Mathematical Modeling Course Research Articles

Computational Thinking Processes in Solving the Corona Epidemic Model: Pre-service Maths Teachers

In the 21st century, pre-service mathematics teachers are expected to have problem-solving skills that are effective, efficient, and solutive and are in line with the mindset of computer experts. In learning mathematics, the concept of computational thinking (CT) is also needed and at this time, many still have difficulty solving mathematical problems in general, especially in solving problems in epidemic mathematical models. The subjects of this study were twenty-seven pre-service mathematics teacher students who took mathematical modeling courses. The researcher used the purposive sampling technique to select two research samples. The research method used was a descriptive qualitative research method in exploring the thinking process of pre-service mathematics teacher students in solving the problem of modeling the epidemic spread of disease. The results showed that the thinking process of the first subject began with identifying the problem and existing information by writing down the data in the form of a graph so as to get a certain pattern, which was then used as the basis for the process of transforming the problem into mathematical language. By adding assumptions related to the existence of environmental limitations in the next epidemic model, the concept of differential equations, in which there are integral properties and natural logarithms, can be used to find the solution to the epidemic model. The second subject was unable to solve the integral at hand. The researcher discovered that pre-service mathematics teacher students who correctly solved the problem in the mathematical model used CT components, namely decomposition, abstraction, pattern recognition, algorithm and mathematical literacy.

"Four New and Three High" Mathematical Modeling Course Construction

After years of inheritance, innovation and integration, the mathematical modeling curriculum has been reformed from the aspects of education concept, training goal, teaching system, teaching material system, course content, teaching method and learning mode. Teaching "four new" design is to organically integrate the ideological and political elements with professional characteristics into the course teaching, innovate the course content, teaching methods and evaluation methods, enhance the students' independent learning ability, and realize the integration of teaching and ideological and political education. The transformation of "three high" innovation resources into teaching: high-level design, high-quality requirements, high-level implementation, relying on high-level scientific research and innovation resources, timely transformation into teaching resources through classroom teaching, extracurricular science and innovation, school-enterprise exchanges and other ways, and focusing on cultivating students' practical ability and innovation ability.

Case Article—Racial Bias in Automated Traffic Law Enforcement and the Price of Unjustness

This case study has been developed for students to practice their data analysis and optimization skills in a contemporary societal issue: that of injustice in automated traffic law enforcement. Specifically, this case study is for students of modern data analysis and statistical modeling courses that focus on hypothesis testing; it also has a component for students in optimization and mathematical modeling courses that focus on linear and network optimization. The case study has been used since Spring 2023 in a combination of two courses from the Industrial Engineering (Analysis of Data, an introduction to probability and statistics) and Civil Engineering (Transportation Systems, an introduction to mathematical modeling and optimization for civil engineers with a focus on transportation) curricula. History: This paper has been accepted for the INFORMS Transactions on Education Special Issue on DEI in ORMS Classrooms. Supplemental Material: The Teaching Note and data files are available at https://www.informs.org/Publications/Subscribe/Access-Restricted-Materials .

Case—Racial Bias in Automated Traffic Law Enforcement and the Price of Unjustness

This case study has been developed for students to practice their data analysis and optimization skills in a contemporary societal issue: that of injustice in automated traffic law enforcement. Specifically, this case study is for students of modern data analysis and statistical modeling courses that focus on hypothesis testing; it also has a component for students in optimization and mathematical modeling courses that focus on linear and network optimization. The case study has been used since Spring 2023 in a combination of two courses from the Industrial Engineering (Analysis of Data, an introduction to probability and statistics) and Civil Engineering (Transportation Systems, an introduction to mathematical modeling and optimization for civil engineers with a focus on transportation) curricula. History: This paper has been accepted for the INFORMS Transactions on Education Special Issue on DEI in ORMS Classrooms.

Математичне моделювання частоти патології вагінального відростка очеревини в дитячій популяції залежно від віку та статі

