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Constructivism learning theory places learners as active subjects in constructing knowledge through learning experiences, social interactions, and reflection on their surroundings. This approach views learning not as a passive process of receiving information, but as an active process of constructing meaning based on the prior knowledge possessed by learners. This paper aims to comprehensively examine the development and definition of constructivist learning theory, its main principles and characteristics, and its implications in the learning process, particularly in the context of primary education. The writing method used is a literature study by analyzing various literature sources in the form of textbooks, scientific journal articles, and other relevant references related to constructivism theory. The results of the study show that constructivist learning emphasizes learner-centered learning, where knowledge is not transferred directly by the teacher but is constructed through a process of assimilation and accommodation. In this approach, teachers act as facilitators who design a conducive learning environment so that students are able to build understanding independently and through social interaction. The application of constructivist learning has been proven to encourage the development of critical thinking, problem solving, cooperation, and meaningful learning. Therefore, constructivist learning theory is relevant to be applied in modern learning as an effort to improve the quality of the learning process and outcomes of students.

The main objective of the Citizenship Education (PKn) course in higher education is to develop students into individuals with nationalist, participatory, and critical characters towards national dynamics. Conventional learning approaches that are still dominant in higher education, such as one-way lectures and memorization of materials, are considered less able to encourage active participation and the development of critical thinking patterns of students in the Citizenship Education (PKn) course. This study aims to identify the effectiveness of the application of innovative learning methods in improving students' activeness and critical thinking skills. Using a descriptive qualitative approach, data were collected through classroom observations, interviews with lecturers and students, and analysis of lecture documents from three study programs at Merdeka University of Malang. The results of the study showed that the application of learning strategies such as Project Based Learning, role playing, utilization of interactive multimedia, collaborative discussions, and nationality-based simulations were able to significantly increase students' participation and critical understanding. This method is relevant to the needs of learning in the era of globalization that demands digital literacy, cross-disciplinary collaboration, and contextual problem solving. Based on these findings, this study recommends the integration of innovative methods into the Civics curriculum in higher education, pedagogical training for lecturers, and the provision of technological infrastructure that supports the implementation of competency-based learning in the era of globalization.

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.

Anxiety is an emotional response to uncertainty or threats that cause feelings of anxiety, worry, excessive tension, which are continuous and can interfere with the patient's process of action and healing, therefore it is necessary to have good and correct therapeutic communication, to build a relationship of mutual trust, empathy, support and help the patient in problem solving. This study aims to identify the Relationship between Nurse Therapeutic Communication and Anxiety Level in Preoperative Patients at Santa Elisabeth Hospital Medan in 2024. The research design uses correlational with a cross sectional approach, purposive sampling technique with a sample of 64 respondents. The instruments used were the nurse therapeutic communication questionnaire and the anxiety questionnaire. The results of the study showed that the majority of therapeutic communication among nurses in the inpatient room of Santa Elisabeth Hospital Medan was in the good category as many as 34 respondents (53.1%), and the level of anxiety of preoperative patients was majority in the medium category as many as 30 respondents (46.9%). The spearman rank statistical test on SPSS obtained a P-Value = 0.000 which means that there is a relationship between the therapeutic communication of nurses and the level of patient anxiety at Santa Elisabeth Hospital Medan. It is expected that the nurses in Pauline's room will further improve therapeutic communication to pre-operative patients.

Fifth grade students' consistently poor reading comprehension abilities, which impeded their overall academic development and participation in language acquisition, served as the driving force for this study. Using a comic assisted problem based learning (PBL) model, the study, which involved 39 students at SDN Purwamekar, aimed to improve learning activities in order to increase teacher and student participation and, eventually, improve fifth grade students' reading comprehension skills. By using comic strips to illustrate issues, this creative method made learning more engaging and accessible for younger students. In order to enable iterative improvements, the study was conducted over two cycles using classroom action research technique. Only 25% of students (eight people) successfully completed the learning objectives in the first cycle, according to preliminary findings, while 75% (24 students) failed, suggesting difficulties with student motivation and comprehension. This led to changes like improving comic material and fostering more cooperative conversations. Significant progress was seen by the second cycle, with 30 students meeting the completion criteria and only four falling short of the objectives, indicating improved engagement and skill growth. In conclusion, the comic assisted PBL model effectively boosted reading comprehension skills among fifth grade students. The research underscores the value of integrating visual aids and problem solving in education, offering practical insights for teachers to create more dynamic classrooms. Nonetheless, factors like time constraints and resource availability warrant further exploration to ensure sustainable implementation in diverse educational settings.

