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JTAM (Jurnal Teori dan Aplikasi Matematika)
Published by Universitas Muhammadiyah Mataram
ISSN : 25977512     EISSN : 26141175     DOI : 10.31764/jtam
Core Subject : Education,
Mathematics
Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model pembelajaran matematika di sekolah dasar sampai perguruan tinggi berbasis pendekatan konstruktivis (PMRI/RME, PBL, CTL, dan sebagainya), (2) Pengembangan media pembelajaran matematika berbasis ICT dan Non-ICT, dan (3) Penelitian atau pengembangan/design research di bidang pendidikan matematika, statistika, analisis matematika, komputasi matematika, dan matematika terapan.
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Articles 25 Documents
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Search results for , issue "Vol 10, No 1 (2026): January" : 25 Documents clear
Arithmetic Adventure: A Role-Playing Game to Support Students’ Mathematical Thinking on Arithmetic Sequences Nurrosyadah, Naqiyyah; Susanti, Ely; Somakim, Somakim
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.35260

Abstract

This study aims to develop an educational Role-Playing Game (RPG) entitled Arithmetic Adventure: The Mystery of Polaria Village to support students’ mathematical thinking on arithmetic sequences. The research employed a Development Research approach using the ADDIE model, which consists of Analyze, Design, Development, Implementation, and Evaluation stages. The subjects were 10th-grade students of SMA Negeri 10 Palembang who had implemented the Merdeka Curriculum. Data were collected through expert validation, student practicality questionnaires, and mathematical thinking ability tests. The results indicated that the RPG obtained an overall average validity score of 4.45, categorized as very valid in terms of content, construct, language, and ICT aspects. Practicality testing showed an average percentage of 86.25%, placing the RPG in the very practical category. Furthermore, the potential effect test revealed that 48.6% of students achieved good, 28.6% very good, and 22.9% fair in mathematical thinking ability, showing improvements in specializing, generalizing, conjecturing, and convincing. These findings demonstrate that Arithmetic Adventure is a valid, practical, and potentially effective educational game for supporting students’ mathematical thinking in arithmetic sequences. The study provides theoretical contributions by reinforcing the role of RPGs in fostering mathematical thinking and practical contributions by offering an innovative alternative medium for mathematics learning. 
The Severe Stunting Cases of Children in Central Java Province Explained by Negative Binomial Regression Model Widiyanto, Rhendy K. P.; Fauzi, Fatkhurokhman; Fauzan, Achmad; Kurnia, Anang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34846

Abstract

Severe stunting, or very short stature among children, remains a critical public health concern in Central Java Province. Robust statistical modelling is essential to identify the key factors associated with these cases and to guide targeted interventions. This study employs count regression models with an offset variable to analyze the factors influencing severe stunting cases across districts in Central Java. By using 2023 official data in districts level taken from the Ministry of Home Affairs and the Statistics Indonesia, we initially utilize a Poisson regression model in this study. However, due to evidence of overdispersion, a Negative Binomial regression model was adopted. Backward elimination was then applied to obtain the most parsimonious model. The Negative Binomial regression successfully addressed overdispersion. Five factors were identified as having a statistically significant influence on severe stunting cases: (1) the proportion of pregnant mothers with Chronic Energy Deficiency receiving nutritious food supplements, (2) the percentage of toddlers (6-23 months) receiving complementary nutritious food, (3) the proportion of households with access to good sanitation, (4) Gross Domestic Product per capita, and (5) the number of local healthcare facilities. These factors have negative relation to the stunting rates, meaning improving these factors will reduce the rates of severe stunting. The findings provide a validated statistical model for severe stunting and offer clear policy directions. To mitigate severe stunting, local governments should prioritize: enhancing nutritious food support for pregnant mothers and toddlers, improving household sanitation, stimulating local economic growth, and increasing accessibility to healthcare facilities.
Geostatistical Co-Kriging Approach for Estimating Total Coliform Bacteria in the Rivers of DKI Jakarta Salsabila, Salwa; Sirodj, Dwi Agustin Nuriani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34391

