Interval: Indonesian Journal of Mathematical Education

Numerical Analysis of Flow Through Venturimeter with Variation of Neck Size to Determine Velocity Coefficient and Pressure Drop

2025-05-01T19:38:32+07:00

Purpose of the study: This study aims to analyze the effect of variations in the size of the venturimeter neck on the velocity coefficient and pressure drop using a numerical simulation method.

Methodology: The method used in this study is numerical simulation using SolidWorks 2014 software. The simulated venturimeter model has a neck length variation of 20 mm and 30 mm, with a throat diameter of 10 mm. The fluid used is water with a temperature of 25°C, and the simulation is carried out in the Reynolds number (Re) range of 1000 to 5000.

Main Findings: The results of the study showed that the greater the velocity of the incoming fluid, the Reynolds number, flow rate, and pressure drop also increased. In addition, the difference in the length of the venturimeter neck affects the pressure drop, where the venturimeter with a longer neck experiences a greater pressure drop due to the longer duration of the fluid flow. The resulting velocity coefficient is also influenced by the velocity of the incoming fluid, where the higher the velocity, the greater the flow rate value.

Novelty/Originality of this study: The novelty in this research lies in the numerical approach in analyzing the relationship between the venturimeter neck size and the velocity coefficient and pressure drop. This approach allows faster and more efficient calculations compared to conventional experimental methods, thus contributing to the development of more accurate and applicable fluid flow measurement techniques.

Mathematics and Combinatorial Thinking: How Computational Ability Influences Problem-Solving in Number Patterns?

2025-05-02T14:23:26+07:00

Purpose of the study: This study aims to analyze students' computational thinking abilities in solving combinatorial problems based on high, medium, and low ability categories.

Methodology: This study uses a descriptive qualitative approach with subjects of 33 students of class VIII I State Islamic Junior High School 2 Bondowoso. Data were collected through written tests, semi-structured interviews, and documentation. Data analysis used the Miles and Huberman model (reduction, presentation, conclusion) with triangulation techniques for validation, comparing test results, interviews, and documentation.

Main Findings: Students with high and medium computational abilities are able to meet all indicators of computational thinking, including identifying and understanding problems, and converting them into combinatorics. Meanwhile, students with low abilities have difficulty in re-understanding the problems found.

Novelty/Originality of this study: This study provides new insights into how students' level of computational thinking ability influences their success in solving combinatorial problems, as well as offers perspectives in developing more effective learning strategies to enhance students' computational thinking ability.

Cultural Values and Their Role in Shaping the Adaptation of Realistic Mathematics Education (RME) in Indonesia: A Mixed-Methods Approach

2025-05-02T14:51:31+07:00

Purpose of the study: The main objective of the study is to analyze how cultural factors influence the implementation of RME in the context of mathematics education in Indonesia.

Methodology: The method used is a qualitative study employing content/document analysis of curriculum guidelines and instructional materials. Additionally, semi-structured interviews were conducted with six educators, and non-participant observations were carried out in three schools to examine the implementation of Realistic Mathematics Education (RME).

Main Findings: The results of the study showed that the success of RME adaptation was influenced by local cultural values, such as community-based approaches and the context of students' daily lives.

Novelty/Originality of this study: The novelty of this research lies in the in-depth analysis of the interaction between RME principles and Indonesian cultural characteristics, providing new insights into the development of more contextual and effective mathematics learning strategies.

Dynamic Analysis and Stability Evaluation of a Discrete Mathematical Model for Flying Fox String Vibrations

2025-05-02T15:04:38+07:00

Purpose of the study: This study aims to find the stability of changes in string deflection and the angle of string deflection when an object is launched along a flying fox.

Methodology:This study uses a model developed by Kusumastuti et al. (2017). There are two models analyzed, namely the discrete model of the string deviation y(t) and the angle of the string deviation θ(t). The analysis steps include model reduction, model discretization, model linearization, fixed point search, and stability analysis. Stability is analyzed based on the eigenvalues it has.

Main Findings:Based on the research conducted, the following eigenvalues were obtained: λ1 = -0.005h + (0.14565h)i, λ2 = -0.005h - (0.14565h)i, λ3 = -0.005h + (0.1331480769h)i, and λ4 = -0.005h - (0.1331480769h)i. The results of the study indicate that the system is in a stable condition (sink) because all eigenvalues obtained are complex numbers with negative real parts. Thus, it can be concluded that the rope deflection, rope deflection velocity, rope deflection angle, and rope deflection angular velocity are in a stable condition.

Novelty/Originality of this study: This study provides a new contribution to the understanding of discrete system dynamics in flying fox string vibrations, by showing that the stability of the system can be analyzed through the negative complex eigenvalues generated from the model.

Exploration Ethnomathematics in Traditional Games of Mancala in Africa and Congklak in Indonesia

2025-05-03T09:53:13+07:00

Purpose of the study: Study this aiming for explore draft ethnomathematics in game traditional Mancala in Africa and congklak in Indonesia use understand relatedness between culture and mathematics in context game.

