 5th grade middle school students. The study was designed using a one-group pretest-posttest weak experimental model within the scope of quantitative research methodology. Following the post-test, a structured questionnaire consisting of closed-ended items was administered to all participating students to collect supplementary data supporting the findings. The sample of this study consists of 5th-grade students, including 35 girls and 24 boys, who were enrolled in a public school in the Selçuklu district of Konya, Türkiye during the 2023-2024 academic year. According to the research findings, unplugged coding activities have been observed to have a significant and positive impact on the problem-solving skills and attitudes towards coding education of 5th-grade middle school students. Specifically, it was found that students gained a broader perspective when faced with problem situations and developed a more systematic and organized approach to solving problems. Additionally, students who initially exhibited hesitant and reluctant attitudes towards coding education showed a more positive attitude towards it after the implementation of the coding activities. The structured questionnaire, used as supplementary data, supported the findings from the pretest-posttest comparison, reinforcing positive changes in students' problem-solving skills and attitudes.

This study aimed to determine the relationship between mathematical communication and problem solving skills and the level of mathematical communication skills and problem solving abilities of seventh grade students of SMPN 2 Kuripan for the academic year 2020/2021. This type of research was ex-post facto research with a quantitative approach. The population in this study were all seventh grade students of SMPN 2 Kuripan with a total of 126 students. The sampling technique used is a non-probability sampling technique with purposive sampling type. Collecting data used were tests to obtain mathematical communication data and problem solving ability data. Data analysis technique used was Pearson product moment. The results of this study indicated that the level of mathematical communication of class VII C students of SMP Negeri 2 Kuripan in solving math problems on the set material as a whole was in the medium category with an average of 12.3. it was found that 6 students had good communication skills or with a percentage (25%), 8 students had moderate communication skills or with a percentage (33.3) 10 students were less capable or with a percentage (41.7) Problem Solving Communication Level students of class VII C SMP Negeri 2 Kuripan in solving math problems on the set material as a whole was in the medium category with an average of 18.21. it was found that 5 students had good problem-solving abilities or with a percentage (20.8%), 10 students had moderate problem-solving abilities or with a percentage (41.7), 9 students had poor problem-solving abilities or with a percentage (37.5). While the results the hypothesis test was 0.337 indicating that there was no significant relationship between mathematical communication and problem solving abilities of class VII students of SMPN 2 Kuripan for the academic year 2020/2021.

Mathematical problem solving ability is the ability of students to find solutions to mathematical problems that cannot be solved immediately or the solution is not yet clear. However, the fact is that student problem solving in Indonesia is still very low. Problem solving is one of the skills that must be mastered by students after learning mathematics. In fact, in elementary school, learning mathematics that develops problem-solving skills has not received much attention from teachers. The teacher's lack of attention to the development of problem-solving skills in the mathematics learning process resulted in students lacking problem-solving skills. One of the learnings that can be done is by applying a mathematics education approach. In addition, students' self-regulation level is still relatively low in learning mathematics. It can be seen from the results of an interview with one of the students of a public elementary school in East Lombok that students still find it difficult to work on questions and do not understand how to do assignments independently. Mathematics parenting learning is one of the new breakthroughs in mathematics learning that can be used by teachers in guiding students to work on math problems independently. The purpose of this study was to analyze the problem-solving and self-regulatory abilities of elementary school students in learning parenting mathematics. This research is a design research research. Design research consists of three phases, namely preliminary design, teaching experiment, and retrospective analysis. This research was conducted at SDN 4 Masbagik Selatan, East Lombok, NTB with research subjects 30 students of class 4A consisting of 14 male students and 16 female students in the 2021/2022 academic year. Data was collected by means of tests (pre-test and post-test) to analyze students' problem-solving abilities in parenting mathematics learning and non-tests (documentation studies, observations, self-regulatory questionnaires, and interviews) were used to analyze students' self-regulatory levels. in parenting mathematics learning. Descriptive statistical analysis was conducted to examine the size of the concentration and distribution of data about the characteristics of the sample/participant and the indicators of the research variables. The data analysis carried out in this study compared the results of the pretest at the preliminary design stage with the results of the post-test at the retrospective analysis stage.

