Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

We describe how an instructor integrated embodiment to teach the Fundamental Homomorphism Theorem (FHT) and preliminary concepts in an undergraduate abstract algebra course. The instructor's use of embodiment reduced levels of abstraction for formal definitions, theorems, and proofs. The instructor's simultaneous use of various forms of embodiment…

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.

Linear algebra is gaining increased attention due to its applications in many modern high-tech industries, such as artificial intelligence, machine learning, and robotics. Coordinate systems underlie many concepts in linear algebra and promote students' spatial thinking of key concepts by imposing a visual aspect to courses that may otherwise be…

The enduring debate surrounding college algebra, traditionally a gateway for STEM pathways, underscores the necessity for curricular evolution in response to the rising popularity of non-STEM majors. This dissertation explores the success of an applied college algebra course designed for non-STEM students. The study aimed to determine whether this…

This research article is about "Introducing a Supportive Framework to Address Students' Misconceptions and Difficulties in Learning Mathematical proof techniques (MPT): A Case of Debark University". This study aims to develop, introduce, and implement a supportive framework to overcome students' misconceptions and difficulties in MPT.…

Numerous studies affirm the importance of students' attitudes for mathematical education. This study uses mathematical autobiographical essays to examine the mathematical experiences and attitudes of undergraduate students enrolled in mathematics classes at a Midwestern University in the United States. The essays of 41 students (20 men, 21 women)…

This article presents a study investigating the use of games in undergraduate mathematics instruction, with a specific focus on students' perspectives regarding post-instructional quiz games. The study explores students' opinions on the implementation of a linear algebra quiz game as a supplementary learning tool. A survey was administered to 78…

The focus of this study was to examine the effect of teaching based on inquiry-based learning versus traditional learning on mathematics achievement scores of undergraduate students enrolled in a college algebra class in a university classified as a Predominantly Black Institution. A college algebra course was chosen in this study due to the…

In this paper, we present a qualitative study on what values students perceive in their abstract algebra course. We interviewed six undergraduates early in their abstract algebra course and then again after their course was completed about what motivated them to learn abstract algebra and what value they saw in the subject. The key finding from…

While the lion's share of mathematics education research in linear algebra has been concerned with the conceptual aspects of students' learning, this study focuses on procedural knowledge that undergraduates can develop in a typical first-year course. The study analyzes the methods that a large cohort of second-semester students applied in a final…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

Though posters have been used as a pedagogical tool in a variety of fields, the literature suggests that the use of posters as an educational assessment tool by the mathematics community has been limited. This is unfortunate given the numerous potential benefits of a poster, including the development of oral communication skills and the ability to…

Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…