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All Journal MUSTEK ANIM HA Al-Jabar : Jurnal Pendidikan Matematika Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) MATAPPA: Jurnal Pengabdian Kepada Masyarakat JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya Jurnal Varian Klorofil: Jurnal Penelitian Ilmu-Ilmu Pertanian MATHEMA: JURNAL PENDIDIKAN MATEMATIKA Edumatica: Jurnal Pendidikan Matematika Jurnal Inovasi Pembelajaran Matematika (JIPM)
Pratama, Rian Ade
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Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Dynamical of Prey Refuge in a Diased Predator-Prey Model with Intraspecific Competition for Predator Pratama, Rian Ade
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19893

Abstract

The predator-prey model described is a population growth model of an eco-epidemiological system with prey protection and predator intraspecific traits. Predation interactions in predator species use response functions. The aim of this research is to examine the local stable balance point and look at the characteristics of species resulting from mathematical modeling interventions. Review of balance point analysis, numerical simulation and analysis of given trajectories. The research results show the shape of the model which is arranged with a composition of 5 balance points. There is one rational balance point to be explained, using the Routh-Hurwitz criterion, . The characteristic equation and associated eigenvalues in the mathematical model are the local asymptotically stable balance points. In the trajectory analysis, local stability is also shown by the model formed. There are differences for each population to reach its point of stability. The role of prey protection behavior is very effective in suppressing the spread of disease. Meanwhile, intraspecific predator interactions are able to balance the decreasing growth of prey populations. If we increase the intraspecific interaction coefficient, we can be sure that the growth of the prey population will both increase significantly. When the number of prey populations increases significantly, of course disease transmission and prey protection become determining factors, the continuation of the model in exosite interactions. In prey populations and susceptible prey to infection, growth does not require a long time compared to the growth of predator populations. The time required to achieve stable growth is rapid for the prey species. Although prey species' growth is more fluctuating compared to predator populations. Predatory species are more likely to be stable from the start of their growth. The significance of predatory growth is only at the beginning of growth, while after that it increases slowly and reaches an ideal equilibrium point. Each species has its own characteristics, so extensive studies are needed on more complex forms of response functions in further research. 
The Impact of Peer Pressure Mathematical Models Armed Criminal Groups with Criminal Mapping Area Pratama, Rian Ade; Ruslau, Maria F V
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16255

Abstract

Model Armed Criminal Groups is mathematically realistic to be considered in the study of mathematical science. The aim of this research is to form a mathematical model of social cases of criminal acts. The given model is a criminal form that adopts the conformity of the conditions in the susceptible, exposed, infected, and recovered (SEIR) disease distribution model. The research method used is literature study and analysis. The research results show that there are 2 non-negative equilibrium, and one of them is stability analysis. Stability analysis is only carried out at equilibrium that does not contain a zero value with the Routh-Hurwitz criteria. In the results of other research the trajectories show that population growth tends not to experience fluctuations, this indicates that the population is growing towards stability rapidly. In case studies in the field, this marks a cycle of crime that quickly subsides or only occurs in a short period of time and does not occur in a sustainable manner. Overall the susceptible population, the exposed population, the infected population, and the recovered population experience the same conditions.
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.
Dynamics of predator–prey populations with allee effects under the influence of two generalist predators Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F V
Desimal: Jurnal Matematika Vol. 8 No. 3 (2025): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v8i3.202528849

Abstract

In this study, we analyze a predator–prey model incorporating a Holling type II functional response, an Allee effect in the prey population, and generalist predator species. The proposed interaction model is formulated as a nonlinear differential system involving three species: one prey species and two generalist predator species. The research methodology combines literature review and analytical investigation. The objectives are to examine the equilibrium points, assess stability using the Routh–Hurwitz criteria, and perform numerical simulations to illustrate population growth trajectories. The analysis reveals eleven equilibrium points, consisting of trivial, semi-trivial, and coexistence equilibria. Among the coexistence equilibria, only one satisfies the local stability conditions, as determined by the characteristic equation associated with the Routh–Hurwitz criteria. The characteristic equation of the model is a complex quartic polynomial. Ecologically, such local stability conditions ensure the persistence of all species within the ecosystem. Numerical simulations are also provided for the proposed model, demonstrating stable conditions for all three populations. However, the population growth patterns of the three species differ significantly. The prey population exhibits pronounced fluctuations: initially showing a gradual change, followed by a rapid increase once predation occurs, eventually reaching a stable state. Interestingly, during predation events, the overall prey population size experiences substantial growth. When predation proceeds without significant hindrance, predator populations also increase simultaneously. The interplay between the Allee effect and the Holling type II functional response plays a critical role in determining the numerical dynamics of the predator–prey system.
ANALYSIS DINAMIC AND BIOECONOMIC OF A PREDATOR-PREY SYSTEM WITH MARINE NATIONAL PARK Pratama, Rian Ade; Wahyudi, Candra Agus
Jurnal Silogisme : Kajian Ilmu Matematika dan Pembelajarannya Vol 8 No 1 (2023): Juni
Publisher : Universitas Muhammadiyah Ponorogo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24269/silogisme.v8i1.6771

