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Kilty, Joel M.; McAllister, Alex M. – PRIMUS, 2020

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and…

Descriptors: Calculus, Teaching Methods, Mathematics Instruction, College Mathematics

Jones, Leslie B.; Hopkins, Britney J. – PRIMUS, 2020

Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…

Descriptors: Mathematics Instruction, Programming, Teaching Methods, College Mathematics

Cline, K.; Fasteen, J.; Francis, A.; Sullivan, E.; Wendt, T. – PRIMUS, 2020

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

Descriptors: College Mathematics, Majors (Students), Programming, Teaching Methods

Ding, Wandi; Florida, Ryan; Summers, Jeffery; Nepal, Puran; Burton, Ben – PRIMUS, 2019

We share our experience and lessons learned from using Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) modeling scenarios in our Differential Equations I class at Middle Tennessee State University. Specific projects with Python codes are presented. Discussions are brought forth on how to…

Descriptors: Calculus, College Mathematics, Mathematics Instruction, Mathematical Models

Ekici, Celil; Plyley, Chris – PRIMUS, 2019

Following a modeling-first approach to differential equations, inquiry-based learning activities on modeling and controlling the growth of locally relevant species, such as lionfish or sea turtles, are developed by the authors. Emerging exemplary practices are presented, building towards a balanced teaching of differential equations involving…

Descriptors: Calculus, Mathematics Instruction, Inquiry, Mathematical Models

Czocher, Jennifer A.; Tague, Jenna; Baker, Greg – PRIMUS, 2019

In this paper, we tell a story of iterative design and continual improvement of an asynchronous technological resource, pencasts, to support development of students' modeling skills while studying at home. Our students were typically engineering majors, enrolled in differential equations as a prerequisite for their subsequent engineering courses.…

Descriptors: Homework, Mathematical Models, Technology Uses in Education, Asynchronous Communication

Sochacki, James S.; Thelwell, Roger; Tongen, Anthony – PRIMUS, 2019

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

Descriptors: Calculus, Mathematics Instruction, Mathematical Models, Problem Solving

Rasmussen, Chris; Dunmyre, Justin; Fortune, Nicholas; Keene, Karen – PRIMUS, 2019

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

Descriptors: Mathematical Models, Teaching Methods, Mathematics Instruction, Inquiry

Anderson, Jeffrey A.; McCusker, Michael V. – PRIMUS, 2019

We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this…

Descriptors: Mathematics Instruction, College Mathematics, Experiential Learning, Learning Activities

Diedrichs, Danilo R. – PRIMUS, 2019

Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a…

Descriptors: Mathematical Models, Equations (Mathematics), Calculus, Industry

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

McCarthy, Chris; Lan, Jie; Li, Jieying – PRIMUS, 2019

We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

Descriptors: Equations (Mathematics), Mathematical Models, Problem Solving, Computer Simulation

Clark, Thomas J. – PRIMUS, 2019

The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…

Descriptors: Equations (Mathematics), Calculus, Mathematical Models, College Mathematics

Bruder, Andrea; Kummel, Miro – PRIMUS, 2019

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

Descriptors: Calculus, Pollution, Inquiry, Problem Based Learning

Linhart, Jean Marie – PRIMUS, 2019

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in…

Descriptors: Census Figures, Equations (Mathematics), Calculus, Mathematical Models