Mathematical Model Of Problem 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.

Mathematical modelling and optimizing design of heliostat field

The heliostat field is a form of solar thermal power plant, The heliostat field is a crucial component of solar thermal power plants and establishing a heliostat field is of great significance for reducing carbon emissions. and is of great significance in reducing carbon emissions This paper focuses on the mathematical modeling and optimization design problem of the heliostat field. For three different design scenarios, firstly, based on the data provided by the China Undergraduate Mathematical Contest in Modeling 2023, a geometric optical efficiency model is proposed to determine the annual average optical efficiency and output thermal power under specific heliostat field design parameters. Secondly, aiming at the optimal design parameters of the solar furnace field under the condition of rated annual average output thermal power is 60 MW\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{MW}$$\\end{document}, Particle Swarm Optimization (PSO) combing with efficiency model is utilized to determine the optimal design parameters of the heliostat field. Finally, this paper uses Quasi-Monte Carlo ray tracing (QMCRT) model to perform simulations, exploring how to obtain the optimal design parameters of the heliostat field with the goals of maximizing the output thermal power and ensuring high efficiency. Furthermore, the influence of normal disturbances on the annual average annual average thermal output power is investigated.

Practicality of Student-Centered Assessment/Learning using Mathematics Modeling Process Worksheets to Improve the Quality of Education

It is necessary to consider reforms to improve the quality of education through assessment/learning. The problem formulation of this research is how to design student-centered assessment/learning using practical mathematical modeling process worksheets to improve the quality of education? This research uses a development research approach developed by Akker, Gravemeijer, McKenney and Nieveen. This development research consists of 3 steps, namely analysis, design and evaluation. In the analysis step, student analysis, curriculum, mathematical modeling and real world problems are implemented. Second step, design and product. In the final step, researchers used a formative evaluation design consisting of self-evaluation, one-to-one, expert review, small group, and field test. Data were analyzed using descriptive analysis methods: (1) walk through, analysis based on solutions and student comments in small groups to obtain student-centered assessment/learning using mathematical modeling process worksheets using the best practical transportation context to improve the quality of education; (2) analyzing the results of the review of small group results. Based on the results of the small group worksheet, the mathematical modeling process is practical for improving the quality of education. Students commented that this mathematical modeling process worksheet was interesting, confusing but challenging and had never been found in their classrooms. Students can solve problems on process worksheets even though the mathematization process has not yet appeared, because students only solve them using informal methods. So, this is a golden opportunity to implement in order to improve the quality of education through assessment/learning. So, a practical mathematical modeling process worksheet is obtained to implement student-centered assessment/learning in order to improve the quality of education.

Method of Identification of Combat Vehicles Based on Yolo

A method for recognizing contours of objects in a video data stream is proposed. Data will be uploaded using a video camera in real time and object recognition will be performed. We will use the YOLO network – a method of identifying and recognizing objects in real time. Recognized objects will be recorded in a video sequence showing the contours of the objects. The approach proposed in the project reasonably synthesizes methods of artificial intelligence, theories of computer vision on the one hand, and pattern recognition on the other; it makes it possible to obtain control influences and mathematical functions for decision-making at every moment of time with the possibility of analyzing the influence of external factors and forecasting the flow of processes, and refers to the fundamental problems of mathematical modeling of real processes. The installation of the neural network is shown in detail. The characteristics of the neural network are shown and its capabilities are substantiated. Approaches to computer vision for object extraction are shown. Well-known methods are methods of expanding areas, methods based on clustering, contour selection, and methods using a histogram. The work envisages building a system for rapid identification of combat vehicles based on the latest image filtering methods developed using deep learning methods. The time spent on identifying the machine will be 10 –20 % shorter, thanks to the developed new information technology for detecting objects in conditions of rapidly changing information.

