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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 26 Documents
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Search results for , issue "Vol 8, No 3 (2024): July" : 26 Documents clear
Discovering Ethnomathematics in Sundanese Gamelan: Explore Mathematics Aspect in Gamelan Supriyadi, Edi; Turmudi, Turmudi; Dahlan, Jarnawi Afgani; Juandi, Dadang; Sugiarni, Rani
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.v8i3.21768

Abstract

Ethnomathematics is important in recent decades, specifically in the production of gamelan instruments. Therefore, this research aimed to examine the intricate relationship between mathematics and cultural craftsmanship in Sundanese gamelan instruments made at Gong Factory in Bogor, West Java. Ethnographic methods were used to observe and describe the practices of gamelan craftsmen and the data collection process comprised carefully selected artists. These individuals actively acquire data by reviewing relevant material, observing, analyzing, and interviewing. Miles and Huberman's framework for data analysis included data reduction, presentation, inference, and verification. The procedures understood the delicate relationship between mathematics and culture in the investigated setting. The results showed that Gong Factory in Bogor preserved and promoted a unique musical heritage. Furthermore, the instruments were known for exceptional sound quality, serving as cultural relics and didactic tools, as well as teaching visitors about the manufacturing process. The factory preserved culture through the manufacture of gamelan instruments including gong, bonang, and saron. In this context, the craftsmanship used mathematical principles, specifically precise proportions and ratios. The instruments' visual and auditory qualities depended on geometry. The results significantly impacted mathematics education by enhancing cross-cultural connections, improving proportional reasoning and mathematical comprehension, and recognizing the wider relevance of principles. Culture, mathematics, and education were connected, showing that conserving Indonesian musical tradition benefited local and global populations.
The Application of the Classical Assumption Test in Multiple Linear Regression Analysis (a Case Study of the Preparation of the Allometric Equations of Young Makila) Mardiatmoko, Gun
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.v8i3.22179

Abstract

The preparation of allometric equations generally uses multiple linear regression equations. The use of this regression equation is usually not carried out through various tests but goes directly to the t test and F test stages. Therefore, this paper aims to provide an example of determining the regression equation through the classical assumption test stages. Makila (Litsea angulata BI) was chosen as an example because it provides environmental services, especially in dealing with climate change and has not been widely studied. The research method used is a quantitative method. Destructive sampling was taken and the material used consisted of 40 young Makila plants planted in polybags next to the greenhouse at the Faculty of Agriculture, Pattimura University, Ambon. The diameter of each sample was measured from the ground surface to a height of 5 cm and numbered 1 to 40. After being coded, the plant samples were cut down and all young trees were divided into stem segments, branches, twigs, leaves and roots. The root segments were collected carefully to facilitate their separation from the soil in polybags. The parts of the roots that still contain soil are cleaned with a machete and brush until they are free of soil and other dirt. Next, each segment was weighed for its wet weight (in g) and dry weight, thus enabling the determination of the biomass content (in g) for each segment. Data analysis was carried out using the Multiple Linear Regression Equation method. The regression model was examined for normality and suitability in predicting independent variables, ensuring there were no issues with multicollinearity, heteroscedasticity, and autocorrelation. The results of the normality test showed that the significance value for the remaining data was 0.813 > 0.05, indicating normal distribution. TThe results of the multicollinearity test show that there is no multicollinearity problem, this is indicated by the VIF value of the two independent variables (tree diameter and tree height each 1.049) < 10 and the Tolerance value (tree diameter and tree height 0.953 each) > 0.100. The results of the heteroscedasticity test show that the two independent variables have a significance value of more than 0.05. The results of the autocorrelation test show the Durbin Watson (DW) value = 1.956 with a range of 1.65 – 2.35 which means there is no correlation problem. The results yielded a multiple linear regression: Y = -1131.146 + 684.799X1 + 4.276X2, where Y is biomass, X1 is the diameter, and X2 is the tree height. Based on the results of the t-test: variable X1 partially affected Y while variable X2 partially had no effect on Y. The F-test indicated that variables X1 and X2 jointly affected Y with R Square: 0.919 or 91.9% and the rest was influenced by other unexplored factors. To simplify biomass prediction and field measurement, a regression equation that used only 1 independent variable, namely tree diameter, was used for the experiment. Allometric equation only used 1 variable, Y = - 1,084,626 + 675,090 X1, where X1 = tree diameter, Y = Total biomass with R = 0.957, and R square = 0.915. The regression equation for young Makila plant provides assurance that the regression equation obtained is accurate in estimation, unbiased and consistent. This is because in data processing classical assumptions have been tested. This equation can save time, costs and energy, as well as make measurements easier in the field so that future researchers can develop allometric equations in other plants for efficiency. 
Application of the Fractal Geometry in Development Surya Majapahit Batik Motif Juhari, Juhari; Pratiwi, Alfrista Anggraini
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.v8i3.22811

