Rangkiang Mathematics Journal

Mathematics Learning Based on Jean Piaget’s Cognitive Development Theory in Vocational Schools

2024-12-28T07:19:28+00:00

This study aims to analyze the application of Merdeka Curriculum in mathematics learning at vocational schools based on Jean Piaget's cognitive development theory. The Merdeka Curriculum is designed to provide flexibility to educators in designing learning that is relevant to student needs, including mathematics subjects that are often considered complex by students. This research includes qualitative research with a case study type. Data were collected through document analysis and interviews. Then the data were analyzed descriptively through data reduction, data presentation, and conclusion drawing. To ensure data validity, source triangulation is used. The results showed that the application of Merdeka Curriculum in mathematics learning can support students’ formal operational cognitive development stage. The project- and problem-based approach, which characterizes the Merdeka Curriculum, develops logical, abstract, and analytical thinking skills that are essential in mathematics. However, there are challenges in its implementation, such as some teachers’ low understanding of learning strategies based on cognitive developmental stages and limited interactive learning media. This research recommends intensive training for mathematics teachers to improve their understanding of cognitive development-based learning strategies and the provision of adequate supporting facilities. With the right approach, the implementation of Merdeka Curriculum in mathematics learning can be more effective in improving students’ cognitive abilities in vocational schools.

Analysis of The Queuing System at Majapahit Gas Station Using Monte Carlo Simulation

2025-08-23T06:46:28+00:00

Queue is a condition of customer accumulation at a service place, which can cause inconvenience to customers, especially if the queue lasts a long time. One of the service stations that often experience long queues is Majapahit Gas Station, especially during peak hours such as in the morning at 07.00-08.00 and in the afternoon at 16.00-17.00. To overcome this problem, it is necessary to apply queue theory and Monte Carlo simulation as an analytical solution. This research aims to improve the effectiveness of service performance at Majapahit Service Station by determining the minimum number of refueling pumps needed during peak hours to minimize queues. Based on the analysis using queue theory and Monte Carlo simulation, it was found that the minimum number of pumps needed in the morning was three units, with a utilization rate of 80.40%. Meanwhile, in the afternoon four pumps are needed with a utilization rate (steady state) of 75.40%. Since the steady state utilization rate is below 100%, the system can be said to be stable, so the possibility of customer accumulation is small.

Middle School Teachers’ Professionalism, Beliefs, and Attitudes on Technology Integration: Implementing Scratch in Coding-Based Mathematics Learning

2025-09-20T01:05:22+00:00

This study addresses the challenge of limited teacher readiness in integrating digital technology into mathematics instruction, particularly through coding-based learning media. It focuses on teacher professionalism by examining their attitudes and beliefs toward the use of Scratch as a tool for developing interactive and contextual mathematics teaching materials. A survey design was employed with twenty junior high school teachers in Bukittinggi City who had previously participated in intensive training on the development of Scratch-based materials. Data were collected using questionnaires, structured interviews, and classroom observations, which served as the main research instruments. The findings reveal that 92% of teachers hold positive beliefs about the integration of digital culture–based technology through Scratch, and 88% perceive it as beneficial for students’ learning. Furthermore, 89% of teachers showed strong engagement and active participation throughout the activities. These results highlight the potential of Scratch to strengthen teachers’ technological pedagogical competence, provide students with more engaging learning experiences, and offer valuable insights for further research on technology-enhanced mathematics education.

The Numbered Heads Together Type Cooperative Learning Model on Students' Understanding of Mathematical Concepts in Grade VIII Mts Negeri 1 Polewali Mandar

2026-02-05T05:02:26+00:00

Learning mathematics at school often present difficulty for students, in particular in understand draft material straight line equation. Students tend experience difficulty in understand gradient, error in determine point cut and not capable drawing graphics, especially if the learning process No support. In case This found p use of learning models in schools the Still not enough diverse. Teachers are more often using a learning model conventional with the teacher playing a role as center information. For overcome problem This requires more learning models active and innovative in increase understanding draft mathematics students. The purpose of study This For know effectiveness of learning models cooperative type Numbered Heads Together (NHT) in increase understanding draft mathematics students on the material straight line equation. Instrument study in study This There is three that is, test understanding draft mathematics, sheets observation implementation learning and questionnaires response students. Data analysis was carried out use analysis descriptive and analytical inferential. Analysis results descriptive show that learning model Numbered Heads Together supports in increase ability understanding draft students and create a learning process more interactive and not monotonous. This study conclude that use of learning media Numbered Heads Together can increase understanding draft student so that impact good on results Study mathematics student.

