Mathematical Modeling Course Research Articles

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.

Гендерные различия предпринимателей, специализирующихся на торговле и информационных технологиях

The article is devoted to the assessment of the creation of new businesses in trade and information and communication sphere. Gender differences in entrepreneurial activity by country are considered. The study examined the specifics of the activities of entrepreneurs engaged in services in such sectors as trade and information and communication services for institutions and organizations, as well as private clients. At the same time, the principles and concepts of the existing development of the sectoral structure of entrepreneurship were taken into account. The implementation of the study consisted of five stages. The information base included the results of questionnaire surveys of respondents-entrepreneurs in 59 states when monitoring the activities of entrepreneurs in 2018. In the course of economic and mathematical modeling, six models were developed that reflect the distribution of the following indicators across the subjects of Russia: the proportion of women and men who have created businesses in trade, in the total number of women and men who have started entrepreneurial activity; the share of women and men who have created businesses in the information and communication sphere in the total number of women and men who have started entrepreneurial activities. In addition, the ratios of specific weights describing the provision of services by women entrepreneurs and men entrepreneurs in the trade sector and the information and communication sphere are calculated. For each of the 59 countries, it was determined whether there is an excess of the values of indicators that characterize the corresponding specific weights of male entrepreneurs and female entrepreneurs. For most countries, these values differed significantly, which indicates gender gaps. In addition, the States with the maximum and minimum values of the indices under consideration were identified. The analysis was carried out, which made it possible to compare the obtained average values with the data reflecting the indicators of Russian entrepreneurs. The share of female entrepreneurs in trade is higher than the share of male entrepreneurs. The share of male entrepreneurs in the field of information and communication services is twice as high as the share of female entrepreneurs. The results of the work can be applied in the development of forecasts for the development of trade and information and communication services in the future.

Evaluation and empirical analysis of the influence of disciplinary competition on innovation practice ability

Mathematical modelling is an embodiment of the application of mathematics in various fields. Exploring the effect of mathematical modeling on the innovative practical ability of college students is conducive to college students’ understanding of mathematical modeling competitions and colleges’ education on mathematical modeling courses. It can also stimulate the confidence of students majoring in mathematics in their majors. On the basis of clarifying the theoretical basis and basic principles of the evaluation of innovative practical ability, this paper combines the characteristics of current college students to construct a college student’s innovation that includes 5 first-level indicators and 15 second-level indicators. Practice system. By the Delphi method and improved analytic hierarchy process we can determine the index weights and the weighted average model of fuzzy mathematics to analyze the collected evaluation membership matrix. We also obtain the membership matrix of the impact of mathematical modeling on the innovative practical ability of college students. Using the principle of maximum membership to get the degree of influence , the research results show that the mathematical modeling competition can improve the innovative and practical ability of college students.

College-level mathematical modelling with mobile devices

PurposeThis work is devoted to increasing the effectiveness of a mathematical modelling lesson with the help of mobile devices. It verifies the authors' hypothesis which states that enabling students to solve mathematical models on mobile devices improves their academic results in the discipline.Design/methodology/approachThe paper describes an experiment conducted among 38 college students in an extracurricular mathematical club where they solved mathematical models with the help of their own smartphones. The authors describe the mathematical models assigned to students, analyse their academic performance and gather their opinions.FindingsThe usage of mobile devices in the mathematical modelling class positively affects students' scores and interest in the subject. The percentage of positive grades among students working on mobile devices is higher than among students working on desktop computers.Originality/valueThe authors discover that in the context of the college-level mathematical modelling course, mobile devices can be successfully used as an alternative replacement for traditional desktop computers.

Designing and Teaching an Undergraduate Mathematical Modeling Course for Mathematics Majors and Minors

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this course to build students' mathematical thought processes and toolbox, ability to analyze and evaluate mathematical models, mathematical modeling skills, and teamwork skills. The course described is intended as an upper division undergraduate course with a prerequisite of differential equations.

