Publication Search

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 aims to describe students’ mathematical problem-solving abilities on the topic of Systems of Linear Equations in Two Variables (SPLDV) based on Polya’s problem-solving stages in relation to their levels of self-efficacy. The research employed a descriptive qualitative approach with three ninth-grade students from SMP Negeri 5 Gresik in the 2024/2025 academic year, selected through purposive sampling to represent high, medium, and low levels of self-efficacy. Data were collected using a self-efficacy questionnaire, problem-solving tests consisting of two contextual essay items on SPLDV, and semi-structured interviews. Data analysis followed the interactive model of Miles, Huberman, and Saldana, encompassing data reduction, display, and conclusion drawing, referring to Polya’s four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. The results revealed that students with high self-efficacy were able to complete all four stages comprehensively and reflectively, demonstrating systematic and accurate reasoning. Students with medium self-efficacy successfully performed the first three stages but failed to verify their final results, while students with low self-efficacy only reached the stage of understanding the problem and struggled to plan or execute solutions. In conclusion, the level of self-efficacy influences students’ mathematical problem-solving performance, particularly in terms of strategic accuracy, procedural precision, and reflective evaluation.

Real analysis is one of the main branches of mathematics that serves as a fundamental foundation for the development of science and technology. This study emphasizes the understanding of basic concepts such as real numbers, limits, continuity, the principle of mathematical induction, as well as deductive and axiomatic approaches as a strong framework for mathematical proofs. This research employs the Systematic Literature Review (SLR) method by examining articles and journals related to both the theoretical aspects and the implementation of real analysis in solving mathematical problems. The findings indicate that the application of Polya’s method, visualization through demonstration, and the use of modern technology such as augmented reality (AR) can enhance the effectiveness of real analysis learning. These approaches help students connect abstract concepts with real applications, thereby strengthening logical, systematic, critical, and rigorous thinking skills. However, several learning difficulties are also identified, including the complexity of the material, weak learning habits, social influences, and inappropriate teaching strategies. Therefore, more applicative, interactive, and contextual learning strategies are needed to support the achievement of learning objectives. The conclusion of this review highlights that the integration of theoretical understanding, problem-solving methods, and innovative technology is a strategic step to improve students’ thinking quality in real analysis courses. Thus, real analysis is not only positioned as a theoretical subject but also as a medium for developing problem-solving abilities and higher-order thinking skills that are relevant to both academic needs and real-world applications.

This study aims to analyze the structure and composition of vegetation on the banks of the Ira River (Wae Ira), Negeri Kamarian, Kairatu District, West Seram Regency. Riparian vegetation plays an important role in maintaining the stability of river ecosystems, both in terms of ecological, hydrological, and biodiversity aspects. The method used in this study is a combination of the continuous strip sampling method and the line plot sampling method, which are applied to four levels of vegetation growth, namely seedlings, saplings, poles, and trees. The results of the analysis show that the vegetation structure in the study area is divided into four strata, with varying species compositions in each stratum. The dominant species found include Pulai (Alstonia scholaris), Pulaka (Cyrtosperma merkusii), Buah rao (Dracontomelon mangiferum), and Salam (Syzygium polyanthum). The highest Importance Value Index (INP) at the tree level is owned by Pulai (Alstonia scholaris) at 54,2. The highest vegetation density is at the seedling level with 52000 individuals/ha and the lowest at the tree level with 341 individuals/ha. The Shannon-Wiener diversity index (H') ranges from 1.87–2.65, indicating a moderate level of diversity. The results of this study indicate that the Ira River border area still has a relatively good vegetation structure and composition, although there are ecological pressures that cause dominance by certain species

This study aims to describe students' critical thinking skills in solving social arithmetic problems based on the Polya stages and FRISCO indicators. The research subjects consisted of three students in grade VIII R-5 MTs Nurul Jadid who were purposively selected to represent the high, medium, and low ability categories out of a total of 21 students. The research method used was a descriptive qualitative approach with instruments in the form of two social arithmetic description questions and semi-structured interview guidelines. Data analysis was carried out by referring to the four stages of problem solving according to Polya (understanding the problem, planning the solution, executing the plan, and re-examination) as well as the six FRISCO critical thinking indicators (Focus, Reason, Inference, Situation, Clarity, Overview). The results of the study showed that students with high abilities were able to solve problems systematically through all stages of Polya and met almost all FRISCO indicators, especially in the aspects of Focus, Reason, and Clarity. Students with moderate ability show sufficient understanding but are inconsistent in planning and implementing solutions, and experience difficulties in the Reason, Situation, and Overview indicators. Students with low abilities experience obstacles from the early stages of understanding problems and do not show significant indicators of critical thinking. These findings indicate that the Polya stage and the FRISCO indicator can be used in a complementary manner to identify and analyze students' critical thinking skills in solving contextual math problems. The implication of this study is the need for a learning strategy that emphasizes strengthening the stages of problem solving and developing explicit critical thinking indicators in the mathematics learning process. This research also opens up opportunities for the development of more structured diagnostic instruments in measuring students' individual critical thinking skills.

Physiological quality deterioration during storage is a major factor contributing to the reduced germination capacity of rice seeds. Revitalization treatments are therefore essential to restore seed viability and promote optimal seedling development. One promising approach involves the application of plant growth regulators (PGRs) from the polyamine group, such as putrescine. This study aimed to assess the effectiveness of varying concentrations and soaking durations of putrescine in improving the viability of deteriorated rice seeds. The experiment was conducted using a Randomized Block Design (RBD) with two factors: putrescine concentrations (0 ppm/ soaking in distilled water only, putrescine 15 ppm, putrescine 20 ppm, and putrescine 25 ppm) and soaking durations (3, 6, and 9 hours). The parameters evaluated included germination percentage and germination rate. Results indicated that treatment with 20 ppm putrescine combined with a 6-hour soaking period yielded the most significant improvement in seed viability. These findings suggest that putrescine treatment can effectively restore the physiological quality of rice seeds affected by storage-induced deterioration.

This study aims to describe the visual thinking of high school students in understanding three-dimensional problems. This research is a descriptive research with a qualitative approach. Two students with medium and high mathematical skills of the female gender were selected as research subjects. Data was collected by giving three-dimensional problem-solving tasks according to Polya's steps and interviews. Students' visual thinking is described based on seeing, recognizing, imagining, and showing. The results of the study show that at the comprehension stage, students with medium and high mathematical skills do looking and seeing, recognizing and imagining at the planning stage, and showing the steps to implement the problem-solving plan appropriately but in a different way, students with medium ability use more concise steps and vice versa for high-ability students; At the re-examination stage, the two subjects showed (showing) the conclusion of the solution solution, but did not show (showing) re-checking.