Rangkiang Mathematics Journal

The Influence of the Discovery Learning Model Assisted by Articulate Storyline on Students' Mathematical Resilience

Abel Garcia Arlis, Yerizon, Muhammad Zaini — Thu, 30 Apr 2026 00:00:00 +0000

This research seeks to examine how the Discovery Learning approach, when supported by Articulate Storyline, impacts students' resilience in mathematics. In an educational landscape rapidly evolving due to technological progress, a key priority for educators is to leverage ICT advancements to elevate teaching and learning standards. This research was conducted at SMAN 2 Rambatan on grade XI students, focusing on mathematics subjects, especially inverse functions and function composition. A quasi-experimental model was applied, structured around a nonequivalent control group design that collected data solely through posttests. Respondents comprised 51 students, divided into experimental (26) and control (25) groups. Data were collected using a 30-item instrument designed to evaluate resilience in mathematics. The analysis revealed that the Discovery Learning model, when supported by Articulate Storyline, significantly enhanced students' mathematical resilience compared to traditional teaching methods (p = 0.031). This finding confirms the importance of developing mathematical resilience through interactive and technology-based learning approaches, which can help students face challenges in the mathematics learning process. This study advances the development of innovative instructional strategies to enhance student academic performance within the framework of 21st-century education.

Life Insurance Premium Calculation Using Markov Chain for Hypertension Patients in Indonesia

Fenni Kurnia Mutiya, Marsika Sepyanda — Thu, 30 Apr 2026 00:00:00 +0000

Long-term care insurance provides death benefits if the insured dies and benefits for medical care costs during the coverage term. One of the products of this insurance is the Annuity Rider, as the Benefit can be modelled with a multi-state model. This paper discusses the calculation of annual premiums with Annuity riders as a Benefit product using a multi-state model for hypertension patients in Indonesia. The premium calculation also utilised Markov Chain transition probabilities. The data used in the Report Survey Kesehatan Indonesia in 2023. The case study was conducted on a 40-year-old male in good health, with LTC insurance coverage for 5 years. It was known that the compensation amount for someone who died was IDR 200,000,000, and the interest rate was 7%. By calculating premiums using the multi-state model, the results yielded an annual premium of IDR 6,486,998. The result of this premium calculation is that the older someone is when they take out insurance, the greater the annual net premium they must pay.

Numerical Investigation for Deterministic Hepatitis B Model using Adomian Decomposition Method

Muhammad Rifki Nisardi, Muh. Nursyam Siduppa, A. Ika Putriani, Nur Rahmi — Thu, 30 Apr 2026 00:00:00 +0000

Numerical solutions are an essential approach to addressing dynamical system problems involving differential equations. This study focuses on solving a modified SITR model for the spread of Hepatitis B using the Adomian Decomposition Method (ADM) to obtain numerical solutions. The advantage of ADM lies in its efficiency and reliability in solving nonlinear problems without requiring linearization. The obtained solutions are presented as polynomial approximations for each compartment in the model. MAPLE software is employed as the primary instrument to implement ADM and perform numerical simulations. The analysis includes examining the behaviour of susceptible, infected, treated, and recovered populations over time. The implications of this study suggest that ADM-based numerical approaches can be a valuable tool for policymakers and health practitioners in predicting disease dynamics and supporting the development of effective intervention strategies for Hepatitis B.

Model Analysis Queue Theory in Fast Food Restaurants in Padang City

Vita Vidayati, Ayu Wulandari, Ira Selvia, Nadiyatul Ghina — Thu, 30 Apr 2026 00:00:00 +0000

Queuing systems represent service processes in which customers wait due to limited service resources. Analysing such systems is essential to ensure efficient service and minimise waiting time. This study aims to examine the queuing system applied at Hokben Sawahan Padang by analysing customer arrival and service rates to determine the appropriate model and system characteristics. A quantitative method was used, with primary data collected through direct observation of arrival and service times. The results indicate that the appropriate model is (M/M/1) with a FIFO discipline. The average number of customers waiting in line (Lq) is 0.52 customers per minute, while the average number in the system (L) is 1.03 customers per minute. The average time spent in the system (W) is 4.9 minutes, and the average waiting time before service (Wq) is 2.4 minutes. The server utilisation level is 50.62%, with an idle rate of 49.38%. These findings suggest that the queuing system is relatively efficient and can be categorised as quite ideal. However, further improvements are needed to increase server utilisation and service effectiveness. Enhancing service quality, cleanliness, comfort, and overall operational performance can improve customer satisfaction and business profitability. The study implies that queue performance indicators, such as waiting time and utilisation rate, can serve as important managerial tools for evaluating and optimising service operations.

Nonparametric Fourier Series Regression for Unemployment Analysis in Banten Province

Bunga Miftahul Barokah, Fadhilah Fitri, Chairina Wirdiastuti — Thu, 30 Apr 2026 00:00:00 +0000

The Open Unemployment Rate (OUR) is a vital indicator of regional economic performance, particularly in Banten Province, which faces disparities in education and poverty. This study models the unemployment rate using two predictors: average years of schooling and poverty level, through a nonparametric Fourier series regression for the 2017–2024 period. This method provides greater flexibility in capturing the nonlinear and fluctuating patterns often observed in socio-economic data. The analysis used secondary data from Statistics Indonesia (BPS), beginning with descriptive statistics and data visualization. Models were evaluated using Generalized Cross-Validation (GCV) and the coefficient of determination (R²). The optimal model was found at K = 3, with a GCV of 2.4057 and an R² of 0.5155. The model effectively captured the non-linear relationships between unemployment, education, and poverty. Although the R² value is moderate, this indicates that including additional explanatory variables could enhance the model’s performance. These findings support the use of Fourier series regression as an alternative approach for labor market analysis, especially when linear methods fall short and provide insights for developing more targeted employment policies.