Formative Assessment of Pre-Service Teachers’ Knowledge on Mathematical Modeling

This document reports how formative assessment strategies promote the knowledge of modeling of pre-service mathematics teachers. This knowledge is understood from content and vehicle points of view. Formative assessment strategies were designed and experimented with 14 participants in a mathematical modeling course offered to pre-service teachers in a Colombian university. Thematic analysis was conducted on lesson plans built by pre-service teachers. In those plans, they evinced knowledge of class management, mathematics teaching, problem solving, and modeling teaching. Finally, the collective construction of assessment rubrics is highlighted. Its contributions and limitations as a formative assessment tool are reported. The role played by the advisors’ feedback and support to pre-service teachers is also presented.

Discrete Zombie Apocalypse A Mathematical Modeling Course Project

For undergraduate mathematical modeling courses, a successful semester project can reinforce key learning objectives while enabling creativity and developing critical thinking skills. However, course directors often struggle in developing novel project ideas and balancing the tradeoff between grading burden and project complexity. At the Military Academy, we take an open-ended and discovery-learning approach to the freshman level math modeling project. This article outlines one successful project involving a Zombie Apocalypse scenario along with student responses. To assist the students, we promote flexibility, scaffold the modeling process with in-progress reviews, and train students on how to write concise executive summaries.

Improving open and rigorous science: ten key future research opportunities related to rigor, reproducibility, and transparency in scientific research

Background: As part of a coordinated effort to expand research activity around rigor, reproducibility, and transparency (RRT) across scientific disciplines, a team of investigators at the Indiana University School of Public Health-Bloomington hosted a workshop in October 2019 with international leaders to discuss key opportunities for RRT research. Objective: The workshop aimed to identify research priorities and opportunities related to RRT. Design: Over two-days, workshop attendees gave presentations and participated in three working groups: (1) Improving Education & Training in RRT, (2) Reducing Statistical Errors and Increasing Analytic Transparency, and (3) Looking Outward: Increasing Truthfulness and Accuracy of Research Communications. Following small-group discussions, the working groups presented their findings, and participants discussed the research opportunities identified. The investigators compiled a list of research priorities, which were circulated to all participants for feedback. Results: Participants identified the following priority research questions: (1) Can RRT-focused statistics and mathematical modeling courses improve statistics practice?; (2) Can specialized training in scientific writing improve transparency?; (3) Does modality (e.g. face to face, online) affect the efficacy RRT-related education?; (4) How can automated programs help identify errors more efficiently?; (5) What is the prevalence and impact of errors in scientific publications (e.g., analytic inconsistencies, statistical errors, and other objective errors)?; (6) Do error prevention workflows reduce errors?; (7) How do we encourage post-publication error correction?; (8) How does ‘spin’ in research communication affect stakeholder understanding and use of research evidence?; (9) Do tools to aid writing research reports increase comprehensiveness and clarity of research reports?; and (10) Is it possible to inculcate scientific values and norms related to truthful, rigorous, accurate, and comprehensive scientific reporting? Conclusion: Participants identified important and relatively unexplored questions related to improving RRT. This list may be useful to the scientific community and investigators seeking to advance meta-science (i.e. research on research).