Abstract

Spatial statistics and geostatistics are essential for analyzing spatially distributed data, particularly in environmental studies where data gaps are prevalent. However, limited studies have applied multivariate geostatistical approaches, particularly Co-Kriging (CK), to assess microbial contamination in tropical urban river systems, where pollution patterns are highly variable and data gaps are frequent. This study employs CK, a multivariate geostatistical interpolation technique, to estimate Total Coliform Bacteria concentrations in the rivers of DKI Jakarta, Indonesia. Total Coliform Bacteria served as the primary variable, with Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) incorporated as secondary variables. A total of 120 sampling points were analyzed, with data collected by Dinas Lingkungan Hidup DKI Jakarta during the second monitoring period in June 2022. Semivariogram modelling identified the Gaussian model as the best fit, yielding the lowest root mean square error (RMSE) of 11.468, which performed better than both the Spherical and Exponential models. Model performance was further evaluated through Leave-One-Out Cross-Validation (LOOCV), in which one data point was systematically removed and re-estimated in multiple iterations to calculate the residuals and assess model accuracy. The CK analysis was performed using RStudio software. CK predictions closely matched observed concentrations, demonstrating strong model performance. At unsampled locations, the estimated mean Total Coliform Bacteria concentration was 7.711 × 10⁶ MPN/100 ml with a standard deviation of 4.406 × 10⁶ MPN/100 ml. The high variance indicates substantial spatial heterogeneity, likely driven by data outliers, weak spatial autocorrelation in COD, and low correlations between Total Coliform–COD and BOD–COD pairs. These findings highlight the potential of geostatistical CK to provide reliable spatial predictions of microbial contamination in urban river systems, thereby supporting evidence-based water quality monitoring and management in densely populated regions. The insights generated in this study can help environmental authorities in DKI Jakarta optimize monitoring strategies, prioritize pollution hotspot interventions, and strengthen urban river health management to protect public health and guide sustainable urban water governance.
Optimization of Rice Production Forecasting using Hybrid ANN-PSO Windasari, Wahyuni; Nugraheni, Anggit Gusti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34879

Abstract

Rice production is a critical component in sustaining national food security, especially Indonesia. The availability of sufficient, affordable, and equitable food is a major challenge for Indonesia. One approach to addressing this challenge is by developing reliable and accurate models for predicting food production. In this study, a hybrid approach that combines Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) algorithms is used to optimize the performance of modeling and prediction of rice production in Central Java, Indonesia. This study uses secondary data in the form of monthly time series data from the Central Java Provincial Statistics Agency (BPS), Meteorology, Climatology, and Geophysics Agency (BMKG), and satellite imagery data with an observation period from January 2019 to December 2024. The input variables in this study include harvested area, precipitation, number of rainy days, atmospheric pressure, wind speed, NDWI, and NDVI while the output variable is rice production in Central Java. The test results using the ANN model provided an RMSE value of 0.1312 and a MSE of 0.0172, while the ANN-PSO model provided an RMSE value of 0.0259 and a MSE of 0.00067. These results indicate that the PSO algorithm is able to optimize the performance of the ANN model in predicting rice production in Central Java. 
Transformation of Junior High School Mathematics Learning: Integration of Interactive Student Worksheet and Virtual Reality Based on Deep Learning Approach Istihapsari, Vita; Kusuma, Jaka Wijaya
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33737