Abstract

In the study of fisheries or marine products in developing countries, the problem of managing marine resources is often faced. Excessive exploitation due to weak legal and supervisory sectors is the most frequently used factor. This research involves a predator-prey mathematical model and provides an intervention variable exploitation, namely harvest. Harvest is carried out on two types of species that inhabit two protected areas of the marine national park zone. One of the objectives of the exploitation variable is to provide benefits for harvesters, such as fishermen. Boundary areas in the marine national park zone and points of equilibrium are assigned to research wetting. Stability analysis using the Routh-Hurwitz criteria indicates the survival of the population. The predator-prey model formed resulted in seven non-negative equilibria, but only one equilibrium point met the research assumptions. Numerical simulations are also provided in trajectories from the initial model formation to the bionomic shape. The basic assumption is that harvesting is carried out in the marine national park zone harvesting is carried out only in a limited way. In the prey one population, more can be harvested in the region than the prey two population. Ecologically, the population of prey one lives in a larger carrying capacity area. In the predator-prey model system, the predator-prey model makes it possible to harvest populations that live in a wider area. The wider the area of the marine national park zone, the more it is permitted to carry out exploitation efforts, provided that it is still limited.
Application of Beddington DeAngelis Response Function in Ecological Mathematical System: Study Fish Endemic Oliv Predator Species in Merauke Pratama, Rian Ade; Ruslau, Maria Fransina Veronica
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 1 (2022): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i1.5340

Abstract

Predator-prey type fishery models Oliv fish is a trans-endemic predator species that inhabits freshwater swamps and brackish water in Merauke, Papua. Maintaining the survival of the Oliv fish species is the main reason for compiling a mathematical model, so that it can be considered by local governments in making ecological policies. Method on model discussed is assembled with the growth of predator-prey populations following the growth of logistics. The response or predatory function corresponding to the behavior of endemic Oliv fish is the Beddington DeAngelis type. The growth of predatory species uses the concept of growth with stage structure, are divided into mature and immature. Research results show there are four equilibrium points of the mathematical model, but only one point becomes the asymptotic stable equilibrium point without harvesting W_4 (x^*,y^*,z^* )=92.823,1311.489,525.957 and equilibrium point with harvesting W_4 (x^*,y^*,z^* )=95.062,92.639,160.466 . Harvesting exploitation efforts are carried out by the community so that the harvesting variables are added with a proportional concept. Simulation of the results of the study shows a stable scheme and harvesting conducted can maintain the number of populations that continue. 
A Bayesian Ordinal Analysis of Students’ Progression Across Van Hiele Levels Ruslau, Maria Fransina Veronica; Pratama, Rian Ade; Meirista, Etriana
Jurnal Varian Vol. 9 No. 1 (2026)
Publisher : Universitas Bumigora

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30812/varian.v9i1.6079

Abstract

Understanding students’ progression across hierarchical levels of geometric reasoning requires analytical approaches that respect ordinal structure and quantify uncertainty. The purpose of this study is to model students’ progression across Van Hiele levels probabilistically and to estimate level-specific transition probabilities under uncertainty using paired pretest–posttest data from Grade 8 and Grade 9 students. The method used in this study is Bayesian ordinal regression with a cumulative logit specification estimated via MCMC sampling. Van Hiele levels were modeled as ordered categorical outcomes, and posterior summaries, transition matrices, and posterior predictive checks were used to characterize progression and assess model adequacy. The results indicate that progression is predominantly upward in both grades, with negligible posterior support for regression. Grade-dependent differences are evident: Grade 8 shows broader, more heterogeneous transitions from a uniformly low baseline, whereas Grade 9 exhibits more constrained, incremental progression from a higher, more dispersed initial distribution. Posterior predictive checks confirm that the model adequately reproduces the observed posttest patterns, supporting the validity of the Bayesian ordinal specification. Pedagogically, these findings imply that students at lower baseline levels tend to undergo broader conceptual shifts, whereas those at higher levels require sustained, targeted instructional support to advance further. These findings indicate that baseline ordinal structure shapes progression dynamics and that Bayesian ordinal modeling offers a coherent alternative to significance-based approaches for analyzing hierarchical learning outcomes. Educationally, this underscores the need to align instruction with students’ initial Van Hiele levels to support optimal conceptual advancement.
Pengaruh Persepsi Penilaian Hasil Belajar Terhadap Keyakinan Guru Tentang Pembelajaran Matematika Nur, Andi Saparuddin; Pratama, Rian Ade; Betaubun, Martha
Edumatica : Jurnal Pendidikan Matematika Vol 16 No 1 (2026): Edumatica: Jurnal Pendidikan matematika (April 2026)
Publisher : Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jambi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22437/edumatica.v16i1.43403

