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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 7, No 3 (2023): July" : 25 Documents clear
Topological Indices of the Relative Coprime Graph of the Dihedral Group Syarifudin, Abdul Gazir; Santi, Laila Maya; Faradiyah, Andi Rafiqa; Wijaya, Verrel Rievaldo; Suwastika, Erma
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14913

Abstract

Assuming that G is a finite group and H is a subgroup of G, the graph known as the relative coprime graph of G with respect to H (denoted as Γ_(G,H)) has vertices corresponding to elements of G. Two distinct vertices x and y are adjacent by an edge if and only if (|x|,|y|)=1 and x or y belongs to H. This paper will focus on  finding the general formula for some topological indices of the relative coprime graph of a dihedral group. The study of topological indices in graph theory offers valuable insights into the structural properties of graphs. This study is conducted by reviewing many past literatures and then from there we infer a new result. The obtained outcomes will include measurements of distance, degree of vertex, and various topological indices such as the first Zagreb index, second Zagreb index, Wiener index, and Harary index that are associated with distance and degree of vertex.
Students’ Visual Reasoning Ability in Solving Quadratic Function in Terms of Learning Style Masduki, Masduki; Savitri, Dhea; Khotimah, Rita Pramujiyanti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.13547

Abstract

Visual reasoning plays an important role in problem-solving and the success of the student’s learning mathematics. This study aims to reveal the students’ visual reasoning ability in solving quadratic function problems in terms of activist, reflector, and pragmatic learning styles. This research used a qualitative approach with a case study were 30 9th-Grade students at one of the public junior high schools in Karanganyar District, Central Java, Indonesia. The Learning Style Questionnaire (LSQ) from Honey and Mumford was used to categorize the students’ learning style. In each category, the researcher selected two students purposively to be interviewed. The researchers used two quadratic equation problems to explore the students’ visual reasoning profile. Before being used, the questions were validated by two experts in mathematics education. The result showed that students with activist learning styles unable to demonstrate all indicators of visual reasoning. The students with pragmatics learning style can exhibit only one indicators of reasoning, namely interpretation. Then, students with reflector and theoretical learning style able to perform all indicators of visual reasoning. Thus, it can be concluded that the student’s learning style affect the visual reasoning ability in solving quadratic function.
Confidence Interval for Variance Function of a Compound Periodic Poisson Process with a Power Function Trend Irawan, Ade; Mangku, I Wayan; Budiarti, Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14836

Abstract

This research is a follow-up research of Utama (2022) on asymptotic distribution of an estimator for variance function of a compound periodic Poisson with the power function trend. The objectives of this research are (i) to formulate a confidence interval for the variance function of a compound periodic Poisson process with a power function trend and (ii) to prove the convergence to 1-α probability of the parameter included in the confidence interval. This research process begins with a review of the existing formulation of the variance function estimator and its asymptotic distribution. Next, the confidence interval for the variance function of the compound periodic Poisson process with a power function trend is formulated and the convergence to 1-α is determined. After obtaining the confidence interval, the research continued by conducting computer simulations to confirmed the results obtained analytically. The results obtained show that the confidence interval for the variance function of a compound periodic Poisson process with a power function trend converges to 1-α both analytically and numerically for different finite time intervals.
RME Based Audiobook Development for Class IV Elementary School Students Sari, Arissona Dia Indah; Herman, Tatang; Sopandi, Wahyu; Jupri, Al
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15074