Abstract

Mathematics learning in junior high schools still faces challenges in building active student engagement, deep conceptual understanding, and the application of technology during the learning process. This study aims to describe the transformation of the implementation of mathematics learning in junior high schools through the integration of interactive Student Worksheets (LKPD) and Virtual Reality (VR) based on the Deep Learning approach. The research employed a qualitative descriptive method, with data collected through classroom observations and interviews involving four classes of grade VII students and interviews with four grade VII mathematics teachers from four different junior high schools. Before implementation, all research instruments including the interactive LKPD, VR media assisted by Artsteps, observation sheets, and interview guidelines were validated by three experts in mathematics education and educational technology, and the results were categorized as very valid. Data were analyzed using the Miles and Huberman model, consisting of four stages: data collection, data reduction, data presentation, and conclusion drawing. The result of this study is that the application of the Deep Learning approach supported by interactive LKPD and VR media received a positive response from teachers and students. Interactive LKPD and VR Media effectively support the Deep Learning stages, namely (1) Introduction of material with context, (2) In-depth presentation of material, (3) Project-based assignments, (4) Discussion and collaboration, (5) In-depth reflection, (6) Provision of constructive feedback, (7) Competency-based assessment (8) Use of technology in learning, (9) Independent learning and self-regulation, (10) Evaluation and development on an ongoing basis. The implementation of learning is in line with the principles of Deep Learning, namely knowledge connectedness, active involvement, critical and reflective thinking, problem-based learning, collaboration, and intrinsic motivation; and also in line with the Deep Learning learning experience, namely understanding, applying and reflecting. These results show that the integration of interactive LKPD and VR media can be an effective strategy to transform mathematics learning at the junior high school level.
Process of Proportional Reasoning Students' Errors in Solving Mathematical Problems Irpan, Samsul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33355

Abstract

Proportional reasoning plays a crucial role in mathematical reasoning, yet many students struggle to coordinate multiplicative relationships when solving mathematical problems. This study aimed to examine the processes behind students’ errors in proportional reasoning and to describe the types of incorrect strategies they used when working through a contextual joint‑work problem. Using a qualitative exploratory descriptive design, data were collected from students’ written solutions, think‑aloud explanations, and interview responses to capture their reasoning processes in depth. The participants were 15 first-semester students from the Mathematics Education Department, Universitas Islam Negeri (UIN) Mataram. Results showed four major categories of incorrect reasoning: intuitive reasoning based on misleading but salient information, additive reasoning that relied on differences rather than multiplicative structures, proportion attempts that identified proportional cues but applied them incorrectly, and other incomplete or unsupported strategies. Additive reasoning emerged as the most dominant pattern across students of varying proficiency, indicating a strong tendency to default to non‑proportional interpretations even when the situation required multiplicative thinking. Although some students recognized structural features such as periodic assistance, they struggled to coordinate unit work or rates, leading to systematically flawed conclusions. These findings suggest that students’ proportional reasoning errors stem from entrenched intuitive and additive tendencies. The study highlights the importance of instructional approaches that explicitly develop unit‑rate reasoning, strengthen multiplicative understanding, and support accurate representation of proportional situations.
Learning Trajectory of Whole Numbers using the Context of Muara Enim Melemang Based on Realistic Mathematics Education (PMRI) M., Arbella Sri Marleny; Zulkardi, Zulkardi; Putri, Ratu Ilma Indra; Hartono, Yusuf
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34937

Abstract

Learning whole numbers in the early grades of elementary school often poses challenges because students must understand abstract concepts and represent them symbolically. This study focuses on developing a Local Instructional Theory (LIT) for learning whole numbers using the Muara Enim melemang cultural context within the Pendidikan Matematika Realistik Indonesia (PMRI) framework. The research contributes both to the development of learning theory (LIT) and to improving the effectiveness of culturally based mathematics learning in Indonesian primary schools. The study employed design research (validation study) consisting of three stages: (1) the preliminary design formulated a Hypothetical Learning Trajectory (HLT) through curriculum analysis and contextual task design; (2) the teaching experiment tested the HLT in classroom practice to explore students’ strategies and interactions; and (3) the retrospective analysis compared the HLT and the Actual Learning Trajectory (ALT) to refine the emerging instructional theory. Findings reveal that the predicted HLT aligned with the ALT. Students successfully developed number sense counting, comparing, ordering, and performing simple operations through concrete representations of lemang. Difficulties mainly appeared in symbolic notation, such as using inequality signs and subtraction symbols. The study’s novelty lies in establishing a local culture-based LIT that bridges PMRI principles with ethnomathematics. Practically, it provides a contextual model teachers can adopt to enhance meaningful mathematics learning in early grades.
Synchonized DAMRI Public Tourist Transportation Route Design using Max-Plus Algebra Yonantha, Krisma; Putra, Dewa Putu Wiadnyana; Rudhito, Marcellinus Andy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33242

