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Journal articles on the topic 'Mathematical modelling problems'

Author: Grafiati

Published: 7 June 2025

Last updated: 26 June 2025

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1

Ural, Alattin. "A Classification of Mathematical Modeling Problems of Prospective Mathematics Teachers." Journal of Educational Issues 6, no. 1 (2020): 98. http://dx.doi.org/10.5296/jei.v6i1.16566.

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The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed using descriptive analysis. The data of the study was obtained from the mathematical modelling problem written by 59 senior mathematics teachers. They were given a 1-week period to write the problems and solutions. The participants took mathematical modelling course for one semester period prior to the research. The problems are the original problems that the participants themselves produced. The mathematical modelling problems produced are categorically as follows: “Which option is more economical” problems, “Profit-making” problems, “Future prediction” problems and “Relationship between two quantities” problems. The mathematical modelling skills used are as follows: to be able to collect appropriate data, organize the data, write dependent and independent variables, write fixed values, visualize the real situation mathematically or geometrically, use mathematical concepts. The mathematical skills used are generally; to be able to do four operations with rational numbers, draw distribution and column graph, write algebraic expression, do arithmetic operation in algebraic rational expressions, write/solve equation and inequality in 1 or 2 variables, write an appropriate mathematical function explaining the data related to the data, solve 1st degree equations in 1 variable, establish proportion, use trigonometric ratios in right triangle, use basic geometry information, draw and interpret a 1st degree inequality in 2 variables.

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Yanık, H. Bahadır, Osman Bağdat, and Murat Koparan. "Investigating Prospective Middle-School Teachers’ Perspectives of Mathematical Modelling Problems." Journal of Qualitative Research in Education 5, no. 1 (2017): 80–101. http://dx.doi.org/10.14689/issn.2148-2624.1.5c1s4m.

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3

Panfilov, D. A., V. V. Romanchikov, and K. N. Krupin. "Solving cross-disciplinary problems by mathematical modelling." IOP Conference Series: Materials Science and Engineering 327 (March 2018): 022080. http://dx.doi.org/10.1088/1757-899x/327/2/022080.

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4

BELLOMO, N., and P. K. MAINI. "PREFACE — CHALLENGING MATHEMATICAL PROBLEMS IN CANCER MODELLING." Mathematical Models and Methods in Applied Sciences 17, supp01 (2007): 1641–45. http://dx.doi.org/10.1142/s0218202507002418.

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5

Copeland, A. H., R. S. Segall, C. D. Ringo, and B. Moore. "Mathematical modelling of inverse problems for oceans." Applied Mathematical Modelling 15, no. 11-12 (1991): 586–95. http://dx.doi.org/10.1016/s0307-904x(09)81004-4.

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6

OMORI, Ryosuke. "Applications, Prospects and Problems in Mathematical Modelling." Journal of Veterinary Epidemiology 26, no. 2 (2022): 88–89. http://dx.doi.org/10.2743/jve.26.88.

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7

Atabekov, Ikram. "Mathematical modelling of some geo-dynamical problems." Journal of Geosciences Insights 1, no. 1 (2023): 1–8. http://dx.doi.org/10.61577/jgi.2023.100001.

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Tectonic earthquakes occur when the stress of Earth’s crust exceeds the instant shear strength. Determining the stress state of a particular area using the equations of mechanics requires knowledge of the boundary conditions, which in most cases seem impossible. This paper proposes the determination of horizontal stresses for the Central Asian territory using the well-known geodynamic hypothesis, according to which the deformation of the Earth’s crust in Central Asia is due to the interaction of the Indian, Arabian, and Eurasian plates. The unknown boundary conditions are reconstructed by solving the inverse problem of elasticity. Some known empirical stresses are used to verify the problem. The solution of the elastic problem makes it possible to set the problem of tectonic creep movements using the Stokes equations. The model is verified by means of horizontal velocity and rotation fields constructed from GPS data. The creep model makes it possible to determine the vertical velocities of the Earth’s crust and supplements the GPS data. The constructed stress state model is used to calculate the variation in the earth’s crust stresses due to earthquakes. A double dipole without a moment is taken as the source mechanism of earthquakes. The boundary element method (BEM) is used for the numerical realization of the model.

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8

Hacia, L. "MATHEMATICAL MODELLING IN ELECTRICAL ENGINEERING." Mathematical Modelling and Analysis 10, no. 3 (2005): 257–74. http://dx.doi.org/10.3846/13926292.2005.9637286.

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Various problems of electrical engineering lead to mathematical models being difference, differential or integral equations. In this paper some mathematical models in certain problems of electrical engineering are presented. Our considerations are restricted to the radiative heat transfer and density theory (Fredholm integral equations). Respecting time in current density problems we get integro‐differential equations or generally Volterra‐Predholm integral equations (heat‐conduction theory). The new numerical method for these equations is analysed. Daugelio elektros inžinerijos problemu sprendimui tenka sudaryti matematinius modelius, kurie dažniausiai būna aprašomi skirtuminemis, diferencialinemis ar integralinemis lygtimis. Šiame darbe apžvelgiami kai kurie modeliai, skirti konkrečiu elektros inžinerijos uždaviniu sprendimui. Apsiribojama šilumos perdavimo proceso su spinduliuote modeliavimu ir tankio pasiskirstymo teorija (Predholmo integralines lygtys) .Ivedus laika, lygtys tankiui tampa integr‐diferencialinemis arba Volteros‐Predholmo integralinemis lygtimis. Darbe pateikiamas ir nagrinejamas naujas skaitinis tokiu lygčiu sprendimo metodas.

