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Problem solving in permutation and combination requires the ability to understand context, choose strategies, and perform calculation procedures accurately. Based on the analysis of students' answers, it was found that difficulties arose consistently at each stage of problem solving according to Polya, namely the problem understanding stage, the planning stage, the plan implementation stage, and the rechecking stage. In general, students' weaknesses are not only related to their understanding of permutation and combination concepts, but also to their inability to apply problem-solving steps systematically. The results of the study indicate the need for a learning approach that not only focuses on mastering formulas, but also strengthens problem literacy, the ability to identify relevant information, and the selection of solution strategies appropriate to the characteristics of the problem. In addition, the habit of reflection through reviewing the process and results of the solution needs to be developed consistently so that students are able to recognize mistakes and improve their accuracy in solving permutation and combination word problems in a more accurate, logical, and structured manner.

This study examines the influence of work discipline, training, and motivation on employee performance at PDAM Tirta Ayu, Tegal Regency. In a public service organization such as PDAM, employee performance is crucial to ensure customer satisfaction and strengthen institutional competitiveness. A quantitative survey method was used with questionnaires distributed to all 115 employees using a saturated sampling technique, as the entire population was included. The independent variables analyzed were work discipline (attitude, compliance with rules, responsibility), training (materials, methods, instructor competence, duration, facilities), and motivation (intrinsic and extrinsic). Employee performance, as the dependent variable, was measured using indicators of work quality, work quantity, teamwork, and problem-solving ability. The data were processed through multiple linear regression to assess simultaneous and partial effects. The research findings revealed that work discipline, training, and motivation each have a positive and significant impact on employee performance, but for training has a positive and insignificant effect, this is shown by the significant results of each significant level for work discipline sig value = 0.000 (<0.05), training sig value = 0.632 (>0.05) and motivation with sig value = 0.000 (<0.05). These results highlight the importance of strengthening employee discipline, implementing well-structured and sustainable training programs, and fostering sustainable motivation strategies. This research provides practical implications for PDAM Tirta Ayu management in designing policies to improve overall employee performance, thereby improving service quality and organizational competitiveness.  

This community engagement program aims to strengthen collaborative governance and social advocacy in Erbil through a data-driven approach that empowers both public institutions and local communities. The initiative responds to the growing need for evidence-based decision-making, particularly in urban areas where socio-economic disparities, limited data literacy, and fragmented public–community communication hinder sustainable development efforts. Using participatory mapping, digital data collection, and community workshops, the program integrates statistical tools and informatics-based solutions to support transparent governance practices. Activities include capacity-building sessions, community needs assessments, data visualization training, and stakeholder forums designed to enhance cooperative problem-solving. Findings show that community members developed increased awareness of data-based decision processes, while local institutions improved their ability to integrate citizen input into planning. Participant feedback confirms higher trust levels, better communication pathways, and enhanced motivation to co-design development initiatives. The program demonstrates that data-driven social advocacy can strengthen relational accountability and foster long-term collaborations between stakeholders. This model offers a scalable and adaptable framework for cities in the Kurdistan Region seeking to implement more inclusive and sustainable governance strategies. Overall, the program contributes to the advancement of participatory governance by embedding statistical literacy and digital tools into community-centered development processes.

This study aims to analyze the basic skills of 21st-century teachers that play a role in creating creative and collaborative learning. Technological developments, changes in student characteristics, and modern educational demands place teachers in the role of facilitators who must master critical thinking, creativity, communication, collaboration, and the ability to integrate technology into the learning process. The results of the study show that mastery of these skills can increase student activity, motivation, and interaction, while also encouraging problem-solving and cooperation skills. In addition to pedagogical aspects, teachers' psychological readiness and attitudes toward the use of technology, including artificial intelligence, also influence the effectiveness of its application in the classroom. This study emphasizes the importance of continuous training, the development of relevant learning media, and institutional support so that teachers can adapt to the changes of the digital era. Thus, the basic skills of 21st-century teachers are an important foundation in realizing innovative and relevant learning for the needs of students.  