Karush Kuhn-Tucker (KKT) Approach for Production Cost Optimization in Falish Kitchen MSMEs, Prabumulih

2026-02-05T04:05:02+00:00

In the production process of Micro, Small, and Medium Enterprises (MSMEs), there is often a lack of careful calculation regarding the optimal production quantity for each type of product, which can lead to cost inefficiencies and suboptimal resource utilization. This study aims to minimize production costs at Dapur Falish MSMEs by applying the Karush Kuhn-Tucker (KKT) method as an optimization approach. The optimization model incorporates various constraints, including limited production capacity, to determine the optimal production levels. This problem is modeled mathematically and then formulated in the form of a Lagrange function. Each equation produced is analyzed systematically to ensure that the solution obtained meets the optimal conditions based on KKT requirements. The results show that the minimum production cost for Dapur Falish is IDR 897,389.7 per month. These findings provide practical insights for MSME owners in improving cost efficiency and support more effective production planning by identifying optimal resource allocation under existing constraints.

Comparison of Generalized Poisson Regression and Negative Binomial Regression Models in Handling Overdispersion in Downtime Cases

2025-08-23T06:43:21+00:00

Downtime in industrial machinery has a significant impact on efficiency and operational costs. To model the number of downtime events, Poisson regression is used, which has several assumptions, including that the response variable must be Poisson distributed, there is no linear relationship between predictor variables (multicollinearity), and the variance is equal to the mean (equidispersion). However, in practice, violations of these assumptions are often encountered, where the variance of the response variable exceeds its mean, known as overdispersion. This issue can be addressed using approaches such as Generalized Poisson Regression (GPR) and Negative Binomial Regression (NBR). In this study, a comparison of the GPR and NBR models will be conducted using secondary data from the cement manufacturing industry in Indonesia, consisting of downtime as the response variable and five predictors: duration of disruptions, number of mechanical and electrical disruptions, raw material availability, and production output. Assumption tests showed no multicollinearity and that the response distribution followed a Poisson distribution, but overdispersion was present. The results show that all predictor variables in the GPR and NBR models are significant except for the duration variable, which does not significantly affect the amount of downtime. The best model is determined based on the smallest Akaike Information Criterion. (AIC) and Root Mean Square Error (RMSE) values. The results show that GPR has an AIC of 148.3074 and an RMSE of 3.608414, while NBR has an AIC of 48.3083 and an RMSE of 3.608534. Based on these criteria, GPR was selected as the superior model.

3D Modeling of the 2010 Mentawai Tsunami Using Optimal Time Stepping

2026-02-05T04:11:13+00:00

The 2010 Mentawai tsunami was a major disaster in Indonesia, triggered by a 7.7 Mw underwater tectonic earthquake southwest of Pagai Island. To enhance disaster mitigation, efficient and accurate computational analysis is essential. This study develops a three-dimensional (3D) tsunami propagation model implementing the Optimal Time Stepping (OTS) method to address the high computational costs typically associated with conventional 3D simulations. Computational data were derived from the USGS earthquake parameters and spatial data of the Mentawai Islands, processed using QGIS software. The simulation evaluated the effectiveness of the OTS method through plane wave and circular wave approaches, utilizing a second-order Runge–Kutta (RK2) scheme for validation. The results demonstrate that the OTS method effectively captures the tsunami propagation patterns with robust numerical stability and significantly higher computational efficiency compared to standard methods. Furthermore, the simulated wave propagation direction aligns with the actual historical movement from the epicenter toward Pagai and Sipora Islands, underscores the method's potential for integration into Indonesia’s tsunami early warning systems.Keywords: 3D modeling, Mentawai tsunami, Optimal Time Stepping (OTS), disaster mitigation.

