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Koss, Lorelei – PRIMUS, 2022

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…

Descriptors: Mathematics Instruction, Learning Activities, Mathematics Tests, Teamwork

Grundmeier, T. A.; Retsek, D.; Berg, A.; Mann, S.; Hamlin Prieto, A. – PRIMUS, 2022

Students' proof abilities were explored in the context of an inquiry-based learning (IBL) approach to teaching an introductory proofs course. IBL is a teaching method that puts the responsibility for proof on students and focuses on student discussion and exploration. Data collected from each of the 70 participants included a portfolio consisting…

Descriptors: Mathematics Instruction, Inquiry, Validity, Mathematical Logic

Palmer, Katrina; Bauldry, William; Bossé, Michael J.; Post, Jaehee – PRIMUS, 2022

Most any students can explain the meaning of "a[superscript b]", for "a" ? R and for "b" ? Z. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" ? R and for "c" ? Z. However, few may be able to explain "a[superscript di]" or…

Descriptors: Mathematics Instruction, Mathematical Concepts, Secondary School Mathematics, College Mathematics

Norton, Douglas E. – PRIMUS, 2022

This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model…

Descriptors: Undergraduate Study, College Mathematics, Mathematical Models, Biological Sciences

Álvarez, James A. M.; Kercher, Andrew; Turner, Kyle; Arnold, Elizabeth G.; Burroughs, Elizabeth A.; Fulton, Elizabeth W. – PRIMUS, 2022

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…

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

Fulton, Elizabeth W.; Arnold, Elizabeth G.; Burroughs, Elizabeth A.; Álvarez, James A. M.; Kercher, Andrew; Turner, Kyle – PRIMUS, 2022

This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into…

Descriptors: High Schools, Secondary School Mathematics, Mathematics Instruction, Undergraduate Study

Andriunas, R.; Boyle, B.; Lazowski, A. – PRIMUS, 2022

This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…

Descriptors: Algebra, Geometry, Matrices, Mathematics Instruction

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

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

Munakata, Mika; Vaidya, Ashwin; Monahan, Ceire; Krupa, Erin – PRIMUS, 2021

This paper describes the development and implementation of course modules intended to encourage creative thinking in an undergraduate general education mathematics course. The modules were designed to address the characteristics of creativity outlined in the literature through explorations of mathematics relevant to non-mathematics majors. A…

Descriptors: Mathematics Instruction, Creative Thinking, Undergraduate Study, College Mathematics

Apkarian, Naneh; Kirin, Dana; Gehrtz, Jessica; Vroom, Kristen – PRIMUS, 2021

The Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

Descriptors: College Mathematics, Undergraduate Study, Mathematics Education, Conferences (Gatherings)

White, D.; Anderson, M. – PRIMUS, 2021

The purpose of this paper is to describe the use of a problem involving superfactorials (a specific product of factorials) that provides an in-depth and comprehensive mathematical experience, encompassing skills that mathematicians view as tantamount to exploration. The problem is easily accessible and fosters creativity and perseverance, thereby…

Descriptors: Mathematics Instruction, College Mathematics, Problem Solving, Mathematics Skills

Fowler, Jim; Snapp, Bart; Johns, Carolyn; Andrews, Darry; Boros, Dan; Clemens, Herb; Ferdinand, Vic; Findell, Brad; Husen, Bill; Johnson, John H.; Lakos, Nela; Miller, Elizabeth; Ramsey, Bobby; Sheldon, Jenny; Talamo, Jim; Carlson, Tim – PRIMUS, 2021

An interactive open-source calculus textbook is compared to a popular commercial textbook. Structured as a non-inferiority study, use of the open-source textbook does not harm student outcomes, and there is evidence that the open-source textbook is better than the commercial textbook in promoting post-course enjoyment of mathematics and confidence…

Descriptors: Mathematics Instruction, College Mathematics, Calculus, Textbooks

Peck, Frederick – PRIMUS, 2021

A deficit perspective is a propensity to locate the source of academic problems in deficiencies within students, their families, their communities, or their membership in social categories (such as race and gender). While the deficit perspective is a common topic of discussion in K-12 mathematics education, it is a much rarer topic of discussion…

Descriptors: Undergraduate Study, College Mathematics, Mathematics Education, Equal Education

Gruber, Sean; Rosca, Raluca I.; Chazan, Daniel; Fleming, Elizabeth; Balady, Steve; VanNetta, Catherine; Okoudjou, Kasso A. – PRIMUS, 2021

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across…

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