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JTAM (Jurnal Teori dan Aplikasi Matematika)
ISSN : 25977512     EISSN : 26141175     DOI : 10.31764/jtam
Core Subject : Education,
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
Callable Bond's Value Analysis Using Binomial Interest Rate Tree Considering Early Redemption and Default Risks Kusnadi, Felivia; Tirtasaputra, Devina Gabriella
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.12125

Abstract

Bonds are known as one of low-risk investments and worth to be considered as a part of an investor's portfolio, however there are still underlying risks that could affect its price. This paper focuses on the effect of early redemption risk and default risk to a bond’s value. Using binomial interest rate tree method and its adjusted for default risk version, this paper wants to analyse how these risks affect Indonesian bonds’ values through simulations, while showing how these bonds can be used to construct the binomial interest rate trees. In the default risk simulation, more assumptions are made because of data limitations, which causes the first period recovery fraction to soar higher than the other periods. The analysis shows that, compared to present value of standard bonds, early redemption risk tends to cause the bond's present value to drop, while on the contrary, default risk tends to cause the bond's present value to rise. The cause of higher present value of bonds with default risk is explained by the high first period recovery fraction. 
Investigating Elementary School Teacher Gestures in Mathematics Teaching and Learning Nasrun, Nasrun; Syawahid, M.; Akib, Irwan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Gestures was an important in mathematics teaching and learning because it can increase student’s cognitive load. however, many teachers pay little attention to gestures in carrying out learning in class. This study aims to describe and compare the gesture of primary school teacher in mathematics teaching and learning. Qualitative of case study used in this study. Two teachers in “Islam Athirah” of elementary schools consist of one senior teacher and one prospective teacher as research subjects. Data was collected through audiovisual material and interview. The teachers were observed and recorded when performing mathematics teaching and learning. Interview were conducted with ten selected students to find out feedback from learning activity. The finding showed that pointing gesture was frequently used in mathematics teaching and learning. Furthermore, senior teacher better in performing gesture than pre-service teacher. Senior teacher has an excellence in pointing and writing gesture, while pre-service teacher has an excellence in performing representing gesture. 
Infographic Development through Instagram to Reduce Mathematics Anxiety and Increase Student Learning Outcomes Sari, Arika; Octaria, Dina; Utari, Rahma Siska; Somakim, Somakim; Hiltrimartin, Cecil; Hartono, Yusuf; Darmawijoyo, Darmawijoyo
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.12512

Abstract

Research is a descriptive research that aims to describe the product development process in the form of infographic learning media in algebra material through Instagram that is appropriate for students to use for independent learning activities. This research focuses on creating infographic media in algebra material through Instagram to reduce mathematics anxiety and improve learning outcomes. The method used in this research is development research using the Sadiman’s model. The stages in this development model are preliminary stage, prototyping stage, and final stage, which from three stages contain of nine steps, namely identification of needs, formulation of objectives, formulation of materials, formulation of success measurement tools, writing of media scripts, production, tests/trials, revisions and the final product. There were 34 students of seventh graders of junior high school participating in this study. Data was collected through interviews, observations, tests, and questionnaires. Data were analyzed quantitatively and qualitatively. The results of the validation test by experts show that 93% of infographics through Instagram as strengthening students' understanding are included in the valid category and are suitable for use in the learning process. In addition, as many as 88% of students experienced an increase in learning outcomes after learning to use infographics through Instagram which indicated that the level of student anxiety in learning mathematics had decreased.
Profile of Junior High School Students’ Symbol Sense Thinking Mutammam, Muhamad Badrul; Wulandari, Evi Novita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.12622

Abstract

Algebra is one of the mathematics materials in junior high school which is synonymous with symbols. There is a concept to assess students' sensitivity to symbols, namely symbol sense. One of the skills that must be possessed by students is thinking skills. The purpose of this study is to describe the thinking process of junior high school students from the symbol sense task. This is qualitative research. The steps in this research is (1) making instruments; (2) selecting subjects; (3) collecting data; and (4) analyzing data.The subjects in the study consisted of four ninth-grade students who had good math and communication skills. Data collection was carried out by giving symbols of sense assignments and followed by task-based interviews. The collected data was then analyzed using the stages of data collection, data condensation, data display, and drawing conclusions. The results showed that all subjects showed good thinking skills. It's just that a student is not good at drawing conclusions because he does not check the answers independently. For the ability of the sense of symbol students lack achievement in two characteristics of the symbol sense. Only two people demonstrated the "friendliness with symbol" characteristic well. This research only examines students' symbol sense thinking on two of the six characteristics of symbol sense. Other researchers can conduct research on the six characteristics of sense symbols thinking.
The Clique Number and The Chromatics Number Of The Coprime Graph for The Generalized Quarternion Group Gayatri, Marena Rahayu; Nurhabibah, Nurhabibah; Aini, Qurratul; Awanis, Zata Yumni; Salwa, Salwa; Wardhana, I Gede Adhitya Wisnu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.13099

Abstract

Graph theory can give a representation of abstract mathematical systems such as groups or rings. We have many graph representations for a group, in this study we use the coprime graph representation for a generalized quaternion group to find the numerical invariants of the graph, which are the clique number and the chromatic number. The main results obtained from this study are the clique number of the coprime graph representation for the generalized quaternion group is equal to the chromatic number of the coprime graph representation for the generalized quaternion group for each case of  the order.
Analysis Dynamics Two Prey of a Predator-Prey Model with Crowley–Martin Response Function Pratama, Rian Ade; Toaha, Syamsuddin
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.v7i3.14506