The pathology of the processus vaginalis of the peritoneum (inguinal hernia, hydrocele testis) is quite widespread among the pediatric population, both in our country and throughout the whole world. More than 99% of inguinal hernias in children are oblique, right-sided localization is more than 3 times more common than left-sided. High interest of scientists in the study of the pathology of the processus vaginalis of the peritoneum is caused by data on the appearance of infertility as a complication of inguinal hernias and dropsy of the testicles. In the structure of the causes of this situation, 30% belongs to the male factor, and this percentage has a constant tendency to increase. This became the reason for an additional study of the mathematical component of the prevalence of the pathology of the processus vaginalis of the peritoneum among the children’s population. Purpose - to create a mathematical model of the prevalence of pathology of the processus vaginalis of the peritoneum depending on age and gender among the children’s population. Materials and methods. 205 patients under the age of 18 who underwent surgical correction of the pathology of non-obliterated processus vaginalis of the peritoneum (inguinal hernia, hydrocele testis) took part in the conducted scientific study. For mathematical modeling, software built into Microsoft Excel was used (Trend line, polynomial regression equation of the 4th degree). Results. In the course of mathematical modeling, characteristic features were identified: they occur both in the female part of the pediatric population and in the male, similar fluctuations are noted in the general pediatric population, namely periods of increase in the frequency of pathology of the vaginal peritoneum, which alternate with periods of its decline. a rapid increase in the frequency of pathology of the vaginal peritoneum, and, accordingly, their surgical correction, in children under 3-4 years of age, followed by a decrease in frequency by the age of 11-13 years. The following slight increase in the frequency of diagnosis of pathology of the vaginal peritoneum and its surgical treatment was detected by the age of 15-16 years, followed by a gradual decrease in the frequency by the age of 18 years Conclusions. Therefore, there are two mathematically confirmed peaks of growth in the frequency of detection of the pathology of the processus vaginalis of the peritoneum, which fall on the age of verticalization of the child and the age of “specialized” loads. The research was carried out in accordance with the principles of the Helsinki Declaration. The study protocol was approved by the Local Ethics Committee of participating institution. The informed consent of the patient was obtained for conducting the studies. No conflict of interest was declared by the authors.

Combat modelling using Lanchester equations

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Using mathematical modelling to provide students with a contextual learning experience of differential equations

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a contextual environment. Teaching mathematics in context has the potential of giving students something to anchor the mathematics to and hence act as cognitive roots With this in mind, in what ways can lecturers use mathematical modelling to provide students with contextual learning experiences of differential equations? A New Zealand study was carried out involving three case studies. Each case study comprised of a mathematical modelling course, lecturer participant and student participants. Modelling examples and activities that involved differential equations were part of all course content. In this paper, I will present information on each course, the main modelling activities each course used, and examples of students' use of differential equations for these activities. Insights discovered into the common practices of the three lecturers regarding using mathematical modelling to teach differential equations will also be presented.

Ortaokul matematik öğretmen adaylarının model oluşturma etkinliği tasarlama yeterlikleri, problem çözmeye yönelik inançları, problem kurmaya yönelik öz-yeterlik inançları ve aralarındaki ilişki

This study aimed to determine the change and the relationship between elementary school mathematics teacher candidates' competence to design model-eliciting activities, their beliefs towards problem-solving, and their self-efficacy beliefs towards problem posing according to gender and overall academic grade point average (GPA). Modeling activities designed by 64 elementary school mathematics teacher candidates in Turkey were evaluated by means of a grading key created in the context of "compliance with MEA design principles". In addition, a scale consisting of 24 items was applied to determine the beliefs of the teacher candidates towards problem-solving, and a 26-imoetem scale was applied to determine their self-efficacy beliefs towards problem-posing, and the responses were analyzed by quantitative methods (one-way multiple variance analysis, correlation analysis, multiple regression test). The findings reveal that elementary school mathematics teacher candidates' proficiency in designing model-eliciting activities is generally at a high level, while their belief in problem-solving and self-efficacy beliefs in problem posing is generally at a moderate level. Based on the studies that concluded that modeling competencies develop as they work on modeling problems and that the experience of mathematical modeling affects their mathematical modeling competencies, it was concluded that modeling problems were used to solve mathematical problems and teach these solutions in the mathematical modeling course they took. It was determined that the linear combinations of teacher candidates' proficiency in designing model-eliciting activities, beliefs in problem-solving, and self-efficacy beliefs in problem-posing did not show a significant difference. The fact that pre-service teachers' beliefs about problem solving and posing are not related to their MEA design competencies is thought to be due to their previous routine mathematical problem solving experiences being more dominant. On the other hand, since the mathematical modeling process is basically considered as a problem-solving process, it was expected that these beliefs of pre-service teachers would be related to MEA design proficiency. It is important to conduct qualitative research with teacher candidates in order to examine this situation in more detail and to reveal the underlying causes.

Mathematical Modeling Instruction Based on ISM In Middle and High Schools to Encourage Path-Obstruction Detection

The mathematical modeling course is one of the courses in the mathematics curriculum that has the most cross-cutting content with other courses, and achieving cross-curricular outreach is an important part of integrated practice implementation. This study uses the ISM method to find 18 factors from 5 dimensions that prevent the promotion of mathematical modeling courses, explains how the components are interconnected, and arranges the link using hierarchies, concludes that social support has the most significant impact on the promotion of mathematical modeling courses, and that their development cannot be achieved without the collaborative efforts of society, schools, teachers, and students. This study makes recommendations for reforming the system for integrating and developing mathematical modeling courses with basic courses, as well as for increasing awareness of and recognition for these courses with the cooperation of multiple parties.

