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Bruder, Andrea; Kohler, Brynja R. – PRIMUS, 2020

Although modeling is an integral process in applied mathematics, students rarely encounter modeling opportunities in their calculus courses. We introduce a laboratory experience as a starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients…

Descriptors: Calculus, Mathematics Instruction, Climate, Food

Breen, Sinéad; O'Shea, Ann – PRIMUS, 2019

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…

Descriptors: Undergraduate Students, Mathematics Instruction, College Mathematics, Learning Activities

Morena, Matthew A.; Smith, Shelly; Talbert, Robert – PRIMUS, 2019

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

Descriptors: Video Technology, Problem Solving, Calculus, Mathematics Instruction

Martin, Taylor E. – PRIMUS, 2019

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

Descriptors: Calculus, Homework, Mathematics Instruction, Mathematical Concepts

Holdener, Judy A.; Jones, Brian D. – PRIMUS, 2019

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

Descriptors: Calculus, Homework, Mathematics Instruction, Story Telling

Gerstle, Kevin – PRIMUS, 2019

At the college level, it can be difficult to engage students outside the classroom through the use of effective homework assignments. Although it is straightforward to create assignments that test the ability to carry out computations as discussed in class, it is more challenging to create assignments that encourage students to think more…

Descriptors: College Mathematics, Mathematics Instruction, Assignments, Creative Thinking

OShaughnessy, J. – PRIMUS, 2019

This paper investigates the advantages of using a two-step homework system. First, technology is used to collect and grade traditional homework. Then, students are expected to present and explain problems from their assignments in class. Several versions of implementation are discussed for different course levels and sizes. Through these methods,…

Descriptors: Mathematics Instruction, College Mathematics, Homework, Educational Technology

Karaali, Gizem; Khadjavi, Lily S. – PRIMUS, 2019

We provide context and motivation for an instructor to use real-life examples in the calculus classroom. To this end we describe two specific project ideas, one related to the devastating impact of methylmercury fungicide in a grain seed supply and the other to a catastrophic methane leak. By using calculus in contexts that have social justice…

Descriptors: Calculus, Mathematics Instruction, Social Justice, Interdisciplinary Approach

Hoke, Kathy; Keough, Lauren; Wares, Joanna – PRIMUS, 2019

In the calculus classroom, integrating applications with the theoretical and procedural conveys the relevance of the material. Since Newton and Leibniz developed calculus in the context of physics and astronomy, applications in these fields tend to predominate. To engage and excite our students, pedagogical considerations must include broader…

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

O'Donovan, Barbara; Geary, Krisan – PRIMUS, 2019

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Calculus

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

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