Negotiation is a strategic communication process in which multiple parties work to reconcile differences and reach mutually beneficial agreements through the exchange of information, interests, and viewpoints. Although traditional theories emphasize analytical elements such as developing a BATNA, crafting offer–counteroffer strategies, and employing persuasive framing, recent research underscores the growing importance of interpersonal competencies in shaping negotiation success. Through a qualitative literature-based approach, this study explores how empathy, assertive communication, and emotional regulation influence negotiation outcomes, examines their relevance in digital negotiation environments, and proposes an integrated training framework for professionals and entrepreneurs. The findings reveal that empathy strengthens a negotiator’s ability to interpret emotional cues, identify underlying concerns, and build trust, thereby minimizing miscommunication. Assertive communication supports clear expression of interests and boundaries while maintaining respect, which enhances collaborative problem-solving. Emotional regulation promotes composure and cognitive flexibility, particularly in high-pressure interactions. In technology-mediated negotiations conducted via email, messaging platforms, or virtual meetings, these skills must be adapted due to limited physical cues and higher risk of misinterpretation, requiring explicit wording and intentional emotional management. The proposed model incorporates empathy training, assertive communication development, emotional regulation practices, and digital negotiation skills to cultivate adaptive and emotionally intelligent negotiators.

In the learning process, there are various important aspects that must be considered, especially by teachers as transmitters of knowledge. The success of learning depends heavily on the teacher's ability to manage the classroom to create a safe, comfortable, and enjoyable learning atmosphere. Therefore, teachers need to choose the right learning method so that learning objectives can be achieved effectively. One method that can be used is Outdoor Learning, which is learning outside the classroom that provides opportunities for students to develop talents and creativity more broadly through direct experience in the open air. Management of the learning environment is also a crucial factor in supporting learning success. Several things that need to be considered include understanding the nature and development of student intelligence, getting to know students individually, utilizing student behavior in organizing learning, and developing critical thinking, creativity, and problem-solving skills. In addition, teachers need to create an attractive classroom, utilize the environment as a learning resource, provide constructive feedback, and differentiate between students' physical and mental activities. The learning environment itself consists of indoor and outdoor environments. The indoor environment includes school facilities such as classrooms, libraries, laboratories, and auditoriums. Meanwhile, the outdoor environment includes places outside the school that can be used as learning resources, such as museums, mosques, monuments, and fields. Prospective teachers need to understand the importance of managing the learning environment and understand the various types and benefits of learning environments to support an effective learning process.  

The development of information and communication technology has driven digital transformation across various sectors, including local governments adopting the Smart Regency concept. Digital literacy plays a vital role in supporting the success of Smart Regency implementation, as it determines citizens’ ability to access, understand, and utilize technology effectively and safely. This study aims to measure the digital literacy level of Sleman Regency residents and analyze its contribution to Smart Regency development. The research employs a survey method by distributing questionnaires to residents in several areas of Sleman. The instrument was designed based on four dimensions of digital literacy: technological ability, digital security, problem-solving, and online communication and collaboration. Data were analyzed using descriptive quantitative techniques to illustrate digital literacy levels based on demographic factors and technology usage intensity. The results indicate that most Sleman residents possess a moderate level of digital literacy, with notable variations in digital security and online collaboration aspects. These findings provide implications for local governments to strengthen digital education programs and expand technology access as part of an inclusive and sustainable Smart Regency development strategy.

This study aims to analyze the effectiveness of the STEM approach and the scientific approach in learning Trigonometry in terms of students’ mathematical problem-solving ability and self-efficacy. The research employed a quasi-experimental method with a nonequivalent comparison group design. The study population consisted of all Grade X MIPA students at MA Al-Ma’had An-Nur in the 2023/2024 academic year, with the sample taken from classes X MIPA 1 and X MIPA 2. Data collection instruments included pre-test and post-test assessments of mathematical problem-solving ability and a student self-efficacy questionnaire. Effectiveness criteria were based on post-test averages exceeding 75 for problem-solving ability and self-efficacy scores above 72, as well as improvements from pre-test results. Data were analyzed using the t-test at a 5% significance level to determine learning effectiveness in both groups. Differences in students’ initial conditions and treatment effects were examined using Hotelling’s T² and the N-Gain score test. An independent-sample t-test of N-Gain was used to compare the superiority between the two approaches. The results indicated that both the STEM and scientific approaches were effective in improving students’ mathematical problem-solving ability and self-efficacy. The STEM approach significantly influenced both variables and was superior in enhancing problem-solving ability, although not superior in improving students’ self-efficacy.

