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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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Construction of Mortality Table for Credit Life Insurance using Whittaker-Henderson Graduation Method Prasetyo, Fajar Eko; Kwon, Hyuk-Sung
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.31941

Abstract

Indonesian Mortality Table III (2011) and Indonesian Mortality Table IV (2019) are still used as a reference for determining life insurance premiums, one of which is determining Credit Life Insurance premium rates. With different and more specific population and risk characteristics, it is necessary to have Mortality Table that reflects the characteristics of the Credit Life Insurance. This study is a quantitative applied study that aims to construct a specialized mortality table reflecting the unique characteristics of Credit Life insurance. First, the crude mortality rates were calculated using Microsoft Excel based on Credit Life Insurance portfolio data obtained from a life insurance company having a fairly large portfolio, during the period from 2017 to 2023. The crude mortality results were then adjusted using a smoothing technique of Whittaker-Henderson method assisted with the R program and Microsoft Excel. After obtaining the smoothed mortality rates, an extrapolation was carried out using Gompertz model assisted with the R program and Microsoft Excel to obtain the mortality rate for ages between 75 and 100 years. The extrapolated results are subsequently compared with the Indonesia Mortality Table III (IMT-III) and Indonesia Mortality Table IV (IMT-IV) to assess the consistency of mortality patterns. The main contribution of this study is the development of a more representative mortality table based on empirical data from credit life insurance portfolios, an area that has not been extensively explored. The findings of this study are expected to improve the accuracy of premium pricing, technical reserve estimation, and risk management for life insurance companies offering credit life insurance products.
Teaching Central Tendency Meaningfully: A Context-Based Trajectory using Water pH Levels Retta, Allen Marga; Putri, Ratu Ilma Indra; Zulkardi, Zulkardi; Susanti, Ely
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32160

Abstract

This study aims to design a contextual learning trajectory using water pH as an anchor to help student’s understand central tendency concepts, including mean, median, and mode. The research employed a design research approach within a qualitative descriptive framework, consisting of three main stages: preliminary design, design experiment, and retrospective analysis. In the preliminary design stage, a Hypothetical Learning Trajectory (HLT) was developed and aligned with the learning objectives, ensuring that the tasks were suitable for fostering students' understanding of the central tendency concepts. The design experiment involved data collection from a pilot experiment with 6 students and teaching experiment with 29 eighth-grade students at the junior high school. Data was gathered using instruments, including student worksheets, video recordings, field notes, and test. The data collected from students’ responses were analyzed to assess their understanding of the concepts. In the retrospective analysis stage, the Actual Learning Trajectory (ALT) was compared with the predicted HLT to identify any discrepancies and assess the effectiveness of the learning activities. The results showed that integrating the PMRI approach with Project-Based Learning (PjBL) successfully engaged students and contributed to their conceptual development, reinforcing the importance of using contextual problems such as water pH in teaching statistical concepts.
Development of Digital Modules Based on Ethnomathematics of Sasak Tribe on Geometry Materials to improve Numeracy Skills of Elementary School Students Hulaipah, Atikatul; Subarinah, Sri; Handika, Ilham
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.33077

Abstract

This study aims to determine the validity and practicality of the Sasak tribe's ethnomathematics-based digital module on geometry material and its effectiveness in improving elementary school students' numeracy skills. This research is highly urgent given the low numeracy skills of elementary school students and the need for learning innovations that are relevant to the local cultural context. Digital modules are a unique innovation for producing contextual and meaningful mathematics learning by integrating Sasak culture with geometry material through an interactive digital approach. This study employs the Research and Development (R&D) method using the ADDIE development model. Research instruments include expert validation questionnaires for media and materials, numeracy test questionnaires, teacher and student response questionnaires, and evaluation tests. The research subjects are fifth-grade students at SDN Gugus IV Perampuan, while the research object is the Sasak ethnic group-based ethnomathematics digital module on geometry material. The data were analyzed descriptively, quantitatively, and qualitatively, with normality, homogeneity, and t-tests to determine the differences in learning outcomes between the experimental and control classes, as well as N-Gain calculations to measure the improvement in elementary school students' numeracy skills. The results of the study show that the Sasak tribe's ethnomathematics-based digital module is highly valid, practical, and effective in improving elementary school students' numeracy skills. The Sasak ethnic mathematics-based digital module meets the requirements for content, presentation, and language validity. This module can help students understand geometric concepts in a contextual and meaningful way. It is very practical for teachers and students to use and effective in improving numeracy skills. Thus, the Sasak ethnic mathematics-based digital module has been proven effective in improving the numeracy skills of fifth-grade students at SDN Gugus IV Perampuan.
The Design of Learning Trajectory for Parabola Equation in Geometry STEM-Based Learning for Flexibility Skills Nopriyanti, Tika Dwi; Zulkardi, Zulkardi; Putri, Ratu Ilma Indra; Aisyah, Nyimas
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32560