This study explored the relationship between 4th-grade students’ functional literacy levels and their problem-solving skills and the effect level of students’ functional literacy experiences on their problem-solving ability. Employing the quantitative research approach, relational survey design, one of the general survey designs, was used in the study. The study universe was 4th-grade students attending public elementary schools in the central districts of Gaziantep. The study was conducted on a sample of 744 4th grade students who were selected by a simple random sampling method. In the study, data were collected with scales related to two different variables, functional literacy and problem-solving. Necessary approvals for the study were taken before the implementation. SPSS 15.0 package program was utilized to analyze the data. Frequency and percentage were performed to determine the demographic information of participating students; arithmetic mean, standard deviation and standard error were performed to determine the functional literacy levels and perception levels of problem-solving skills; Pearson product-moment correlation coefficient to determine the relationship between functional literacy and its sub-dimensions, and perceptions of problem-solving skills; and finally, multiple regression analysis calculations were made to determine the predictive power of functional literacy and its sub-dimensions on perceptions of problem-solving skills. According to the study results, students’ functional literacy levels were at a medium level and their problem-solving skills were at a partially high level. Also, there was a positive significant relationship between the students’ functional literacy levels and their problem-solving skills. Furthermore, it was determined that functional literacy and its sub-dimensions significantly predicted students’ problem-solving skills. The study results were discussed within the framework of the related literature.

The study aimed at identifying the role of metacognitive experiences (ME), such as feeling of difficulty, estimate of solution correctness and estimate of effort exerted, in the formation of one’s self-concept in the mathematics domain and in self-regulation. The idea was that when one enters an achievement situation, one’s self-concept in the respective domain will influence the ME evoked in response to the task at hand. The ME, in their turn, will influence and shape one’s task-specific self-concept and through it one’s more general self-concept in the respective academic domain. To test these predictions a longitudinal study was designed, in which 172 students of 5th and 6th grade participated. On the first testing, they were given a questionnaire tapping their self-concept in mathematics and two verbal mathematical problems. Before and after problem solving, ME were measured on a 4-point scale. After that, a questionnaire addressing their self-concept in verbal mathematical tasks was administered. On the second testing, one week later, the same process was repeated, with two more mathematical problems, which were more difficult than the initial two. On the third testing, the same procedure was followed with all 4 mathematical problems. Students’ ability in mathematics was represented by their respective school marks. Path analysis confirmed the predictions stated. It was found that exisiting self-concept influences ME which, along with information from task processing, feed back on self-concept and update it. Thus self-regulation becomes more adaptive to reality demands.

The aim of this study is to examine the development of critical thinking, problem-solving, and creativity skills among 7th-grade students from low socioeconomic backgrounds, and to analyze this developmental process using children's books within the framework of the flipped learning model. In this context, action research, one of the qualitative research methods, was employed. The study was conducted over a period of 12 weeks during the fall semester of the 2022–2023 academic year at a secondary school with a low socioeconomic profile, located in a central district of a major city in the western part of the Eastern Anatolia region. The participants consisted of twenty 7th-grade students who exhibited deficiencies in critical thinking, problem-solving, and creative thinking skills, selected through criterion sampling. Different data collection tools were utilized at various stages of the research. While the Cornell Critical Thinking Test and the Torrance Tests of Creative Thinking were used to gather quantitative data, qualitative data were collected through observation notes, the researcher's diary, audio and video recordings, and interviews with teachers, students, and families, as well as student projects created based on the activities related to the books. Quantitative data were analyzed using correlation analysis and the Kendall’s W test to determine inter-rater agreement. Qualitative data were analyzed using the thematic analysis method. As a result of the analyses, it was concluded that the students showed improvement in their critical thinking and problem-solving skills. Although there was also an improvement in their creative thinking skills, it was not as pronounced as the other two skill areas.

