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T. Clark – PRIMUS, 2024
A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
George Ashline; Bret Findley; Mitchell Andrea; Dylan Wawruck – PRIMUS, 2024
We describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of…
Descriptors: Learning Activities, Mathematics Instruction, Calculus, Chemistry
Smith, Joseph R.; Snapp, Bart; Madar, Savva; Brown, Jonathan R.; Fowler, Jim; Andersen, Maeve; Porter, Christopher D.; Orban, Chris – PRIMUS, 2023
We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…
Descriptors: STEM Education, Telecommunications, Handheld Devices, Computer Simulation
Landi, Amanda K.; Minden, Kaethe – PRIMUS, 2023
In this paper, we assess the pedagogical approaches we employ in our US-based undergraduate mathematics courses during the COVID-19 pandemic. Our goal is to share anecdotal evidence on the use of math journals, oral exams, and learning portfolios in the synchronous online mathematics classroom. We reflect on our experience using artifacts of…
Descriptors: Metacognition, COVID-19, Pandemics, Teaching Methods
Soosloff, Elisa; Huey, Maryann; Alexander, Daniel S. – PRIMUS, 2023
In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…
Descriptors: Mathematics Instruction, Visual Aids, Prior Learning, Teaching Methods
Yu, F. – PRIMUS, 2023
A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these…
Descriptors: Mathematics Instruction, College Mathematics, Calculus, Mathematical Concepts
Wang, A. Tingxiu; Çelik, B. Mehmet; Webster, C. Pamela – PRIMUS, 2023
Texas A&M University-Commerce has implemented supplemental instruction (SI) for Calculus since the fall of 2013. A direct display of the ABC rates from fall 2005 to spring 2021 only presents fluctuation from semester to semester, and one can hardly deduce that the ABC rates are increasing. In this paper, the "moving average"…
Descriptors: Supplementary Education, Mathematics Instruction, Calculus, College Mathematics
Reed, Zackery; Tallman, Michael A.; Oehrtman, Michael – PRIMUS, 2023
We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…
Descriptors: Mathematics Instruction, Calculus, Mathematical Concepts, Concept Formation
Alayont, Feryal; Karaali, Gizem; Pehlivan, Lerna – PRIMUS, 2023
In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within…
Descriptors: Textbooks, Textbook Evaluation, Calculus, Mathematics Instruction
Mangum, Amanda; Sorrells, Jessica – PRIMUS, 2023
We present a system for math placement and intervention that pairs ALEKS PPL with an online, standards-based "bridge" course designed to prepare students interested in STEM for PreCalculus. To determine the efficacy of this system we studied ALEKS PPL placement scores, bridge course grades, ALEKS concept mastery percentages, and…
Descriptors: Grading, Mathematics Instruction, Standards, Mastery Learning
MacArthur, Kelly; Dobie, Tracy E. – PRIMUS, 2023
Collaborative assessment techniques are needed to align with shifting approaches to learning that center peer interaction. Furthermore, it is critical to understand how collaborative assessments work for students belonging to historically marginalized groups. This study reports the perspectives of four mixed race and Latina/Hispanic women…
Descriptors: Calculus, Mathematics Instruction, Mathematics Tests, College Faculty
Oremland, Lucy S.; Dunmyre, Justin R.; Fortune, Nicholas – PRIMUS, 2022
In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the…
Descriptors: Inquiry, Active Learning, Mathematical Models, Calculus
Douventzidis, Andrew; Landquist, Eric – PRIMUS, 2022
The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its…
Descriptors: Numbers, Food, Rating Scales, Sensory Experience
Nievergelt, Yves – PRIMUS, 2022
This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Undergraduate Students
Aligning Calculus with Life Sciences Disciplines: The Argument for Integrating Statistical Reasoning
Luque, Antoni; Mullinix, James; Anderson, Matt; Williams, Kathy S.; Bowers, Janet – PRIMUS, 2022
Governmental and educational organizations have pointed out that students coming into the biological sciences require stronger skills in statistics and data modeling that are not usually addressed in typical engineering-based calculus courses. Our work here documents how faculty in biology and mathematics addressed this issue at a large urban…
Descriptors: Mathematics Instruction, Calculus, Undergraduate Students, STEM Education