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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
Shelton, Therese; Laurent, Theresa; Agyemang-Barimah, Beulah – PRIMUS, 2019
We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…
Descriptors: Equations (Mathematics), Active Learning, Calculus, Pharmacology
Amy Graham Goodman – ProQuest LLC, 2021
The goal of learning analytics is to optimize learning and the environments in which it occurs. Since 2011, when learning analytics was defined as a separate and distinct area of academic inquiry, the literature has identified a need for research that presents evidence of effective learning analytics, as well as, learning analytics research that…
Descriptors: Metacognition, Learning Analytics, Calculus, Mathematics Instruction
Liang, Senfeng – International Journal of Research in Education and Science, 2016
Although the mathematics community has long accepted the concept of limit as the foundation of modern Calculus, the concept of limit itself has been marginalized in undergraduate Calculus education. In this paper, I analyze the strategy of conceptual conflict to teach the concept of limit with the aid of an online tool--Desmos graphing calculator.…
Descriptors: Graphing Calculators, Mathematics, Mathematics Instruction, Mathematical Concepts
Ting, M.-Y.; Kuo, B.-C. – Journal of Computer Assisted Learning, 2016
The purpose of this study was to investigate the effect of a calculus system that was designed using an adaptive dynamic assessment (DA) framework on performance in the "finding an area using an integral". In this study, adaptive testing and dynamic assessment were combined to provide different test items depending on students'…
Descriptors: Calculus, Alternative Assessment, Models, Test Items
Winkel, Brian J. – International Journal of Mathematical Education in Science and Technology, 2012
This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…
Descriptors: Mathematical Models, Calculus, Diseases, Class Activities
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
Sawtelle, Vashti; Brewe, Eric; Kramer, Laird H. – Journal of Research in Science Teaching, 2012
The quantitative results of Sources of Self-Efficacy in Science Courses-Physics (SOSESC-P) are presented as a logistic regression predicting the passing of students in introductory Physics with Calculus I, overall as well as disaggregated by gender. Self-efficacy as a theory to explain human behavior change [Bandura [1977] "Psychological…
Descriptors: Higher Education, Introductory Courses, Physics, Calculus
Swinyard, Craig; Larsen, Sean – Journal for Research in Mathematics Education, 2012
The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…
Descriptors: Mathematics Education, Learner Engagement, Models, Experiments
Rash, Agnes M.; Winkel, Brian J. – PRIMUS, 2009
This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…
Descriptors: Equations (Mathematics), Probability, Calculus, Mathematics Instruction
Gordon, Sheldon P. – PRIMUS, 2008
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Descriptors: Calculus, Mathematics Instruction, Calculators, Spreadsheets
Marland, Eric; Palmer, Katrina M.; Salinas, Rene A. – PRIMUS, 2008
In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…
Descriptors: Mathematics Instruction, Biology, Integrated Curriculum, Equations (Mathematics)

Anderson, Malcolm; Bloom, Lyn; Mueller, Ute; Pedler, Pender – International Journal of Mathematical Education in Science and Technology, 1999
Considers some changes that the use of graphics calculators impose on the assessment of calculus and mathematical modeling at the undergraduate level. Suggests some of the ways in which the assessment of mathematical tasks can be modified as the mechanics of calculation become routine and questions of analysis and interpretation assume greater…
Descriptors: Calculus, College Mathematics, Graphing Calculators, Higher Education

Dancis, Jerome – Primus, 2001
Students in a freshmen calculus course should become fluent in modeling physical phenomena represented by integrals, in particular geometric formulas for volumes and arc length and physical formulas for work. Describes how to train students to became fluent in such modeling and derivation of standard integral formulas. Indicates that these lessons…
Descriptors: Calculus, College Mathematics, Higher Education, Mathematical Models

Sims, Brailey – Australian Mathematics Teacher, 1975
The fundamental results of integration theory are shown to follow from an axiomatic definition of the integral as a real valued function whose domain is a subset of the set of real valued functions of a real variable. (SD)
Descriptors: Calculus, College Mathematics, Curriculum, Higher Education