An FCM–TOPSIS-Based Model for Grouping and Ranking Priority Regions for Poverty Alleviation: A Case Study of Indonesian Provinces

2026-03-01T12:35:54+00:00

Poverty in Indonesia is a multidimensional problem that reflects regional disparities and cannot be adequately represented by a single indicator. Differences in socioeconomic conditions among provinces require more targeted poverty alleviation policies. This study aims to map and prioritize poverty alleviation areas in Indonesia by integrating the Fuzzy C-Means (FCM) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods. The novelty of this study lies in combining fuzzy clustering and multi-criteria decision-making to identify groups of provinces with similar socioeconomic characteristics and determine intervention priorities within each group. Secondary data from the Central Statistics Agency in 2025 covering 38 provinces and eight welfare indicators were analyzed. FCM was used to cluster provinces, while TOPSIS was applied to rank poverty alleviation priorities. The results produced three clusters with distinct socioeconomic characteristics. Cluster 1, consisting of Central Papua and Papua Pegunungan, showed the highest socioeconomic vulnerability. Cluster 2 represented provinces with moderate conditions, while Cluster 3 comprised provinces with relatively better development indicators. TOPSIS results identified Central Papua, West Papua, and South Papua as the highest-priority provinces in Clusters 1, 2, and 3, respectively. The integrated FCM–TOPSIS approach provides a comprehensive framework for targeted and effective poverty alleviation planning.

Time Series-Based Transformer for Forecasting SOE Dividends as Danantara’s Investment Fund Source

2026-02-05T07:18:51+00:00

In recent years, dividend allocation from State-Owned Enterprises (SOEs) has become increasingly important following the establishment of Daya Anagata Nusantara (Danantara) on February 4, 2025, a national investment management institution tasked with optimizing state assets outside the state budget, where SOE dividends contribute approximately 40% to 45% of total managed assets. Accurately estimating future dividends is crucial for Danantara to plan and allocate productive investments efficiently and establish a basis for future evaluation. SOE dividend distribution is influenced by internal factors such as net profit and external macroeconomic conditions, including inflation, Bank Indonesia's benchmark interest rate (BI Rate), the Rupiah exchange rate against the US dollar, Gross Domestic Product (GDP), and the money supply. This applied research uses a time series-based Transformer model with a self-attention mechanism to capture short-term and long-term dependencies across multivariate financial and macroeconomic data. The secondary dataset consists of annual SOE dividends, net profit, and Indonesian macroeconomic indicators obtained from the Ministry of SOEs and Bank Indonesia covering 35 observations from 1990 to 2024. Model accuracy is evaluated using the Mean Absolute Percentage Error (MAPE). The results show that the best model is achieved with parameters of 450 epochs, a d_model dimension of 128, four multi-head self-attention heads, and four layers, yielding a testing MAPE of 31.81%, which is categorized as reasonably suitable for forecasting. Forecasting results for the five-year horizon show an initial downward adjustment in SOE dividend values before increasing significantly in the fourth projection year and moderating in the final year, providing a valuable quantitative reference for strategic investment planning by Danantara.

The Effect of Implementing the Problem-Based Learning Model on the Systematic Communication Skills of Grade XI Students at SMAN 2 Padang

2026-10-31T12:55:40+00:00

This study was motivated by the low level of students’ mathematical communication skills in mathematics learning. One learning model that can encourage students to participate actively in the problem-solving process is Problem Based Learning (PBL). This study aimed to determine and describe the mathematical communication skills of students taught using the PBL model compared to those taught using direct instruction in Grade XI, Phase F, at SMA Negeri 2 Padang. This research employed a quasi-experimental method with a The Nonequivalent Posttest-Only Control Group Design. The research sample consisted of 66 students, comprising 29 students in the experimental class taught using the PBL model and 37 students in the control class taught using direct instruction. Data on students’ mathematical communication skills were collected through a posttest consisting of essay questions developed based on three indicators of mathematical communication skills. The data were analyzed using descriptive statistics and the Mann-Whitney U test. The results showed that the mean score of the experimental class was 80.90, while the control class obtained a mean score of 77.59. However, the Mann-Whitney U test yielded an Asymp. Sig. (2-tailed) value of 0.658, which was greater than the significance level of 0.05. Therefore, there was insufficient statistical evidence to conclude that the mathematical communication skills of students taught using the PBL model were better than those of students taught using direct instruction.