Improving high school students’ perceptions of mathematics through a mathematical modelling course

Abstract Literature shows there is support for adding connection and relevancy in mathematics for students through the use of real-world context and data in mathematical modelling. A teaching unit on mathematical modelling was designed within the context of future affordable housing for the local surrounding area. The teaching unit was implemented, and data were collected to address the research question: ‘How does exposure to mathematical modelling influence students’ perceptions and understandings of mathematical modelling?’ Data were collected through pre- and post-teaching unit surveys and post-teaching unit student interviews. Pre- and post-surveys were used to establish any changes in students’ perception towards mathematics, understanding of mathematical modelling and perceived relevance of mathematical modelling use to their own lives. Student interviews gained further insight into the student experience and associated perception changes. Statistical analysis of the survey responses included both hypothesis and nonparametric testing. Interviews were analysed using a thematic qualitative approach. Our analysis showed that a greater understanding of mathematical modelling was achieved, with many students unfamiliar with the concept prior to the teaching unit. It was also found that through the real-world context of the mathematical modelling unit, students had a new-found interest in mathematics.

Empirical Efficiency Modeling of Online + Offline Teaching Evaluation Mode of Courses Based on 6G Real-Time Image Transmission Architecture

Putting forward the requirements of the 6G-oriented space-earth integrated information network architecture, and put forward a flexible and reconfigurable space-earth integrated information network architecture on this basis. On the basis of the research, it puts forward the countermeasures and suggestions to improve the evaluation mode of college English online teaching. From the aspects of curriculum structure, curriculum implementation, evaluation feedback, teacher team construction and talent training, the innovative teaching mode of "online micro-course" integrated into mathematical modeling courses is studied. A set of experimental teaching plans based on small modeling projects and corresponding teaching methods are proposed. The system of learning evaluation, and the effect of curriculum reform was analyzed through empirical teaching.

Talking about the Present Situation, Problems and Strategies of Information Technology in the Integration of Mathematical Modeling Courses

With the development of information age in China, information technology has been widely used in mathematics education and teaching. According to the High School Mathematics Curriculum Standards (2017 Edition) issued in 2018, China's emphasis on mathematical modeling has been further enhanced, and the core quality of mathematical modeling has become one of the six core qualities. This paper analyzes the current situation and problems of the integration of information technology and mathematical modeling courses, and finally gives some strategies, hoping to have some guiding significance in the future mathematical education and teaching.

数学建模课程的教学现状分析

数学建模课程的教学现状分析

ПАРАЛЕЛЬНЕ ВИЗНАЧЕННЯ СПЕКТРУ СИМЕТРИЧНИХ ТЕПЛИЦЕВИХ МАТРИЦЬ З ПЕРЕТВОРЕННЯМИ ЛЕВІНСОНА-ДАРБІНА

Purpose. The paper investigates modern approaches to mathematical modeling of random fields using correlation matrices of superhigh dimensions. Methodology. Techniques for constructing surrogate models focused on reducing the high dimension of stochastic input spaces have been considered. A comparative analysis of modern numerical methods for searching for eigenvalues of filled matrices has been carried out with an assessment of the possibilities of parallelizing the computation process. To determine the range of the distribution spectrum of eigenvalues of symmetric Toeplitz matrices and subsequent localization of eigenvalues, the use of Gershgorin circles has been proposed. As test matrices, we used the generation of random vectors of arbitrary dimensions, followed by the formation of symmetric Toeplitz matrices on such vectors. Results. The studies have been carried out both for serial and parallel implementations of computational processes. When testing, the main tasks were aimed at conducting a comparative analysis of the accuracy of the solutions obtained, at estimating the coefficient of the ratio of the total number of partitioning problems to those that led to obtaining an eigenvalue. Scientific novelty. The use of a parallel procedure for separating and refining all matrix eigenvalues using a priority search for the smallest(s), largest(s) of eigenvalues has been justified. A software application has been developed for separating and refining all eigenvalues of symmetric Toeplitz filled matrices, which are formed in the course of mathematical modeling of random fields. Practical significance. The proposed software product can be used in numerical simulators for the implementation of mathematical models of groundwater flows and physicochemical processes of dissolution in deep aquifers.