Mathematical modeling of heat exchange for efficient automated control systems

The article deals with the problem of mathematical modeling of heat transfer processes, taking into account a large number of factors affecting these processes and a variety of mathematical modeling methods. The article discusses the idea of developing a universal and flexible model that could quickly adapt to different initial modeling conditions and take into account various parameters for further use of the mathematical model in the synthesis of automatic control systems. The paper discusses the main aspects of mathematical modeling of heat transfer and the creation of a mathematical model in distributed heat exchanger parameters with the possibility of changing the properties and parameters of the equipment. The paper analyzes previous studies and identifies the problems of existing methods of mathematical modeling of heat transfer, such as lack of versatility, complexity, and insufficient accuracy. The paper goes on to review different approaches to mathematical modeling of heat transfer, such as models with a group of parameters, models in distributed parameters, and models based on artificial intelligence. The article provides an overview of model implementation methods and their advantages and disadvantages. Based on this analysis, the authors propose a new mathematical model of heat transfer in distributed parameters, which should be universal, easy to use, and accurate in accordance with the requirements of synthesizing automated control systems. The authors also outline the methodology for achieving this goal, which includes the implementation of the geometry of the heat exchanger, the implementation of conditions and mathematical modeling, as well as the study of the influence of parameters and the formation of transients. The general conclusion of the article is that the developed mathematical model of heat transfer can be used to synthesize automatic control systems for heat exchange processes in various industries.

SYNTHESIS OF MATHEMATICAL MODELS FOR MONITORING THE TECHNICAL CONDITION OF VEHICLES DURING THEIR OPERATION

One of the problems of mathematical modeling of monitoring the technical condition of vehicles during their operation is the lack of practical recommendations regarding the use of various types of modeling for specific diagnostic tests. A distinctive feature of monitoring the technical condition of the elements of vehicles during their intensive operation is the uncertainty of the nature of the loads, which makes it impossible to use traditional diagnostic methods and encourages to move to their complex use. In these conditions, the informational support of conclusions about the suitability of products for further operation and the assessment of the residual resource of the equipment becomes especially relevant. The need to create intelligent support for monitoring the technical condition of vehicles during operation is due to the fact that the uncertainty of the nature of the magnitude of loads during the operation of complex structures complicates the use of existing information. The synthesis of mathematical models of the technical state of metal structures, which are based on the general principle of transforming the degradation of the structure into a fixed signal of different nature of origin, has been performed. The presented structuring is considered as informational support for intelligent monitoring of changes in the properties of transport objects, each of which has a specific purpose. The novelty of the structuring of the main models is a practical focus on solving the issues of their functional purpose in relation to test operations in the monitoring and diagnosis of vehicles and the identification of developing defects. On the basis of the synthesis of mathematical models, analysis of their shortcomings, advantages and possibilities of use for monitoring transport devices during their operation, their main properties from the position of their time series, field of knowledge, methods of implementation and rationality of application were established. Distinctive features have been established and the classification of mathematical models has been performed, which makes it possible to significantly simplify the selection of appropriate models, to ensure the correct use of the mathematical apparatus and analytical ideas about the possibilities of assessing the remaining resource and the quality of monitoring in general.

Metacognitive Strategies for Mathematical Modeling with Engineering Groups of Students: Adaptation and Validation of a Questionnaire

A sequential exploratory mixed-methods study is implemented to develop an instrument that allows for the evaluation of the metacognitive strategies used by engineering groups of students when solving mathematical modeling problems. The findings of the qualitative study guided by observations and interviews reveal the use of metacognitive strategies of ‘planning’, ‘monitoring and, if necessary, regulation’, and ‘evaluation’. In this article, we present the final categories of the qualitative analysis and discuss how these data were shaped into a theoretical construct and items of an instrument to measure metacognitive strategies. The psychometric properties of the instrument are analyzed, and it is argued that it has a similar interpretation among males and females, as there are no significant differences in these results. The development of the present study demonstrates how the qualitative method can support the adaptation of an instrument to measure metacognitive strategies, thus contributing to validity and applicability.

Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems

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.

Contributions and problems of mathematical models in COVID‐19 prevention in Japan

AbstractThis article reviews the essential role of mathematical models in understanding and combatting the pandemic of novel coronaviruses, in particular focusing the advance in the use of mathematical models in disease control in Japan. Highlighting the integral role of mathematical models in public health, the article introduces a model that factors in the heterogeneity of infectious contacts, concentrating on the effectiveness of testing and isolation, alongside a model that involves economic losses. The models exhibit how, given such heterogeneity, milder behavioral restrictions can still achieve suppression, rigorous testing and isolation can effectively curb the spread, and containment measures can mitigate economic losses. These models aid in grasping the complicated dynamics of disease transmission and optimizing interventions. The knowledge of population ecology is also considered effective for public health in statistical analysis, organizing concepts using dynamic mathematical models, which lead to policy proposals and deepen understanding. Evolution theory may help the understanding of virulence subject to change. However, effective prevention necessitates not only models but also the practical implementation of efficacious measures. The cooperation of various disciplines is particularly crucial in achieving a balance between health measures, economic interests, and human rights. Moreover, the article acknowledges the limitations of models and underscores the significance of real‐world execution. Overall, the article advocates for a broader outlook to tackle future pandemics and related challenges, underscoring the importance of ongoing academic cooperation and global governance to effectively address emerging infectious diseases and their far‐reaching implications.