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Lei, Jinzhi. "Viewpoints on modelling: Comments on "Achilles and the tortoise: Some caveats to mathematical modelling in biology"." Mathematics in Applied Sciences and Engineering 1, no. 1 (2020): 85–90. http://dx.doi.org/10.5206/mase/10267.

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Mathematical modelling has been proven to be useful in understanding some problems from biological science, provided that it is used properly. However, it has also attracted some criticisms as partially presented in a recent opinion article \cite{Gilbert2018} from biological community. This note intends to clarify some confusion and misunderstanding in regard to mathematically modelling by commenting on those critiques raised in \cite{Gilbert2018}, with a hope of initiating some further discussion so that both applied mathematicians and biologist can better use mathematical modelling and better understand the results from modelling.

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10

Herrero, Miguel A., and José M. López. "Bone Formation: Biological Aspects and Modelling Problems." Journal of Theoretical Medicine 6, no. 1 (2005): 41–55. http://dx.doi.org/10.1080/10273660412331336883.

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In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentation.

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11

Shemelova, O. "Mathematical modeling in chemical technology processes." Bulletin of Science and Practice 4, no. 12 (2018): 20–23. https://doi.org/10.5281/zenodo.2252778.

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In the practice of researching the processes of chemical technology with the help of mathematical modelling, it is relatively easy to change the parameters of the investigated object and to determine their influence on the quality of its work as a whole. This is possible because the deformation of the process model is studied not on the physical model, but directly on the mathematical model when using a computer.

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12

Dolgonosov, A. M., A. G. Prudkovskii, E. A. Zaitseva, N. K. Kolotilina, and A. A. Dolgonosov. "Mathematical Modelling in Analytical Chromatography: Problems and Solutions." Journal of Analytical Chemistry 76, no. 11 (2021): 1233–44. http://dx.doi.org/10.1134/s1061934821110046.

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Abstract Based on an analysis of the results of original research performed in the Laboratory of Sorption Methods of the Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Sciences within the project “Mathematical Chromatograph,” the review covers the aim and strategy of the imitation modeling of high-performance chromatography; associated problems of the theory of intermolecular interactions; classifications of polar stationary phases by their selectivity; descriptions of the kinetics and dynamics of sorption processes, choice of the composition of multicomponent mobile phases in HPLC and ion chromatography using the method of the dynamic map of a chromatographic system; and the development of alternating gradient modes using a mathematical experiment.

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13

Descloux, Jean, Michel Flueck, and Jacques Rappaz. "Modelling and mathematical results arising from ferromagnetic problems." Science China Mathematics 55, no. 5 (2011): 1053–67. http://dx.doi.org/10.1007/s11425-011-4306-6.

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14

Bravo de la Parra, Rafael, and Jean-Christophe Poggiale. "Theoretical ecology and mathematical modelling: Problems and methods." Ecological Modelling 188, no. 1 (2005): 1–2. http://dx.doi.org/10.1016/j.ecolmodel.2005.05.005.

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15

Verschaffel, Lieven, Wim Van Dooren, Brian Greer, and Swapna Mukhopadhyay. "Reconceptualising Word Problems as Exercises in Mathematical Modelling." Journal für Mathematik-Didaktik 31, no. 1 (2010): 9–29. http://dx.doi.org/10.1007/s13138-010-0007-x.

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16

Sri, Irawati, Manuharawati, and Abadi. "Levels and competence in solving mathematical modelling problems: a case of preservice teachers." Perspektivy Nauki i Obrazovania, no. 1 (February 28, 2025): 732–45. https://doi.org/10.32744/pse.2025.1.47.

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The problem and the aim of the study. Mathematical modelling has become an important topic in mathematics education. However, many students are not accustomed to dealing with mathematical modelling problems, which are characterized by reality relation, relevance, authenticity, openness, and the promoting sub-competencies. Students are more familiar with solving problems where all necessary data is clearly presented, despite the fact that real-life situations rarely provide complete information upfront. The ability of students to solve modelling problems is closely linked to their teachers' capabilities. In this article, we explore the modelling competencies of preservice teachers in solving mathematical modelling problems. The exploration is based on six levels of mathematical modelling competence and describes the process of solving these mathematical modelling problems through various sub-competencies. Research methods. The research is descriptive and employs a qualitative approach. The subjects in this study were 34 preservice mathematics teachers. We used instruments in the form of mathematical modelling problems and interview guidelines. Based on the written responses and interview results, we categorized the subjects according to their modeling competency levels. The categorization of modelling competency levels is based on Ludwig and Xu’s framework, while the process of solving the mathematical modelling problem is analyzed using the Blum and Leiß modeling cycle. The description of the process of solving the mathematical modelling problem was provided by a representative from each competency level who provided an insightful answer. The data was analyzed through the stages of condensation, display, and conclusion. KEYWORDS Results. According to our research findings, the distribution of subjects across competency levels is as follows: 5.88% are at level 5, 2.94% are at level 4, 5.88% are at level 3, 11.76% are at level 2, 64.71% are at level 1, and 8.82% are at level 0. We provide a detailed description of the process of solving the mathematical modelling problem based on their respective mathematical modelling sub-competencies of one subject from each level. Conclusion. Based on the research results, the majority of preservice teachers are at level 1 (64.71%), indicating that they can understand the problem, but struggle to progress to the next stages. This is concerning because they believe they already have enough information to solve the problem, whereas solving the problem requires making assumptions. These findings reveal that the modelling competence of preservice teachers is relatively low, and it is important to focus on finding solutions to improve this. The difficulties encountered by the subjects include challenges in understanding the problem, difficulty organizing and simplifying the provided information, inability to differentiate between essential and nonessential elements, lack of algebraic skills, and limited use of various forms of representation. 

