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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 26 Documents
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Search results for , issue "Vol 8, No 3 (2024): July" : 26 Documents clear
Characteristic Polynomial and Eigenproblem of Triangular Matrix over Interval Min-Plus Algebra Rahmawati, Anita Dwi; Siswanto, Siswanto; Wibowo, Supriyadi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22305

Abstract

A min-plus algebra is a linear algebra over the semiring R_ε', equipped with the operations “"⊕'=min" ” and “⊗=+”. In min-plus algebra, there is the concept of characteristic polynomial obtained from permanent of matrix. Min-plus algebra can be extended to an interval min-plus algebra, which is a set 〖 I(R)〗_ε' equipped with the operations ¯("⊕'" ) and ¯("⊗" ). Matrix over interval min-plus algebra has some special forms, one of which is a triangular matrix. The concept of characteristic polynomial and eigenproblem can be applied to a triangular matrix. There is a more concise formula for solving the eigenproblem of triangular matrix because this matrix is a special form of matrix. This research will discuss the characteristic polynomial and solving eigenproblem of triangular matrix over interval min-plus algebra using its characteristic polynomials. The research method used is a literature study. From the research results, the permanent formula and characteristic polynomial formula of the triangular matrix are obtained. It is also obtained that the smallest corner of the characteristic polynomial is the principal eigenvalue and the vector eigen corresponding to the principal eigenvalue can be obtained through the matrix A_λ. For readers who are interested in this topic, can research about characteristic polynomial and eigenproblem of matrices with other special forms over min-plus interval algebra.
Development of Mathematical Maturity through the Amalgamation of Computational Thinking and Technology-Enhanced Learning Prabawa, Harsa Wara; Rosjanuardi, Rizky; Nurlaelah, Elah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.23766

Abstract

Advancements in technology and global information infrastructure have transformed education, leveraging a constructivist approach that enhances knowledge construction through student interaction with computer applications. The research aimed to explore the facilitation of enhancing mathematical maturity through the integration of technology in mathematics education using computational thinking. This research employed a qualitative method with a case study approach. The participants in this study were 15 Grade XI students from various classes of the Vocational High School, selected from a total of 159 students. The data collection techniques used in this research included observation and open-ended test instruments. The data analysis techniques involved data reduction, data presentation, and conclusion drawing. The research results show: (1) technology enhances mathematics education; (2) computers deepen mathematical understanding; (3) technology creates contextual learning environments for problem-solving; (4) combining computational thinking and technology aids in mastering mathematical concepts. The conclusion is that integrating computational thinking with technology-enhanced learning significantly fosters mathematical maturity among students.
Equating by Using Circle Equation Approach: Applied Mathematics Formula for Prevent Discrimination Iriyadi, Deni; Rustam, Ahmad; Hartati, Hevriana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22195

Abstract

This study aims to determine the accuracy of the equating method that uses a circle equation approach in terms of its circular arc (Simplified Circle Arc). This research uses 2015 National Examination data from two questions packages. Using the number of preliminary samples as many as 2135 on the X and 2271 test devices on the Y test. After doing a Rasch analysis using a Mean Square Outfit (MNSQ), the data was acquired and analyzed. Following this, replication was performed up to a maximum of 50 times for each kind of data distribution. For each replication, up to a maximum of 50 respondents were selected from the original data set to be used as data for score equalization. The Root Mean Square Error (RMSE) statistic is then used to analyze the outcomes of the equating score. The results showed that the average RMSE group that has the same distribution will provide a lower RMSE value compared to groups that have different data distributions. The low average RMSE value indicates the accuracy of the equal of the scores performed. Thus, the use of the SCA method is highly recommended to equalize scores, especially in small samples in classes at school to prevent discrimination in grading.
Dual Optimization of Weighted Fuzzy Time-Series Forecasting: Particle Swarm Optimization and Lagrange Quadratic Programming Zamelina, Armando Jacquis Federal; Astutik, Suci; Fitriani, Rahma
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22554