A PROPOSAL FOR AN INNOVATIVE APPROACH TO EXTENDED MODELLING CYCLES INCORPORATING PROBLEM-POSING FROM A CREATIVITY PERSPECTIVE

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.

Математичне моделювання динамічних впливів на будівельні конструкції

The solution of the problem of mathematical modeling of dynamic influences on building structures is considered in general and in connection with important scientific and practical tasks. In modern conditions, special attention should be paid to the problems of taking into account dynamic influences, parameters of load-bearing structures of buildings that affect their structural reliability and safety. For many years, information about catastrophic destruction of buildings and structures has been appearing more often, which are the result not only of errors that arose during the construction of facilities, but also due to dynamic influences that arose during their operation. A buildable technical system will be used in advance with the technical parameters set, which is responsible for the control of the process of the preparation of structures, the installation of the equipment, during the operation and operation. The development will be carried out and the sporud will be constantly used to promote the development of future technologies, the development and the establishment of the future, as well as the development of dynamic developments in the future. In particular, it is important to understand the development of the engineering and geological minds of the spores, as they have known the front deformation of the non-essential axis of the runt foundations. Various methods are used for structural dynamics, such as modal analysis, response spectrum analysis, time analysis, and finite element analysis. These methods include mathematical modeling, numerical simulation, and computational methods to predict the behavior and response of a structure under dynamic load conditions. Knowing the frequency and form of the structure, it is possible to estimate the dynamic reaction of the design to the application. For the purpose of including the transfer of the world, the destruction of internal forces in the real parts of the construction. Analyses of the response to the additional assessment of the characteristics of the construction, the identification of critical areas and the re-conversion, which the project is able to meet the criteria.

Using different digital tools in designing and solving mathematical modelling problems

While existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers’ designing and solving mathematical modelling problems by using different digital tools through the collaboration of two different courses in their education program. The GeoGebra-supported modelling cycle was adopted as the conceptual framework of the study. The case study was used to design the research. The participants of the study were three volunteer pre-service secondary mathematics teachers, who were able to use and integrate digital tools in mathematics education. The pre-service teachers were asked to design a mathematical modelling problem by integrating different digital tools as the final assignment in both courses. The designed mathematical modelling problem, the video records of pre-service teachers’ explanations including the designing and solving process, and the video records of the focus group interview were the data of the study. The results showed that the pre-service teachers were able to design and solve an effective and comprehensive mathematical modelling problem using technology by combining their skills that they had learnt through different courses. In particular, they were able to use different digital tools in both designing and solving a mathematical modelling problem. Their solution also led to the extension of the adopted framework by adding new technological actions into the modelling stages.

STAGES OF ACCUMULATION OF OIL DROPLETS AND GAS BUBBLES IN THE DOME FOR CASES OF DEEP-SEA SPILLS: PART 2

In a previously published article, the problem of mathematical modeling of the operation and installation of a special device – a separator dome designed to collect hydrocarbons for cases of deep-sea leaks was given, three initial stages of modeling the installation of the device were described. This paper describes in detail the remaining stages of installing the dome: the accumulation of a layer of gas, the final stage of installing the dome, when the tubes for pumping oil and gas are connected to the device and the device begins to work in stationary mode. Let's take a closer look at each of the stages. The fourth stage of the dome installation is associated with the achievement of a given height (at which the gas bubbles have not yet passed into the hydrate state) and the beginning of the migration of gas bubbles inside the dome. First, the gas bubbles migrate into layer of liquid immiscible with water, then in the oil layer. During this process, all the gas coming from the jet completely enters the tank. At the fifth stage, gas accumulations inside the tank are considered. At the sixth stage, the study of the accumulation of layers of gas and oil continues, but at the same time the reservoir itself sinks to the bottom of the reservoir at a constant speed. This is necessary to subsequently secure the dome and prevent oil and gas from leaking out of the dome. The seventh stage is the final one. At this stage, we believe that the dome is fixed on the ocean floor, pipes for pumping oil and gas are connected to it. As a result of the created mathematical model of the dome-separator operation, dependences characterizing the process of installation and functioning of the dome, the temperature dependences of gas and oil layers accumulated inside the dome, as well as the dynamics of accumulation of the corresponding layers in the dome are obtained. The characteristic start and end times of each of the stages are described.

