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Diamond, Harvey – PRIMUS, 2023

This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

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

Zolt, Holly; Wrightsman, Elizabeth; Ford, Lucinda; Patterson, Cody L. – PRIMUS, 2023

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

Descriptors: Mathematical Concepts, Mathematics Education, Calculus, Online Courses

Gordon, Sheldon P.; Gordon, Florence S. – PRIMUS, 2023

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

Descriptors: College Mathematics, Introductory Courses, Statistics Education, Algebra

Madamanchi, Aasakiran; Thomas, Madison; Magana, Alejandra; Heiland, Randy; Macklin, Paul – PRIMUS, 2022

There is growing awareness of the need for mathematics and computing to quantitatively understand the complex dynamics and feedbacks in the life sciences. Although several institutions and research groups are conducting pioneering multidisciplinary research, communication and education across fields remain a bottleneck. The opportunity is ripe for…

Descriptors: Mathematics Instruction, Biological Sciences, Interdisciplinary Approach, Computation

Hossain, M. Alamgir; Menz, Petra M.; Stockie, John M. – PRIMUS, 2022

We present a question bank consisting of over 250 multiple-choice and true--false questions covering a broad range of material typically taught in an introductory undergraduate course in numerical analysis or computational science. The questions are ideal for polling students during lectures by means of a student response system that uses…

Descriptors: Audience Response Systems, Undergraduate Study, Telecommunications, Handheld Devices

Reed, Zackery; Tallman, Michael A.; Oehrtman, Michael; Carlson, Marilyn P. – PRIMUS, 2022

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

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

Toney, Allison F.; Boul, Stephen D. – PRIMUS, 2022

Based on our work teaching undergraduate Calculus courses, we offer insight into teaching the chain rule to reduce cognitive load for students. A particularly difficult topic for students to grasp, problems likely arise due to student struggles with the concept of function and, particularly, function composition relative to when they first…

Descriptors: College Mathematics, Undergraduate Study, Mathematics Instruction, Difficulty Level

Melkonian, Vardges – PRIMUS, 2019

This paper discusses a game that can be used for introducing the binary representation of integers in an interactive and fun environment. The game is introduced in the way it is presented in an undergraduate Discrete Mathematics class. Variations of the game are discussed, particularly its extension to base-three representation of integers. It is…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Educational Games

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

Kostadinov, Boyan; Thiel, Johann; Singh, Satyanand – PRIMUS, 2019

The goal of this paper is to promote the use of R and Python as high-level, free, open-source programming environments that can be used as a computational and visualization tool for teaching differential equations. Both R and Python also allow for creating reproducible dynamic documents using Markdown, which combines live code, plain text, and…

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

Lynch, Frank H.; Page, Breeanna S. – PRIMUS, 2018

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

Descriptors: Calculus, Problem Solving, Word Problems (Mathematics), Mathematics Instruction

Daugulis, Peteris; Sondore, Anita – PRIMUS, 2018

Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…

Descriptors: Mathematics Instruction, Matrices, Visualization, Multiplication

Robertson, Robert L. – PRIMUS, 2017

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

Descriptors: Mathematics Instruction, Teaching Methods, Probability, Computation

Pudwell, Lara – PRIMUS, 2017

In this paper, we discuss the Experimental Mathematics course taught at Valparaiso University since 2009. We focus on aspects of the course that facilitate students' abilities to ask and explore their own research questions.

Descriptors: Inquiry, Mathematics, Mathematics Instruction, Mathematics Education

Toews, Carl – PRIMUS, 2017

Inquiry-based pedagogies have a strong presence in proof-based undergraduate mathematics courses, but can be difficult to implement in courses that are large, procedural, or highly computational. An introductory course in statistics would thus seem an unlikely candidate for an inquiry-based approach, as these courses typically steer well clear of…

Descriptors: Computation, Inquiry, Introductory Courses, Statistics