INTERDISCIPLINARY ANALYSIS OF DEMOGRAPHIC PROCESSES IN RELATION TO THE CENTER - PERIPHERY MODEL

. It is necessary to have knowledge about world dynamics, identifying systemic patterns in: economic, political, socio-cultural, scientific, technological and educational spheres to analyze possible scenarios of the future. Often, such foresight models are based on the analysis of existing trends in world economic development, but they do not pay attention to nonlinear processes, institutional traps, and scientific and technological changes. In the case of the position of the system far from the equilibrium state, some of the models used explicitly imply an intensification of convergence processes. This can be interpreted as an increase in destructive tendencies with an intensification of the demographic crisis. The system finds itself in an institutional trap. The problem of making forecasts of population growth is solved in a complex way, when demographic forecasts are correlated with the economic development of society. Methodologically, this study continues the approach of dividing a single system into a number of subsystems (hierarchical approach). The subject of this study is population growth in the subsystems of a certain single “economic community”, taking into account the socio-economic development of this system. It is assumed that in the system under consideration, it is possible to clearly distinguish the Center and the Periphery (in this way we will be able to distinguish the subsystems). A similar problem was solved by the authors earlier in the course of mathematical modeling of the population size based on the stratum model. The developed approach will allow considering complex systems where simplified approaches doesn’t work.

Об использовании ГИС-инструментария в практическом курсе математико-картографического моделирования

GIS is closely related to mathematical cartographic modeling, as they work with spatially coordinated data. geoinformation technologies used to study the spatio-temporal structure, connections and dynamics of geosystems are mainly based on the methods of cartographic analysis and mathematical-cartographic modeling. The purpose of mastering the discipline “Mathematical and cartographic modeling” is to form students’ theoretical knowledge and practical skills in the field of mathematical and cartographic modeling, the acquisition of general and special knowledge by students, as well as practical skills in constructing thematic content of maps based on modern computer and geoinformation technologies. The course must meet the requirements of the time and assume the use of modern gIS technologies when performing practical tasks. When studying the discipline, students get acquainted with the place and role of mathematical and cartographic modeling in the structures of geographic information systems, acquire skills in working with various sources of spatial information, independently systematize and analyze data. The functionality of GIS packages allows you to construct thematic content of maps based on the analysis of spatial data and geoinformation modeling. Some mathematical and cartographic models are created easily and simply, the construction of individual models requires the development of additional scripts, programs, etc. The acquisition by students of practical skills in constructing thematic content of maps based on modern computer and geoinformation technologies should be accompanied by the formation of ideas about the mathematical methods used, knowledge of how a particular tool works. This article is devoted to researching the possibilities of using GIS technologies in the practical course of mathematical and cartographic modeling. The main attention is paid to the construction of models of the structure of the spatial characteristics of geographic phenomena.

Mathematical modeling of the influence of defects in structures of an on-farm network of rice systems on their operational reliability

This article presents the results of mathematical modeling of the effects of defects in the structures of an on-farm network of rice systems over a long period of work on their operational reliability. This year marks the ninety years since the first rice system was built in 1929 in the Kuban. In the Krasnodar Territory, rice systems have been used that have been in continuous operation for more than thirty years. Therefore, it is necessary to scientifically substantiate the costs of maintenance and overhaul, and a numerical experiment was carried out on various defects in the structures of the on-farm network of rice systems. Based on field studies, mathematical modeling was performed for the most common defects by the ground- penetrating radar (GPR) sounding—a transverse crack crossing the drainage structure, as well as the destruction of the sides of the well. All calculations were performed on the SCAD Office calculation complex. In the course of mathematical modeling, it was found that the drainage pipeline with a well has a margin of operational reliability, which decreases over the years of use of the structure. In the formulation of mathematical modeling of a model of a drainage structure with a well without defects and damages, the aim was to establish the adequacy of the solid-state model of the stress-strain state at maximum water pressure with existing field tests under various boundary conditions. According to the data of the technical analysis of operational reliability, the operational reliability of the structures of the on-farm network of rice systems is determined and characterized. Provision of the operational reliability of rice systems is to carry out engineering, technical and land reclamation measures for sustainable and effective water conservation, rational use and development of the water management complex as a whole.

Improving open and rigorous science: ten key future research opportunities related to rigor, reproducibility, and transparency in scientific research.