Моделирование работы газотурбинной установки SGT5-4000F с исследованием влияния режимных и климатических факторов на устойчивость горения в камере сгорания

When regulating gas turbine units, it is necessary to be confident in the stable combustion process in the combustion chambers, considering the dynamics of the processes and changes of external climatic factors. Many scientific studies are devoted to the problems of experimental research and mathematical modeling of processes in combustion chambers. The possibilities of flame failure, expansion of the lower limit of combustion, determination of the stable position of the flame front and other issues have been assessed. Even though the problem of design of mathematical models and their use remains relevant. The purpose of this research is to model and study the influence of operation and climatic factors on the stability of combustion in the combustion chamber of the SGT5-4000F gas turbine unit. The subject of the research is the SGT5-4000F gas turbine unit with a low-emission combustion chamber. The simulation model of the gas turbine unit has been developed in the environment of dynamic modeling of technical systems SimInTech. The research is carried out using theoretical methods of calculating fuel combustion, thermodynamic foundations of the theory of gas turbine engines, methods of mathematical and simulation modeling, as well as data from the archive of automated process control systems. A simulation model of SGT5-4000F gas turbine unit has been developed. It is distinguished by the ability to assess the proximity of the compressor operating mode to the stability limit and determine the boundaries of stable combustion procedure in the combustion chamber, considering environmental climatic factors. The authors have studied the stability of the compressor and combustion chamber. The results of the experimental studies of a gas turbine unit in the operating load range from 113 to 282 MW and in the range of outside air temperature from –12 to 30 °C have shown that the combustion process in the combustion chamber is unvarying over the entire operational stress spectrum. The results obtained are verified by comparing model values with technological parameters of a gas turbine unit taken from the archive of the power plant control system. The authors have assessed the influence of electrical load on the performance indicators of a gas turbine unit at outdoor temperatures of +30, +15 and –12 °C. According to the results of simulation modeling, the model of SGT5-4000F gas turbine unit is found to be adequate. The developed model can be used as a tool at the stage of functional and technological design of automated control systems for the development of effective automatic control systems.

Robust generation expansion planning in power grids under renewable energy penetration via honey badger algorithm

Robust reliability Generation Expansion Planning (GEP) turns out to be a crucial step for an efficient energy management system in a modern power grid, especially under renewable energy employment. The integration of all such components in a GEP model makes it a large-scale, nonlinear, and mixed-variable mathematical modeling problem. In this paper, the presence of wind energy uncertainty is analyzed. Both long and short-term uncertainties are incorporated into the proposed GEP model. The first step concerns the impact of long-term wind uncertainties through the annual variations of the capacity credit of two real sites in Egypt at Zafaranh and Shark El-ouinate. The second step deals with the short-term uncertainties of each wind site. The wind speed uncertainty of each wind site is modeled by probability distribution function. Then, wind power is estimated from the wind power curve for each wind site and Monte-Carlo Simulation is performed. Fast Gas Turbine and/or Pump Hydro Storage are incorporated to cope with short-term uncertainties. Sensitivity analysis is implemented for 3, 6, and 12 stages as short and long planning horizons to minimize the total costs with wind energy penetration and emission reduction over planning horizons. Also, a novel Honey Badger Algorithm (HBA) with model modifications such as Virtual Mapping Procedure, Penalty Factor Approach, and the Modified of Intelligent Initial Population Generation is utilized for solving the proposed GEP problem. The obtained results are compared with other algorithms to ensure the superior performance of the proposed HBA. According to the results of the applicable test systems, the proposed HBA performs better than the others, with percentage reductions over CSA, AO, BES, and PSO ranging up to 4.2, 2.72, 2.7, and 3.4%, respectively.

