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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 540 Documents
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The (Strong) Rainbow Connection Number of Join Of Ladder and Trivial Graph Kartika, Dinda; Febrian, Didi; Surbakti, Nurul Maulida
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.11704

Abstract

Let G = (V,E) be a nontrivial, finite, and connected graph. A function c from E to {1,2,...,k},k ∈ N, can be considered as a rainbow k-coloring if every two vertices x and y in G has an x- y path. Therefore, no two path's edges receive the same color; this condition is called a “rainbow path”. The smallest positive integer k, designated by rc(G), is the G rainbow connection number. Thus, G has a rainbow k-coloring. Meanwhile, the c function is considered as a strong rainbow k-coloring within the condition for every two vertices x and y in G have an x - y rainbow path whose length is the distance between x and y. The smallest positive integer k, such as G, has a strong rainbow k-coloring; such a condition is called a strong rainbow connection number of G, denoted by src(G). In this research, the rainbow connection number and strong rainbow connection number are determined from the graph resulting from the join operation between the ladder graph and the trivial graph, denoted by rc(L_n∨K_1) and src(L_n∨K_1) respectively. So, rc (L_n∨K_1 )= src (L_n∨K_1 )=2,"for" 3≤n≤4 and rc (L_n∨K_1 )=3, while src(L_n∨K_1 )=⌈n/2⌉,"for" n≥5. 
Development of Malay Deli Songket Motifs Based on Symmetry Groups Mingka, Rizka Annisa; Kartika, Dinda; Suwanto, Fevi Rahmawati
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10279

Abstract

One of the tribes in North Sumatra Province that has a wide variety of art is the Deli Malays, especially the Songket motifs. Songket is a type of traditional Indonesian weaving that should be preserved to maintain Indonesia’s wealth. The motifs in the Malay Deli Songket can be analyzed because of its symmetrical pattern. In this study, the author developed the Malay Deli Songket motif based on the concept of the symmetry group. The motif development was carried out with the Matlab program based on the frieze group pattern and the crystallography group pattern. The Frieze pattern, often called the Frieze Group, is a symmetry group created from one-way translation, forming a linear pattern that repeats one way. The crystallography group has 17 crystallographic patterns formed by a specific transformation from each type of unit lattice. Through the development of motifs, 6 new Songket motifs were obtained based on the Frieze pattern in 11 observed Malay Deli Songket motifs, namely the Moon Orchid motif, the Orchid motif, the Balong Ayam motif, the Coffee Flowers motif, the Tobacco Leaves 1 and 2 motifs, the Corn motif, the Paddy motif, the Tampuk Manggis motif, the Tobacco motif, and the Ulam Raja motif. In 4 previously observed Malay Deli Songket motifs, 11 new Songket motifs were obtained for crystallography patterns: the Deli Tobacco Leaves motif, the Coffee motif, the Tampuk Gelugor motif, and the Undang Kupu-Kupu motif. 
Percentile Bootstrap Interval on Univariate Local Polynomial Regression Prediction Mansyur, Abil; Simamora, Elmanani; Ahmad, Ahmad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.11752

Abstract

This study offers a new technique for constructing percentile bootstrap intervals to predict the regression of univariate local polynomials. Bootstrap regression uses resampling derived from paired and residual bootstrap methods. The main objective of this study is to perform a comparative analysis between the two resampling methods by considering the nominal coverage probability. Resampling uses a nonparametric bootstrap technique with the return method, where each sample point has an equal chance of being selected. The principle of nonparametric bootstrapping uses the original sample data as a source of diversity in contrast to parametric bootstrapping, where the variety comes from generating a particular distribution. The simulation results show that the paired and residual bootstrap interval coverage probabilities are close to nominal coverage. The results showed no significant difference between paired bootstrap interval and percentile residual. Increasing the bootstrap sample size sufficiently large gives the scatterplot smoothness of the confidence interval. Applying the smoothing parameter by choice gives a second-order polynomial regression with a smoother distribution than the first-order polynomial regression. The scatterplot shows that the second-degree polynomial regression can capture the data curvature feature compared to the first-degree polynomial. The bands made from second-degree polynomials give a narrower width than first-degree polynomials. In contrast, applying optimal smoothing parameters to the model provides different conclusions by using smoothing parameters based on choice. In addition to the differences based on the scatterplot, the bootstrap estimates of the coverage probability are also other. Selecting smoothing parameters based on a particular value provides probability coverage with the paired bootstrap method for the first-degree local polynomial regression is 0.93, while the second-degree local polynomial is 0.96. The probability of coverage based on the residual bootstrap method for the first-degree local polynomial regression is 0.95, while the second-degree local polynomial is 0.96. The probability coverage based on the optimal parameters of the paired bootstrap method for the first-degree local polynomial regression is 0.945, while the second-degree local polynomial is 0.93. The residual bootstrap method gives the first-degree local polynomial regression of 0.95, while the second-degree local polynomial is 0.93. In general, both bootstrap methods work well for estimating prediction confidence intervals.
The Development of Project Based Learning Module for Vocational High Schools to Improve Critical Thingking Skills Baidowi, Baidowi; Arjudin, Arjudin; Novitasari, Dwi; Kertiyani, Ni Made Intan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.11806

