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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

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

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

Sears, Ruthmae; Kersaint, Gladis; Burgos, Fernando; Wooten, Rebecca – PRIMUS, 2019

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses,…

Descriptors: Middle School Mathematics, Preservice Teachers, Knowledge Level, Mathematics Education

Pinter, Mike; Jones, Linda – PRIMUS, 2019

We describe a successful collaboration between mathematics and psychological science faculty members to create a learning community for our students that linked sections of introductory mathematical reasoning and psychological science courses. The students in our learning community were in their second or third semester. The learning community is…

Descriptors: Mathematics Instruction, College Mathematics, Interdisciplinary Approach, College Faculty

Cardetti, Fabiana; LeMay, Steven – PRIMUS, 2019

In this article we present the results of a study focused on engaging students in argumentation to support their growth as mathematical learners, which in turn strengthens their science learning experiences. We identify five argumentation categories that promote the learning of argumentation skills and enrich mathematical reasoning at the…

Descriptors: Persuasive Discourse, Abstract Reasoning, Mathematics Skills, Science Process Skills

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

Jordan, Daniel R. – PRIMUS, 2019

Workshops can be a powerful tool to support students as they develop proof-writing skills. In a workshop, each student writes a proof, provides feedback on other students' work, and reflects on critiques from peers. Workshops can be used in any class that emphasizes writing proofs or other forms of mathematical writing. They are highly efficient…

Descriptors: Workshops, Mathematical Logic, Mathematics Skills, Mathematics Instruction

Stange, Katherine E. – PRIMUS, 2018

Standards-based grading, in which grading should be designed to communicate to students their current level of mastery with regards to well-articulated standards, is becoming popular at the K-12 level. As yet, the literature addressing standards-based grading at the university level is scarce. In this paper, I document my attempts to put into…

Descriptors: Academic Standards, Grading, Introductory Courses, College Mathematics