Article Per Year (5 Year)
p-Index From 2021 - 2026
0.444
P-Index
This Author published in this journals
All Journal JURNAL PENELITIAN ILMU PENDIDIKAN Jurnal Natural
Musthofa Musthofa
Universitas Negeri Yogyakarta
Decision Sciences, Operations Research & Management Education

Published : 2 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 2 Documents
Search

 1 
Math trails in mathematics education: A systematic literature review on contextual learning, student engagement, and spatial reasoning (2013 – 2025) Muhammad Ainun Niam; Musthofa Musthofa
Jurnal Penelitian Ilmu Pendidikan Vol. 18 No. 2 (2025): July–December
Publisher : Fakultas Ilmu Pendidikan, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/jpip.v18i2.93486

Abstract

Mathematics education has faced persistent challenges in student engagement, spatial reasoning, and real-world relevance. Among innovative approaches, math trails have emerged in the last decade to integrate contextual, spatial, and technology-enhanced learning experiences. This study presents a systematic review (2013–2025) examining how math trails contribute to contextual learning, enhance student engagement, and develop spatial reasoning skills. Following PRISMA 2020 guidelines, 50 relevant peer-reviewed studies were identified via Boolean searches in major databases (Scopus, ERIC, SpringerLink, MDPI, etc.) and analyzed using thematic synthesis. Three major themes were identified. First, math trails situate mathematics in authentic contexts, linking mathematical ideas to real environments and encouraging students to model real-world situations. Second, math trails promote active, collaborative learning that increases student interest and participation. Third, math trails improve spatial reasoning through tasks involving navigation, measurement, and visual-spatial problem-solving in outdoor settings. The literature goes on to say that using mobile apps and tasks that are relevant to students' cultures can improve math trails when they are used with clear learning goals and reflection. Overall, the findings suggest that math trails are a multidimensional pedagogical approach that bridges theory and practice, yielding both cognitive and affective benefits. Future research should investigate long-term impacts, cross-context adaptations, and scalable models for broader classroom adoption.
Constructing modified binary de Bruijn sequences via cycle joining based on the prefer-complement algorithm Musthofa Musthofa; Agus Maman Abadi; Karyati Karyati; Lusi Harini
Jurnal Natural Vol. 26 No. 2 (2026)
Publisher : Faculty of Mathematics and Natural Science (FMIPA), Universitas Syiah Kuala

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jn.v26i2.407

Abstract

This paper presents a generalized implementation of the cycle joining algorithm for generating binary sequences corresponding to modified de Bruijn sequences of order . The proposed approach can be interpreted in terms of a modified de Bruijn graph, where vertices represent binary strings of length and edges correspond to allowable transitions under the modification rules. The algorithm can be applied to any integer  and can start from any chosen initial vertex. The procedure begins by constructing an initial sequence using the prefer-complement algorithm. The method can produce multiple disjoint cycles, which are iteratively extended and joined into a single sequence. A key challenge in cycle joining is identifying suitable conjugate pairs for merging cycles. In this approach, conjugate pairs are efficiently determined through the algorithm’s structured scheme, simplifying the joining process. The resulting sequence achieves the maximal length , which corresponds to a modified de Bruijn sequence. The flexibility of the algorithm allows it to accommodate varying initial vertices, making it highly adaptable for sequence generation. Its ability to systematically join multiple cycles into a single sequence corresponding to a modified de Bruijn sequence demonstrates potential applications in cryptographic keystream generation, pseudorandom binary sequence design, and other areas requiring structured yet complex binary sequences.
Co-Authors Agus Maman Abadi Harini, Lusi Karyati Karyati Muhammad Ainun Niam