Abstract

Critical thinking is one of the skills needed by vocational high school students in the world of work and has a positive impact on students' fieldwork practices. Therefore the aim of this research is to produce a mathematics module focused on critical thinking skills using a project-based learning model. Thiagarajan's 4D development model, namely define, design, develop, and dissemination, is used in this research and development model. Validation tests, questionnaires, observations, interviews, and critical thinking tests were used to collect data. Data analysis was carried out quantitatively and qualitatively. Quantitative analysis uses descriptive statistical tests and T-tests while qualitative analysis comes from suggestions and input from media experts, materials, practitioners, teachers, and students. The results showed that: (1) the mathematics module for grade 11th vocational high school met valid criteria based on the assessment of material experts, media experts, practitioners, teachers, and students; and (2) with a sig score of 0.000 from the T-test, students who took the module these have better critical thinking skills than those who don't. So that this module can be classified as effective for use in learning. This indicates that this module meets the requirements for use in learning.
Mathematical Model of the Central Lombok Regency People’s Interest towards the COVID-19 Vaccination Himmah, Elok Faiqotul; Riana, Riana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10310

Abstract

The COVID-19 vaccination program as an effort to prevent COVID-19 infection is still less attractive to the public in some areas in Indonesia, one of which is Central Lombok Regency. This is indicated by data on the number of complete vaccine recipients who still have not reached the threshold value for the formation of herd immunity. The factors that influence people's interest in COVID-19 vaccination can be analyzed using a mathematical model. This study aims to obtain a mathematical model of the interest of the people of Central Lombok Regency towards COVID-19 vaccination and to find out what factors most influence the interest of the people of Central Lombok Regency towards COVID-19 vaccination. The method used in this research is quantitative descriptive method. The data collection technique used a questionnaire that was given randomly to 332 respondents, namely the people of Central Lombok Regency in the age range of 12 to 70 years. Data analysis was based on multiple linear regression analysis with classical assumption tests, namely normality, multicollinearity, and heteroscedasticity tests. The results of the study obtained a mathematical model of the interest of the people of Central Lombok Regency towards COVID-19 vaccination. Variable of trust in the vaccine effectiveness and trust in the government are the factors that influenced the interest of the people of Central Lombok Regency towards COVID-19 vaccination.
Employing Nearpod as a Resource to Encourage Active Students in BYOD Mathematics Learning Model Yanuarto, Wanda Nugroho; Setyaningsih, Eka; Amri, Khofifatul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.11864

Abstract

In the period of the last few decades, more complex technology have been integrated into our daily lives. Therefore, teachers are advocating that students BYOD (bring your own device). This aims are investigated the activities of students during the lesson, which enables teachers to evaluate their students' progress in learning. In addition to this, students' learning experiences and raise their levels of satisfaction with their education with Nearpod and the dynamic interaction that occurs between them. Descriptive statistics were used for the analysis. Descriptive data for the questions and items were compiled in Excel, and included frequency, percentage, mean, and standard deviation. The goal of this research is to explore how female students feel about using Nearpod in conjunction with a video-conferencing learning system on a Bring Your Own Device (BYOD) learning platform. This study was conducted at Universitas Muhammadiyah Purwokerto (n = 78 students) and Purwokerto Secondary School in Central Java (n = 83 students and 9 teachers), during the even semester of the 2020/2021 school year. The objectives of this study required the development and administration of a questionnaire to all of the women enrolled in the "Mathematics Education" course. Researchers concluded from their study that students are open to using their own devices in class and are willing to benefit from the affordances provided by the BYOD platform and the Nearpod to engage in active learning during lectures. Therefore, there has to be more work done by universities to figure out which of the growing elements of education should be prioritized in order to create the best possible conditions for instruction and learning. 
Application of Markov Chain to Prediction Poverty in Banten Province Ningsi, Besse Arnawisuda; Putri, Dinda Novianda
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10057