Analysis of Students' Errors Based on Newman's Errors in Solving Mathematical Reasoning Problems

Redy Williantama Zulhafendi, Yerizon Yerizon, Fitrani Dwina, Shinta Sari — Thu, 30 Apr 2026 00:00:00 +0000

Mathematical reasoning is one of the essential competencies that students must possess to face the challenges of 21st-century learning. However, many students still struggle to solve problems that assess their mathematical reasoning. This study aims to analyse the types of errors students make using Newman’s Error Analysis procedure. The research employed a descriptive qualitative method, with 37 twelfth-grade high school students selected through purposive sampling. Data were collected through a mathematical reasoning ability test and interviews. The quantitative data from the test were analysed descriptively to identify error patterns, while the qualitative data from interviews were analysed thematically through data reduction, data display, and conclusion drawing. Most students made errors in three main stages, namely understanding the problem concept, transforming verbal information into appropriate mathematical representations, and applying mathematical procedures or algorithms correctly. Furthermore, the analysis showed that conceptual misunderstanding was the most prevalent type of error, often leading to subsequent transformation and process-skill errors. These findings suggest that teachers need to design learning interventions that strengthen conceptual comprehension and develop students’ systematic problem-solving strategies.

The Impact of Math Walks on Enhancing Mathematical Fluency in Elementary Students

Büşra Usluoğlu, Veli Toptaş — Thu, 30 Apr 2026 00:00:00 +0000

Mathematical fluency encompasses not only paper-and-pencil operations but also skills supported through games, activities, and real-life experiences. Math walks are experiential learning activities that enable students to explore mathematical concepts beyond the classroom by connecting movement, the environment, and problem-solving. This study aimed to examine the effects of math walk activities developed for fourth-grade primary school students on their mathematical fluency skills. A mixed-methods design was employed in the study. Quantitative data were obtained through a single-group pretest–posttest design administered to 20 students. In contrast, qualitative data were collected using semi-structured interviews to explore students’ views regarding the implementation process. The findings revealed a statistically significant improvement in students’ overall mathematical fluency scores following the math walk activities (p < .05), particularly in procedural, conceptual, and game-based fluency dimensions, whereas improvement in digital fluency remained limited. The results indicate that math walks provide an effective learning environment that supports the development of mathematical fluency by promoting active participation and real-life mathematical engagement. The study suggests integrating math walk activities into mathematics curricula and expanding activity-based approaches that foster mathematical fluency in elementary education.

Evaluation of Mathematics History Learning: Improving Students' Journal Writing and Presentation Skills for Publication

Vivekanantharasa Raveenthiran, Hafizatunnisa Hafizatunnisa — Thu, 30 Apr 2026 00:00:00 +0000

The History of Mathematics Learning course is often taught theoretically and descriptively, thus not fully encouraging students to develop applicable academic skills, particularly in scientific writing and publication. In fact, scientific journal publication is an important indicator in strengthening students' academic literacy. This study aims to evaluate the effectiveness of a project-based learning program for scientific journal writing and presentation in improving students' academic competencies. The method used is a qualitative approach with a program evaluation design based on the CIPP (Context, Input, Process, and Product) model. The study subjects comprised 57 students in the Mathematics Education Study Program who were taking the History of Mathematics Learning course. The instruments used consisted of interview guidelines, observation sheets, and documentation of student articles. Data analysis was conducted qualitatively through thematic analysis and document analysis techniques. The results show that this program is relevant to students' academic needs, supported by good resource readiness, and implemented systematically through a cycle of presentations and revisions that build a scientific culture. The scientific articles produced by students showed a significant quality improvement, with the majority successfully submitted to SINTA-indexed national journals. These findings suggest that integrating scientific journal writing into mathematics history courses not only enhances students’ critical thinking and academic literacy but also helps prepare future educators for scholarly publication, highlighting broader implications for mathematics education.

Analysis of Nonlinear Oscillation Models with External Forcing Using the Multiple Scales Method

Ayuni Kemala Safira, Aminatus Sa’adah, Rani Sulvianuri, Yoli Agnesia — Thu, 30 Apr 2026 00:00:00 +0000

Nonlinear effects accompanied by external forces can cause the behaviour of the system to become more complex and difficult to explain using linear analysis. Therefore, analytical methods are needed to obtain approximate solutions. This paper presents an analysis of approximate solutions to nonlinear oscillation models subject to periodic external forces. The analysis was conducted using the Multiple Scales Method, a perturbation technique for obtaining asymptotic solutions to nonlinear differential equations. This approach is carried out by introducing several time scales and developing solutions as series in ε. The differential equations that model the system are analysed to orders. and to obtain approximate solutions that describe the oscillation dynamics of the system. The analysis was performed under two main conditions: when the external force frequency approached the system's natural frequency (main resonance) and when the two were not close. In the non-resonance condition, several special cases were also examined: non-resonant, superharmonic resonance, subharmonic resonance, and low excitation frequency. The results show that first-order asymptotic solutions agree well with numerical solutions. The system response is influenced by parameters such as the amplitude and frequency of the external force, as well as the damping parameter. These findings support further research on more complex nonlinear systems and have practical applications in the design of vibration absorbers and rotating mechanical components to control resonance and improve system stability.