Abstract

The flexibility of mathematical thinking among prospective mathematics teachers remains relatively low, primarily due to learning approaches that do not meaningfully connect mathematical concepts with real-world contexts. This study aims to design and implement a STEM-based learning trajectory on the topic of parabolic equations to foster the development of mathematical thinking flexibility in prospective teachers. The research employs a design research approach consisting of two stages: a pilot experiment to test and refine the learning trajectory, and a teaching experiment to implement and evaluate its effectiveness. The participants were students who had completed an Analytical Geometry course. Data were collected through activity sheets, Desmos documentation, video recordings, and interviews. Data were analyzed using a retrospective analysis method, which involved three main steps: (1) organizing data from various sources, (2) conducting within-case analysis to trace students' thought processes throughout each activity, and (3) synthesizing patterns across cases to identify the development of mathematical flexibility. The results show that the learning trajectory consisting of four main activities: video analysis, elevation angle experiments, graphing parabolas using Desmos, and determining parabolic equations effectively facilitated the development of mathematical flexibility in three aspects: representational, conceptual, and procedural. Students demonstrated the ability to shift between different representations, understand the interconnections among mathematical concepts, and adapt problem-solving strategies to contextual situations. The teaching experiment also revealed increased student engagement, higher quality of discussion, and a greater diversity of strategies employed. This study recommends the integration of real-world contexts, such as football throw-ins, to support STEM-based mathematics instruction aimed at developing flexible mathematical thinking in prospective teachers.
Assessing Solar Energy Potential through Sunshine Hour Interpolation using Spatiotemporal Kriging with Local Drift Nugroho, Salma Fitri; Fitriani, Rahma; Iriany, Atiek
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32048

Abstract

Solar energy is a key renewable resource, particularly valuable in tropical regions like Bali, where sunlight is consistently available throughout the year. Accurate estimation of sunshine duration is essential for assessing solar energy potential, as it directly affects photovoltaic (PV) system performace and informs strategic planning for renewable energy development. This study aims to develop a spatiotemporal statistical interpolation model to estimate and predict sunshine duration patterns across Bali, thereby enhancing the planning and deployment of solar energy infrastructure. This quantitative research applies space-time kriging with local drift using sunshine duration data (in hours) collected from four meteorological stations between 2019 and 2023. The method effectively captures spatial and temporal dependencies by integrating local drift as a deterministic trend component. Among several models tested, the Gaussian-Gaussian-Gaussian (Gau-Gau-Gau) combination delivered the best performance, with an RMSE of 2.3085. The results show a clear seasonal cycle, with higher sunshine duration during the dry season (May–October) and lower values in the wet season (November–March). Northern and eastern Bali, particularly Buleleng and Karangasem, demonstrate the highest solar potential, while central mountainous areas show lower sunshine exposure due to cloud coverage. These results offer not only a methodological contribution through the application of spatiotemporal kriging with local drift, but also a practical framework for decision-makers. The insights can guide strategic placement of solar farms, optimize energy yield forecasts, and support resilient infrastructure planning in line with Bali’s climatic realities and energy needs.
Effectiveness of Traditional Game-Based Learning: using Panjat Pinang Context to Improve Students’ Mathematical Modelling Skills Amarta, Nadiati; Darmawijoyo, Darmowijoyo; Hartono, Yusuf
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32592