Abstract

The Mandelbrot and Julia sets are generated through iterative mathematical functions applied to points in the complex plane. These operations enable the detailed and intricate patterns characteristic of these fractals, allowing for modifications and zooming to explore different regions of the sets. TThe Mojokerto Surya Majapahit batik motif is a motif that has eight corners. One way to develop a Mojokerto batik motif that is similar to Surya Majapahit is by applying the science of fractal geometry. Fractal geometry studies a fractal pattern that can change shape according to input parameters and the number of iterations carried out. This research was conducted to determine the application of Mandelbrot and Julia’s fractal geometry using geometric transformations to obtain batik motif variants that is similar to Surya Majapahit. There are three steps in forming this motif variant. First, generating Mandelbrot fractals and Julia fractals. Second, the patterns generated by Mandelbrot and Julia are applied using geometric transformations. The geometric transformations that will be used are rotation, dilation, and translation. Finally, these patterns will be modified by combining patterns implementing logic operations using Python computer applications. The results of this research obtained four variants of batik motif that is similar to Surya Majapahit. The difference in each variant lies in the order of transformation. Variant 1 and variant 3 can be carried out by changing the sequence of geometric transformations, namely rotation, translation and dilationVariant 1 is obtained by applying rotation, dilation, and translation to the Mandelbrot and Julia pattern. Variant 2 is obtained with the Mandelbrot pattern applying rotation, dilation with two different scales, and translation, while the Julia pattern only applied rotation and translation. Variant 3 is obtained by applying rotation, dilation and translation to the Mandelbrot and Julia pattern. Variant 4 is obtained with the Mandelbrot pattern applied by rotation, dilation with three different scales, and translation, while the Julia pattern was applied only by rotation and translation. Meanwhile variants 2 and 4 apply different rotations, dilation scales, namely 0.451 and 0.318, and translation to the Mandelbrot pattern.
Implementation of Data Mining and Spatial Mapping in Determining National Food Security Clusterization Sifriyani, Sifriyani; Budiantara, I Nyoman; Mardianto, M. Fariz Fadillah; Febriyani, Eka Riche; Chairunnisa, Nurul Rizky; Putri, Asyifa Charmadya
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.v8i3.19912