Background: As part of a coordinated effort to expand research activity around rigor, reproducibility, and transparency (RRT) across scientific disciplines, a team of investigators at the Indiana University School of Public Health-Bloomington hosted a workshop in October 2019 with international leaders to discuss key opportunities for RRT research. Objective: The workshop aimed to identify research priorities and opportunities related to RRT. Design: Over two-days, workshop attendees gave presentations and participated in three working groups: (1) Improving Education & Training in RRT, (2) Reducing Statistical Errors and Increasing Analytic Transparency, and (3) Looking Outward: Increasing Truthfulness and Accuracy of Research Communications. Following small-group discussions, the working groups presented their findings, and participants discussed the research opportunities identified. The investigators compiled a list of research priorities, which were circulated to all participants for feedback. Results: Participants identified the following priority research questions: (1) Can RRT-focused statistics and mathematical modeling courses improve statistics practice?; (2) Can specialized training in scientific writing improve transparency?; (3) Does modality (e.g. face to face, online) affect the efficacy RRT-related education?; (4) How can automated programs help identify errors more efficiently?; (5) What is the prevalence and impact of errors in scientific publications (e.g., analytic inconsistencies, statistical errors, and other objective errors)?; (6) Do error prevention workflows reduce errors?; (7) How do we encourage post-publication error correction?; (8) How does 'spin' in research communication affect stakeholder understanding and use of research evidence?; (9) Do tools to aid writing research reports increase comprehensiveness and clarity of research reports?; and (10) Is it possible to inculcate scientific values and norms related to truthful, rigorous, accurate, and comprehensive scientific reporting? Conclusion: Participants identified important and relatively unexplored questions related to improving RRT. This list may be useful to the scientific community and investigators seeking to advance meta-science (i.e. research on research).

Evaluating Pre-Service Teachers’ Design of Mathematical Modelling Tasks

This study aims to examine pre-service teachers’ competencies in designing authentic mathematical modelling tasks. The participants of this study were 22 pre-service teachers enrolled in a mathematical modelling course during their second year in a mathematics teacher education program. The participants designed 20 problems, which were evaluated based on four criteria for mathematical modelling: reality, openness, complexity, and model eliciting. The results indicate that even though the participants were successful in developing problems that had real-world scenarios, only five of them were classified as modelling problems. The majority of the problems fulfilled the reality criterion (12 out of 17); only five of them fulfilled the criteria of openness and model eliciting, and only six of them fulfilled the criterion of complexity. These findings contribute to the importance of supporting teachers’ competencies in the teaching and learning of mathematical modelling for integration into K-12 classrooms.

A Classification of Mathematical Modeling Problems of Prospective Mathematics Teachers

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.

The Compatibility of Model Eliciting Activities of Secondary School Teacher Candidates with Design Principles

The purpose of this study is the investigation of the compatibility of model eliciting activities of secondary school teacher candidates with design principles. This study was conducted in the scope of Mathematical Modelling course with the students who were the secondary school mathematics teacher candidates. The participants of this case study were thirty-nine mathematics teacher candidates who worked in eight groups. The data of this study consisted of eight model eliciting activities which were created within the eight groups and their analysis. The activities created by the groups were analyzed by document analysis method in terms of design principles that were defined for model eliciting activities. It was concluded that the created model eliciting activities satisfied the construct share ability and reusability principle at minimum while they satisfied the reality principle at maximum. The effective prototype principle could not be determined. It can be ensured that the secondary school mathematics teacher candidates gain more experience by making more implementations related to model eliciting activities. The implementation of model eliciting activities in class can be effective in reducing the modelling deficiencies of secondary school mathematics teacher candidates.