Abstract

The predator-prey model has been extensively developed in recent research. This research is an applied literature study with a proposed dynamics model using the Crowley–Martin response function, namely the development of the Beddington-DeAngelis response function. The aim of this research is to construct a mathematical model of the predator-prey model, equilibrium analysis and population trajectories analysis. The results showed that the predator-prey model produced seven non-negative equilibrium points, but only one equilibrium point was tested for stability. Stability analysis produces negative eigenvalues indicating fulfillment of the Routh-Hurwitz criteria so that the equilibrium point is locally asymtotically stable. Analysis of the stability of the equilibrium point indicates stable population growth over a long period of time. Numerical simulation is also given to see the trajectories of the population growth movement. The population growth of first prey and second prey is not much different, significant growth occurs at the beginning of the growth period, while after reaching the peak the trajectory growth slopes towards a stable point. Different growth is shown by the predator population, which grows linearly with time. The growth of predators is very significant because predators have the freedom to eat resources. Various types of trajectory patterns in ecological parameters show good results for population growth with the given assumptions.
The Ideal Over Semiring of the Non-Negative Integer Adillah, Aisyah Nur; Hasnani, Fitriana; Fatimah, Meryta Febrilian; Puspita, Nikken Prima
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.v7i3.14997

Abstract

Assumed that (S,+,.) is a semiring. Semiring is a algebra structure as a generalization of a ring. A set I⊆S is called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I for every s in semiring S.  Based on this definition, there is a special condition namely prime ideal P, when for any αβ∈P, then we could prove that α or β are elements of ideal P. Furthermore, an ideal I of S is irreducible if Ia is an intersection ideal from any ideal A and B on S, then I=A or I=B. We also know the strongly notion of the irreducible concept. The ideal I of S is a strongly irreducible ideal when I is a subset of the intersection of A and B (ideal of S), then I is a subset of A, or I is a subset of B. In this paper, we discussed the characteristics of the semiring of the non-negative integer set. We showed that pZ^+ is an ideal of semiring of the non-negative integer Z^+ over addition and multiplication. We find a characteristic that 〖pZ〗^+  is a prime ideal and also a strongly irreducible ideal of the semiring Z^+ with p is a prime number.
Differences in Students' Algebraic Thinking in Online and Offline Learning Abdillah, Abdillah; Mastuti, Ajeng Gelora; Kasliyanto, Kasliyanto; Buamona, Rasna
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.v7i3.13916

Abstract

Mathematics teachers still have to create their creativity in online and offline learning. Therefore, mathematics teachers must pay attention to the assignments given to their students. One of the higher-order thinking skills that teachers must consider is algebraic thinking. This study aims to describe students' algebraic thinking as impact of online and offline learning. Researchers want to see the difference in algebraic thinking between students who are given online mathematics learning and students who are given offline mathematics learning. This study uses a qualitative research approach. Participants in this study consisted of 30 students taken from 2 junior high schools taken in the city of Ambon. The research procedure carried out in this research process is the stage of giving questions and thinking hard, as well as the interview stage. The interview guide was made based on indicators of algebraic thinking (Herbert & Brown, 1997). The results showed that the algebraic thinking skills of students who were subjects of online learning were said to be incomplete because they experienced construction holes at the stage of looking for patterns and generalizations. In contrast, students who were subjects of offline learning had complete algebraic thinking according to the algebraic thinking process.
Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula Budiarti, Retno; Intansari, Kumala; Purnaba, I Gusti Putu; Septyanto, Fendy
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.v7i3.15109

Abstract

Quantifying dependence among variables is the core of all modelling efforts in financial models. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. The COVID-19 pandemic is an extreme event that has caused the collapse of various economic activities which resulted in the decline of stock prices. The modelling of extreme events is therefore important to mitigate huge financial losses. Extreme-value copula can be suitable to quantify dependencies among assets under an extreme event. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data. This model was applied in the portfolio of the IDX Composite Index (IHSG), Straits Times Index (STI) and Kuala Lumpur Stock Exchange (KLSE). Each individual asset return is modelled by the ARMA-GARCH and the joint distribution is modelled using extreme value copulas. This empirical study showed that Gumbel copula is the most appropriate extreme value copulas for the three indices. The results of this study are expected to be used as a basis for investors in the formation of a portfolio consisting of 2 financial assets and a portfolio consisting of 3 financial assets. 
Mathematical Reasoning Ability of Male and Female Students in Problem Base Learning Negara, Habibi Ratu Perwira
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.v7i3.15023

Abstract

Considering the objectives and standards of the mathematics learning process, mathematical reasoning is an ability that students are expected to have. Nonetheless, the mathematical reasoning abilities of Indonesian students are still inadequate, and learning resources are still inadequate. The researcher then tries to solve it by combining the problem-based learning (PBL) paradigm with the use of GeoGebra in the classroom. The aim of this research is to identify and analyze the effect of GeoGebra and Gender-assisted problem-based learning (PBL) models on students' mathematical reasoning abilities. The study involved 35 students of XI State Senior High School at one of the schools in Mataram City. The research instrument used a mathematical reasoning ability test consisting of five essay questions. The study applied a one-group pretest-posttest design to observe the increase in students' mathematical reasoning abilities. Mathematical reasoning ability tests were given before and after the implementation of the GeoGebra-assisted PBL model. Data analysis used descriptive statistics, paired t-tests, and independent t-tests. The results of the analysis show that improving students' mathematical reasoning abilities can be done by applying the GeoGebra-assisted PBL model in the classroom. Observation of the psychological aspects of Gender showed significant results in students' mathematical reasoning abilities.