Abstract

The transportation system is a crucial infrastructure for supporting connectivity between each National Strategic Tourist Area (NSTA) tourist destination of Yogyakarta. Management of transportation network and scheduling departure of transportation services are not yet optimal. This study aims to design a synchronized DPTT route and schedule that covers the entire service area using max-plus algebra. This type of study is applied research. The scheduling problem will focus on determining the number of fleets serving all routes with departure periods below 60 minutes. This research was conducted through literature review, field observations and online maps using Google Maps, and computation using the Scilab program. The results show that time travel between 8 tourist destinations are organized into a strongly connected directed graph with 20 routes. Departures are modeled as a linear discrete-event system over max-plus algebra. Computation in Scilab produce a baseline departure period of 90 minutes. We evaluate by adding 2, 8, 10, or 12 of buses by reinforcing the longest route. The simulation shows that the addition of 10 and 12 buses in certain section can reduce the departure period to 56 and 48 minutes respectively. The results demonstrate that targeted fleet additions and network reconnection, guided by max-plus synchronization, can substantially improve service regularity and passenger connectivity.
A Daily Transition Analysis of Disaster Events in Riau Islands using Markov Chains: Dominant Disaster Identification and Risk Assessment Hayati, Nahrul; Anggraeni, Andini Setyo; Sulistyono, Eko
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34024

Abstract

Objectives: This study employs a Markov Chain approach to analyze daily disaster transition patterns in the Riau Islands, with the primary objectives of identifying dominant hazards, quantifying long-term disaster risks, and providing evidence-based recommendations for disaster management. Methods: The research utilized daily disaster records from Indonesia’s National Disaster Management Agency (BNPB) for 2024. A dominant state classification approach was applied to handle days with multiple disaster occurrences, followed by the construction of a transition probability matrix and steady-state analysis to determine long-term disaster distribution. Results: The analysis reveals that no disaster conditions represent the most prevalent state in the region. Among actual disasters, wildfires demonstrate the highest persistence, followed by extreme weather events, floods, and landslides. The transition patterns indicate that most disasters occur as isolated events rather than consecutive sequences, though wildfires show a tendency for temporal clustering. Conclusion: The study provides two key contributions. Methodologically, it demonstrates an effective approach for simplifying complex multi disaster daily data. Practically, it offers scientific evidence for prioritizing wildfire management in the Riau Islands while maintaining preparedness for other episodic disasters. These findings support the development of targeted early warning systems and resource allocation strategies for local disaster management agencies.
Statblithz Game Media Development to Train Students' Mathematical Problem-Solving Skills Afifah, Ani; Wulandari, Alya; Darmayanti, Rani; Santiago, Paulo Vitor da Silva; Karim, Samuel
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.35179

Abstract

Mathematical problem-solving skills are essential for students to succeed in the 21st century, yet many struggle to apply mathematical concepts in real-life situations. This research addresses the need for innovative learning media by developing Statblithz Game, an educational game designed to train and enhance students’ mathematical problem-solving abilities. The study employed a Research and Development approach using the ADDIE model, involving stages of analysis, design, development, implementation, and evaluation. Participants included middle school students who engaged with the prototype and provided feedback through questionnaires, expert validations, and pre- and post-tests measuring problem-solving performance. The results indicated that Statblithz Game is highly feasible, with expert validation scores averaging 89%. Moreover, students’ problem-solving test scores improved by an average of 25% after using the game. In conclusion, the Statblithz Game effectively enhances mathematical problem-solving skills and offers an engaging alternative to traditional mathematics instruction. The impact of this research lies in providing educators with an innovative and interactive tool that can foster critical thinking and improve student learning outcomes in mathematics.

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