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Calkins, Susanna; Grannan, Sharisse; Siefken, Jason – PRIMUS, 2020

This study explores the impact of Peer-Assisted Reflection (PAR), a structured active learning strategy that emphasizes peer feedback and reflection, on students' perceptions of mathematical thinking, and of the roles their peers and their instructors play in their learning process. This study also examines the impact of PAR on the students'…

Descriptors: Reflection, Peer Influence, Active Learning, Feedback (Response)

Das, Tushar; George, Whitney; Warnberg, Nathan – PRIMUS, 2020

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

Descriptors: Mathematics Education, Mathematical Concepts, Symbols (Mathematics), College Mathematics

Boyce, Steven; O'Halloran, Joyce – PRIMUS, 2020

We describe the process of adjusting the balance between computer-based learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format…

Descriptors: Active Learning, College Students, Algebra, Mathematics Instruction

Coggins, Porter E., III; Glatzer, Tim – PRIMUS, 2020

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Descriptors: Mathematics Instruction, Matrices, Technology, Addition

Garcia, Stephan Ramon; Horn, Roger A. – PRIMUS, 2020

Linear algebra is best done with block matrices. As evidence in support of this thesis, we present numerous examples suitable for classroom presentation.

Descriptors: Mathematics Instruction, Algebra, Teaching Methods, Matrices

Krouss, Paul; Lesseig, Kristin – PRIMUS, 2020

Introductory and remedial courses in college mathematics often serve as a gateway to student success. However, these university courses have seen little innovation despite historically low success rates. We sought to address deficits of the traditional lecture model and enhance student learning in an introductory college algebra course through the…

Descriptors: Educational Technology, Technology Uses in Education, Homework, Video Technology

Adiredja, Aditya P.; Bélanger-Rioux, Rosalie; Zandieh, Michelle – PRIMUS, 2020

In this paper we share a classroom implementation of a task about basis in linear algebra, which was originally developed for research about the topic. The task asks students to construct an everyday situation that captures the definition of basis, and then to critique it mathematically. Using this task, the original research study uncovered…

Descriptors: Mathematics Instruction, Algebra, Relevance (Education), Teaching Methods

Cline, K.; Fasteen, J.; Francis, A.; Sullivan, E.; Wendt, T. – PRIMUS, 2020

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

Descriptors: College Mathematics, Majors (Students), Programming, Teaching Methods

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

Cilli-Turner, Emily; Dunmyre, Justin; Mahoney, Thomas; Wiley, Chad – PRIMUS, 2020

While you may be ready to make the change to implementing Mastery Grading, you may still wonder exactly how to do this. This paper seeks to compile recommendations on implementing mastery grading from various sources as well as examples from our own experiences. The reader should expect a detailed overview of the components involved in mastery…

Descriptors: Grading, Mastery Learning, Evaluation Methods, Program Implementation

Elsinger, Jason; Lewis, Drew – PRIMUS, 2020

This article describes a framework of Standards-Based Grading suitable for use in a variety of mathematics courses. We detail our experience adapting this framework to various courses, ranging from Pre-calculus to Differential Equations, at four different institutions, including both small liberal arts colleges and large universities, and in class…

Descriptors: Academic Standards, Grading, Mathematics Education, College Mathematics

Harsy, Amanda – PRIMUS, 2020

As educators, it is important for us to recognize that our assessment methods affect student attitudes. If we want students to learn from their mistakes and counteract a fixed-mindset of learning, perhaps we should look at what we incentivize in the classroom. Some professors are attempting to counteract math and test anxiety, poor STEM retention,…

Descriptors: Testing, Mastery Tests, Mastery Learning, Mathematics Instruction

Zimmerman, Jane K. – PRIMUS, 2020

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra…

Descriptors: Grading, Standards, Mathematics Instruction, College Mathematics

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

Anderson, Jeffrey A.; McCusker, Michael V. – PRIMUS, 2019

We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this…

Descriptors: Mathematics Instruction, College Mathematics, Experiential Learning, Learning Activities