This study aims to determine the implementation and challenges  of the Promblem Based Learning (PBL) learning model and contextual approach to students. So, by knowing the results of the implementation, it is hoped that teachers can improve the way to teach students better. The method used in this study is descriptive qualitative with interviews via chat via whatsapp and provides google from to be filled in by Yuselvin Beo Wesso as a PPG student who teaches at SMP Negeri 6 Banjarmasin grade 8. She was chosen because she was a student of the Teacher Professional Program and also directly taught at school. The results obtained are the advantages and disadvantages of this model and approach. The advantage of this model is that it helps students to hone critical thinking skills through problem solving that can build students' connectivity with learning. The shortcoming faced in its application is that students find it difficult if they are directly asked for problem-solving discussions. In addition, the challenge faced is that teachers must be able to design learning that varies with the context of problem-solving and not all students can construct their experiences into written text. Therefore, efforts are made by applying the jigsaw method. The result of the application of this model and approach is that the students are quite good. Students can work together to complete assignments and be able to bring up topics relevant to daily life.

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 analyze the errors made by eleventh-grade students of SMA Swasta Eria in solving word problems related to quadratic equations and quadratic function graphs using Newman’s error taxonomy. The research employed a descriptive qualitative method involving 25 students who were given essay-type tests to measure both conceptual understanding and problem-solving skills. Data were collected from students’ written answers and analyzed according to Newman’s stages, which include reading, comprehension, transformation, process skills, and encoding. The findings reveal that errors occurred across all stages, with transformation errors and encoding errors being the most dominant. These mistakes generally stemmed from students’ inability to extract key information into correct mathematical models, inaccuracies in arithmetic operations, and insufficient understanding of fundamental quadratic concepts and their graphical representations. The results highlight the importance of instructional approaches that emphasize conceptual understanding, varied practice problems, and proper mathematical notation. Regular application of Newman’s error analysis is expected to help teachers provide more targeted feedback and improve students’ problem-solving abilities.

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.

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 describe the understanding of high school students in solving high, medium, and low category HOTS (Higher Order Thinking Skills) problems and to explore the students' responses in solving problems related to the material of SPLTV (System of Linear Equations with Three Variables). This research is qualitative in nature, using a descriptive method. The subject selection technique used purposive sampling, involving three students from class X IPA/IPS SMAIT Nurul Fajri, with a total of 19 students. The data collection techniques included written tests on mathematical concept understanding using HOTS, interviews, and documentation. Based on the research results, it was found that the students' understanding of mathematical concepts in solving HOTS problems varied. The subject NF-17, with high ability, was able to answer well, including restating the concepts studied in problems 1, 2, and 4, classifying objects based on concepts, applying concepts algorithmically, relating various mathematical concepts internally or externally, providing examples or counterexamples, and presenting concepts in various representations in problems 1, 3, and 4. The subject NF-18, with medium ability, showed more limited results. Although able to restate concepts in problem 4, this subject could only classify objects based on concepts and apply concepts algorithmically in problems 1 and 4. This subject could only provide examples or counterexamples in problem 1. The subject NF-10, with low ability, was only able to restate concepts studied in problem 1 and did not show more in-depth understanding in other problems. These findings indicate variations in students' understanding of mathematical concepts in the SPLTV material.

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.