Abstract

Learning mathematics at the Elementary School (SD) level is an important basis in building a good understanding of mathematical concepts in students. However, students often experience difficulties in understanding abstract and complex mathematical concepts. This can have an impact on reducing students' interest in learning mathematics. To overcome this problem, an audiobook based on RME (Realistic Mathematics Education) was developed which emphasizes the quality of sound recordings that are close to the experience of listening to voices directly, especially for mathematics materials at the elementary level. The research method used in this study is a research and development approach using the ADDIE model developed by Robert Maribe Branch. The ADDIE model is a development model consisting of five stages, namely analysis, design, development, implementation, and evaluation. The results of the study show that audiobooks based on RME are valid and can be implemented in learning. Based on these results, the RME-based audiobook is ready to be implemented on a large scale and used as an effective alternative learning media in increasing conceptual understanding and interest in learning mathematics for fourth grade elementary school students in multiplication material.
Biclustering Performance Evaluation of Cheng and Church Algorithm and Iterative Signature Algorithm Sumertajaya, I Made Sumertajaya; Ningsih, Wiwik Andriyani Lestari; Saefuddin, Asep; Rohaeti, Embay
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14778

Abstract

Biclustering has been widely applied in recent years. Various algorithms have been developed to perform biclustering applied to various cases. However, only a few studies have evaluated the performance of bicluster algorithms. Therefore, this study evaluates the performance of biclustering algorithms, namely the Cheng and Church algorithm (CC algorithm) and the Iterative Signature Algorithm (ISA). Evaluation of the performance of the biclustering algorithm is carried out in the form of a comparative study of biclustering results in terms of membership, characteristics, distribution of biclustering results, and performance evaluation. The performance evaluation uses two evaluation functions: the intra-bicluster and the inter-bicluster. The results show that, from an intra-bicluster evaluation perspective, the optimal bicluster group of the CC algorithm produces bicluster quality which tends to be better than the ISA. The biclustering results between the two algorithms in inter-bicluster evaluation produce a deficient level of similarity (20-31 percent). This is indicated by the differences in the results of regional membership and the characteristics of the identifying variables. The biclustering results of the CC algorithm tend to be homogeneous and have local characteristics. Meanwhile, the results of biclustering ISA tend to be heterogeneous and have global characteristics. In addition, the results of biclustering ISA are also robust.
Creativity Profile of Students in Constructing Mathematics Learning Media Hidayati, Wiwin Sri; Tristanti, Lia Budi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15223

Abstract

Students must be equipped with creativity as a 21st century skill. The research objective was to obtain a profile of student creativity in constructing learning media. The method used is observation and in-depth interviews. The researcher is the main instrument and observation guide and interview guide as a supporting instrument. The research subject was one of the students of the mathematics education study program taking the mathematics learning media course. The results of student creativity research, namely the subject of creating new ideas in constructing different mathematics teaching aids, using the basic concepts of multiplication and division of positive integer operations that are formed on boards and there is a touch of technology in the form of lights and barcodes. Subjects apply creative ideas as real contributions in the form of the KoKagi Ke Wort demonstration tool. The creative idea is evident in the use of lights and barcodes that can be copied using a smartphone, so that learning videos and material on prime numbers can be displayed through the LCD projector. Learning videos and practice questions for studying at home via can also be accessed via the link from the barcode.
Prime Graph over Cartesian Product over Rings and Its Complement Fatimah, Farah Maulidya; Krisnawati, Vira Hari; Hidayat, Noor
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14987

Abstract

Graph theory is a branch of algebra that is growing rapidly both in concept and application studies. This graph application can be used in chemistry, transportation, cryptographic problems, coding theory, design communication network, etc. There is currently a bridge between graphs and algebra, especially an algebraic structures, namely theory of graph algebra. One of researchs on graph algebra is a graph that formed by prime ring elements or called prime graph over ring R. The prime graph over commutative ring R (PG(R))) is a graph construction with set of vertices V(PG(R))=R and two vertices x and y are adjacent if satisfy xRy={0}, for x≠y. Girth is the shortest cycle length contains in PG(R) or can be written gr(PG(R)). Order in PG(R) denoted by |V(PG(R))| and size in PG(R) denoted by |E(PG(R))|. In this paper, we discussed prime graph over cartesian product over rings Z_m×Z_n and its complement. We focused only for m=p_1, n=p_2 and m=p_1, n=〖p_2〗^2, where p_1 and p_2 are prime numbers. Then, we obtained some properties related to order and size, degree, and girth. We also observe some examples. Moreover, we found that a correction in the statement of (Pawar & Joshi, 2019) about the complement graph over prime graph over a ring and gave a counter example for that. 
Analysis of the Student Numerical Literacy in Completing the Division Count and Multiplication Operation of the 6th Grade Elementary School Round Number Triwahyuningtyas, Dyah; Hanum, Abdila Ayu Hanna Mulya; Suastika, I Ketut; Sesanti, Nyamik Rahayu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.13555