Abstract

This study aims to develop a context-based Learner Worsheet (LKPD) on comparison material using the traditional game of panjat pinang to enhance the mathematical modelling skills of seventh-grade junior high school. The research employed a design research approach with the Tessmer model, consisting of preliminary and formative evaluation stages. Instrument included expert validation sheets (to assess content, construct, and language), practicality questionnaires, and a mathematical modelling ability test (covering understanding tasks, mathematising, working mathematically, and explaining results). Data analysis involved calculating percentage scores for validity and practicality, along with descriptive analysis of students’ mathematical modelling performance. The results indicate that the LKPD achieved high validity with an average score of 84,77% and good practicality with an average score of 81,25%. Field testing demonstrated its potential to improve students’ performance in all four stages of mathematical modelling. In conclusion, integrating panjat pinang as a cultural context creates meaningful learning experiences, making the concept of comparison more accessible and engaging. The LKPD can serve as an effective alternative mathematics teaching material and a reference for developing other culturally relevant resources. 
Preservice Mathematics Teachers’ Self-Efficacy and Competence in using Visual Representations for Teaching Fractions Suryanti, Sri; Wijaya, Agung Putra; Firdaus, Ahmad Qolfathiriyus
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32207

Abstract

Visual representation is crucial for enhancing students' conceptual understanding of fractions and correcting misconceptions. This explanatory-sequential mixed study assessed Indonesian preservice mathematics teachers' perceptions, self-efficacy, and implementation competencies using visual representations in fraction learning and identified gaps among these three aspects. A total of 251 students from three study programs participated in a validated online survey (α = 0.89). Quantitative data were analyzed using descriptive statistics. Seven participants were then purposefully selected for semi-structured interviews; transcripts were analyzed using Braun & Clarke's six-stage thematic analysis with researcher triangulation. The results showed that although prospective teachers had a very high perception of the pedagogical value of visual representations (M = 4.41; SD = 0.153; 78.9% agreed/strongly agreed), their self-efficacy level was only in the moderate category (M = 3.21; SD = 0.617), with only 28.3% showing high efficacy, and 61.3% were in the medium category. Implementation competence was even lower, with only 17% of participants being able to select and explain visual models pedagogically and 27.8% meeting the sufficient criteria in the teaching reasoning test. The combined analysis of quantitative and qualitative data confirmed the existence of a systemic gap between strong conceptual understanding and limited practical skills, which was mainly caused by uncertainty in model selection, minimal misconception-oriented practical experience, and weak pedagogical reflection. Integrating high-fidelity micro-teaching, representational scenario-based simulations, and video reflections is recommended to enhance self-efficacy and implementation competency.Visual representation is crucial for enhancing students' conceptual understanding of fractions and correcting misconceptions.This explanatory-sequential mixed study assessed Indonesian preservice mathematics teachers' perceptions, self-efficacy, and implementation competencies using visual representations in fraction learning and identified gaps among these three aspects. A total of 251 students from three study programs participated in a validated online survey (α = 0.89). Quantitative data were analyzed using descriptive statistics. Seven participants were then purposefully selected for semi-structured interviews; transcripts were analyzed using Braun & Clarke's six-stage thematic analysis with researcher triangulation.The results showed that although prospective teachers had a very high perception of the pedagogical value of visual representations (M = 4.41; SD = 0.153; 78.9% agreed/strongly agreed), their self-efficacy level was only in the moderate category (M = 3.21; SD = 0.617), with only 28.3% showing high efficacy, and 61.3% were in the medium category. Implementation competence was even lower, with only 17% of participants being able to select and explain visual models pedagogically and 27.8% meeting the sufficient criteria in the teaching reasoning test. The combined analysis of quantitative and qualitative data confirmed the existence of a systemic gap between strong conceptual understanding and limited practical skills, which was mainly caused by uncertainty in model selection, minimal misconception-oriented practical experience, and weak pedagogical reflection. Integrating high-fidelity micro-teaching, representational scenario-based simulations, and video reflections is recommended to enhance self-efficacy and implementation competency.
Enhancing Adaptive Particle Swarm Optimization Based on Human Social Learning with Human Learning Strategies for the Traveling Salesman Problem Qomah, Yusti; Silalahi, Bib Paruhum; Bakhtiar, Toni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.31466