The problem of this research is the ability of students' mathematical problem solving which is influenced by interest in learning. The aims of this study were 1) to see how well students could apply problem-solving skills, 2) to see students' learning interests and 3) to understand what obstacles students experienced in working on problem-solving ability tests. This research uses a qualitative approach and applies descriptive research. The subjects in this study were 22 students in class VIII of Christian Private Middle School BNKP Telukdalam 2022/2023 Academic Year. There are three research instruments used, namely tests of students' problem solving abilities, questionnaires of student interest in learning and interviews. Data analysis techniques according to Miles and Huberman. The results showed that the students' abilities in terms of exponentials and root forms were sufficient, where there were 17 students who were in the sufficient category and 5 in the insufficient category. The results of the analysis of students' interest in learning were 2 students with high learning interest, 14 students with moderate learning interest and 6 students with low learning interest. So it can be concluded that students' problem-solving abilities are still quite sufficient and students' learning interest is in the medium category. So the suggestions put forward by researchers are 1) it is hoped that students often practice problem solving skills and increase their interest in learning mathematics, 2) Teachers are more aware of the challenges facing students.

The purpose of this study is to test: (1) classical mastery of problem-solving abilities in Realistic Mathematics Education Learning assisted with fun cards, (2) whether problem-solving abilities in Realistic Mathematics Education Learning Approach is better than learning with PBL, (3) the influence of students' learning responsibility towards problem-solving skills with the Realistic Mathematics Education approach, and (4) describe students' problem-solving abilities in terms of learning responsibility. This study uses a mixed method of sequential explanatory design, the population in this study was the seventh-grade students of one of Junior High School 36 Semarang the academic year of 2018/2019. The results showed that (1) students' problem-solving abilities through the Realistic Mathematics Education Learning Approach assisted with fun cards met classical learning completeness criteria, (2) problem-solving abilities of students who obtained Realistic Mathematics Education Learning assisted with fun cards are better than students who learn with Problem-Based Models Learning, (3) learning responsibilities have a positive effect on students' problem-solving skills in Realistic Mathematics Education Learning assisted with fun cards, (4) students' problem-solving abilities in terms of responsibility through the RME learning approach assisted with fun cards.

Effective mathematics learning is characterized by students' ability to solve mathematical problems independently. One strategy that has been known in improving students' problem-solving skills is a problem-based approach. This study aims to explore and analyze the effectiveness of problem-based mathematics learning strategies in improving students' problem-solving abilities. Qualitative methods were used in this study by conducting literature studies and library research to collect data from various relevant sources. Findings from this study reveal that problem-based math learning strategies make a significant contribution in improving students' problem-solving abilities. With this approach, students are not only taught to remember facts and formulas, but also trained to apply mathematical knowledge in real-world situations. In addition, this strategy also encourages students to develop critical, creative, and analytical thinking skills that are essential in problem solving. The results of this study provide valuable insights for educators in designing and implementing more effective mathematics learning to improve students' problem-solving abilities

The purpose of this study is to describe the effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on students' problem solving and mathematical communication skills, describe the effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on problem solving skills, and describe the effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on students' mathematical communication skills. This type of research is Quasi Experimental using Nonequivalent Control Group Design. This research was conducted at SMP Negeri 1 Malinau, North Kalimantan City with 60 students from two 9th grade classes. The instruments used in this study were descriptive test questions of problem solving ability, mathematical communication and observation sheets for the implementation of Outdoor Learning Math learning activities using GPS-based mobile technology-assisted math traces. The results showed that there was an effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on students' problem solving and mathematical communication skills together, there was no effect of Outdoor Learning Math using mobile technology-assisted math traces on problem solving skills, and there was no effect of Outdoor Learning Math using GPS-based mobile technology-assisted math traces on mathematical communication skills. Therefore, for future researchers to expand the scope of materials such as geometry, statistics and probability, algebra, arithmetic and add student motivation variables.