This study aims to identify and analyze effective learning strategies for improving Qur’an reading and writing skills among elementary school students. The ability to read and write the Qur’an serves as an essential foundation for students’ spiritual, moral, and cognitive development, shaping their Islamic character from an early age. This research employs a descriptive approach using a literature study method that reviews various sources, including books, journals, and previous studies related to Qur’an learning at the elementary school level. The findings indicate that a combination of several innovative strategies proves to be highly effective in enhancing Qur’an literacy skills. These strategies include the use of engaging and interactive digital learning media, the application of contextual learning approaches that connect Qur’anic teachings to students’ daily lives, and the implementation of the Problem-Based Learning model to foster critical thinking and problem-solving skills. Furthermore, strengthening students’ intrinsic motivation through a supportive and religious learning environment plays a crucial role in maintaining learning interest and discipline. The integrated implementation of these strategies not only improves students’ technical ability to read and write the Qur’an but also reinforces their character, responsibility, and spiritual awareness in the context of Islamic education at the elementary level.

Critical thinking is an essential skill in the modern era, characterized by rapid changes in the workplace and the dynamics of daily life. In a time when information is readily accessible and challenges are increasingly complex, individuals are required not only to master technical skills (hard skills), but also to possess the ability to analyze, evaluate, and critically respond to information. These skills are the foundation for making informed, wise, and adaptive decisions. Case studies from various recent news outlets in Indonesia show that many young people, especially Gen Z, still face difficulties entering the workforce due to a lack of soft skills and mental preparedness. This phenomenon is evident in increasing reports of unpreparedness for work pressure, poor communication skills, and a lack of problem-solving skills. Through an analysis of the literature and news reports, this article explores the relationship between critical thinking skills and the real-world challenges faced by Gen Z. Furthermore, it offers practical recommendations for developing critical thinking capacity so that young people can better adapt, improve professional performance, and respond to various issues in daily life more maturely and responsibly.  

This study aims to determine the effect of the application of PQ4R (Preview, Question, Read, Reflect, Recite, Review) learning strategies on the mathematical problem-solving ability and confidence of students at SMAN 1 Sembakung, Nunukan Regency. The background of this research is the low ability of students to solve mathematical problem-solving problems and their lack of confidence in facing academic challenges. The PQ4R strategy was chosen because it is considered to be able to encourage active student engagement, build deep understanding, and strengthen confidence through structured learning steps. This study uses a quantitative method with a quasi-experimental design of the pretest-posttest control group design. The research sample consisted of 73 students in grade XI who were divided into experimental and control groups at random. The research instruments include problem-solving ability tests and confidence questionnaires. The data analysis technique used t-test and MANOVA (Hotelling's Trace) after meeting the normality and homogeneity tests. The results showed that PQ4R learning strategies had a significant effect on students' mathematical problem-solving skills and confidence. The experimental group experienced a higher score increase than the control group. Thus, the PQ4R strategy can be an effective learning alternative to improve the quality of mathematics learning as well as students' affective aspects such as confidence.

This study aims to analyze the influence of the Problem-Based Learning (PBL) model assisted by e-LKPD on students’ problem-solving abilities and self-confidence in vocational high schools. Specifically, the objectives are: (1) to examine the simultaneous effect of the PBL model assisted by e-LKPD on both variables, (2) to determine its effect on problem-solving ability, and (3) to evaluate its effect on self-confidence. A quantitative approach with a quasi-experimental pretest–posttest control group design was applied. The population consisted of all 10th-grade students at SMK Negeri 1 Tarakan, while the sample was selected using purposive sampling, resulting in class X Marketing 1 (35 students) as the experimental group and class X Culinary 2 (34 students) as the control group. Research instruments included a problem-solving test and a self-confidence questionnaire. Hypothesis testing utilized Hotelling’s T² and independent sample t-tests. The findings showed that 97% of students in the experimental class met the Learning Objectives Mastery (KKTP), compared to only 18% in the control group. Improvement in the experimental group was categorized as high, whereas in the control group it was moderate. Self-confidence also increased significantly in the experimental group, with most students moving from low to high categories. Hotelling’s Trace (Fcount = 77.109, p < 0.001) and t-tests confirmed significant effects on both problem-solving (tcount = 11.657) and self-confidence (tcount = 8.140), proving that the PBL model assisted by e-LKPD effectively enhances students’ abilities and confidence.