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17

Sodré, Gleison De Jesus Marinho. "Mathematical Modelling and Didactic Moments." Acta Scientiae 23, no. 3 (2021): 96–122. http://dx.doi.org/10.17648/acta.scientiae.6543.

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Background: from the perspective of mathematics education, an important issue addressed vehemently in international conferences on mathematical modelling teaching, regardless of the theoretical current adopted on the concept, is how we can teach modelling? Objective: to highlight the didactic moments announced by the anthropological theory of the didactic in the process of studying problems in concrete contexts in mathematical modelling. Design: a study and research path was conducted based on theoretical and methodological tools of the anthropological theory of the didactic. Settings and participants: preservice teachers of a degree course of a public institution, who had to solve a problem of application in savings. Data collection and analysis: From an empirical excerpt of a study developed by Sodré (2019) with preservice teachers. Results: the elements found in the empirical research confirm the hypothesis that regardless of the path taken in the modelling process, one or more didactic moments is/are performed. Conclusions: ultimately, the study of problems in concrete contexts, besides highlighting the encounter of teachers with different didactic moments, revealed the remarkable dependence between mathematical and non-mathematical know-how that stimulates us to further investigations.

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18

Korobkin, Alexander, Emilian I. Părău, and Jean-Marc Vanden-Broeck. "The mathematical challenges and modelling of hydroelasticity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1947 (2011): 2803–12. http://dx.doi.org/10.1098/rsta.2011.0116.

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Hydroelasticity brings together hydrodynamics and elastic theories. It is concerned with deformations of elastic bodies responding to hydrodynamic excitations, which themselves depend on elastic deformation. This Theme Issue is intended to identify and to outline mathematical problems of modern hydroelasticity and to review recent developments in this area, including physically and mathematically elaborated models and the techniques used in their analysis.

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19

Irawati, Sri, Manuharawati, and Abadi. "Levels and competence in solving mathematical modelling problems: a case of preservice teachers." Perspectives of science and Education 73, no. 1 (2025): 732–45. https://doi.org/10.32744/pse.2025.1.47.

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The problem and the aim of the study. Mathematical modelling has become an important topic in mathematics education. However, many students are not accustomed to dealing with mathematical modelling problems, which are characterized by reality relation, relevance, authenticity, openness, and the promoting sub-competencies. Students are more familiar with solving problems where all necessary data is clearly presented, despite the fact that real-life situations rarely provide complete information upfront. The ability of students to solve modelling problems is closely linked to their teachers' capabilities. In this article, we explore the modelling competencies of preservice teachers in solving mathematical modelling problems. The exploration is based on six levels of mathematical modelling competence and describes the process of solving these mathematical modelling problems through various sub-competencies. Research methods. The research is descriptive and employs a qualitative approach. The subjects in this study were 34 preservice mathematics teachers. We used instruments in the form of mathematical modelling problems and interview guidelines. Based on the written responses and interview results, we categorized the subjects according to their modeling competency levels. The categorization of modelling competency levels is based on Ludwig and Xu’s framework, while the process of solving the mathematical modelling problem is analyzed using the Blum and Leiß modeling cycle. The description of the process of solving the mathematical modelling problem was provided by a representative from each competency level who provided an insightful answer. The data was analyzed through the stages of condensation, display, and conclusion. KEYWORDS Results. According to our research findings, the distribution of subjects across competency levels is as follows: 5.88% are at level 5, 2.94% are at level 4, 5.88% are at level 3, 11.76% are at level 2, 64.71% are at level 1, and 8.82% are at level 0. We provide a detailed description of the process of solving the mathematical modelling problem based on their respective mathematical modelling sub-competencies of one subject from each level. Conclusion. Based on the research results, the majority of preservice teachers are at level 1 (64.71%), indicating that they can understand the problem, but struggle to progress to the next stages. This is concerning because they believe they already have enough information to solve the problem, whereas solving the problem requires making assumptions. These findings reveal that the modelling competence of preservice teachers is relatively low, and it is important to focus on finding solutions to improve this. The difficulties encountered by the subjects include challenges in understanding the problem, difficulty organizing and simplifying the provided information, inability to differentiate between essential and non essential elements, lack of algebraic skills, and limited use of various forms of representation.

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20

Yang, Xian Hua, Lotfollah Shafai, and Abdel Razik Sebak. "On the nature of wire grid modelling for numerical solutions of electromagnetic problems." Canadian Journal of Physics 71, no. 11-12 (1993): 564–70. http://dx.doi.org/10.1139/p93-085.

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Wire grid modelling has been used successfully for solving radiation and scattering problems of complicated structures, but its mathematical basis remains unclear. In this paper, we prove mathematically that wire grid modelling is equivalent to the point-matching method with subdomain basis functions. Other questions arising from applications of wire grid modelling, such as the selection of wire radius based on the "same surface area rule" and difficulties in satisfying the boundary conditions are considered and explained based on this equivalence.

