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INDONESIA
Pythagoras: Jurnal Matematika dan Pendidikan Matematika
Published by Universitas Negeri Yogyakarta
ISSN : 19784538     EISSN : 2527421X     DOI : 10.21831
Core Subject : Education,
Education Mathematics
Arjuna Subject : -
Articles 308 Documents
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Digital Project Development Study: How Does Scratch Accommodate Students' Numeracy and Logical Thinking Skills? Ummah, Siti Khoiruli; Effendi, Moh Mahfud; Rosyadi, Alfiani Athma Putri
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 20 No. 2 (2025)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v20i2.82415

Abstract

Numeracy and logical thinking skills need to be accommodated in lectures, especially logic and algorithm lectures. The purpose of this study is to develop a digital project-based lecture design assisted by the Scratch Application to accommodate students' numeracy and logical thinking skills. The research method uses the ADDIE (Analysis, Design, Develop, Implementation, Evaluation) development model with 20 students as trial subjects. The research instruments used were observations of the implementation of the lecture model and the provision of tests so that the data analysis technique used was using inferential statistical tests to see the effectiveness of the lecture model compared to the lecture model using the discussion method. The results of the study showed a digital project in the form of making simple animations in the form of games by applying mathematical logic rules when compiling scripts. The use of branching and looping algorithms is able to accommodate students' abilities in logical thinking so that there is a systematic thinking pattern. In conclusion, the digital project-based lecture design assisted by Scratch has significant differences with the lecture model using the discussion method based on students' numeracy and logical thinking skills.
Kerangka SPIKR untuk Mengajarkan Keterampilan Kolaborasi Antardisiplin Ilmu bagi Statistisi dan Data Saintis Indonesia Mualifah, Laily Nissa Atul; Vance, Eric Alan
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 20 No. 2 (2025)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v20i2.82940

Abstract

Di abad ke-21, dengan pesatnya peningkatan volume data dan kompleksitas masalah, statistisi dan data saintis tidak lagi mampu menyelesaikan permasalahan hanya berdasarkan bidang keilmuan mereka saja. Mereka kini dituntut untuk berkolaborasi dengan profesional dari berbagai disiplin ilmu guna mendorong inovasi dan kreativitas dalam pemecahan masalah. Keterampilan kolaborasi ini bukanlah keterampilan yang spesifik pada disiplin ilmu tertentu, melainkan keterampilan umum yang dapat diajarkan dan dipelajari oleh berbagai pihak dari semua bidang ilmu. Penelitian ini memperkenalkan kerangka SPIKR, yaitu suatu kerangka yang dirancang untuk mengajarkan keterampilan kolaborasi antardisiplin ilmu kepada statistisi dan data saintis Indonesia. Kerangka SPIKR terdiri dari lima komponen utama: Sikap, Pola Pertemuan, Isi Proyek, Komunikasi, dan Relasi. Hasil penelitian kami menunjukkan bahwa setiap komponen dalam SPIKR memiliki peran yang sangat penting dalam meningkatkan keterampilan kolaborasi antardisiplin ilmu di kalangan statistisi dan data saintis Indonesia. Untuk mengajarkan SPIKR dengan efisien, kami menemukan bahwa metode pembelajaran berbasis kelompok dan memfasilitasi mahasiswa untuk melakukan kolaborasi nyata dengan mitra kolaborasi dari disiplin ilmu yang berbeda terbukti menjadi pendekatan yang sangat efektif dalam meningkatkan keterampilan non-teknis kolaborasi.
Comparative Study of Lightweight Deep Learning Architectures for Potato Plant Disease Detection Faisol, Ahmad; Rudhistiar, Deddy; Puspasari, Betty Dewi
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 20 No. 2 (2025)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v20i2.90854