Investigation of the stability of trajectories for three-dimensional nonlinear dynamic system using an accompanying coordinate reference

The development of methods of stability analysis and the study of various types of dynamic systems stability belongs to an urgent scientific direction. Among the problems solved in the framework of this direction, an important place is occupied by the problems of finding conditions for stability and stabilization in the sense of N.E. Zhukovsky of trajectories of dynamic systems modeled by systems of three nonlinear differential equations of the first order. The aim of the work is to study the stability in the Zhukovsky sense of the trajectories of a dynamic system described by three autonomous nonlinear first-order differential equations using a differential geometric method called the accompanying coordinate reference method. The formulation of the stability problem in the Zhukovsky sense of the trajectories of dynamic systems described by systems of three nonlinear differential equations of the first order is considered. The definitions of stability of trajectories of a three-dimensional nonlinear system are specified. Using the accompanying coordinate reference, the conditions of exponential stability and instability according to Zhukovsky are obtained. The results can be used in studying the stability of processes in systems of natural science and technology, as well as in solving theoretical and applied problems of mathematical modeling and qualitative research of trajectories of nonlinear dynamic systems.

A Comparative Study of Mathematical Modelling Problems in High School Mathematics Textbooks—Taking People’s Education Edition A, Jiangsu Education Edition and Hubei Education Edition as Examples

A Comparative Study of Mathematical Modelling Problems in High School Mathematics Textbooks—Taking People’s Education Edition A, Jiangsu Education Edition and Hubei Education Edition as Examples

Analysis of models and development of a software package for assessing the impact of vibration effects of vehicles on urban infrastructure

The direction associated with the construction and research of models that can be used to predict the impact of vibration effects of vehicles on surrounding infrastructure facilities is relevant given the increasing pace of civil engineering in large cities and taking into account the expansion of transport networks. The development of models for evaluating vibration effects and for subsequent use in monitoring and diagnostic systems requires the use of modern methods of nonlinear analysis, discrete mathematics, as well as tools for the development of expert systems and artificial intelligence technologies. The purpose of the article is to obtain the results of the analysis of a complex mathematical model of spatial interactions, the development of algorithmic support and a description of the structure of a software package for assessing the impact of vibration effects of vehicles on urban infrastructure. A model of spatial interactions is proposed to assess the levels of vibration exposure with the construction of a graph of the placement of objects connected by vibration propagation channels and using the mathematical apparatus of modeling hybrid dynamic systems, expert knowledge and fuzzy rules of logical inference. Examples of constructing a model of spatial interactions taking into account three objects of vibrational observation are considered. The VibCalcAlg algorithm has been developed to calculate the states of a three-component model. The structure of the VibCalc software package is described, which includes a block of fuzzy logic, a block of model construction and a block of visualization. The results can be used in solving mathematical modeling problems related to the assessment and prediction of vibration impacts in the field of transport and civil engineering, as well as in solving environmental protection problems. The results are aimed at improving intelligent monitoring systems and decision support systems in the design, construction and operation of transport facilities.

Mathematical modeling and research of transport flows and processes of transport systems of cities

The problem of mathematical modeling and research of transport flows and processes of transport systems of cities is set and solved. Related works, methods, modeling of traffic flow intensity as a first-order autoregression process, finding estimates of process model parameters with a standard normal random component are considered.

Model Oluşturma Etkinliklerinde Matematiksel İlişkilendirmelerin Belirlenmesi: Tasarımcı Olarak Matematik Öğretmen Adaylarıyla Bir Durum Çalışması

This paper aimed to explore mathematical connections that pre-service elementary mathematics teachers identified in model-eliciting activities that they designed. The study used a qualitative, in-depth exploratory case study approach conducted with a total of 42 undergraduate students selected using a purposive sampling method. Data were collected from mathematical modeling problems prepared by pre-service mathematics teachers and from written assignments in which pre-service teachers evaluated their problems in terms of mathematical connections. Data analysis utilized open coding to identify and label common patterns thematically. Results showed that most of the problems designed were consistent with the principles of the model-eliciting activities. A cross-case analysis of model-eliciting activities revealed that four types of mathematical connections were identified: (i) connections to real-world situations, (ii) connections between mathematical concepts, (iii) connections between different modes of representation, and (iv) connections to other disciplines. The mathematical connections identified in the modeling activities did not seem to be mutually exclusive, but rather supportive and sometimes overlapping. Pre-service mathematics teachers’ identification of mathematical connections in modeling problems reflects both their awareness of mathematical connections and their perception that the skills required for the mathematical modeling process are directly related to mathematical connection skills. Therefore, it is important that pre-service mathematics teachers have a comprehensive understanding of mathematical connections and believe that this is an essential element of the modeling process so that the various dimensions of mathematical connections, along with relevant mathematical, pedagogical, and curricular knowledge, can be effectively integrated into model-eliciting activities.