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21

Friedman, Avner. "Free boundary problems in biology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2050 (2015): 20140368. http://dx.doi.org/10.1098/rsta.2014.0368.

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In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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22

Gelrud, Ya D., L. I. Shestakova, E. V. Gusev, V. L. Kodkin, and V. I. Shiriaev. "Modelling political processes in a multicriterial setting." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 24, no. 3 (2024): 111–23. http://dx.doi.org/10.14529/ctcr240310.

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A political process is a complex management system that includes, for instance, economics, electoral processes, and ecology. To make decisions when managing such a system, it is necessary to use some rules that allow to intentionally choose the best or an acceptable option. Such rules are called performance criteria. This paper discusses problems that affect different aspects of the management systems of political processes, and when choosing a solution, it is necessary to evaluate options using several criteria. These are called multicriteria problems. They emerge in strategic planning of a system, its forecasting and development. The goal of the study is to consider methods and tools of solving multicriteria problems ari-sing while managing political processes. We discuss mathematical methods that help discard solutions, which are, in all respects, worse than others, and choose a compromise option from the remaining ones. Methods. We analyzed various methods of choosing a compromise solution, their advantages and disadvantages, and identified their areas of use. First, we consider various options for condensing the criteria and illustrate their positive and negative sides. Then, we describe the procedure for constructing a set of Pareto optimal solutions. Another method is the method of successive concessions, which is a procedure for choosing a solution in a dialogue (interactive) setting. Finally, we describe a decision-making procedure based on the analytic hierarchy process. Results. The paper shows the effectiveness of applying mathematical methods to solve multicriteria problems in managing political processes. The paper concludes with an example of a solution of a management problem in accordance with all the requirements we consider. Conclusion. The use of mathematical modeling and methods to solve multi-criteria management problems helps politicians make efficient decisions in their work and provides them with communication tools by using professional mathematical language.

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23

Guseynov, Sharif E., and Jekaterina V. Aleksejeva. "Mathematical Modelling of Aquatic Ecosystem." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 3 (June 16, 2015): 92. http://dx.doi.org/10.17770/etr2015vol3.192.

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<p class="R-AbstractKeywords"><span lang="EN-US">In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used</span><span lang="EN-US">. </span></p>

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Sarjana, Ketut, Laila Hayati, and Wahidaturrahmi Wahidaturrahmi. "Mathematical modelling and verbal abilities: How they determine students’ ability to solve mathematical word problems?" Beta: Jurnal Tadris Matematika 13, no. 2 (2020): 117–29. http://dx.doi.org/10.20414/betajtm.v13i2.390.

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 [English]: This study aims to determine the level of lower secondary school students’ ability in solving mathematical word problems and how much both mathematical modelling ability and verbal ability influence the ability to solve word problems in the implementation of Kurikulum 2013 (Curriculum 2013). This study involved 411 students as samples determined by stratified proportional random sampling technique. The test used was declared valid through construct validity and reliability with Cronbach's alpha. Data were analyzed descriptively and inferentially. Descriptively, the students' ability in solving mathematical word problems was classified as medium. Meanwhile, inferentially, results were obtained indicating that: (1) students' verbal ability is significantly influential on the ability to solve word problems by 47.6%; (2) the students’ ability in mathematical modelling is significantly influential on the ability to solve word problems by 84.6%; and (3) students' verbal and mathematical modelling abilities are significantly influential on the ability to solve word problems by 87.8%. This indicates that the increase in students' ability to solve mathematical word problems will be more optimal if the verbal ability and the mathematical modelling ability are considered simultaneously, rather than focusing on one ability only. Keywords: Verbal ability, Mathematical modelling, word problems, Curriculum 2013 [Bahasa]: Penelitian ini bertujuan menentukan tingkat kemampuan siswa SMP menyelesaikan soal cerita matematika dan seberapa besar pengaruh kemampuan membuat model matematika dan verbal terhadap kemampuan menyelesaikan soal cerita pada pelaksaaan kurikulum 2013. Penelitian ini melibatkan 411 siswa sebagai sampel yang ditentukan melalui teknik stratified porposional random sampling. Tes yang digunakan dinyatakan valid melalui uji validitas konstruk dan reliabel dengan Alpha Cronbach. Data dianalisis secara deskriptif dan inferensial. Secara deskriptif, kemampuan siswa dalam menyelesaikan soal cerita matematika masih tergolong sedang. Sedangkan secara inferensial diperoleh hasil bahwa (1) kemampuan verbal siswa berpengaruh secara signifikan terhadap kemampuan menyelesaikan soal cerita, dengan kemampuan verbal 47,6%; 2) kemampuan siswa dalam membuat model matematika berpengaruh secara signifikan terhadap kemampuan menyelesaikan soal cerita, dengan kemampuan membuat model matematika 84,6%; 3) kemampuan verbal dan membuat model matematika siswa berpengaruh secara signifikan terhadap kemampuan menyelesaikan soal cerita, dengan kemampuan verbal dan membuat model matematika sebesar 87,8%. Hal ini mengindikasikan bahwa peningkatan kemampuan siswa dalam menyelesaikan soal cerita matematika akan lebih optimal jika kemampuan verbal dan kemampuan membuat model matematika diperhatikan secara bersamaan dibandingkan hanya fokus pada salah satu kemampuan saja. Kata kunci : Kemampuan verbal, Model matematika, Soal cerita, Kurikulum 2013

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Okamoto, Hidemichi. "A PROPOSAL FOR AN INNOVATIVE APPROACH TO EXTENDED MODELLING CYCLES INCORPORATING PROBLEM-POSING FROM A CREATIVITY PERSPECTIVE." International Journal of Advanced Research 12, no. 03 (2024): 943–49. http://dx.doi.org/10.21474/ijar01/18477.

