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Jean Marie Linhart – International Journal of Mathematical Education in Science and Technology, 2024
The historic total global human population dataset is available on Wikipedia and provides an opportunity for modelling with simple models such as the exponential and logistic differential equations for population. Using the per-capita population growth rate (PPGR) predicted by these two models and estimated PPGR from the data, we are able to…
Descriptors: Calculus, Population Growth, Mathematical Models
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Samuel Cuthbertson; Mark Ian Nelson – International Journal of Mathematical Education in Science and Technology, 2025
We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer…
Descriptors: War, Mathematical Models, Calculus, Problem Solving
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Liang Kong – International Journal of Mathematical Education in Science and Technology, 2024
The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by…
Descriptors: Mathematics Instruction, Teaching Methods, Advanced Courses, Epidemiology
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Lu, Yu; Chen, Penghe; Pian, Yang; Zheng, Vincent W. – IEEE Transactions on Learning Technologies, 2022
In this article, we advocate for and propose a novel concept map driven knowledge tracing (CMKT) model, which utilizes educational concept map for learner modeling. This article particularly addresses the issue of learner data sparseness caused by the unwillingness to practice and irregular learning behaviors on the learner side. CMKT considers…
Descriptors: Concept Mapping, Learning Processes, Prediction, Models
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Ernest C. Davenport Jr.; Mark L. Davison; Kyungin Park – Journal of Educational and Behavioral Statistics, 2024
The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show…
Descriptors: High School Students, Mathematics Instruction, Mathematics Achievement, Grade 9
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Jablonski, Simone – Educational Studies in Mathematics, 2023
Mathematical modelling emphasizes the connection between mathematics and reality -- still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It…
Descriptors: Mathematics Instruction, Mathematical Models, Secondary School Students, Secondary School Mathematics
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L. H. A. Monteiro – International Journal of Mathematical Education in Science and Technology, 2025
Cybersex is the use of the Internet and its services to achieve sexual arousal and pleasure. This use, however, can become excessive and uncontrolled. Common consequences of a problematic engagement in online sexual activities are the deterioration of real-life romantic relationships and the occurrence of sexual dysfunctions, even in young…
Descriptors: Mathematical Models, Internet, Computer Mediated Communication, Sexuality
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Zeynep Gül Dertli; Bahadir Yildiz – Anatolian Journal of Education, 2025
Mathematical modelling and modelling activities are important for making sense of mathematical concepts in different extracurricular and daily life contexts. However, teachers may have difficulties in designing these activities in a way to establish meaningful relationships with real life, in accordance with the modeling process and the objectives…
Descriptors: Prompting, Engineering, Mathematical Models, Mathematics Activities
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Fabiana Zama – International Journal of Mathematical Education in Science and Technology, 2024
This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for…
Descriptors: Masters Programs, Mathematical Models, Graduate Students, Microbiology
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Kontorovich, Igor'; Li, Tianqing – International Journal of Science and Mathematics Education, 2023
Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…
Descriptors: Undergraduate Students, Calculus, Graphs, Mathematical Models
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Tianjiao Wang; Xiaona Xia – SAGE Open, 2023
The study of learning behaviors with multi features is of great significance for interactive cooperation. The data prediction and decision are to realize the comprehensive analysis and value mining. In this study, hierarchical learning behavior based on feature cluster is proposed. Based on the massive data in interactive learning environment, the…
Descriptors: Cluster Grouping, Mathematical Models, Artificial Intelligence, Learning Analytics
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Yu-Cheng Chen; Xin-Yu Chen; Zhi-Yuan Lin; Shan-Jing Yao; Dong-Qiang Lin – Journal of Chemical Education, 2023
The utilization of modeling tools has gained significant attention recently. These models typically involve a series of partial differential equations, which can be challenging for novice modelers. This paper presented an approach in practical teaching of modeling tools for ion-exchange chromatography with three parts: model introduction, model…
Descriptors: Chemistry, Mathematical Models, Case Studies, Science Instruction
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J. T. Sandefur – International Journal of Mathematical Education in Science and Technology, 2024
In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line…
Descriptors: Population Growth, Sustainability, Agricultural Production, Mathematical Models
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Omar A. Naranjo; Steven R. Jones – International Journal of Science and Mathematics Education, 2024
Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students' understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study…
Descriptors: Equations (Mathematics), Mathematical Models, Relevance (Education), Mathematics Skills
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Seonyoung Hwang; Sunyoung Han – Journal of Mathematics Teacher Education, 2025
This study aimed to observe the competencies of pre-service mathematics teachers in designing mathematical modeling tasks. The participants were 45 pre-service mathematics teachers enrolled in a Mathematics Education Theory course at a university in Seoul, South Korea. Data were collected from surveys and task development reports. The participants…
Descriptors: Preservice Teachers, Mathematics Teachers, Teacher Competencies, Mathematical Models
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