Students are less able to work on mathematical problems due to difficulties understanding information and connecting real problems into mathematical models, resulting in low problem-solving abilities and mathematical self-concept. This study aims to (1) determine students’ problem solving ability with mathematical modeling through the Means-Ends Analysis (MEA) model based on blended learning to achieve classical completeness (2) to determine students’ problem solving ability with mathematical modeling through the MEA model based on blended learning and online PBL learning, (3) to determine the effect of mathematical self-concept on students’ problem solving abilities, (4) describe the students’ problem solving ability with mathematical modeling based on the mathematical self-concept. The research method used was a mixed-method. The population of this study was students of class VIII Junior High School 2 Purbalingga in the academic year 2021/2022, with students of class VIII B (experimental group) and VIII H (control group) taken by simple random sampling method. In the qualitative study, six subjects were taken from the experimental group using purposive sampling. The results showed that the problem-solving ability with mathematical modeling through the MEA model based on blended learning had not yet achieved classical completeness, but the test results with this model were better than the results of the online PBL model. Mathematical self-concept has a positive effect on students' problem solving abilities by 41.3%. Previously, subjects with high mathematical self-concept tended to fulfill all indicators of problem solving ability with mathematical modeling, while subjects with mathematical self-concept tended to have different achievement indicators.

This study aimed to investigate the effect of critical reading (CR) practices in science courses on academic achievement, science performance level, and problem-solving skills. The experimental method and factorial design were used. The study was conducted with 102 seventh-grade students from a public school in Turkey during the 2014–2015 academic year. Experimental and control groups were formed. CR practices were followed in the experimental group and teaching practices appropriate to the curriculum were used in the control group. Data were collected with the “Multiple-Choice Academic Achievement Test” to determine the students’ academic level in the “Human and Environment Unit: The Science Performance Level Test” to determine their science performance level and the “Logical Thinking Group Test” to determine the level of their problem-solving skills. The variables of academic achievement and science performance levels were labeled “Academic Performance.” Independent samples two-way ANOVA was applied to analyze the data using SPSS 18.0 software. The results revealed that the students in the experimental group, who were taught science using CR practices, were significantly more successful than the students in the control group, whose teaching was appropriate to the current curriculum in terms of academic achievement, science performance level, and problem-solving skills. It is of critical importance to use such innovative practices, which combine various disciplines, to allow students to excel at reading, which is a basic skill, at all educational levels in order to raise contemporary and social individuals.

Twenty first century learning demands that students possess critical thinking, creativity, and problem-solving skills. However, physics education in Indonesia particularly in the topic of renewable energy is still conducted using conventional methods and lacks active student involvement. In fact, this topic has the potential to foster higher-order thinking skills. This study aims to analyze the need for the development of a Problem-Based Learning (PBL) based Electronic Student Worksheet (E-SWS) to improve students' problem-solving abilities. A needs analysis was conducted to gain a comprehensive understanding of the learning conditions, challenges encountered, and appropriate teaching material specifications. The method used was descriptive with a mixed quantitative and qualitative approach, utilizing questionnaires and interviews. The research findings indicate that: (1) students feel bored and unmotivated when learning physics; (2) the learning models and media used are not optimal in enhancing understanding and thinking skills; (3) the teaching materials, particularly the student worksheets, are not yet technology-based and the content is inadequate; and (4) students’ problem-solving abilities are still low, reaching only 38.9%. These findings highlight the need to develop a PBL-based E-SWS as a solution to enhance students’ learning interest and problem-solving skills in the digital era

Toys are commonly used as educational tools for children. Beyond supporting their pedagogical development, children also explore and make sense of their environment through play and toys. The use of toys in education has become increasingly widespread over time, as they help foster skills such as exploration, inquiry, collaboration, and understanding cause-and-effect relationships. Activities like toy-making further contribute to the development of engineering-related skills in children, which are integral to the widely adopted STEM (Science, Technology, Engineering, and Mathematics) approach. The purpose of this study is to examine the impact of a STEM-based instructional approach supported by toy design on 6th-grade students’ analogical reasoning, problem-solving, and engineering design skills within the context of support and movement systems. The study group consisted of 28 6th-grade middle school students. The topic was selected based on the 2018 Turkish Science Curriculum. A mixed-methods research design was employed. The quantitative phase utilized a one-group pre-test/post-test experimental design, while the qualitative phase involved content analysis of students’ design products. Data were collected using the Analogical Reasoning Test, the Problem-Solving Skills Questionnaire, and the Engineering Design Rubric. Both quantitative and qualitative data analysis methods were applied. The findings showed that toy design activities related to support and movement systems significantly improved students’ analogical reasoning, problem-solving abilities, and engineering design skills.