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Many studies have shown that mathematical modelling, creativity, and problem-posing activities are deeply related. However, there is a lack of research that poses mathematical modelling problems. Additionally,only few studies have conducted statistical analyses of the relationship between creativity in problem-posing and creativity in psychology. The purpose of this research is to conduct a survey to quantitatively evaluate creativity, and to propose a more effective modelling cycle based on the survey results. This study focuses on fluency a creativity factor that is measured by the number of problems posed by students. The survey results showed a moderate positive correlation between fluency in posing mathematical modelling problems and creativity in psychology (r = 0.44, p <0.01). Based on the results, an extended modelling cycle is proposed and discussed.

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Suweken, Gede. "Modelling School Zone Border as Rich Modelling Problem for Secondary School Students." Emerging Science Journal 8, no. 5 (2024): 1991–2002. http://dx.doi.org/10.28991/esj-2024-08-05-019.

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This article explores the potential of using the school zoning problem in Indonesia as a vehicle for teaching mathematical modeling to secondary school students. This problem is highly suitable for students as a modeling challenge because it is (i) contextual, (ii) rich, (iii) challenging, and (iv) within students' Zone of Proximal Development (ZPD). School zoning involves a concept called Voronoi, essentially a partitioning problem. For simpler or special-case problems, these partitions can be created using concepts already taught in secondary schools, such as perpendicular bisectors and radical axes. However, for more complex problems with multiple sites, an algorithm is required, which involves advanced mathematical concepts beyond the typical secondary curriculum. Yet, with the rise of visual programming languages like Scratch, Snap!, StarLogo, and TurboWarp, it becomes possible to tackle these partitioning challenges using coding and only basic mathematical principles. This approach not only enhances students' understanding of foundational mathematical concepts but also fosters the integration of computational thinking and coding within mathematics. In summary, the school zoning problem serves as an ideal topic for mathematical modeling for secondary school students, promoting the integration of mathematical concepts, computational thinking, and coding skills. Doi: 10.28991/ESJ-2024-08-05-019 Full Text: PDF

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HESELEVA, Kateryna, and Tetiana DUMANSKA. "FORMATION OF THE SKILLS OF MATHEMATICAL MODELING OF APP LIED PROBLEMS USING THE METHODS OF DIFFERENTIAL EQUATIONS." Collection of scientific papers Kamianets-Podilsky Ivan Ohienko National University Pedagogical series 29 (December 14, 2023): 110–13. http://dx.doi.org/10.32626/2307-4507.2023-29.110-113.

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The article focuses attention on the need to learn how to solve applied problems, substantiates the need to master the skills of mathematical modelling as a universal method of solving applied and practical problems, presents the experience of students of higher education in forming the skills of mathematical modelling of applied problems using the methods of differential equations, reveals interdisciplinary connections, examples of solving geometric and physical problems from the topic “Differential Equations” are given. Problem solving was carried out in three stages, namely: building a mathematical model, studying the model and interpreting the result.

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Kanaev, A. A., V. Yu Glotov, V. M. Goloviznin, V. G. Kondakov, and A. E. Kiselev. "Mathematical modelling of hydrogen safety problems with CABARET scheme." Journal of Physics: Conference Series 1392 (November 2019): 012039. http://dx.doi.org/10.1088/1742-6596/1392/1/012039.

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REUBEN, A. J., and A. G. SHANNON. "Some Problems in the Mathematical Modelling of Erythrocyte Sedimentation." Mathematical Medicine and Biology 7, no. 3 (1990): 145–56. http://dx.doi.org/10.1093/imammb/7.3.145.

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Jiashen, Fan, Fei Weishui, and Chong-Shien Tsai. "Some mathematical modelling problems of seismic response of structures." Applied Mathematical Modelling 14, no. 9 (1990): 475–81. http://dx.doi.org/10.1016/0307-904x(90)90172-2.

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Copeland, A. H., C. D. Ringo, B. Moore, and R. S. Segall. "Mathematical modelling of singular value decomposition problems for oceans." Applied Mathematical Modelling 17, no. 10 (1993): 536–46. http://dx.doi.org/10.1016/0307-904x(93)90083-s.

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Khatibi, R. H., R. Lincoln, D. Jackson, S. Surendran, C. Whitlow, and J. Schellekens. "Systemic data management for mathematical modelling of environmental problems." Management of Environmental Quality: An International Journal 15, no. 3 (2004): 318–30. http://dx.doi.org/10.1108/14777830410531289.

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Adamu Alfaki, Hassan, Muhammad Kabir Dauda, Ahmed Mohammed Gimba, and Mohammed Abdullahi Ahmed. "On Modelling and Simulation of Electric Circuit Problems." Malaysian Journal of Computing and Applied Mathematics 3, no. 1 (2020): 24–29. http://dx.doi.org/10.37231/myjcam.2020.3.1.39.