Abstract

Particle Swarm Optimization (PSO) is a widely used metaheuristic approach for solving optimization problems. Recent developments in this field involve the adaptation of human learning behaviors to enhance algorithmic performance. One such adaptation is the Adaptive Particle Swarm Optimization based on Human Social Learning (APSO-HSL), a variant of PSO that incorporates human inspired learning strategies. This study aims to enhance the performance of APSO-HSL on the Traveling Salesman Problem (TSP) by incorporating additional human learning strategies. The proposed algorithm, named Modified Adaptive Particle Swarm Optimization–Human Learning Strategies (MAPSO-HLS), integrates learning mechanisms from Human Learning Optimization (HLO), including individual, random, and social learning. This research is classified as applied research and algorithmic experimentation, focusing on the development and modification of a metaheuristic algorithm to solve a well-known combinatorial optimization problem. Benchmark datasets from the Traveling Salesman Problem Library (TSPLIB) are used for evaluation, and all computations and experiments are implemented in Python. The performance of MAPSO-HLS is compared with the exact method in terms of shortest distance and computation time. The results of the study indicate that the MAPSO-HLS algorithm is capable of producing TSP solutions with low total distance deviation, below 10%, compared to exact solutions across all tested datasets. This reflects a high level of solution accuracy. In addition, MAPSO-HLS demonstrates better time efficiency than the exact ILP method, particularly for datasets with a large number of cities. The integration of human learning strategies within the adaptive PSO framework provides significant advantages in terms of both efficiency and effectiveness in solving TSP.
Game-Based Learning Utilised Kahoot! Application for Mathematics Literacy and Motivation Among Primary Students: Experimental Study Yanuarto, Wanda Nugroho; Hanum, Latifah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.33105

Abstract

This study explores how game-based learning using the Kahoot! application can enhance mathematics literacy and learning motivation among primary school students. Employing a quantitative experimental approach, the research involved two student groups: the experimental group engaged in math lessons incorporating Kahoot!, while the control group received conventional teacher-centered instruction. A total of sixty elementary students took part in the study. To evaluate outcomes, mathematics literacy was assessed through pre-tests and post-tests, while a motivation questionnaire gauged students' engagement and attitudes toward learning math. The findings showed that the experimental group experienced significantly greater gains in both mathematics literacy and motivation. The interactive, game-like nature of Kahoot! created a more enjoyable and participatory learning atmosphere, promoting better understanding of mathematical concepts. These results indicate that game-based learning tools like Kahoot! can enhance academic performance and foster a more positive attitude toward mathematics. The study underscores the potential of digital learning innovations to make classrooms more interactive and student-focused, ultimately supporting the development of key mathematical skills in primary education.
Complexity of Graphs with Wheel Graph and Fan Graph as their Blocks Alexander, Alexander; Fran, Fransiskus; Kusumastuti, Nilamsari
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32776

Abstract

The complexity of a graphs remains an active area of research within graph theory. Let G be an undirected connected graph. Graph G is said as a non-separable graph if it does not have cut-vertex. A maximal non-separable subgraph of graph G is called a block of G. Every connected graph G has at least one spanning tree. The complexity of the graph G is the number of spanning trees in G, denoted by τ(G), and can be determined using the matrix tree theorem. The matrix used in this theorem is the Laplacian matrix, which related to the number of spanning trees in a graph. This research aims to formulate the complexity of graphs with wheel graph W_n and fan graph F_n as their blocks. The focus of this research is on graphs whose blocks are wheel graph W_n and fan graph F_n, specifically the m-wheel graph W_(n,m), the dragonfly graph 〖Dg〗_n, and the generalized dragonfly graph 〖Dg〗_n^((3,3) ). This study utilizes a qualitative and theoretical approach grounded in mathematical analysis. It involves a thorough review of relevant books and journal articles. The theoretical contributions of this research include deeper understanding about complexity of graph and elucidating the relationship between the complexity of graphs and their blocks. In this research, the complexity of graphs is determined using the matrix tree theorem, which involves calculating the cofactor of the Laplacian matrix. Based on τ(W_n ) and τ(F_n ), the results obtained in this study are τ(W_(n,m) )=(τ(W_n ))^m, τ(〖Dg〗_n )=(τ(F_(n+2) ))^2 and  τ(〖Dg〗_n^((3,3) ) )=(τ(F_(n+2) ))^3 . The results of this study show that the complexity of a graph is related to the complexity of its blocks.

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