This study investigates the algebraic reasoning processes of university students when expanding mathematical expressions in the context of nonroutine problem-solving. The research adopts a qualitative approach to explore how students interpret algebraic structures, apply symbolic transformations, and construct logical explanations while working through unfamiliar tasks. Data were collected through written tests, task-based interviews, and detailed analysis of students’ solution strategies. The findings reveal significant variation in students’ ability to generalize patterns, recognize structural relationships, and justify algebraic procedures. Students with strong conceptual understanding demonstrated flexible reasoning, coherent explanations, and appropriate use of algebraic properties. In contrast, students who relied heavily on procedural rules often struggled with symbolic manipulation, produced fragmented reasoning, and exhibited misconceptions related to variables and distributive operations. These results highlight the importance of fostering conceptual understanding, metacognitive awareness, and reasoning-oriented instruction in university mathematics. The study provides insights for educators seeking to design learning environments that promote deeper algebraic thinking and enhance students’ ability to solve complex, nonroutine problems.

In the modern computing era, servers face significant challenges in data storage due to hardware failures, cyber attacks, or human errors. The problem highlighted focuses on the impact of file systems on three critical aspects: data integrity (accuracy and consistency of data without corruption), data recovery (the ability to restore data after a failure), and failure resilience (fault tolerance, such as redundancy and journaling to prevent downtime). The main issue is that traditional file systems like FAT32 or NTFS are often susceptible to fragmentation, metadata loss, or long recovery times, which can lead to data loss of up to 20-30% on enterprise servers, especially in high-traffic environments like cloud computing.A simple problem-solving process is conducted through a straightforward comparative analysis approach: (1) A literature review of popular file systems (ext4, ZFS, Btrfs); (2) Failure simulations using tools like fsck and stress testing on virtual servers (e.g., via KVM or Docker); and (3) Measuring performance metrics with benchmarking tools like Bonnie++ for I/O throughput, recovery time, and error rates. This process is designed to be simple, requiring only a virtual lab setup without expensive hardware, and is analyzed quantitatively with descriptive statistics.The solution to the problem indicates that advanced file systems like ZFS or Btrfs provide significant improvements: data integrity is up to 95% more secure through automatic checksums, data recovery is achieved in minutes through snapshots and RAID integration, and failure resilience is higher with copy-on-write features. The main recommendation is to migrate to journaling-based file systems for servers, combined with automated backups, which can reduce the risk of downtime by up to 50%. This research provides practical guidance for system administrators to enhance server reliability without excessive additional costs.

The use of technological resources, especially the internet, has a very important role in supporting the effectiveness of the implementation of the flipped classroom model. Through internet access, students can prepare before face-to-face learning by watching learning videos, reading materials, or doing exercises independently. This allows the classroom teaching and learning process to be more interactive, where face-to-face time can be focused on discussion, problem-solving, and application of concepts. Based on survey data collected from students of SMK Dewata Bali Denpasar, it is known that optimal use of the internet helps increase students' understanding and interest in learning science subjects. However, as time went by, it was found that some of the material was still difficult for students to understand and remember. Therefore, educators need to choose the learning platform that is most effective in supporting the implementation of this model. Using the ELECTRE (Elimination and Choice Expressing Reality) method, this study assessed various platforms such as features, price, ease of use, and user survey results. The results show that Google Classroom is the most suitable and efficient platform to support reverse learning because of its ability to integrate various learning media, ease of access, and support for interaction between teachers and students.

This study aims to determine the effect of the combined learning model of Problem Solving with Numbered Head Together (NHT) on the character of mutual cooperation and critical reasoning abilities of fourth-grade students of SD Negeri Kanigoro 03. This type of research uses a quantitative approach with a Posttest Only Non-Equivalent Control Group Design. The research subjects consisted of two classes, namely class IV A as the experimental group and class IV B as the control group, each consisting of 23 students. The research instruments included an observation sheet of mutual cooperation character and a critical reasoning ability test. Data analysis was carried out through normality, homogeneity, and t-test using SPSS with a significance level of 5%. The results showed that the data were normally distributed and homogeneous. The t-test produced a calculated t value of 2.940 > t table 2.015 with a significance of 0.019 for the character of mutual cooperation and a calculated t value of 2.343 > t table 2.015 with a significance of 0.024 for critical reasoning abilities. These results demonstrate that the combined Problem Solving and NHT models significantly enhance students' mutual cooperation and critical reasoning skills. Therefore, implementing this model effectively develops students' cognitive competencies and character, aligned with the Pancasila student profile.

The problem addressed in this community service project is the low understanding of PKBM Permata Paket B students in applying mathematics to everyday life. The objective of this study is to improve students' understanding of mathematics through context-based learning, as well as to stimulate their interest and independence in solving problems involving numbers. The method used is a contextual teaching approach involving group discussions, problem-solving exercises, and real-life problem applications. The results show that context-based mathematics learning significantly improved students' understanding of budgeting, expenses, and personal finance management. Students also showed increased active participation in learning activities and a better ability to connect mathematical theory with practical problems in their daily lives. This program also had a positive impact on social empowerment, increasing students' independence in managing their daily lives. However, challenges related to understanding more complex concepts remain, and it is recommended to use more varied methods and extend the learning time in the future.