Abstract

This study proposes a cluster analysis of provinces based on national food security data. The research objective is to determine provincial clusters based on food indicators which include rice harvest area, distribution of rice stocks, percentage of trade margin and transportation of rice distribution, percentage of average per capita expenditure, and total per capita consumption of rice. The source of observation data for the Rice Harvested Area by Province variable is the Ministry of Agriculture, Central Bureau of Statistics and Agriculture Services throughout Indonesia. This study uses data mining techniques in data processing with the K-Medoids algorithm. The K-Medoids method is a clustering method that functions to break down data sets into several groups. The advantage of this method is that it can overcome the weakness of the K-Means method which is sensitive to outliers. Another advantage of this algorithm is that the results of the clustering process do not depend on the order in which the dataset is entered. The k-medoids clustering method can be applied to food security data by province. From grouping the data obtained three clusters, with silhouette coefficient values for cluster 1, cluster 2, and cluster 3 respectively 0.33; 0.32; and 0.44. With the largest silhouette coefficient value obtained in cluster 3 and the cluster has entered into a strong cluster structure. The research results can provide information to the government about food security grouping data in Indonesia which has an impact on the distribution and availability of food in Indonesia.
Forecasting Roof Tiles Production with Comparison of SMA and DMA Methods Based on n-th Ordo 2 and 4 Yel, Mesra Betty; Tundo, Tundo; Arinal, Veri
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.v8i3.22225

Abstract

This research aims to predict roof tile production trends at one of the roof tile companies in Kebumen to assist company management in determining and providing management recommendations for the tile production that occurs. A comparison of Single Moving Average (SMA) and Double Moving Average (DMA) Forecasting methods was used to better accommodate trends in roof tile production data optimally. Where the forecast is presented for several steps ahead, and is equipped with a value measuring the accuracy of the forecast using Mean Absolute Percentage Error (MAPE), on roof tile production transaction data over 60 months, namely January-December 2019 to January-December 2023 to produce a monthly forecast for predicting roof tile production with n-th ordo 2 and 4. The total sample of training data processed was 1,415,987 records which were roof tile production transaction data, as well as data in January 2024 as test data (to test the accuracy of the forecast). The results of testing the forecast results produced a MAPE calculation of 6.6% for SMA with n-th ordo 2, while for n-th ordo 4 it was 7.2%. The MAPE value for DMA is 6.3% for n-th ordo 2, while for n-th ordo 4 it is 8.2%, which means the accuracy level is very good, namely above 90%. Based on the MAPE results obtained, the DMA method with n-th ordo 2 is a suitable method for carrying out periodic forecasting for roof tile companies in carrying out the production process to maintain stability and avoid unexpected events.
Improving the Accuracy of Discrepancies in Farmers' Purchasing and Selling Index Prediction by Incorporating Weather Factors Yulianti, Silvina Rosita; Effendie, Adhitya Ronnie; Susyanto, Nanang
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.v8i3.22584

Abstract

One measure that can be used to see the level of farmer welfare is the farmer exchange rate (NTP), which is a comparative calculation between the price index received by farmers (IJ) and the price index paid by farmers (IB), expressed as a percentage. In reality, NTP cannot explain the actual welfare situation of farmers because the ratio value has the potential to produce biased values. Another alternative that can be used to look at farmer welfare with less potential bias is to look at the difference between the sales index and the farmer purchasing index (ID). ID data forecasting can be a reference for developing and optimizing things that need to be improved in the agricultural sector. Despite the fact that a number of external factors, such as variations in the weather throughout the year, had a significant impact on the ID value, previous research used the ARIMA model to forecast without taking exogenous factors into account. Therefore, the goal of this research is to identify the optimal ARIMAX regression model for achieving accurate forecasting results with minimal error values. This research was carried out with limitations using data from the Central Statistics Agency and the Meteorological, Climatological, and Geophysical Agency in Central Java from 2008 to 2023. The first method in this research is to prepare the data, which involved collecting secondary data such as IJ and IB along with climate data such as rainfall, duration of sunlight, air pressure, wind speed, and rice prices. Next, calculate the difference between IJ and IB to determine the ID value. Then, verify the ID data's stationarity and perform AR and MA calculations. After determining the AR and MA values, construct an ARIMAX model that incorporates external factors, search for the optimal model, and utilize the optimal model to make future predictions. The results show that the accuracy of the ARIMAX model (1,1,0) has a better value than the accuracy of the ARIMA model (1,1,0), and the results obtained in this study are better than previous studies. The authors hope that the findings of this research will serve as a benchmark for the forecasting analysis of time series data in the agricultural sector, providing the local government with a foundation for policy decisions.
Analysis of Multi-Input ARIMA Interventions with Additive Outlier for Forecasting Price of Crude Oil West Texas Intermediate Nabil, Ilhan Nail; Satyahadewi, Neva; Huda, Nur'ainul Miftahul
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.v8i3.22147