Abstract

Time series Forecasting is one of crucial techniques that helps with strategic decision-making and mitigating potential risks –One of which is Weighted fuzzy time series (WFTS). Moreover, the interval length of the WFTS plays a crucial role in its modelization and accuracy in predicting future values. Therefore, this research implements a dual optimization on WFTS, which are (1) Particle Swarm Optimization to find the optimum interval length of the WFTS and (2) a Lagrange quadratic to optimize the weight of the fuzzy interval. In this research, a univariate Average Air Temperature located in Malang is used to perform forecasting model. The dataset is taken from BMKG-Indonesia. This research aims to acquire an optimized interval length on fuzzy time series forecasting, i.e., improving its accuracy by finding the optimal interval length. Based on the result, the proposed dual optimization model outperforms the classical WFTS on forecasting. The proposed model excels based on the evaluation matrix values. It has been noticed also that implementing PSO to find the optimum interval length has improved the accuracy of the classical WFTS. The classical WFTS has MAPE and RMSE of 2.4 and 0.73, respectively, while the proposed dual optimized model has 1.01 and 0.3. This approach identifies the best interval values and provides optimum weights related to each data point, providing solid insights for air temperature forecasting. 
Confirmatory Factor Analysis to Reduce the Knowledge and Economic Dimensions of the Behavior of Cerebral Palsy Parents Khasanah, Al Um Aniswatun; Yuliana, Sri; Ikrom, Dhofirul Fadhil Dzil; Sholiha, Sangidatus; Dewi, Wardhani Utami
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22952

Abstract

This research is important to understand the behavior of parents of Cerebral Palsy (CP) children by reducing the complexity in understanding knowledge and economic dimensions, thus providing a structured approach to identifying factors that influence the psychology of children with CP. This study aimed to identify and reduce the dimensions that influence the behavior of parents of children with CFA.This study aimed to reduce the socio-economic dimensions and knowledge of the behavior of parents of Cerebral Palsy (CP) children using CFA. A quantitative approach with a cross-sectional design was used in this study to comprehensively examine the behavior of parents of children with CP. Purposive sampling was used to select 200 participants from various backgrounds. The instrument used was a 28-item questionnaire which was distributed online to collect data. The questionnaire has gone through rigorous testing, including CFA, determinant KMO test, Bartlett test PCA, and grouping of variables based on identified factors.Research methods , a quantitative approach with cross-sectional design, and purposive sampling were used to select 200 parents of children with CP from various backgrounds. The instrument in the form of a questionnaire with 28 statement items was distributed online. Data analysis was carried out using CFA, including the determinant test, Kaiser-Meyer-Olkin (KMO) test, Bartlett test, Principal Components Analysis (PCA), and grouping variables based on factors. Research in Lampung shows that the number of boys with CP is slightly higher, with the majority aged 1-5 years. Factor analysis identified three main dimensions: parental knowledge about CP, family economic situation, and parental behavior. Better knowledge and a stable economic situation are positively correlated with better parental behavior in caring for children with CP. Many parents experience high levels of stress due to the physical, emotional, and financial burden of caring for a child with CP. The research conclusion shows that the 28 statement items were successfully reduced to three main dimensions (knowledge, economics, and behavior) which have a significant relationship in the care of children with CP. These findings suggest the need for interventions to increase parental knowledge about CP and family economic stability to increase parental participation in child care.Findings the sex distribution of children with cerebral palsy in Lampung showed a slight excess in the number of boys, with the majority of children being in the age range of 1-5 years. Factor analysis identified three main dimensions: parental knowledge of CP, family economic situation, and parental behavior, where better knowledge and stable economic situation positively correlated with better parental behavior in caring for children with CP. Many parents experience high levels of stress in caring for a child with CP because of the physical, emotional, and financial burden that the condition brings. In conclusion, the 28 items of the statement are reduced to 3 dimensions or factors, including knowledge, economics, and behavior. Each dimension has a relationship with each other significantly to the behavior of parents of CP children.
Improving Creative Thinking Skills through Open-ended Problems in Mathematics Education in terms of Adversity Quotient (Types of Climbers and Campers) Sa'idah, Ulya; Budiyono, Budiyono; Siswanto, Siswanto; Usodo, Budi; Hendriyanto, Agus
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.21612