This study aims to determine the differences in problem-solving and critical thinking skills between students taught using the Reciprocal Teaching and Problem-Based Learning models in class X of SMK Ki Hajar Dewantara Kotapinang for the 2021-2022 academic year. This is a quantitative study using a quasi-experimental design. The population consists of all class X students at SMK Ki Hajar Dewantara Kotapinang in the 2021-2022 academic year, totaling 111 students. The sample used was class X AKUNTANSI 1 and X AKUNTANSI 2, each consisting of 20 students, chosen as experimental classes using Cluster Random Sampling. Data were collected from pre-tests and post-tests with problem-solving and critical thinking skill test items, then analyzed descriptively and followed by Two-Way ANOVA. The findings indicate: 1) There is no difference in problem-solving ability between students taught using the Reciprocal Teaching model and the Problem-Based Learning model in class X of SMK Ki Hajar Dewantara Kotapinang, with F_observed = 0.320 < F_table(α= 0.05) = 3.978; 2) There is a difference in critical thinking skills between students taught using the Reciprocal Teaching model and the Problem-Based Learning model in class X of SMK Ki Hajar Dewantara Kotapinang, with F_observed = 5.128 > F_table(α= 0.05) = 3.978; 3) There is a difference in both problem-solving and critical thinking skills between students taught using the Reciprocal Teaching model and the Problem-Based Learning model in class X of SMK Ki Hajar Dewantara Kotapinang, with F_observed = 0.026 > F_table(α= 0.05) = 3.936; 4) There is no interaction between the Reciprocal Teaching and Problem-Based Learning models in class X of SMK Ki Hajar Dewantara Kotapinang, with F_observed = 0.459 < F_table(α= 0.05) = 3.936.

This study aims to determine the significant influence of mathematical resilience on students' mathematical problem-solving ability, as well as measure the magnitude of this influence. The approach used is quantitative with an ex post facto (comparative causal) design, where variables have occurred before the study was conducted. The research population included all grade XII students at MAS Miftahussalam Medan, with a sample of 33 students selected through simple random sampling techniques. The research instrument consisted of a questionnaire to measure mathematical resilience and a test to measure mathematical problem-solving ability. The validity and reliability of the instruments were tested through preliminary trials. Data analysis was carried out through a prerequisite test (normality and linearity), followed by a simple linear regression test, t-test, and determination coefficient. The results of the analysis showed a regression equation Y = 16.803 + 0.273X, with a value of t_hitung = 3.784 > t_tabel = 2.039 at a significance level of 5%, so that H₀ was rejected and H₁ was accepted. The determination coefficient of 0.316 showed that mathematical resilience contributed 31.6% to students' mathematical problem-solving ability, while 68.4% was influenced by other factors. These findings confirm the importance of strengthening mathematical resilience in an effort to improve students' problem-solving skills more effectively.

This study investigates the use of experimental statistical analysis as an instructional approach to enhance students’ understanding of variable relationships in science learning. Many students tend to memorize experimental results without comprehending the underlying relationships between variables, resulting in limited analytical reasoning and superficial understanding. To address this issue, the present study explores how integrating basic statistical tools-such as mean, correlation, and regression-into experimental activities can strengthen conceptual comprehension, analytical reasoning, and scientific literacy. Grounded in constructivist and inquiry-based learning frameworks, the research emphasizes active engagement, where students participate in data collection, analysis, and interpretation to draw evidence-based conclusions. The study employed a quasi-experimental design involving science students divided into experimental and control groups. Both groups conducted similar laboratory experiments, but only the experimental group received explicit instruction in statistical analysis. Data were collected through pre-tests and post-tests to measure changes in students’ understanding of variable relationships. The results indicated a 25% improvement in the experimental group’s comprehension and reasoning ability compared to the control group. Students who applied statistical analysis demonstrated greater proficiency in interpreting data, identifying causal patterns, and connecting theoretical knowledge to experimental findings. In contrast, students taught through traditional narrative-based instruction showed minimal gains and relied heavily on memorization. The findings highlight the effectiveness of integrating statistical reasoning in promoting critical thinking, problem-solving, and scientific reasoning skills.