Abstract

Potato leaf diseases pose a significant threat to crop productivity and global food security, necessitating accurate and reliable diagnostic systems for early detection. Although deep learning based image classification has shown promising results in plant disease recognition, many existing studies rely on simple train test splits, insufficient handling of class imbalance, and limited statistical analysis. This study presents a comprehensive evaluation of multiple pretrained convolutional neural network architectures for multi class potato leaf condition classification, including disease categories and a healthy class. DenseNet121, EfficientNetV2 S, InceptionV3, MobileNetV3 Small, ResNet50, and Xception were evaluated using a stratified K fold cross validation framework. Class imbalance was addressed through class weighted loss functions, and model performance was assessed using accuracy, macro averaged F1 score, and weighted F1 score reported as mean values with 95% confidence intervals. The experimental results indicate that ResNet50 achieved the best overall performance with a mean accuracy of 99.07% ± 0.38% and a macro F1 score of 98.24% ± 0.80%, demonstrating strong and consistent classification across all classes. Lightweight architectures such as MobileNetV3 Small also delivered competitive results with an accuracy of 97.77% ± 0.59%, highlighting their suitability for deployment in resource constrained agricultural environments. These findings emphasize the importance of statistically robust evaluation and imbalance aware training strategies for developing reliable deep learning based systems in precision agriculture.
Exploring Spatial Nonstationarity in the Number of Motor Vehicles in East Java Using Robust Geographically Weighted Regression with an MM-Estimator Isnaini, Bayutama; Isnandar Slamet; Sulandari, Winita; Khoirunissa, Husna Afanyn
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 20 No. 2 (2025)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v20i2.90866

Abstract

The number of motor vehicles in each region is quite diverse, not least in East Java Province. The variety of number of motor vehicles can be affected by local factors that are important to study so that vehicle growth can be adequately anticipated. On the other hand, economic growth incentives are influenced by people's purchasing power. In addition, motor vehicles are one of the essential things in the sustainability of economic activities. This study aims to evaluate a robust, geographically weighted regression model with an MM-estimator (RGWR MM-estimator), which is considered suitable for analyzing the number of motor vehicles in East Java. The results showed that the RGWR MM-estimator model generates an estimate of the number of motor vehicles based on the HDI explanatory variables, road length, sex ratio, poverty gap index, and the number of colleges that is accurate compared to other models formed. In addition, there are significant differences in the influence of the five explanatory variables in each region. Districts/cities located near the capital of East Java Province tend to have many explanatory variables that have a significant effect compared to regencies/cities far from the provincial capital.
Mathematical Model of Preventing The Spread of Dengue Disease in Yogyakarta Using Wolbachia Mosquitoes Syahla Kamila Harsono Putri; Fitriana Yuli Saptaningtyas; Hartono; Fithri Annisatun Lathifah; Fugo Takasu
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 20 No. 1 (2025)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v20i1.91115

Abstract

The purpose of this study is to explain the mathematical model of preventing the spread of dengue fever in the Special Region of Yogyakarta by involving Wolbachia mosquitoes, explain the equilibrium point and stability analysis and conduct numerical simulations. The model used in this study is SIS-SI model, using population data of Yogyakarta Special Region Province in 2023. The steps involved include forming the SIS-SI mathematical model, determining the disease-free and endemic equilibrium points, calculating the basic reproduction number, analyzing the stability of the equilibrium point, and conducting numerical simulation. The results showed that the disease-free equilibrium point is asymptotically stable when . The endemic equilibrium point is asymptotically stable when . Research has shown that is related to the inhibitory effect of Wolbachia bacteria ( ). When , , the threshold for disease spread. If , the disease will not spread in the population, conversly if , the disease will spread. Based on the numerical simulations conducted, it was observed that the smaller the inhibitory effect of Wolbachia bacteria on dengue replication in mosquitoes, the more effective Wolbachia bacteria are in suppressing the spread of dengue virus. As a result, this leads to the disappearance of dengue disease from the population.
Kompleksitas Graf Cocktail Party dan Graf Sandat Berdasarkan Spektrum Laplacian Fransiskus Fran; Suryani Suryani; Bayu Prihandono
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 21 No. 1 (2026)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v21i1.87662