Abstract

Creative thinking is one of the abilities that students must have. This research aims to explore creative thinking skills in solving open-ended problems in grade 7 students at a junior high school in Surakarta. This research uses a qualitative method. The instruments used are questionnaires, questions, and interviews. The test instrument uses one open-ended question on algebra material. The sampling method was carried out by purposive sampling where the subject was selected based on the results of the Adversity Response Profile (ARP) questionnaire score. The research subjects were 7th-grade students at one of Surakarta's private junior high schools who had studied algebraic form operations. Data were collected through tests and interviews with 4 research subjects. The data validity used was method triangulation. The results of the study show that all subjects can go through all stages of the creative thinking process although there are differences in each stage. In the preparation stage, climbers-type students do not need a long time to understand the problem. Unlike the campers, they take time to understand the problem by reading it repeatedly. At the incubation stage, students pause to look for ideas for solving the problem. At the illumination stage, students have different ways of solving the problem. At the verification stage, climbers-type students recalculate the answers written to check their correctness. While campers type students only skim the answers they write. Climbers-type students do not give up easily and do not experience difficulties in solving problems, while campers-type students take longer to understand the problem and almost give up in solving the problem. Based on the findings obtained, teachers need to consider the different types of students' creative thinking in designing class activities in order to improve students' creative thinking abilities through classroom learning.
Analysis of the Single Index Model Optimal Portfolio Using the Sharpe and Treynor Measurement Index Related to Covid-19 Salsabila, Yumna Hanum; Sulistianingsih, Evy; Debataraja, Naomi Nessyana; Martha, Shantika
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.21249

Abstract

The optimum portfolio is the preferred choice among investors for determining the most favorable combination of projected return and risk. This study seeks to ascertain the ideal portfolio performance of companies in the IDX30 index on the Indonesia Stock Exchange and know the value of the stock weight in each period, over three specific periods: before to the Covid-19 pandemic, at the peak of Covid-19 cases, and after a decline in Covid-19 instances. Stocks listed on IDX30 are stock companies that have high liquidity and large capitalization value on the capital market. The pre-Covid-19 era spanned from March 2019 to February 2020. The time of peak Covid-19 occurrences occurred from April 2021 to March 2022. Lastly, the period of declining Covid-19 instances extended from September 2022 to August 2023. The study employs the Single Index Model (SIM), using the Sharpe and Treynor measurement indices. The SIM will identify the relationship between the returns from each security and market returns to construct a portfolio. Meanwhile, Sharpe and Treynor Index measures the performance of portfolio. Based on the results of the analysis of optimal portfolio formation from 30 samples of IDX30 stocks, 4 stocks were obtained (ARTO, BBCA, BBRI, and BRPT) in the period before the Covid-19 pandemic, 14 stocks (ADRO, AKRA, ASII, BBCA, BBNI, BMRI, EMTK, ESSA, INCO, ITMG, MDKA, PTBA, TLKM, and UNTR) in the period when Covid-19 cases were peaking, and 7 stocks (AKRA, AMRT, BBCA, BBNI, BMRI, BRPT, and MEDC) in the period when Covid-19 cases were sloping. The Sharpe measurement index assessment had an average value in the period before the Covid-19 pandemic 1,7836; in the period when Covid-19 cases peaked it was 1,6051, and in the period when Covid-19 cases were sloping it was 0,7236. Meanwhile, the Treynor measurement index had an average value of in the period before the Covid-19 pandemic 0,8507; in the period when Covid-19 cases peaked it was 0,4095; and in the period when Covid-19 cases sloped it was 0,1317. The best period that has the highest Sharpe and Treynor index values is the period before the Covid-19 pandemic. The expected return value of the portfolio that was formed was 0,0601 in period I, 0,0509 in period II, and 0,0210 in period III. Meanwhile, the portfolio risk formed in period I was 0,1086, in period II it was 0,0150, and in period III it was 0,0089.
Chi-Square Feature Selection with Pseudo-Labelling in Natural Language Processing Afriyani, Sintia; Surono, Sugiyarto; Solihin, Iwan Mahmud
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22751