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Differential equations are of fundamental importance in Mathematics, Physical Sciences and Engineering Mathematics. Many mathematical relations and physical laws appeared in the form of such equations. This paper reviewed an application of these equations in solving mathematical model on electric circuit problems using the First order linear differential equation. The analytical approached in solving the equations confirmed that solving electric circuits using first order linear ordinary differential equations gives accurate and reliable result. Therefore, the application is of importance and great need. However, complex problems need higher order differential equations, which are nonlinear and have entirely different approach in finding their solutions.

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LACEY, A. A., M. G. HENNESSY, P. HARVEY, and R. F. KATZ. "Mathematical modelling of Tyndall star initiation." European Journal of Applied Mathematics 26, no. 5 (2015): 615–45. http://dx.doi.org/10.1017/s095679251500042x.

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The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid–liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface; it leads to an interesting class of free boundary problems that treat the melt region as infinitesimally thin.

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Kohar, Ahmad W., Dayat Hidayat, Nina R. Prihartiwi, and Evangelista L. W. Palupi. "Preservice Teachers in Real-world Problem-Posing: Can They Turn a Context into Mathematical Modelling Problems?" SHS Web of Conferences 149 (2022): 01032. http://dx.doi.org/10.1051/shsconf/202214901032.

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While problem-posing respecting real-world situations can be a promising approach for fostering modelling competence, research on modelling through problem posing is scant. This present paper aims to characterize the mathematical tasks designed by prospective teachers regarding the criteria of a modelling problem. Data were collected from fifty mathematical tasks posed by twenty-five preservice teachers as participants at a public university in Surabaya, Indonesia, within a summative test of an assessment course.The problem-posing task asked the participants to pose two different mathematical tasks from a given realworld situation. To analyze, the participants’ responses were coded as solvable or unsolvable tasks and then further coded regarding two aspects of modelling problem i.e., connection to reality and openness of a problem. Our analysis revealed that the participants tended to pose problems with authentic connections rather than artificial connections to reality. However, only a few of the posed problems were indicated to promote openness in terms of either various mathematical models or an unclear initial state, which is the crucial indicator of a modelling problem. Implications regarding modelling competence via problem-posing in preservice teacher education are discussed.

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Talekar, P. R. "Integrating Indian Knowledge System in Medical Problems Based on Mathematical Models." International Journal of Advance and Applied Research 5, no. 12 (2024): 74–77. https://doi.org/10.5281/zenodo.11653824.

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Integrating traditional Indian knowledge systems with modern medical practices offers a promising avenue for addressing healthcare challenges. This paper explores the potential of integrating Indian knowledge systems with mathematical modelling techniques to tackle medical problems. Drawing from ancient Indian texts, contemporary medical research, and mathematical modelling methodologies, we discuss how this integration can enhance understanding, diagnosis, and treatment of various medical conditions. Through case studies and theoretical discussions, we illustrate the effectiveness of this approach and its implications for advancing healthcare globally.

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董, 清艳. "Exploring the Development of Materials for High School Mathematical Modelling Activities: From Application Problems to Modelling Problems." Creative Education Studies 11, no. 09 (2023): 2534–41. http://dx.doi.org/10.12677/ces.2023.119374.

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Zhang, Hongzhi, and L. Varlamova. "THE APPLICATION OF ORDINARY DIFFERENTIAL EQUATIONS IN MATHEMATICAL MODELLING." Scientific heritage, no. 139 (June 25, 2024): 81–83. https://doi.org/10.5281/zenodo.12526009.

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As an important branch of mathematics, ordinary differential equations have a wide range of applications in many fields. We are able to analyse and predict practical problems in depth by constructing appropriate models of ordinary differential equations. This paper demonstrates the application of ordinary differential equations in mathematical modelling by constructing mathematical models for practical problems in particle motion, concentration problems, economic and financial forecasting, and so on.

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Tasarib, Aslipah, Roslinda Rosli, and Azmin Sham Rambely. "Impacts and challenges of mathematical modelling activities on students’ learning development: A systematic literature review." Eurasia Journal of Mathematics, Science and Technology Education 21, no. 5 (2025): em2641. https://doi.org/10.29333/ejmste/16398.

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Mathematical modelling is essential in mathematics education, presenting real-world problems in mathematical terms. This systematic literature review aims to evaluate the effectiveness of mathematical modelling in education and its implications for teaching and learning. The review used the PRISMA approach and a systematic search of electronic databases to identify relevant articles. The review identified key themes, including the impact of mathematical modelling activities on students’ learning development and the challenges of these activities. It identified patterns and trends in students’ achievement and skills through modelling activities, the effectiveness of enhancing mathematical learning development, and the challenges in implementing mathematical modelling. Key findings revealed the varying impact of different approaches on diverse modelling tasks. The review emphasized the need for educators to prepare for mathematical modelling practices and suggested that their effectiveness depends on task nature, learners’ age, and learning context. Future research should refined best practices, standardize classroom materials, and explore innovative approaches.

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Nielsen, S. N. "Matrices and graphs — Stability problems in mathematical ecology." Ecological Modelling 77, no. 1 (1995): 86–87. http://dx.doi.org/10.1016/0304-3800(95)90034-9.

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Fajri, Hardian Mei, Arita Marini, and Suyono Suyono. "A bibliometric study on mathematical modelling in elementary schools in the Scopus database between 1990-2024." Eurasia Journal of Mathematics, Science and Technology Education 21, no. 2 (2025): em2577. https://doi.org/10.29333/ejmste/15916.

