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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group Evi Yuniartika Asmarani; Sahin Two Lestari; Dara Purnamasari; Abdul Gazir Syarifudin; Salwa Salwa; I Gede Adhitya Wisnu Wardhana
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.16991

Abstract

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .
Integration of Ethnoscience in the Development of a Problem-Based Learning–Based Science E-Module as a Contextual Learning Medium Salwa Salwa; Mahrus Mahrus; Masayu Febiyanti; Kanaya Hasnah Al-Fadhilah
Indonesian Journal of Educational Innovation Vol. 2 No. 1 (2026): January - April
Publisher : Yayasan Siti Widhatul Faeha Salahudin Syawal

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65622/ijei.v2i1.251

Abstract

This study developed a Problem-Based Learning (PBL)-based science e-module integrating local ethnoscience from Lombok, Indonesia, and examined its validity, practicality, and effectiveness in improving students’ problem-solving skills and cognitive outcomes. Using the ADDIE model within a Research and Development (R&D) framework combined with a quasi-experimental design, four ethnoscience contexts of the Sasak community, traditional weaving dye techniques, Rinjani terraced irrigation, coastal salt production, and clay stove cooking, were systematically embedded as authentic problem scenarios across five PBL phases. Expert validation yielded a mean score of 90.1% (very valid). Student response surveys indicated 88.4% practicality. Pre-test and post-test analysis using N-gain showed a score of 0.63 (moderate-high) for the experimental group versus 0.35 for the control group, with a statistically significant difference (p < 0.001). Problem-solving skills improved across all four Polya indicators (N-gain 0.52–0.61). The ethnoscience-PBL e-module constitutes a contextually grounded digital learning medium that enhances scientific competence while valorizing indigenous cultural knowledge within the Merdeka Belajar curriculum.
Instructional Models for Enhancing Science Literacy Skills: A Literature Review Irman Muliadi; Lalu Azikri Amrullah; Ahmad Hardyan Isnaini; Neli Yuliani; Salwa Salwa; Shelliana Iqlima
Indonesian Journal of Innovation and Educational Technology Vol. 1 No. 1 (2026): Edisi Januari-Juni 2026
Publisher : Indonesian Publication Center

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.67434/ijiet.v1i1.2440

Abstract

The low 2022 PISA scores highlight a serious challenge for scientific literacy in Indonesia, triggering the need for a transformation from conventional models toward pedagogical innovation. This study aims to analyze effective learning models for enhancing scientific literacy in the digital era. Using a Systematic Literature Review (SLR) method with the PRISMA model, this research reviewed 20 selected articles within the 2019–2026 interval. The analysis identified nine primary models and approaches proven to significantly improve scientific literacy: inquiry-based learning, problem-based learning (PBL), project-based learning (PjBL), STEAM-PjBL, guided inquiry, discovery learning, differentiated instruction, the ethnoscience approach, and the RADEC model. Findings indicate that these models, supported by technology integration such as interactive e-books and digital media, produce N-Gain scores in the medium to high categories. The ethnoscience approach also proved to enhance learning relevance through local wisdom. Despite their effectiveness, implementation still faces obstacles related to school facilities and teacher competency readiness. This study concludes that the synergy between student-centered innovative models and the reinforcement of teacher TPACK is crucial for creating meaningful, competitive, and adaptive science education for the modern era.
The Effectiveness of Problem-Based Learning E-Modules on Students' Problem-Solving Skills and Cognitive Learning Outcomes: A Systematic Review Salwa Salwa; Neli Juliani; Irman Muliadi; Sumarti Sumarti
Indonesian Journal of Innovation and Educational Technology Vol. 1 No. 1 (2026): Edisi Januari-Juni 2026
Publisher : Indonesian Publication Center

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.67434/ijiet.v1i1.2491

Abstract

This systematic literature review (SLR) evaluates the effectiveness of Problem-Based Learning (PBL)-integrated e-modules in enhancing students' problem-solving skills and cognitive learning outcomes. Following the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines, a comprehensive search was conducted across Google Scholar, Garuda (SINTA), ERIC, and Scopus databases for articles published between 2016 and 2025. From an initial pool of 76 identified studies, 25 met the predefined inclusion and exclusion criteria for analysis. The findings demonstrate that PBL-based e-modules significantly improve problem-solving skills, evidenced by an average N-gain ranging from 0.60 to 0.78 (medium to high category). Similarly, cognitive learning outcomes showed a marked increase, with average score improvements of 15% to 35% from pre-test to post-test. Key factors contributing to this effectiveness include the structured problem-based approach, interactive e-module features, and the integration of contextual real-world issues. This review concludes that PBL-based e-modules are a potent instructional tool for fostering critical skills and academic achievement across various educational levels.
The Effectiveness of Problem-Based Learning E-Modules on Students' Science Literacy: A Systematic Literature Review Shelliana Iqlima; Neli Yuliani; Asyil Arifah; Irman Muliadi; Salwa Salwa
Indonesian Journal of Teacher Education Vol. 7 No. 1 (2026): Edisi Januari-Juni 2026
Publisher : Indonesian Publication Center

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.67434/ijte.v7i1.2194

Abstract

Science literacy is a fundamental competency that reflects students’ ability to understand and apply science knowledge in real-world contexts. The integration of Problem-Based Learning (PBL) into digital E-Modules has emerged as a promising innovation to improve this competency. This study analyzes the effectiveness of PBL-based E-Modules on students’ science literacy through a Systematic Literature Review (SLR) with PRISMA guidelines. Ten national and international articles published between 2016 and 2025, retrieved from Google Scholar, Garuda (SINTA), and ERIC databases, were selected and analyzed. The analysis reveals a positive trend in which PBL-based E-Modules generally and effectively support the improvement of science literacy across various educational levels. Three major themes emerge: (1) effectiveness of E-Modules in enhancing science literacy indicators through multimodal and interactive content; (2) the role of PBL in stimulating scientific reasoning and authentic problem-solving; and (3) integration of contextual and ethnoscience approaches as a catalyst for meaningful learning. These findings confirm that the synergy between interactive digital media and PBL is the key mechanism for transforming students’ science literacy in 21st-century education.