Abstract

The number of poor people in Banten Province is in the third lowest position in Java Island under the Special Region Province of the Capital Jakarta and Yogyakarta Special Region Province in 2018-2020 until finally it is in the second lowest position in 2021. However, this does not mean that the problem of poverty is no longer a top priority. This study aims to apply the Markov chain in predicting poverty in Banten Province. According to Marli et al. (2018) The Markov chain is a method that studies the properties of a variable in the present based on its past properties to estimate the properties of these variables in the future. In this research, the type of research used is applied research and used secondary data sourced from the Central Statistics Agency (BPS) Banten Province. The poverty prediction results for Pandeglang Regency in 2022, 2023 and 2024-2025 will increase by 2%, 0.46%, and 0.02%, respectively. Lebak Regency in 2022 will increase by 2%, in 2023 and in 2024-2025 it will decrease by 0.66% and 0.01%, respectively. Tangerang Regency in 2022 will decrease by 4%, in 2023 it will increase by 0.99%, and will fall back in 2024-2025 by 0.01%. Serang Regency in 2022 will increase by 1%, in 2023-2025 it will decrease by 0.83%. Tangerang City in 2022 remains, in 2023 and 2024-2025 it will increase by 0.53% and 0.01%, respectively. The city of Cilegon in 2022 remains, in 2023 it will increase by 0.18% and 2024-2025 will decrease by 0.01%. Serang City in 2022 remains, in 2023-2025 it will decrease by 0.71%. South Tangerang City in 2022 will decrease by 1%, in 2023-2025 it will increase by 0.04%. The steady state probability of Pandeglang Regency is 17.48%, Lebak Regency is 17.33%, Tangerang Regency is 27.98%, Serang Regency is 10.17%, Tangerang City is 15.54%, Cilegon City is 2.17%, Serang City is 5.29% and South Tangerang City is 4.04%..
An η-Intuitionistic Fuzzy Rings Structure Hidayahningrum, Syafitri; Hidayat, Noor; Marjono, Marjono
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.11833

Abstract

In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research. 
Distribution Route Optimization of Zakat Al-Fitr Based on the Branch-and-Bound Algorithm Mussafi, Noor Saif Muhammad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10375

Abstract

The short interval between the collecting and distribution of zakat al-fitr is a recurring issue. As a result, ‘amil does not always pay attention to the ideal route, leading in inefficient transportation expenditures. This study aims to minimize the amount of vehicle mileage that affects fuel consumption. The branch-and-bound algorithm was employed to overcome the distribution route optimization problem by proposing the shortest circuit that traverses each district exactly once and returns to its original district. The procedures involve data collecting, graph analysis, branch-and-bound analysis, MATLAB code development, and the recommendation of the best route. The results indicate that the branch-and-bound algorithm can numerically solve the distribution route optimization corresponding to traveling salesman problem. Furthermore, according to a case study of zakat al-fitr distribution conducted by Eradication of Illiteracy Al Quran (PBHA), the total optimal distance of the computational-based algorithm was 152.9 km, with inter-village routes starting from Sidorejo and then via Sumberarum, Pendoworejo, Gerbosari, Banjaroyo, Banjarasri, Sendangagung, Tuksono, Argodadi, Triwidadi, Jatimulyo, Giripurwo, and ends in Sidorejo. 
Analogical Reasoning in Mathematical Theorems Hardiani, Nur; Kristayulita, Kristayulita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10783

Abstract

Analogical reasoning is one of the most powerful tools of mathematical thinking. For example, to prove a theorem it is necessary to see similarities with the previous theorem. This study aims to classify analogies in mathematics courses and examples. This classification is based on research results. The research was conducted use qualitative research. The research subjects are 12 lecturers who teach mathematics courses and study program managers. Analogical reasoning instruments are unstructured interview guidelines and observation sheets. Interview guides and observation sheets were made to be able to reveal mathematics analogical reasoning in the Mathematics Education Study Program course. The results of the research show that there are 3 types of analogy classifications in mathematics courses, namely definition analogy, theorem-defining analogy, and theorem analogy. First, the definition of similarity in the same or different courses. Second, the similarities between definitions and theorems in the same or different courses. Third, the theorem similarities in the same or different subjects. Our classification is related to theorems and analogical properties in several courses in the curriculum of the Mathematics Education Study Program. The analogy can be applied to certain mathematical topics related to real life. Meanwhile, to analyze other aspects of reasoning through analogy needs to be studied further.

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