The limitation and countermeasures of mathematical modeling course in finance and economics universities

The limitation and countermeasures of mathematical modeling course in finance and economics universities

Prediction model for different progressions of Atherosclerosis in ApoE-/- mice based on lipidomics

Atherosclerosis (AS) is a progressive disease with a complex pathogenesis which is characterized by dyslipidemia and changes in the vascular wall composition. According to the degree of lesions, atherosclerosis can be divided into four stages: hyperlipidemia, lipid stria, fiber plaque, and atherosclerotic plaque. The present study aimed to establish a prediction model for the different pathological stages of AS based on lipidomics. ApoE-/- mice and C57BL/6 mice fed a normal diet were divided into seven groups according to the feeding time (8, 12, 16, 20, 24, 28, and 32 weeks). The changes in the lipid composition and serum content were detected using ultra-performance liquid chromatography coupled with quadrupole time-of-flight high-definition mass spectrometry (UPLC-Q-TOF/MS). Through the results of serum total cholesterol, triglyceridelow density lipoprotein at each time and HE staining of the head and arm artery, the seven time points of the model group were corresponding to the four courses of atherosclerosis. In accordance with the lipid data of each course of AS and mathematical modeling, this study established a multi-index prediction model of the different processes of AS. Notably, while establishing the model, several indicators were combined with one of four dimension reduction methods, such as principal component logistics regression method, cumulative logistics regression method, Partial least squares-discriminant analysis(PLS-DA), and canonical discriminant analysis (CDA). The error rate of the four methods were 28.5%, 16.22%, 18.24%, and 14.86%, respectively. CDA had the lowest error rate and the best prediction accuracy of the AS different courses for the training and verification sets after 5-fold cross-validation of this model. This study showed that lipidomics combined with mathematical methods could establish a non-invasive and accurate model for the prediction of AS.

What does mathematical modelling have to offer mathematics education? Insights from students' perspectives on mathematical modelling

The student experience with mathematical modelling has the potential to differ in nature to the experience of a typical mathematics student. The research reported in this paper forms part of a broader study looking into tertiary learning experiences for mathematical modelling. This paper reports on: What are the student experiences when learning to mathematically model? How might these experiences inform mathematics education? Data were collected across two different tertiary mathematical modelling courses in the form of student interviews. Student interviews were analysed, using reflective thematic analysis, to identify themes relating to the collective student learning experience. The results show that modelling provides an opportunity for students to be actively involved with their learning. Being open-minded was a key behaviour for a productive student experience.

Methodological aspects of teaching mathematical modeling in the system of university education

The problem of formation of practice- and professionally-oriented skills by means of general subject areas in the conditions of constant modernization of educational standards of higher professional education and realization of the concept of development of mathematical education is investigated in the work. The problem of convergence in the educational process of theoretical and applied mathematics is studied, which, in fact, is solved by means of e(ective use of ideas and methods of mathematical modeling. There is a cross-cutting content and methodological line of mathematical models, in the implementation of which the greatest potential for increasing the motivation of students to mathematical activities. It is shown that this approach is a carrier of innovation, novelty in the content of mathematical courses and methods of their teaching and practice-oriented orientation. The inseparable connection between the methodology of cognition and the methodology of practical integrity of the study of applied problems of natural sciences, which are studied in various mathematical courses of higher education institutions for the further formation of professional competencies in the course of mathematical modeling.

Математическое моделирование процесса удаления растительности при проведении мелиоративных работ

In the article, based on the analysis of the process of removing vegetation during reclamation work, it is shown that in order to perform them at the lowest amount of current and capital costs, it is necessary to take into account the limited nature of certain types of resources, the requirements for certain types of work, and other factors. In the course of mathematical modeling, it was taken into account that the number of technical means for performing the planned work should not exceed the amount of machines available on the farm, bought again and attracted from other farms, minus those to be withdrawn from the balance sheet and leased during this period. When establishing the amount of fuels and lubricants for a specific period when performing mechanized work, it is necessary to keep in mind the intensity of use of machines. When planning the number of machines and their use, it is necessary to take into account the seasonal nature of the work and the limited reserves for replenishing the staff of machine operators. Specific restrictions are formulated that allow for a comprehensive planning of the use of machines and the labor of machine operators. As a result of the research, it was found that the development of a plan for the optimal distribution of the fleet of machines allows you to establish the best option for using machines, the efficiency of performing specific operations of the technological process by individual machines, ensuring that the existing machines perform work in the optimal time, which ultimately helps to increase the profitability of operating machines on 15-35%.

Perceptions of Pre-Service Teachers Regarding the Model Eliciting Activities

This study aims to examine the perceptions of pre-service mathematics teachers about mathematical modelling activities. Participants of the study comprised 23 pre-service mathematics teachers who undertook a course on mathematical modelling. A 12-hour mathematical modelling course revealed the perceptions of participants. After it, the participants found/developed a modelling problem and explained why they evaluated it as a model eliciting activity (MEA). MEA found/developed by participants were examined by taking the principles of developing MEA into consideration. Results showed that many participants considered having more than one solution, the principle based on real-life context, and suitability for group work for MEA. The participants did not focus on the model documentation principle. Based on this result, faculty members can help pre-service teachers by using activities that can be considered appropriate for this principle in modelling education.