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All Journal SAINSMAT BAREKENG: Jurnal Ilmu Matematika dan Terapan Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika SAINSMAT: Jurnal Ilmiah Ilmu Pengetahuan Alam Ininnawa: Jurnal Pengabdian Masyarakat Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat (JHP2M) SMART: Jurnal Pengabdian Kepada Masyarakat Journal of Mathematics, Computation and Statistics (JMATHCOS)
Ja'faruddin, Ja'faruddin
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Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Environmental Science Library & Information Science Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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Penggunaan Partitioning Around Medoids (PAM) dalam Klasterisasi Tingkat Kesejahteraan Kabupaten/Kota di Provinsi Sulawesi Selatan Thaha, Irwan; Ja'faruddin, Ja'faruddin; Ningsih, Rika Rahayu
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 8 No. 4 (2025): Volume 8 Nomor 4 Tahun 2025
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v8i4.7083

Abstract

Penelitian ini merupakan penelitian kuantitatif untuk mengelompokkan Tingkat Kesejahteraan Kabupaten/Kota di Provinsi Sulawesi Selatan menggunakan metode PAM. Algoritma PAM yang biasa dikenal dengan K-Medoids adalah algoritma yang mengimplementasikan objek yaitu medoid sebagai pusat di setiap klaster. Data yang digunakan pada penelitian ini adalah Umur Harapan Hidup (X1), Angka Melek Huruf  (X2), Persentase Pengeluaran Per Kapita Untuk Makanan (X3), Persentase Penduduk Miskin (X4), Tingkat Partisipasi Angkatan Kerja (X5), dan Gini Rasio (X6) di Sulawesi Selatan Tahun 2023 yang didapat dari  website Badan Pusat Statistik. Data dianalisis dengan mencoba beberapa jumlah klaster k=2,3,4 dan 5 dan dievaluasi menggunakan metode Silhouette Coefficient untuk menentukan jumlah klaster yang paling optimal. Hasil penelitian menunjukkan penerapan algoritma PAM menghasilkan nilai Sillhouette Coefficient sebesar 0,31 dengan jumlah k sebanyak 2 klaster. Klaster 1 terdiri 8 kabupaten/kota yaitu Kep. Selayar, Jeneponto, Pangkajene dan Kepulauan, Enrekang, Luwu, Tana Toraja, Luwu Utara, dan Toraja Utara dengan karakteristik  (X1), (X2), dan  (X5) bernilai rendah, sedangkan (X3), (X4), dan (X6) bernilai tinggi. Klaster 2 terdiri dari 16 kabupaten/kota yaitu Bulukumba, Bantaeng, Takalar, Gowa, Sinjai, Maros, Barru, Bone, Soppeng, Wajo, Sidenreng Rappang, Pinrang, Luwu Timur, Kota Makassar, Kota Palopo, dan Kota Pare-Pare dengan karakteristik (X1), (X2), dan  (X5) yang Tinggi, sedangkan (X3), (X4), dan (X6) bernilai rendah.
The The Effect of The Problem Based Learning Model Integrated with Culturally Responsive Teaching on The Numeracy Skills and Mathematical Dispositions Ja'faruddin, Ja'faruddin; Amin, Resky Fadila; Awi Dassa
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 8 No. 4 (2025): Volume 8 Nomor 4 Tahun 2025
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v8i4.7182

Abstract

This study analyzes the effectiveness of implementing Culturally Responsive Teaching (CRT) within a Problem Based Learning (PBL) framework in mathematics instruction at SMP Negeri 2 Takalar and examines its impact on students’ numeracy skills and mathematical dispositions. This research employed a pre-experimental one-group pretest–posttest design involving 28 eighth-grade students, using numeracy tests, classroom observations, student response questionnaires, and mathematical disposition scales as instruments. The findings show that CRT was implemented effectively through the integration of local cultural contexts, inclusive interactions, and active student participation. Students’ numeracy skills improved significantly, with posttest scores surpassing the Minimum Mastery Criteria (KKM) and N-Gain values falling within the medium to high categories. Student activity levels were categorized as active, responses were positive, and mathematical dispositions increased to the medium category. These results indicate that the application of CRT contributes to enhancing students’ numeracy skills and supports mathematics learning that is more meaningful, contextual, and culturally grounded.
The Coefficient Parallelisator Matrix: A Diagonal Similarity Operator for Symmetry Preservation in Knot Semantic Logic Ja'faruddin, Ja'faruddin; Ashari, Nur Wahidin; Baharuddin, Baharuddin; Asyari, Syahrullah; Fadiyah, Wulan Nur; Farhan, Muhammad
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.10762

Abstract

This study introduces the Coefficient Parallelisator Matrix (CPM) as a novel diagonal similarity operator designed to preserve structural and semantic symmetry within the framework of Knot Semantic Logic (KSL). The CPM formalizes the process of parallelization in linguistic and conceptual structures by transforming semantic matrices through similarity operations that maintain eigenvalues, determinants, and symmetry invariants. Each element of the CPM acts as a scaling coefficient, re- balancing semantic weights while conserving the overall interpretive equilibrium of the text. Mathematically, the transformation A′ = MAM−1 establishes a spectral equivalence between the original and parallelized structures, ensuring that both share identical eigen-spectra, determinant, and Hermitian invariants. This invariance reflects a form of semantic gauge symmetry, wherein the un- derlying topology of meaning remains stable despite local transformations in semantic intensity. Conceptually, the operator bridges linguistic theory, topology, and algebraic representation, providing a formal mechanism for analyzing reflective relations such as parallelism, chiasmus, and concentric composition. The findings extend the mathematical foundation of KSL by establishing the Coefficient Parallelisator as an analytical framework for quantifying semantic symmetry—enabling deeper integration between mathematical logic, structural linguistics, and computational semantics.
Co-Authors Ahmad Faisal Amin, Resky Fadila Ardiyanti, Fifi Aris, Fauzan Abdillah Awi Dassa Azzahra, Aulia Baharuddin Baharuddin Fadiyah, Wulan Nur Fajar Arwadi Faruq, Ahmad Al Hassan, Muhammad Nasiru Hisyam Ihsan Irwan Irwan jelita, jelita Khaerati Khaerati, Khaerati Latif, Lhenny Ardillah Mahdiyah, Muyassarah Muhammad Ammar Naufal Muhammad Farhan Muhammad, Fadhel Musyawir, Musyawir Mutmainnah , Nadia Nasrullah Nasrullah Ningsih, Rika Rahayu Novianti, Gita Eka Nurdin Arsyad, Nurdin Nurdin, Nurazizah Nyulle, Rusdianto Pratiwi, Annisa Triananda Pratiwi, Nur Hikmah Kanzha Qalzum, Umrah Nur risaldi, risaldi Saputra, Andika Ardel Satrina, Satrina Sitandi , Flora Frisilia Syahrullah Asyari, Syahrullah Syam , Delia Mustika Syamsuddin Mas'ud Takdirming, Takdirming Thaha, Irwan Utary, Utary Wahidin Ashari, Nur Wahyuni, Maya Sari Wihda, Wihdatul Ummi