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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.
Arjuna Subject : -
Articles 540 Documents
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Measuring Changes of Students’ Statistical Reasoning Taught by Ethnomathematics Approach Assisted TinkerPlots: A Stacking Analysis Study Ramadhani, Rahmi; Saragih, Sahat; Maulida, Rizki; Simanjuntak, Sinta Makito Br
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8375

Abstract

This study aims to use the Rasch model stacking analysis technique to assess students' statistical reasoning abilities in descriptive statistics learning utilizing a TinkerPlots-assisted ethnomathematics approach in Nias cultural environment. This research is a quasi-experimental study that uses pre-and post-test control group designs. The stacking technique is used to examine how students' statistical reasoning abilities change in the presence of the intervention. The sample for this study is students in the 12th year at Gunungsitoli High School in the Nias Islands, Sumatera Utara region. Students are administered an exam that consists of five essay questions. Their responses are evaluated using a rubric that incorporates diagnostic criteria and a response certainty index. The data is analyzed using the Rasch Partial Credit Model with WINTSTEPS 4.5.5. The results indicate that students in the experimental group improved their statistical reasoning abilities more than students in the control group when they used TinkerPlots-assisted ethnomathematics in Nias cultural environment (the group with an ordinary learning approach). Along with the intervention, it is discovered that changes in student learning capacities are achievable in some situations due to pupils receiving the correct response or cheating. In other circumstances, pupils who undergo negative changes may respond inappropriately due to carelessness, boredom, or misconceptions. Additionally, these findings demonstrate that some children provide correct responses following intervention on certain items. According to the findings of this study, stacking analysis approaches are critical for describing each change in student abilities as a result of each person and each item. 
On the Explicit Formula for Eigenvalues, Determinant, and Inverse of Circulant Matrices Aliatiningtyas, Nur; Guritman, Sugi; Wulandari, Teduh
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8616

Abstract

Determining eigenvalues, determinants, and inverse for a general matrix is computationally hard work, especially when the size of the matrix is large enough. But, if the matrix has a special type of entry, then there is an opportunity to make it much easier by giving its explicit formulation. In this article, we derive explicit formulas for determining eigenvalues, determinants, and inverses of circulant matrices with entries in the first row of those matrices in any formation of a sequence of numbers. The main method of our study is exploiting the circulant property of the matrix and associating it with cyclic group theory to get the results of the formulation. In every discussion of those concepts, we also present some computation remarks. 
Validity, Practicality, and Effectiveness of Ludo Cartesius Learning Media to Improve Understanding of Mathematical Concepts Sumadi, Iman Putra; Kusmayadi, Tri Atmojo; Fitriana, Laila
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8477

Abstract

Abstract mathematics learning requires media in outlining the material so that it can be well received by students. Media can help students understand and recall explanations from the teacher and test students' understanding more deeply. This research was conducted with the aim of knowing the validity of Ludo Cartesius' learning media to improve understanding of mathematical concepts in class VIII students at junior high school. This research will apply development research design with ADDIE approach developed by Robert Maribe Brach. The ADDIE stages include analysis, design, development, implementation, and evaluation. The Population in this study were all eighth grade students at junior high school. The research sample was 27 students who were taken randomly using cluster random sampling technique. The instruments used include media expert assessment sheets, material expert assessments, student and teacher response questionnaires, as well as pretest and posttest understanding of mathematical concepts. The average value of media experts from the three validators of Dokar's media is 95.61. The average value of media experts from the three validators of Dokar's media is 92.36. The results showed that the Dokar media was categorized as "very valid" in terms of media experts and material experts and this media was suitable for use in class VIII students at junior high school. Dokar media is classified as practical media based on the average percentage of student and teacher responses, namely 86.23% and 85.83%. Dokar media is an effective medium based on the t-test (paired sample t-test) p value (0.000)<α (0.05) so that the posttest score is better than the pretest.
The Effect of Susceptible Immigrants in a System Dynamic on the Spread of Malaria in Indonesia Aprianti, Euis; Jaharuddin, Jaharuddin; Nugrahani, Endar H.
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8630