Methodology: With use approach qualitative ethnography, research this collect data through observation participatory, interview in-depth, and documentation to Mancala players in Ghana and congklak in Sumatra, as well as educators at school basis. Research results show that second game this involving draft mathematics like pattern numbers, distribution strategy, operations count, and thinking logical and probable.

Main Findings: Experienced players show natural mathematical thinking through efficient strategies. While Mancala remains popular in Ghana, congklak is declining in Indonesia. Observations indicate traditional games have strong potential in culture-based math education. Thus, preservation and innovation are needed to integrate them contextually into learning.

Novelty/Originality of this study: The novelty of this research lies in the exploration of the concept of ethnomathematics in the games Mancala in Africa and congklak in Indonesia through a qualitative ethnographic approach, which has not been studied in depth.

Modeling the Spruce Budworm Population: A Numerical Approach Using Heun and Runge-Kutta Methods

2025-05-03T14:03:10+07:00

Purpose of the study: The purpose of this study is to determine the numerical solution of the spruce caterpillar model using the Heun method and the Third Order Runge-Kutta method, as well as to analyze the errors associated with both methods.

Methodology: The type of research used in this study is library research. In this study, the data will be analyzed numerically from the data entry stage, data processing and results. The results obtained are from the Heun programming method and the Runge iteration method that have been determined previously. Kutta-Order Three will produce data with the smallest error in the number of.

Main Findings:The results of the study showed the solution of the Pinus Lice model for the initial values of B(t₀) = 2, S(t₀) = 10 cm, E(t₀) = 2 cm, at t = 5 years, with h = 0.05. Using the Heun method, it was obtained that B ≈ 3, S = 14.9058 cm, and E = 1.0047 cm, while the Third Order Runge-Kutta method produced B ≈ 3, S = 14.9057 cm, and E = 1.0046 cm. The error calculation showed that the B error was smaller with the Heun method, while the S and E errors were smaller with the Third Order Runge-Kutta method.

Novelty/Originality of this study: The novelty of this study lies in the comparative analysis of the errors of the Heun Method and the Third Order Runge-Kutta Method in modeling the dynamics of spruce budworm populations with specific biological parameters.

Fun Strategies for Learning Mathematics: Exploring the Potential of Combinatorial Game Theory in Discrete Mathematics

2025-05-04T20:42:51+07:00

Purpose of the study: This study aims to examine the effectiveness of using combinatorial game theory in discrete mathematics learning to improve students' understanding and interest in learning.

Methodology: Using the Mixed Methods approach, quantitative data were collected through a quasi-experimental design with a pretest-posttest control group, while qualitative data were obtained through interviews and observations. The sample consisted of 60 grade XI students divided into experimental and control classes.

Main Findings: The results of the analysis showed that the average gain score of students' conceptual understanding in the experimental class (0.68) was significantly higher than the control class (0.32) with a t-test significance value of 0.001 (p < 0.05). In addition, the motivation questionnaire showed an increase in the average score from 2.9 to 4.1 on a Likert scale of 1–5.

Novelty/Originality of this study: Qualitative findings reinforce that game-based strategies encourage active participation, collaboration, and positive perceptions toward discrete mathematical theory.

Modification of the Fourth Order Runge Kutta Method Based on the Contra Harmonic Average

2025-05-05T12:05:25+07:00

Purpose of the Study
This study aims to modify the fourth-order Runge-Kutta method based on the contra harmonic mean. The research discusses the theoretical modification of the fourth-order Runge-Kutta method.

Methodology
The research was conducted using a literature study method. The study begins by introducing the general form of the Runge-Kutta method up to the nth order. This general form is then specialized to the fourth order. Additionally, the concept of the contra harmonic mean is introduced. After obtaining the general form of the fourth-order Runge-Kutta method and the contra harmonic mean, these two general forms are modified to derive a new formula.

Main Findings
Based on the results, the modified fourth-order Runge-Kutta method has the following equation form:
yi+1 = yi + (h/4) * [(k1^2 + k2^2) / (k1 + k2) + 2 * (k2^2 + k3^2) / (k2 + k3) + (k3^2 + k4^2) / (k3 + k4)],
with an error of order O(h^5). Numerical simulations demonstrate that the modified method provides better results compared to the original fourth-order Runge-Kutta method.

Novelty/Originality of this Study
The numerical simulations using the RKKCM method show improved accuracy compared to the unmodified fourth-order Runge-Kutta method, highlighting the innovation and contribution of this study.

Application of Adams-Bashforth-Moulton Method on Logistic Equation in Predicting Population Growth

2025-05-05T12:24:10+07:00

Purpose of the study: This study aims to obtain population growth prediction results using the Adams-Bashforth-Moulton method.

Methodology: This type of research is applied research. In this study, the Adams-Bashforth-Moulton method was applied by solving the problem of population growth in South Sulawesi Province.

Main Findings: The logistic equation for population growth with a step size of h = 1 and the capacity of South Sulawesi Province is 20,000,000 people, with a growth rate of 2%. The numerical solution of the logistic equation for population growth at time t = 2020 with an optimal step size of ℎ = 1 is 8,944,168 people.

Novelty/Originality of this study: This research is unique in the form of applying the Adams-Bashforth-Moulton method to solve problems in calculating population growth in South Sulawesi Province.