Abstract

Crude oil is a liquid characterized by a thick texture and blackish color. It is composed of complex hydrocarbon compounds with various benefits that are spread around the world. Crude oil derived from fossil fuels can be used as primary fuels, such as gasoline, and is the most important of the energy resources. Based on that, crude oil play a crucial role in the global economy movement because can be used as the main sources of energy all over the world. However, one of the benchmarks for crude oil from the USA is West Texas Intermediate (WTI). Known to produce high-quality oil, the price of crude oil of WTI fluctuates. In addition, fluctuations occur because of several factors, such as the availability of oil supplies, the embargo on oil imports, and the COVID-19 pandemic. The research aims to analyze price forecasting that occurs over the next five months and the accuracy level of the method used. The data that exists outliers is usually removed from forecasting that contains outliers, but that can affect the estimation result in the model. So, in this research intervention and outlier factors are added to the research to overcome the constraints In this study, the Multi-Input ARIMA Intervention and Additive Outlier (AO) method are used by modelling ARIMA pre-intervention and then. After that, the procedure is adding intervention factorsand additive outlier with iterative procedures. Multi-Input ARIMA Intervention and Additive Outlier (AO) are used to determine the magnitude of fluctuations that occur. Data shocks causing outlier data can be used by adding AO factors. WTI oil price data was retrieved from investing.com with monthly data from January 2011 to June 2023. Based on the results of Mmulti-Iinput ARIMA intervention with Additive Outlier method, it has been determined that the movement of WTI oil prices in the next five months will increase compared to the last five periods of actual data. Because of incrased price of crude oil, it will impact of the economic growth all over the world. So, the government better controlled the price of crude oil at lower price. . withMulti-Input ARIMA interventions resulting in AIC, MAPE, and RMSE model each 941.490, 6.979%, and 5.913 . So, Multi-Input and AO proven can be used to forecast data with fluctuate that data occur. 
Biplot Analysis Methods for Selecting the Consumer's Preferences of Primary Needs in Java Island Indonesia Jajang, Jajang; Supriyanto, Supriyanto; Maryani, Sri; Bawono, Icuk Rangga; Novandari, Weni; Gunawan, Diah Setyorini; Naufalin, Rifda
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.v8i3.22264

Abstract

The effect of COVID-19 pandemic in February 2020 had changingchanged human consumption pattern. Most people especially for lower and middle communitycommunities, they only be able to fulfils the primary needs. The COVID-19 pandemic had been made some companies done a work termination. Therefore, people is required to sort out and choose needs that are on a priority scale. This article used biplot methods to analyze behavior of the consumers consumer's primary needs during the COVID-19 pandemic. Respondents number of this research are 100 respondents from 4 districts in Java Island who filled out the questioner. In some references, biplot analysis methods focus on agriculture field such as determining the best genotypes and habitats of plants. Rarely of them cosider in economic point of view for example in consumers’ preferences. As we known that biplot analysis is a valuable technique for identifying environtmental condition. It is superior to other statistical methodologies because of its superior predictive accuracy. This method represent a grapics of multivariate data that plot information between the observation and variables in cartesian coordinates. Therefore, the goal of this study examines the consumers' preferences in the Java Island, Indonesia, using biplot analysis to assess preferences of primary needs such rice, cooking oil and margarine in four districts, Bekasi, Madiun, Tasikmalaya, Banyumas, in Java Island were conducted. Regarding to the result of principal component analysis, it shows that consumers have same priority to choose the brand of the cooking oil. It was shown from score of PC1 and PC2 values. The result provide helpful information about the consumer preferences of primary needs during COVID-19 from four districts in Java Island.  
Implementation of Gamma Regression and Gamma Geographically Weighted Regression on Case Poverty in Bengkulu Province Azagi, Ilham Alifa; Sumertajaya, I Made; Saefuddin, Asep
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.v8i3.22930

