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Thomas J. Pfaff – PRIMUS, 2024
The logistic differential equation is ubiquitous in calculus and differential equations textbooks. If the model is developed from first principles in these courses, it is usually done in an abstract mathematical way, rather than in one based in ecology. In this short note, we look at examples of how the model is derived in mathematical texts and…
Descriptors: Calculus, Mathematics Instruction, Textbooks, Ecology
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Forest Mannan – International Journal of Mathematical Education in Science and Technology, 2024
This article considers starting with an existing SIMIODE modeling scenario [Winkel, B. (2015). 1-031-CoolIt-ModelingScenario. SIMIODE (Version 2.0). "QUBES Educational Resources." https://doi.org/10.25334/3WG8-EC31] that develops Newton's law of cooling by considering data on the cooling of a beaker of water in a room, and expanding upon…
Descriptors: Calculus, Mathematical Models, Programming, Heat
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Ferrarello, Daniela; Gionfriddo, Mario; Grasso, Federico; Mammana, Maria Flavia – ZDM: Mathematics Education, 2022
The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…
Descriptors: Graphs, Mathematics, Mathematical Models, Middle School Students
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van der Hoff, Q.; Harding, A. – International Journal of Mathematical Education in Science and Technology, 2019
It is well-known that the Lotka-Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka-Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit…
Descriptors: Calculus, Mathematical Models, Mathematics, Biology
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Miranda, Vicente Carrión; Pluvinage, François; Adjiage, Robert – ZDM: The International Journal on Mathematics Education, 2016
Approximating given real-valued functions by affine functions is among the most basic activities with functions. In this study we examine two contexts in which two such approximations are performed. The first involves a microscopic representation of functions for the study of tangents; the second a macroscopic representation of functions for the…
Descriptors: College Freshmen, College Mathematics, Calculus, Mathematics
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Merrotsy, Peter – Australian Senior Mathematics Journal, 2016
The leap into the wonderful world of differential calculus can be daunting for many students, and hence it is important to ensure that the landing is as gentle as possible. When the product rule, for example, is met in the "Australian Curriculum: Mathematics", sound pedagogy would suggest developing and presenting the result in a form…
Descriptors: Foreign Countries, Mathematics, Mathematics Instruction, Mathematics Education
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Oldenburg, Reinhard – International Journal for Technology in Mathematics Education, 2015
Quantifier Elimination is a procedure that allows simplification of logical formulas that contain quantifiers. Many mathematical concepts are defined in terms of quantifiers and especially in calculus their use has been identified as an obstacle in the learning process. The automatic deduction provided by quantifier elimination thus allows…
Descriptors: Mathematical Concepts, Mathematical Formulas, Mathematical Applications, Calculus
Massachusetts Department of Elementary and Secondary Education, 2017
This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…
Descriptors: Elementary School Mathematics, Middle School Mathematics, Secondary School Mathematics, Preschool Education
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Deakin, Michael A. B. – International Journal of Mathematical Education in Science and Technology, 2011
The story is often told of the calculation by G.I. Taylor of the yield of the first ever atomic bomb exploded in New Mexico in 1945. It has indeed become a staple of the classroom whenever dimensional analysis is taught. However, while it is true that Taylor succeeded in calculating this figure at a time when it was still classified, most versions…
Descriptors: Mathematical Models, Mathematics, Equations (Mathematics), Computation
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Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S. – International Journal of Research in Education and Science, 2016
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
Descriptors: Mathematical Models, STEM Education, Standardized Tests, Mathematics Achievement
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012
In this article, the author reports results in their efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in their model. They have offered the reader two sets of data and several approaches to determine the rate of sublimation of a piece of solid dry ice. They presented several models…
Descriptors: Computation, Scientific Concepts, Mathematical Models, Models
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Padula, Janice – Australian Senior Mathematics Journal, 2012
When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…
Descriptors: Teaching Methods, Graphs, Mathematics Instruction, Mathematics Teachers
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2010
We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity…
Descriptors: Mathematical Models, Calculus, Mathematics Education, Mathematics Instruction
Holm, Jennifer, Ed.; Mathieu-Soucy, Sarah, Ed.; Oesterle, Susan, Ed. – Canadian Mathematics Education Study Group, 2017
This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…
Descriptors: Foreign Countries, Mathematics Instruction, Writing Exercises, Mathematical Concepts
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Rozema, Edward – College Mathematics Journal, 2007
Recent events have led to an increased interest in emerging infectious diseases. This article applies various deterministic models to the SARS epidemic of 2003 and a measles outbreak in the Netherlands in 1999-2000. We take a historical approach beginning with the well-known logistic curve and a lesser-known extension popularized by Pearl and Reed…
Descriptors: Foreign Countries, Calculus, Mathematics Instruction, History
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