This study aims to: (1) produce e-LKPD based on problem-based learning oriented to mathematical problem-solving ability and self-confidence of high school students on the material of equations and quadratic functions and (2) describe the feasibility of PBL-based e-LKPD oriented to mathematical problem- solving ability and self-confidence of high school students on the material of equations and quadratic functions seen from the aspects of validity,  practicality, and effectiveness. This type of research is research and development using the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The research was conducted at SMA Negeri 1 Malinau with the research subject of class X-3 students totaling 35 students. Data collection was carried out using interview techniques, observation, e-LKPD validation sheets, pretest-posttest, and questionnaires. To determine the validity, the e-LKPD assessment sheet of material and media experts was used, practicality used student and teacher response questionnaires, and effectiveness used mathematics problem solving ability test questions and student self-confidence questionnaires. Data analysis consisted of qualitative data analysis and quantitative data analysis. Qualitative data analysis was conducted by analyzing the results of interviews, observations, and comments or suggestions given to make improvements to the e-LKPD products developed. Quantitative data analysis was conducted by converting quantitative data into qualitative data in the form of certain categories, normality test using shapiro-wilk, t-test with paired samples test, and N-Gain score. The results showed: (1) PBL-based e-LKPDs oriented towards mathematical problem solving skills and self-confidence of high school students on the material of quadratic equations and functions have been produced, (2) PBL-based e-LKPDs developed meet product feasibility, namely valid with excellent categories based on material and media experts; practical with very practical categories based on teacher responses and practical based on student responses; effective on math problem solving skills with classical completeness of 77%, the t-test results obtained a significance value of 0.000 <0.05 which means that there is a difference in the average ability to solve mathematical problems before and after learning using e-LKPD, the N-Gain result is 0.65 with moderate criteria, and effective on student self-confidence with an increase in the average score of each indicator before and after learning,  the N-Gain result is 0.49 with moderate criteria, and the t-test results with a significance value of 0.000 < 0.05.

This study aims to develop a contextual learning-based mathematics test instrument focused on Statistics and intended for eighth-grade junior high school (SMP) students. The instrument developed consists of essay questions designed by integrating real-life situations to make them more relevant and meaningful for students. This contextual approach is expected to help students understand statistical concepts more deeply and improve their ability to solve mathematical problems related to everyday life. In the instrument development process, a series of analyses were conducted to test the quality of the test items, including validity, reliability, discriminating power, and difficulty level. The validity of the test items was tested using the correlation between item scores and total scores, with the results showing that all test items had a correlation coefficient greater than the r value of the table, thus being declared valid. Meanwhile, the reliability coefficient obtained was 0.84, indicating that this instrument has a high level of consistency and is suitable for use in measurement. Analysis of the discriminating power showed that each test item had excellent ability to differentiate students with high and low abilities. The analysis of the difficulty level showed balanced variations, namely from easy, medium, to difficult categories. This variation is important to accommodate differences in student ability levels and reflect the diversity in the context of the problems presented. Overall, the results of this study indicate that the developed test instrument is of excellent quality and can be used as an evaluation tool to measure students' mathematical problem-solving abilities. Furthermore, this instrument supports more contextual, interactive, and meaningful statistics learning.

This study investigates the implementation of the discovery learning model to enhance the learning independence of Grade V students in the IPAS subject at MIS Nurul Yaqin. The problem arises from limited learning facilities, which reduce opportunities for activities that stimulate creativity, as well as students’ limited ability to recognize and describe shapes and colors in detail. This Classroom Action Research applied the Kemmis and McTaggart model with Grade V students as the research subjects. Data were collected through observation, questionnaires, interviews, and documentation, and analyzed descriptively in both quantitative and qualitative forms. The results show that Discovery Learning effectively improved students’ independence in learning. Through its exploratory approach, students actively engaged in questioning, observing, experimenting, and drawing conclusions in meaningful activities. Improvements were noted in self-confidence, task discipline, initiative in managing learning, motivation to understand material, and responsibility for outcomes. Active participation at each stage—from problem formulation to reflection—enhanced mastery of the properties of light and their applications, while also fostering critical, creative, and responsible learning behavior. Furthermore, the study found that the implementation of Discovery Learning encouraged collaborative interaction among students, allowing them to share ideas, test hypotheses, and provide peer feedback. This created a more student-centered learning atmosphere, shifting the focus from teacher instruction to student exploration. Quantitative results showed that student independence increased significantly, with success rates rising from 47.80% in Cycle I, when learning was still teacher-centered, to 84.76% in Cycle II, as students became more actively engaged both physically and mentally. These findings highlight the importance of using student-centered approaches such as Discovery Learning to develop independence, critical thinking, and motivation. The model not only supported better academic outcomes but also prepared students with essential lifelong learning skills that can be applied across subjects and in real-life problem solving.