Abstract

Spatial analysis involves leveraging spatial references inherent in the data being analyzed. The method to be used in spatial analysis is the Geographically Weighted Regression (GWR) method. GWR is an extension of the linear regression model at each location by adding a weighting function to the model. Generally, the GWR model uses residuals with a normal distribution in its analysis. One distribution that can be used is the gamma distribution. With the development of methods in statistics, when a response variable follows a gamma distribution, analysis is performed using Gamma Regression (GR). GR analysis is conducted because the response variable meets the gamma distribution assumption. One method used for spatial effects with a gamma-distributed response variable is the Gamma Geographically Weighted Regression (GGWR) method. In 2022, Bengkulu Province was among the ten poorest provinces in Indonesia. Therefore, the main objective is to compare the GR and GGWR models and analyze the factors affecting poverty in Bengkulu Province using these models. The results of this study show that the GR model has an R² accuracy of 87.93%, while the GGWR model has an R² accuracy of 95.87%. This indicates that the best model for the analysis is the GGWR. An example of the GGWR model equation for poverty in Bengkulu Province is Y=exp⁡(-6.039+3.15×〖10〗^(-6) X_1-0.055X_2+0.156X_4-0.00021X_5+0.004X_7-0.021X_8-0.006X_9+4.794×〖10〗^(-5) X_10). The factors influencing the GGWR model in Bengkulu Province are Population, Life Expectancy, Average Years of Schooling, Adjusted Per Capita Expenditure, School Participation Rate, Per Capita Expenditure on Food, Households Receiving Rice for the Poor, and Gross Regional Domestic Product. The benefit of this research is to serve as a reference for the provincial government of Bengkulu regarding the variables that influence poverty. It is expected that this will help the government reduce the poverty rate in Bengkulu Province. 
Integrating Ethnomathematics Through Traditional Maluku Snacks to Enhance Geometric Understanding of Junior High Students Purba, Pratiwi Bernadetta; Nurwijaya, Sugian
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.v8i3.20526

Abstract

This study explores the potensial of utilizing traditional Maluku snacks (pom poms, bagea, embal kacang, sagu lempeng, serut kenari) as pedagogical tools to enhance students’ understanding of geometric conceps. The aim of this research is to describe how to integrate Ethnomathematics through traditional Maluku snacks to improve junior high school students' understanding of geometry concepts. This research was carried out in November 2023 at Yos Sudarso Junior High School Dobo. The subjects in this research were 30 grade 8 students. In this research, students used traditional Maluku snacks to understand geometric concepts through demonstrations and discussions. This research uses a qualitative approach where the type of research is descriptive qualitative. The data collection technique in this research is through observation using students’ worksheets, interviews, and documentation using a recording device. Furthermore, data analysis in this research is qualitative analysis with stages of data reduction, data presentation, and drawing conclusions. The results of the research are that students understand the concept of 2D shapes in traditional Maluku snacks: pom-poms (triangles and rectangles), bagea (circles), serut kenari (circles and rectangles), sagu lempeng (trapezoids and rectangles), and embal kacang (rectangle). The concept of 3D shapes in traditional Maluku snacks: pom-poms (triangular prisms), bagea (balls), serut kenari (tubes), sagu lempeng (trapezoidal prisms), and embal kacang (cube-shaped). The integration of ethnomathematics in learning can include learning experiences to the formation of mathematical concepts, especially geometry, mathematical problems, the use of terms in geometry. It is hoped that the integration of ethnomathematics in geometry learning at school can develop meaningful learning.

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