Abstract

This study aims to evaluate the effectiveness of the Chi-Square feature selection method in improving the classification accuracy of linear Support Vector Machine, K-Nearest Neighbors and Random Forest in natural language processing when combined with classification algorithms as well as introducing Pseudo-Labelling techniques to improve semi-supervised classification performance. This research is important in the context of NLP as accurate feature selection can significantly improve model performance by reducing data noise and focusing on the most relevant information, while Pseudo-Labelling techniques help maximise unlabelled data, which is particularly useful when labelled data is sparse. The research methodology involves collecting relevant datasets, thus applying the Chi-Square method to filter out significant features, and applying Pseudo-Labelling techniques to train semi-supervised models. In this study, the dataset used in this research is the text data of public comments related to the 2024 Presidential General Election, which is obtained from the Twitter scrapping process. The characteristics of this dataset include various comments and opinions from the public related to presidential candidates, including political views, support, and criticism of these candidates. The experimental results show a significant improvement in classification accuracy to 0.9200, with precision of 0.8893, recall of 0.9200, and F1-score of 0.8828. The integration of Pseudo-Labelling techniques prominently improves the performance of semi-supervised classification, suggesting that the combination of Chi-Square and Pseudo-Labelling methods can improve classification systems in various natural language processing applications. This opens up opportunities to develop more efficient methodologies in improving classification accuracy and effectiveness in natural language processing tasks, especially in the domains of linear Support Vector Machine, K-Nearest Neighbors and Random Forest well as semi-supervised learning.
Modelling of Forecasting ASEAN-5 Stock Price Index Using GSTAR Model Zakiyah, Tuti; Windasari, Wahyuni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22738

Abstract

This research aims to apply the Generalized Space-Time Autoregressive (GSTAR) model to predict stock price indices in ASEAN-5 countries. Generalized Space Time Autoregressive (GSTAR) model is one of the most common used space-time model to modeling and predicting spatial and time series data. The GSTAR model produces a space-time model that adopts the stages of the Autoregressive Integrated Moving Average (ARIMA) model. This research uses parameter estimation using the Maximum Likelihood method, which is a method used to estimate parameter values by maximizing the probability function seen based on observations. This research uses secondary data in the form of Stock Price Index data from 5 countries in Asia, namely the Composite Stock Price Index (JCI), Philippine Stock Exchange (PSEi), Strait Time Index (STI), Kuala Lumpur Composite Index (KLCI), and Thailand Stock Exchange Index (SETI). Stock Price Index data was divided into in-sample data for Generalized Space-Time Autoregressive (GSTAR) modelling and out-sample data used to validate presumptive results. In-sample data was taken from January 4, 2021, to December 29, 2023, and then out-sample data for presumptive was as many as 5 from January 2, 2024, to January 8, 2024. From the modeling results, it was found that the mean MAPE value of the GSTAR model was smaller than that of the ARIMA model. Moreover, based on the presumptive results for the following 5 periods using the GSTAR (2.1) I(1) model, a Mean Absolute Percentage Error (MAPE) of less than 10% in each location. The values shows that GSTAR model is more accurate than the ARIMA model.
Kanoma: Learning Media to Improve Students’ Understanding Mathematical Concepts Sigarini, Khofifah Aluh; Fitriana, Laila; Setiawan, Rubono
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.23076

Abstract

This research was conducted to determine the validity, practicality, and effectiveness of Kanoma’s learning media in improving the understanding of mathematical concepts in high school students in class X. This research applied development research design with the PLOMP approach developed by Tjeerd Plomp. The stages of development using the PLOMP approach include preliminary investigation, product design, construction, testing, and implementation. The population in this research were all ten-grade students at a vocational high school. The research sample consisted of 16 students in the experimental class and 14 students in the control class. These students were selected randomly using the cluster random sampling technique. The instruments utilized in the study included assessments by media experts, questionnaires for students and teachers, and pretest and posttest evaluations of mathematical understanding. The instruments given to media experts is used to validate the Kanoma media and its content. The questionnaires for students and teachers were used to test the practicality of the developed Kanoma media. These quistionnaires gathered feedback on how easy and useful the media was in a classroom setting. The pretest and posttest were designed to measure students’ understanding of mathematical concepts related to finding the roots of quadratic equations. The average value given by material experts from the two validators of Kanoma’s media is 0.82. The average value given by media experts from the two validators is 0.90. The results show that the Kanoma media was categorized as “very valid” by both material and media experts. This indicates that media was suitable for use by class X students in senior high school. Kanoma media is also classified as practical based on the average percentage of student and teacher responses. The responses from students scored 73%, categorized as “practice”. The responses from teachers scored 81%, categorized as “very practice.” Kanoma media is effective based on the Mann-Whitney Asyptotic Sig. (0.002) <α (0.05). The results showed a significant improvement in mathematical understanding. Students who used the Kanoma media had a better grasp of the mathematical concepts than those who did not.

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