Abstract

The spread of malaria is a serious public health problem, including in Indonesia. The mathematical model is formulated to describe the dynamic nature of the spread of malaria. The model used in this article is the SIR-SI model. This article discusses the stability of the fixed point analyzed using the Jacobian matrix and Routh-Hurwitz criteria, bifurcation analysis using the Castillo-Chaves and Song Theorem, and numerical simulation of the effect of the rate of susceptible immigrants on the dynamics of the malaria by using data on malaria cases in Indonesia. The results of the analysis show that the stability of the fixed point is related to the basic reproduction number determined by the next-generation matrix, and bifurcation occurs when the basic reproduction number is equal to one. The results of numerical simulations show that in order to suppress the spread of malaria, it is necessary to reduce the rate of susceptible immigrants. 
Frieze Group in Generating Traditional Cloth Motifs of the East Nusa Tenggara Province Nataliani, Yessica
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8568

Abstract

Ethnomathematics studies the relationship between mathematics and culture. Indonesia has many traditional cultures. One of them is traditional cloth. The traditional cloth from East Nusa Tenggara (NTT) province is called tenun ikat. Since the motif of tenun ikat consists of symmetrical and repeated patterns, it can be generated using Frieze groups. The Frieze groups are the plane symmetry groups of patterns whose subgroups of translations are isomorphic to Z. There are seven groups in the Frieze groups, i.e., F_1, F_2, F_3, F_4, F_5, F_6, and F_7. Translation, reflection, rotation, and glide reflection are the transformation used in the Frieze groups. In this paper, Frieze groups are used to generate digital tenun ikat motifs from the basic pattern. Since one piece of original tenun ikat may consist of some basic patterns, the basic patterns are identified first, and then each of them is generated into the desired pattern, according to the suitable Frieze groups. Furthermore, a GUI Matlab program is developed to generate the Frieze groups. Three motifs of tenun ikat are presented to demonstrate the implementation of Frieze groups. With the Frieze group, users can generate other patterns from a basic pattern, so users can generate new motifs of tenun ikat without leaving the cultural characteristics of NTT province. 
Comparing Five Machine Learning-Based Regression Models for Predicting the Study Period of Mathematics Students at IPB University Nurdiati, Sri; Najib, Mohamad Khoirun
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8408

Abstract

Grade point average (GPA) is initial information for supervisors to characterize their supervised students. One model that can be used to predict a student's study period based on GPA is a machine learning-based regression model so that supervisors can apply the right strategy for their students. Therefore, this study aims to implement and select a machine learning-based regression model to predict a student's study period based on GPA in semesters 1-6. Several regression models used are least-square regression, ridge regression, Huber regression, quantile regression, and quantile regression with l_2-regularization provided by Machine Learning in Julia (MLJ). The model is evaluated and selected based on several criteria such as maximum error, RMSE, and MAPE. The results showed that the least-square regression model gave the worst evaluation results, although the calculation method was easy and fast. Meanwhile, the quantile regression model provided the best evaluation results. The quantile regression model without regularization gives the smallest RMSE (2.31 months) and MAPE (3.56%), while the quantile regression model with l_2-regularization has a better maximum error (4.9 months). The resulting model can be used by supervisors to predict the study period of their supervised students so that supervisors can characterize their students and can design appropriate strategies. Thus, the student's study period is expected to be accelerated with a high-quality final project.
Inclusion Properties of Henstock-Orlicz Spaces Herlinawati, Elin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8618