Abstract

The background of this study is that students are unable to solve the problems and problems of daily life and which of the students associated with literacy, are unable to think critically and be able to reason in understanding the concept of division operations and multiplication integers. The aim of this study was to describe numerical literacy in the division and multiplication operations of integers in 6th grade elementary school. Research type use descriptive with a qualitative approach. Research instrument consist of interview instrument, observation instrument, and test subject. Research has found no significant obstacle, the study subject can complete most numerical literacy components on the test issue. Research subjects has not been able to dominate numerical literacy of patterns and statistic intact, but some of the components appearing on the subject have not been fully resolved.
Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers Agustito, Denik; Kuncoro, Krida Singgih; Istiqomah, Istiqomah; Hendriyanto, Agus
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15039

Abstract

The purpose of this paper is to introduce the idea of how to construct transfinite numbers and study transfinite arithmetic. The research method used is a literature review, which involves collecting various sources such as scientific papers and books related to Cantorian set theory, infinity, ordinal or transfinite arithmetic, as well as the connection between infinity and theology. The study also involves constructing the objects of study, namely ordinal numbers such as finite ordinals and transfinite ordinals, and examining their arithmetic properties. The results of this research include the methods of constructing both finite and transfinite ordinal numbers using two generation principles. Both finite and transfinite ordinal numbers are defined as well-orderings that are also transitive sets. Arithmetic of finite ordinal numbers is well-known, but the arithmetic of transfinite ordinal numbers will be introduced in this paper, including addition, multiplication, and exponentiation.
Learning Media Recommendations and Criteria for the Validity of Junior High School Mathematics Learning Media Books Sripatmi, Sripatmi; Azmi, Syahrul; Junaidi, Junaidi; Wulandari, Nourma Pramestie; Lu’luilmaknun, Ulfa
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14907

Abstract

The low quality of education and the achievement of school accreditation, where one of the assessed aspects is the learning process that should be technology-based, demand teachers to develop instructional media.This research aims to develop reference books and obtain mathematical learning media criteria for junior high school. The research method used is Design Research. Research steps are identification and analysis of problems, drafting prototypes, testing prototypes, and improvements. Research is carried out by reviewing the theories, research results, then developing a learning media reference book that will be used as a teacher's guide in developing mathematics learning media for junior high school. The book that has been developed is further validated by three experts in the field of mathematical learning media. validator consists of lecturers and mathematics teachers for junior high school. The conclusion of this study is that interactive learning is the right learning medium in mathematics learning. Some interactive media that affect math learning outcomes are interactive powerpoints, learning videos, and geogebra media. for the development of learning media, a mathematics learning media reference book was developed for junior high school. References have valid criteria on aspects of the material, language, presentation of materials, and infographics.This research aims to develop reference books and establish criteria for mathematical learning media for junior high school. The research method used is Design Research, which involves the following steps: problem identification and analysis, prototype drafting, prototype testing, and improvement. The research is conducted by reviewing theories and research findings, followed by the development of a learning media reference book that will serve as a teacher's guide for creating mathematics learning media for junior high school. The developed book is then validated by three experts in the field of mathematical learning media, including lecturers and mathematics teachers for junior high school. The conclusion of this study is that interactive learning is an effective medium for mathematics education. Some interactive media that have an impact on math learning outcomes include interactive PowerPoints, instructional videos, and Geogebra. To further enhance the development of learning media, a mathematics learning media reference book has been created specifically for junior high school. This reference book meets valid criteria in terms of material aspects, language usage, presentation of content, and infographics.

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