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Adiredja, Aditya P. – PRIMUS, 2021

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

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

Petrilli, Salvatore J., Jr. – PRIMUS, 2021

The Department of Mathematics and Computer Science at Adelphi University engaged in a year-long program revision of its mathematics major, which was initiated by a longitudinal study and the publication of the 2015 Curriculum Guide by the MAA's Committee on Undergraduate Programs in Mathematics. This paper stands as a short story, so to speak, of…

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

Engelke Infante, N. – PRIMUS, 2021

In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…

Descriptors: Mathematics Instruction, College Mathematics, Calculus, Schemata (Cognition)

Bleiler-Baxter, Sarah K.; Pair, Jeffrey D.; Reed, Samuel D. – PRIMUS, 2021

Students often view their role as that of a replicator, rather than a creator, of mathematical arguments. We aimed to engage our students more fully in the creation process, helping them to see themselves as legitimate proof creators. In this paper, we describe an instructional activity (i.e., the "group proof activity") that is…

Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic

Becker, Paul; Medwid, Mark – PRIMUS, 2021

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

Descriptors: College Mathematics, Mathematics Instruction, Undergraduate Students, Assignments

Seager, Suzanne – PRIMUS, 2020

For many of my students, Real Analysis I is the first, and only, analysis course they will ever take, and these students tend to be overwhelmed by epsilon-delta proofs. To help them I reordered Real Analysis I to start with an "Analysis Boot Camp" in the first 2 weeks of class, which focuses on working with inequalities, absolute value,…

Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Concepts, Concept Formation

Flórez, Rigoberto; Mukherjee, Antara – PRIMUS, 2020

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

Descriptors: Mathematics Instruction, College Mathematics, Secondary School Mathematics, Undergraduate Study

Durst, Susan; Kaschner, Scott R. – PRIMUS, 2020

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

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

Karaali, Gizem; Yih, Samuel – PRIMUS, 2020

When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. In this article we explore three specific statements from abstract algebra that involve the number…

Descriptors: Mathematics Instruction, College Mathematics, Algebra, Numbers

Cooper, Andrew A. – PRIMUS, 2020

Mastery grading is an approach to grading in which students are assigned term grades based on whether they meet certain enumerated objectives, rather than accumulating points. In this note, I describe my experiences using a mastery system, which I call techniques grading, which applies the insights behind the standards-based and specifications…

Descriptors: Academic Standards, Grading, Mastery Learning, Evaluation Methods

Carlisle, Sylvia – PRIMUS, 2020

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…

Descriptors: Grading, Standards, Mathematics Instruction, Calculus

Weir, Rachel J. – PRIMUS, 2020

Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Student Centered Learning

Selbach-Allen, Megan E.; Greenwald, Sarah J.; Ksir, Amy E.; Thomley, Jill E. – PRIMUS, 2020

In this paper, we compare and contrast our experiences in using standards-based grading in different courses and across two separate institutions to explore the related tradeoffs and subtleties in designing and implementing such grading systems, guided by innovation diffusion theory. We summarize our individual courses, use Linda Nilson's criteria…

Descriptors: Grading, Standards, Evaluation Methods, College Faculty

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

Klima, V. – PRIMUS, 2019

As teachers of mathematics we encourage our students to ask good questions, and we strive to help our students find and understand answers to these questions. This journey can be made more meaningful if students conclude by reflecting on their learning process. If we find careful questioning and reflection important, we should include such…

Descriptors: Homework, Mathematics Instruction, College Mathematics, Color