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Mathematical modelling is an approach to bridge real-world problems into mathematics as an effort to improve students’ mathematical literacy. The purpose of this study is to conduct a bibliometric analysis of published articles related to mathematical modelling in elementary school. This research uses bibliometric analysis method. This study used the Scopus database scanned with the keywords “mathematical modelling” and “elementary school” with a time span of 1990-2024 obtained as many as 78 articles. The data collected was then analyzed using R-software and VOSviewer applications. The results of this study found that the development trend of mathematical modelling research in elementary schools significantly increased after 2015-2023 with a percentage of 67.95%. The top researchers who have the most influence are dominated by authors from Germany and Denmark. Furthermore, in recent years the dominant topics in mathematical modelling research studies in elementary schools such as mathematical modelling cycle, development, mathematical modelling competency, mathematical concept, mathematical knowledge, modeling process, mathematical modelling task, empirical study, and creative thinking. It is hoped that future research can focus on the literature of mathematical modelling carried out on the subject of high school to college level and include analysis on the literature in the years 1960-1990 which is the campaign period and the early years of integrating mathematical modelling into the curriculum of various countries in the world.

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Tangkawsakul, Sakon, Weerawat Thaikam, and Songchai Ugsonkid. "Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems." Journal of Education and Learning 13, no. 3 (2024): 133. http://dx.doi.org/10.5539/jel.v13n3p133.

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Real-world mathematical problem (RWMP) solving and posing are important aspects of teaching and learning mathematical modelling, as well as developing a mathematization disposition for both teachers and students. Several researchers have explored blockages or difficulties in such modelling processes and in problem posing. However, prior research has identified difficulties that the pre-service mathematics teachers (PSMTs) encountered when they tried to pose a modelling problem by choosing the general topic themselves, as there is little known about possible obstacles that PSMTs can encounter when trying to pose a real-world problem relevant to a given mathematical topic. The current study explored the difficulties encountered by PSMTs in a RWMP-posing activity. The target group was 23 PSMTs with prior experience in mathematical modelling and mathematical problem posing. The findings showed that the PSMTs struggled with: (a) task organization, which involved selecting and understanding mathematical knowledge; (b) specialized content knowledge, which included a lack of real-world knowledge and difficulty in connecting mathematical concepts to real-world contexts; and (c) individual considerations of aptness, which encompassed authenticity, interest, complexity, language, and relevance to task organization. The PSMTs applied various strategies to complete the posing task, such as using problem-posing and solving heuristics, adapting existing problems, sharing and discussing with friends, and considering the perspective of a typical student. The implications of these findings should help in developing preparatory instructional practices for mathematics teachers.

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Lu, Xiaoli, and Gabriele Kaiser. "Can mathematical modelling work as a creativity-demanding activity? An empirical study in China." ZDM – Mathematics Education 54, no. 1 (2021): 67–81. http://dx.doi.org/10.1007/s11858-021-01316-4.

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AbstractCreativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling has recently been introduced as one of the six core competencies in the Chinese mathematical curriculum and is built on students’ ability to solve real-world problems using mathematical means. As mathematical modelling is characterised by openness regarding the understanding of complex real-world problems and the complex relationship between the real world and mathematics, for the strengthening of creativity, mathematical modelling activities seem to be adequate to accomplish this purpose. In this paper, we describe a study with 71 upper secondary school students, 50 pre-service mathematics teachers, and 66 in-service mathematics teachers, based on an extended didactical framework regarding mathematical modelling as a creativity-demanding activity. The results of the study indicate a significant correlation between modelling competencies and creativity aspects. Especially significant correlations between the adequacy of the modelling approaches and the two creativity aspects of usefulness and fluency could be identified, as well as a significant negative correlation between usefulness and originality. The results of the correlational analysis of relationships among the four criteria were not always consistent in the three participant groups. Overall, the results have implications for the promotion of creativity for various expertise groups and demonstrate the dependency of the modelling activities on the mathematical knowledge of the participants and the mathematical topic with which they are dealing.

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Wei, Yicheng, Qiaoping Zhang, and Jing Guo. "Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies." Education Sciences 12, no. 12 (2022): 923. http://dx.doi.org/10.3390/educsci12120923.

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STEM education has been promoted in schools worldwide to cultivate students’ 21st-century skills. Mathematical modelling is a valuable method for developing STEM education. However, in this respect, more attention is given to secondary level or above compared with kindergarten or primary level. Teaching mathematics at the primary level is closely related to authentic problems, which is a crucial characteristic of mathematical modelling activities. After screening 239 publications from various databases, we reviewed 10 empirical studies on mathematical modelling at the primary level. In this systematic review, we analysed the following three aspects: (1) the use of professional development intervention methods/strategies to enhance the intervention effects and the competencies of primary teachers to utilize mathematical modelling; (2) the effects of mathematical modelling on primary students and methods of improving their mathematical modelling skills; and (3) methods used to assess the modelling skills of primary school teachers and students. The results indicate that professional development interventions can enhance the teaching quality of mathematical modelling. The components of the interventions should include an introduction to the pedagogy of mathematical modelling, clarifying the role of the teacher and the student in mathematical modelling activities. Through mathematical modelling, students can generate mathematical ideas, explore mathematical theorems independently, develop critical thinking, and improve their metacognitive and communicative skills. The competency of mathematical modelling is often determined using formative assessments of teachers and students. Because limitations still exist in conducting primary-level modelling activities, schools should utilise more standardised assessment methods, provide universal teacher training, and grant more opportunities for primary school students to participate in mathematical modelling activities. The lack of research on cross-cultural contexts should draw the attention of future research.