Abstract

Misalkan adalah graf terhubung dan tidak berarah. Setiap graf terhubung memiliki pohon perentang, yaitu subgraf yang terdiri dari seluruh simpul dalam graf dan membentuk pohon. Kompleksitas graf , yang dinotasikan dengan , merupakan banyaknya pohon perentang pada graf . Dalam artikel ini, digunakan pendekatan spektrum Laplacian untuk menentukan kompleksitas graf, khususnya graf Cocktail Party dan graf Sandat. Spektrum Laplacian merupakan matriks yang dibentuk dari susunan nilai eigen matriks Laplacian dan multiplisitasnya. Penelitian diawali dengan menentukan matriks adjacency dan matriks degree dari graf Cocktail Party untuk dan graf Sandat untuk , kemudian dibentuk matriks Laplacian serta polinomial karakteristik matriks Laplaciannya. Selanjutnya, dirumuskan formula polinomial karakteristik ke- matriks Laplacian masing-masing graf. Pembuktian kebenaran formula polinomial karakteristik dilakukan dengan memanfaatkan matriks blok. Berdasarkan hasil tersebut, dirumuskan dan dibuktikan formula spektrum Laplacian, serta formula kompleksitas graf untuk graf Cocktail Party dan Sandat. Hasil dari penelitian ini adalah rumusan spektrum Laplacian dan kompleksitas dari graf Cocktail Party serta graf Sandat.
Eksplorasi Kemampuan Metakognitif Siswa SMP dalam Pembelajaran Etno-PBL Berdasarkan Self-Esteem Ratna Rustina; Dhoriva Urwatul Wutsqa; Jaslin Ikhsan
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 21 No. 1 (2026)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v21i1.96856

Abstract

Kemampuan metakognitif siswa dalam pembelajaran matematika, yang mencakup perencanaan, pemantauan, dan evaluasi, sangat berkaitan dengan self-esteem karena tingkat kepercayaan diri memengaruhi kemampuan siswa dalam mengelola proses berpikirnya, sehingga penerapan model Etno-Problem Based Learning (Etno-PBL) yang kontekstual berbasis budaya dapat menjadi sarana untuk mengembangkan keduanya secara lebih optimal. Penelitian ini bertujuan untuk mendeskripsikan kemampuan metakognitif siswa SMP dalam pembelajaran Etno-PBL berdasarkan self-esteem. Penelitian ini menggunakan pendekatan deskriptif kualitatif dengan subjek enam siswa kelas IX yang dipilih secara purposive berdasarkan kategori self-esteem (tinggi, sedang, dan rendah). Instrumen penelitian meliputi angket self-esteem, tes kemampuan metakognitif, serta pedoman wawancara semi-terstruktur. Teknik pengumpulan data dilakukan melalui pemberian angket, tes, dan wawancara mendalam. Data dianalisis menggunakan model analisis Miles dan Huberman yang meliputi reduksi data, penyajian data, dan penarikan Kesimpulan. Hasil penelitian menunjukkan bahwa kemampuan metakognitif siswa bervariasi sesuai dengan tingkat self-esteem. Siswa dengan self-esteem tinggi menunjukkan kemampuan metakognitif yang lengkap dan reflektif, siswa dengan self-esteem sedang menunjukkan kemampuan yang cukup namun belum konsisten, sedangkan siswa dengan self-esteem rendah menunjukkan kemampuan metakognitif yang masih lemah dan tidak terstruktur.
Integrasi Joyful Learning dalam Project-Based Learning untuk Meningkatkan Kemampuan Numerasi Elis Nurhayati
PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika Vol. 21 No. 1 (2026)
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/pythagoras.v21i1.96902

Abstract

Low students’ numeracy ability remains a significant issue in learning, which is partly caused by limited active engagement and less engaging learning environments. The integration of the Joyful Learning approach within the Project-Based Learning (PjBL) model offers an alternative solution by creating interactive, enjoyable, and meaningful learning experiences throughout project-based learning stages. This study employed a quasi-experimental method with a nonequivalent control group design involving experimental and control groups. The subjects consisted of three schools, each comprising two classes. Data were collected through numeracy tests (pretest and posttest). The results showed that the average numeracy ability of students in the experimental class increased from 38.63 to 77.63, while the control class increased from 36.49 to 62.94. The improvement in the experimental class was consistently higher than that of the control class across all schools. Overall, the N-gain score in the experimental class was in the medium to high category with an average of 0.64, whereas the control class was in the medium category with a score of 0.42. Specifically, the N-gain values in the experimental class were 0.69 (School A), 0.61 (School B), and 0.60 (School C), which were higher than those of the control class, namely 0.55, 0.37, and 0.33. These findings indicate that the integration of Joyful Learning within Project-Based Learning is effective in improving students’ numeracy skills and can serve as an innovative instructional strategy in mathematics learning.

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