Developing a learning design of mathematical modelling courses on understanding basic concept of mathematical modelling

The approach to learning mathematical modelling is an approach that focuses on mathematics learning by using the context of real world phenomena so that the use of mathematics can be used in describing a process of understanding, simplifying, and solving problems in the form of mathematical modelling in order to have deeper understanding. Therefore, undergraduate students of the mathematics education as prospective mathematics teachers in schools need to get in-depth competencies related to mathematical modelling learning. These competencies were obtained by students in mathematics modelling courses. Based on the importance of mathematical modelling courses for students of mathematics education study programs need to be made in the design of learning in the subject of mathematical modelling based on the development of questions according to the characteristics of mathematical modelling. This study aims to generate local instruction theory in mathematics modelling courses after lectures are based on designing modelling task. Therefore this research will refer to design research methods in learning by constructing the Hypothetical Learning Trajectory (HLT) which will become Local Instruction Theory in the subject of mathematical modelling. In this paper, we focussed on the first step on HLT that is the basic concept of mathematical modelling. The results of this study are forming hypotheses, developing learning designs, and testing the truth according to research design methodology.

数学建模课程教学改革与实践：以西安电子科技大学为例

数学建模课程教学改革与实践：以西安电子科技大学为例

Modeling of the influence of non-stationary waves in three-component medium in the formation of a plasma jet

This article discusses the mathematical description of the physical processes of transformation of composite substances of a plasma jet. A mathematical model describing the propagation of elastic waves in a three-component medium was developed for the prediction and planning of the use of plasma deposition technology, in particular in the study of the kinematic characteristics of the plasma flow. Also in the course of mathematical modeling the table of coefficients of compressibility of liquid (plasma jet) and gas and velocities of longitudinal and transverse elastic waves is obtained. Graphs of the velocity of propagation of longitudinal and transverse waves in the plasma coating material on its physical and mechanical characteristics-compressibility coefficients are plotted.

АНАЛІЗ ЕКОНОМІЧНОЇ ЕФЕКТИВНОСТІ ДІЯЛЬНОСТІ ОБ’ЄДНАНИХ ТЕРИТОРІАЛЬНИХ ГРОМАД В РЕГІОНАХ УКРАЇНИ

The article investigates the economic effectiveness of the the united territorial communities’ activities in terms of groups formed by the number of united territorial communities’ inhabitants and provides recommendations for optimizing the structure of the united territorial communities. An in-depth statistical analysis of the financial activities of united territorial communities in Ukraine in 2018 has been conducted. It revealed that the income of the united territorial communities is subject to lognormal distribution law. In the course of economic and mathematical modeling, two approaches have been proposed to maximize the economic effectiveness of the activities of the united territorial communities. In the first approach, the goal was to maximize the volume of own revenues of all united territorial communities of Ukraine, and in the second approach, to minimize the amount of expenditures on the management of the united territorial communities. It is determined that the second approach is optimal. The criteria for defining the effectiveness of territorial communities are : indicators of their own income, management costs and received subsidies in the calculation. The number of residents in different groups of united territorial communities was selected as the model optimizer. Higher economic effectiveness was found to be characteristic of the large united territorial communities. It is proposed to develop a set of economic norms and measures that would stimulate the consolidation of the small united territorial communities. Recommendations have been made to improve the existing structure of united territorial communities in the Rivne region in order to minimize the amount of management expenditures.

Reduction of angular velocities of AIST-2D spacecraft using a system of kinetic moment dumping

The efficiency of a magnetic system of kinetic moment dumping in solving the problem of stabilizing Aist-2D spacecraft without using information on angular velocity is investigated. We defined the conditions under which the magnetic moment produced by electromagnets constitutes a useful control mechanical moment. Boundary conditions for preventing emergence of the parasitic moment are also defined. The paper presents the solution of the problem of forming the vector of the kinetic moment of the system spacecraft + control moment gyro according to the information on the vector of geomagnetic induction of the Earth. We defined the dependence of the time taken by the algorithm of angular speed reduction on the value and direction of the projections of the vector of spacecraft angular speeds at the time of algorithm actuation. The results obtained in the course of mathematical modeling and natural experiment on the spacecraft, the process of dumping angular speeds in providing the solution of the problem of attitude determination with the use of star sensors are compared.