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Bucur, Amelia. "About Applications of the Fixed Point Theory." Scientific Bulletin 22, no. 1 (2017): 13–17. http://dx.doi.org/10.1515/bsaft-2017-0002.

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Abstract The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

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Pisano, Raffaele, and Paolo Bussotti. "OPEN PROBLEMS IN MATHEMATICAL MODELLING AND PHYSICAL EXPERIMENTS. EXPLORING EXPONENTIAL FUNCTION." Problems of Education in the 21st Century 50, no. 1 (2012): 56–69. http://dx.doi.org/10.33225/pec/12.50.56.

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Generally speaking the exponential function has large applications and it is used by many non physicians and non mathematicians, too. Nevertheless some crucial and practical problems happen for its mathematical understanding. Mostly, this part of mathematical cognitive programmes introduce it from the mathematical strictly point of view. On the contrary, since both physics experiments make a vast use of it, in this paper the exponential function will be explained starting from physical experiments and only later a mathematical modelling of it will be organized. The relationship physics-mathematics-geometry is crucial and indispensable in this kind of integrated and history&science education. The history and epistemology of mathematics and physics can be a significant means to make the epistemological and didactical research more profound and clear. Key words: interdisciplinary, elementary functions, geometric transformations, epistemological teaching, thermology and calorimetry.

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Jeulin, Dominique. "MODELLING RANDOM MEDIA." Image Analysis & Stereology 21, no. 4 (2011): 31. http://dx.doi.org/10.5566/ias.v21.ps31-s40.

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Basic random structure models (random sets and random function models) are introduced for the simulation of images and of microstructures. Their implementation requires the use of image analysis tools defined in mathematical morphology.They can be used for solving problems of physics of random media.

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Quarteroni, A., A. Manzoni, and C. Vergara. "The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications." Acta Numerica 26 (May 1, 2017): 365–590. http://dx.doi.org/10.1017/s0962492917000046.

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Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. In this review article we will address the two principal components of the cardiovascular system: arterial circulation and heart function. We will systematically describe all aspects of the problem, ranging from data imaging acquisition, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, proposing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the physiological processes involved, and the need to devise computational methods that are stable, reliable and efficient. Critical issues involve filtering the data, identifying the parameters of mathematical models, devising optimal treatments and accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are of paramount importance when solving problems with high complexity, which would otherwise be out of reach.

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Tomczyk, Krzysztof. "Problems in Modelling Charge Output Accelerometers." Metrology and Measurement Systems 23, no. 4 (2016): 645–59. http://dx.doi.org/10.1515/mms-2016-0045.

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Abstract The paper presents major issues associated with the problem of modelling change output accelerometers. The presented solutions are based on the weighted least squares (WLS) method using transformation of the complex frequency response of the sensors. The main assumptions of the WLS method and a mathematical model of charge output accelerometers are presented in first two sections of this paper. In the next sections applying the WLS method to estimation of the accelerometer model parameters is discussed and the associated uncertainties are determined. Finally, the results of modelling a PCB357B73 charge output accelerometer are analysed in the last section of this paper. All calculations were executed using the MathCad software program. The main stages of these calculations are presented in Appendices A−E.

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Shazhdekeyeva, Nurgul, Salamat Idrissov, Bahyt Barsay, Aigul Myrzasheva, and Toidyk Akhmurzina. "Ethnomathematical problems in the context of the ethnocultural content of mathematical education." Scientific Herald of Uzhhorod University Series Physics 2024, no. 55 (2024): 1343–51. http://dx.doi.org/10.54919/physics/55.2024.134fp3.

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Relevance. The relevance of this study lies in the fact that modelling the content of ethnomathematical problems determines the range of mathematical competencies and skills, including mathematical reasoning and problem-solving, the cycle of which comprises the corresponding ethnocultural processes. Modelling measures how effectively the state prepares students to use mathematics in all aspects of their personal, civic, and professional life so that they become rational, committed, and thinking members of modern society.Purpose. The purpose of this study is to investigate the modelling of ethnomathematical problems necessary for the successful establishment and development of mathematical competencies of students in grades 5�6.Methodology. These problems include the use of concepts, properties, procedures, and tools to describe, explain, and predict phenomena, which, in turn, help to draw informed conclusions and make informed decisions.Results. The role of ethnomathematical problems in a rapidly changing world driven by new technology and trends, where students in grades 5�6 are creative and actively involved in learning, can be of great importance and enable the children to make non-standard decisions on behalf of themselves or the society they live in. This puts at the forefront the capacity for mathematical thinking, which has always been part of the development of teaching competencies. Modern technological advances also require students to understand the concepts of computational thinking that are part of mathematical skills. The ability of modelling allows enables logical reasoning, as well as allows honestly and convincingly presenting arguments, which are becoming an increasingly important structure of ethnocultural practice in the modern world.Conclusions. The practical significance lies in the definition of mathematical means of folk pedagogy, which allows developing a methodology and technology of teaching to structure and model the content of ethnomathematical tasks.

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