This study aims to compare the effectiveness of the Deep Learning and Differentiated Instruction models in improving junior high school students’ mathematical problem-solving and reasoning abilities. The background of this research stems from the low level of mathematical literacy among Indonesian students, which demands innovative and reflective learning approaches. A quasi-experimental method was used with a Nonequivalent Control Group Design. The sample consisted of two eighth-grade classes at SMP Negeri Satu Atap 01 Ciseeng, each receiving different instructional treatments: one class was taught using the Deep Learning approach, and the other using the Differentiated Instruction approach. The instruments employed included mathematical problem-solving tests, observation sheets, and student perception questionnaires. The data analysis results indicated that the class taught with the Deep Learning model experienced a more significant improvement in mathematical reasoning ability compared to the class using Differentiated Instruction. These findings suggest that Deep Learning-based instruction is more effective in promoting students’ higher-order thinking skills. It encourages deeper engagement with mathematical concepts, fosters critical and analytical thinking, and allows students to construct knowledge through meaningful learning experiences. However, Differentiated Instruction remains relevant in providing learning comfort and addressing diverse student needs, making it beneficial in inclusive classroom settings. The theoretical and practical implications of this research highlight the importance of integrating both depth of thinking (Deep Learning) and flexibility in learning (Differentiation) within mathematics instruction. Such integration could offer a balanced learning environment that supports both cognitive development and emotional engagement, leading to more effective and equitable mathematics education. In conclusion, this study recommends educators and curriculum developers to consider incorporating Deep Learning strategies to enhance students’ mathematical reasoning while maintaining the adaptive and student-centered principles of Differentiated Instruction. Future research could explore hybrid learning models that combine the strengths of both approaches to maximize student outcomes in mathematics learning.

Penelitian ini bertujuan untuk mengetahui pengaruh kWh meter yang bermasalah terhadap efektivitas kWh Jual. Penggambilan data pemakaian kWh meter bermasalah pelanggan di PT. PLN (Persero) ULP Muara Enim. Metode yang digunakan ACMT (Aplikasi Catat Meter Terpusat) dan anlisa RCPS (Root Cause Problem Solving). Hasil penelitian ini Terdapat peningkatan nilai kWh setelah dilakukan penggantian pada kWh meter bermasalah, yang sebelumnya rata-rata pemakaian hanya 3.282 kWh setelah di lakukan penggantian rata-rata pemakaian meningkat menjadi 4.011 kWh   maka terdapat selisih rata-rata pemakaian sebesar 729 kWh. Penggantian kWh meter macet dan buram meningkatkan efektifitas kWh   jual sebesar 24,97 %. Terdapat selisih biaya yang merupakan kerugian yang selama ini ditanggung oleh PT. PLN sebesar Rp.824.560,-/bulan. Dengan dilakukannya penggantian kWh meter bermasalah ini diharapkan akan meminimalisir kesalahan yang dapat menimbulkan kerugian pada PT. PLN (Persero).

This research aimed to know how does puzzle game conduct in developing children cognitive in age 5 to 6 years old at TK Negeri Pembina of Sorong Regency. The result of this research indicated that there was an influence on puzzle game toward cognitive development of before and after using puzzle game. It meant that the use puzzle game can help to stimulate the childrens’ cognitive development, especially on the ability if problem solving for students in age 5 to 6 years old. For this research had function to describe the effectiveness of puzzle game ini increasing childrens’ cognitive development in age 5 to 6 years old. To collect the data, this researcy used observation sheet, interview and documentation. The result of observation sheets and interview, the research applied puzzle game to be able improve cognitive development of students class B in age 5 to 6 years old.

This study examined the effectiveness of applying the Logan Avenue Problem Solving (LAPS-Heuristic) learning model on mathematics learning outcomes among Class VII students at Wusto Imam An-Nasai Gowa using a one-group pretest–posttest design. The population consisted of all seventh-grade students enrolled in the even semester of the 2024/2025 academic year. A learning outcome test was employed as the primary research instrument to measure students’ performance before and after the implementation of the learning model. The data analysis involved descriptive statistical methods combined with gain tests to assess the extent of improvement. The findings revealed that students’ mathematics achievement fell predominantly within the very high category, with 53.85% of learners classified in this range, indicating a notable increase in category levels compared to their pretest performance. Furthermore, the percentage of students who successfully met the required minimum competency standards after the application of the LAPS-Heuristic model reached 96.15%. This outcome clearly illustrates that the vast majority of students—over 85%—achieved or exceeded the established passing threshold, suggesting that the integration of the LAPS-Heuristic approach was highly effective in enhancing mathematics learning outcomes. Overall, the results underscore that the LAPS-Heuristic learning model can serve as a practical and impactful strategy to improve student engagement, comprehension, and mastery of mathematical concepts in junior high school settings.