Abstract

The paradigm in assessing mathematics learning outcomes has turned, especially after the pandemic and the enactment of the Kurikulum Merdeka. Assessment serves to not only determine learning objectives, but also as a process and tool for learning. Nevertheless, attitudes toward the assessment of mathematics learning outcomes can be mediated by several factors, such as the teachers' conceptions of mathematics learning. This study aims to examine the effect of perceptions of assessments on teachers' beliefs about mathematics learning. This study employed a correlational design involving 69 mathematics teachers from 20 provinces in Indonesia. Student characteristics are classified by gender, educational stage, teaching experience, and highest academic qualification. A Google Form was distributed through WhatsApp groups to obtain data. The data were analyzed using simple analysis, contingency correlation, and SEM analysis. Results indicate that teachers generally continue to use AoL format rather than AfL and AaL in assessing mathematics learning outcomes. The association between differentiation factors and mathematics teachers’ beliefs was generally weak to very weak. School level and teaching experience showed a low correlation with mathematics teachers' beliefs. The mediating role of teachers' beliefs about learning assessment accounted for 32% teachers' beliefs about mathematics learning. This study emphasizes the necessity for educational interventions that promote practical classrooms applications to develop teachers’ attitudes of the importance of AfL and AaL. Future researchers may conduct longitudinal studies with a larger number of participants and a more equal distribution of characteristics to minimize bias and obtain most comprehensive results
ImageStat EDU: Developing an interactive digital image-based tool for statistical visualization and learning Ruslau, Maria Fransina Veronica; Nurhayati, Nurhayati; Pratama, Rian Ade; Kamariah, Kamariah
Al-Jabar: Jurnal Pendidikan Matematika Vol 17 No 3 (2026): Al-Jabar : Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/

Abstract

Purpose: This study aimed to develop and preliminarily evaluate ImageStat EDU, an interactive digital image-based tool designed to support statistical visualization and learning, particularly in descriptive statistics, histogram interpretation, and introductory probability distributions.Method: The study employed a Research and Development approach using the ADDIE model. Product evaluation involved three expert validators representing mathematics/statistics content, instructional media and ICT, and pedagogy, followed by a small-scale implementation with 15 undergraduate mathematics education students enrolled in a statistics course. Data were collected using expert validation sheets, a user response questionnaire, and pretest–posttest assessments. Expert and student responses were analyzed descriptively, while changes in student performance were examined using a paired-sample t-test, a Wilcoxon signed-rank test, and Cohen’s.Findings: Expert evaluation showed substantial improvement following prototype revision, with the final overall evaluation reaching 96.67%. Students also reported high perceived practicality and usefulness, with an overall response of 92.00%. The mean score increased from 36.88 on the pretest to 65.17 on the posttest, with a large within-participant effect size ( ). Parametric and nonparametric analyses consistently indicated higher posttest performance. However, these findings represent preliminary changes within a small, uncontrolled sample and should not be interpreted as evidence of causal effectiveness.Significance: ImageStat EDU demonstrates the potential of using image-derived pixel data to connect visual information, numerical summaries, histograms, and distributional representations within an interactive statistics learning environment. The study provides preliminary evidence supporting further investigation of image-based statistical exploration in mathematics teacher education using larger and comparative research designs.
Co-Authors Amil Siddik, A. Muh. Aminah, R. Iin Siti Andi Saparuddin Nur Betaubun, Martha Dadi, Oswaldus Ika Paridawati Iriani, Cindy Dian Kamariah Kamariah, Kamariah Kasbawati Kasbawati Maria Fransina Veronica Ruslau Meirista, Etriana Nur?aini, Khumaeroh Dwi Nurbaiti Amir Nurhayati Nurhayati Nurhayati, Nurhayati Palobo, Markus Ruslau, Maria F V Ruslau, Maria F V. Ruslau, Maria F. V. Ruslau, Maria Fransina Veronica Suryani, Dessy Rizki syamsuddin Toaha Taufik, Abdul Rachman Wahyudi, Candra Agus