Abstract

Henstock-Orlicz spaces were generally introduced by Hazarika and Kalita in 2021. In general, a function is Lebesgue integral if only if that function and its modulus are Henstock-Kurzweil integrable functions. Moreover, suppose a function is a finite measurable function with compact supports. In that case, the function is a Henstock-Kurzweil integrable function if only if the function is a Lebesgue integrable function. Due to these properties, Henstock-Orlicz spaces were constructed by utilizing Young functions. This definition is almost similar to the definition of Orlicz spaces, but by embedding the Henstock-Kurzweil integral, and the norm used is the Luxembourg norm. Therefore, an analysis of properties in these spaces is needed carried out more deeply. This research was using a literature study on inclusion properties from scientific journals, especially those related to the Orlicz Spaces. And based on the definition of Henstock-Orlicz spaces and its norm, we formulate a hypothesis regarding the inlcusion properties. By deductive proof, we proof the hypothesis and state it as theorem. In this study, we obtain sufficient and necessary conditions for the inclusion properties in Henstock-Orlicz spaces. 
Simulated Annealing Algorithm for Determining Travelling Salesman Problem Solution and Its Comparison with Branch and Bound Method Silalahi, Bib Paruhum; Sahara, Farahdila; Hanum, Farida; Mayyani, Hidayatul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8481

Abstract

Travelling Salesman Problem (TSP) is a problem where a person must visit some places, starting from one city and then moving on to the next city with the conditions that the places visited can only be passed precisely once and then back to the starting city. TSP is an NP-hard, an important problem in operations research. TSP problems can be solved by an exact method or an approximation method, namely the metaheuristic method. This research aims to solve the TSP problem with an approximation method called the Simulated Annealing (SA), and then compare the results of this approximation method with the exact Branch and Bound method. The results indicated that the SA method could accomplish TSP problems. However, like other metaheuristic methods, SA only accomplishes it using an approach to get good results. Still, it cannot be determined that SA has the most optimal results, but the time needed by the SA method is faster than the Branch and Bound method. In case I, the percentage difference between the distance generated using the SA method with the B-and-B method is 0%, in case II it is 7% and in case III it is 8%.  
Identifying Significant Factors Affecting the Human Development Index in East Java Using Ordinal Logistic Regression Model Farida, Yuniar; Nurfadila, Monika Refiana; Yuliati, Dian
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8301

Abstract

The achievement of human development can be reviewed from the Human Development Index (HDI), which is sourced from indicators of health, education, and state income. East Java Province is the second-most populous province in Indonesia which has a high work intensity in economic aspects and abundant natural and human resources. However, judging from the level of the human development index, East Java Province occupies the lowest position compared to other provinces on the island of Java. This study aims to identify significant factors affecting East Java's HDI using ordinal logistic regression. The data from Indonesia Statistics (Indonesian: Badan Pusat Statistik, BPS) of East Java province in 2020 includes seven variables, namely Gross Regional Domestic Product (GRDP), high school participation rate, infant mortality rate, health facilities, population density, labor force participation rate, and open unemployment rate. This study produced two ordinal logistic regression models in medium category HDI and high category HDI with a classification accuracy value of 97.37%. From this model obtained, a significant factor affecting the HDI of East Java is the participation rate of high school and health facilities.
Improving Conceptual Understanding Through STEM-Based Mathematics Learning Tonra, Wilda Syam; Syam Tonra, Winda; Ikhsan, Muhammad; Achmad, Fatoni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8682

Abstract

This study aims to improve conceptual understanding through STEM-based mathematics learning. The research method was pre-experimental research with one-group pretest-posttest design. The population is grade 8 of one of school in Ternate City. The method of sampling is random sampling. Research variable in the research, the independent variable is STEM-based learning and the dependent variable is the conceptual understanding. The validity of test that will be used in this research is content validity. Data analysis technique are descriptive and inferential. A test given to measure conceptual understanding The indicators are (1) restating a concept and providing examples, (2) Implementing specific procedures or operations, (3) Use algorithm to solve a problem. The results of the study is that students’ conceptual understanding is improving of the circle concept through STEM-based mathematics learning. The increase of conceptual understanding can be seen in the average value obtained, where for the pretest it is 40.41 then after the STEM is applied and the posttest is carried out the average value has increased to 83.73. Therefore, STEM-based mathematics learning is one of approaches that can improve conceptual understanding, and promotes the use of hands-on activities to solve problems in everyday life

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