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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

Krause, Andrew J.; Maccombs, Ryan J.; Wong, Willie W. Y. – PRIMUS, 2021

Our traditional model of calculus instruction at a large public research university emphasized factual knowledge and procedural fluency with few realistic applications, leaving a chasm between classroom mathematics and disciplinary practice. Amid an ongoing effort by our department to improve undergraduate learning outcomes, we replaced…

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

Greene, M.; von Renesse, C. – PRIMUS, 2017

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…

Descriptors: Mathematics Instruction, Learning Activities, Mathematics Activities, Inquiry

Pinzon, D.; Pinzon, K.; Stackpole, M. – PRIMUS, 2016

In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

Descriptors: College Mathematics, Undergraduate Study, Algebra, Active Learning

Smith, Michael D. – PRIMUS, 2016

The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Mathematical Logic

Lenz, Laurie – PRIMUS, 2015

Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college.…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Liberal Arts

Cook, John Paul – PRIMUS, 2015

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

Descriptors: Mathematics Instruction, Liberal Arts, College Mathematics, Undergraduate Study

McGee, Daniel; Moore-Russo, Deborah; Martinez-Planell, Rafael – PRIMUS, 2015

Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…

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

Mayfield, Betty – PRIMUS, 2014

The benefits of including the study of the history of mathematics in the education of mathematics majors have been discussed at length elsewhere. Many colleges and universities now offer a History of Mathematics course for mathematics majors, for mathematics education majors, or for general credit. At Hood College, we emphasize our commitment to…

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

Barnett, Janet – PRIMUS, 2014

Much has been written about the benefits to be derived by incorporating the history of mathematics into its teaching. Of the various ways to do this, the use of original sources is among the most thrilling for the insights and the challenges it offers for students and instructors alike. In this paper, we describe examples of one particular…

Descriptors: College Mathematics, Undergraduate Study, History, Teaching Methods

Bardzell, Michael; Poimenidou, Eirini – PRIMUS, 2011

In this article we present, as a case study, results of undergraduate research involving binomial coefficients modulo a prime "p." We will discuss how undergraduates were involved in the project, even with a minimal mathematical background beforehand. There are two main avenues of exploration described to discover these binomial…

Descriptors: Mathematics Curriculum, Undergraduate Study, Class Activities, Learning Activities

Peer reviewed

Zarzycki, Piotr – Primus, 1992

Presents eight techniques for teaching undergraduate mathematics whose main aims are (1) learning how to pose problems in an easier and more attractive form; (2) fostering usage of mathematical symbolism; and (3) checking the level of comprehension of the principal ideas. Examples illustrate each technique. (Author/MDH)

Descriptors: Competition, Elementary Secondary Education, Enrichment Activities, Higher Education

Peer reviewed

Reiter, Clifford A. – Primus, 1992

Computational environments that provide integrated numeric, symbolic, and graphical capabilities provide new opportunities for laboratories in Numerical Analysis. Hermite interpolation is one topic that can benefit from such an environment. Describes a laboratory session using Mathematica that allows students to actively experience Hermite…

Descriptors: College Mathematics, Computer Assisted Instruction, Discovery Learning, Estimation (Mathematics)

Peer reviewed

Francis, Richard L. – Primus, 1992

Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting…

Descriptors: College Mathematics, Higher Education, Learning Activities, Mathematical Concepts

Peer reviewed

Lutzer, Carl V. – Primus, 2001

Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)

Descriptors: Calculus, Higher Education, Learning Activities, Mathematics Education