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,…

This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable…

Introductory mathematics courses at postsecondary institutions simultaneously function as gateways and gatekeepers to degrees and careers in Science, Technology, Engineering, and Mathematics (STEM) for historically minoritized and marginalized students. While these courses provide access to higher education, they also thwart student STEM pathways…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

In an effort to make math courses more relevant and improve success rates in college math, various organizations and colleges developed a new model of math education that has come to be called "math pathways." Math pathways enable students to take different paths through the math curriculum, depending on their course of study. With math…

Low success rates in developmental mathematics courses have caused a growing concern for many institutions including moderately selective four-year universities. As a result, institutions have adopted various course redesign models, such as the emporium and replacement models, which take advantage of interactive online learning tools. Though these…

The traditional mathematics pre-requisite model creates obstacles for pre-service educators by increasing the number of semesters to graduation. Extended time results in additional financial burdens for students in developmental courses along with increased risk of student drop out. Education majors, with little or no room for electives in their…

The purpose of this study was to compare students' performances in a freshmen level quantitative reasoning course (QR) under three different instructional models. A cohort of 155 freshmen students was placed in one of the three models: needing a prerequisite course, corequisite (students enroll simultaneously in QR course and a course that…

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of…

This paper is a case study of the teaching of an undergraduate abstract algebra course, in particular the way the instructor presented proofs. It describes a framework for proof writing based on Selden and Selden (2009) and the work of Alcock (2010) on modes of thought that support proof writing. The paper offers a case study of the teaching of a…

A method of solving the Schrodinger equation using a basis set expansion is described and used to calculate energy levels and wavefunctions of the hindered rotation of ethane and the ring puckering of cyclopentene. The calculations were performed using a computer algebra package and the calculations are straightforward enough for undergraduates to…

This material shows how to use basic techniques, principles of counting, and geometry to count squares on geoboards. The methods are elementary in that the proofs are easily conceptualized. A discussion of other approaches illustrates that easily stated problems may lead to very difficult and sophisticated methods. (MP)

Describes the development of an interactive teaching and learning model involving Desktop Videoconferencing (DVC) and other audiographic facilities for undergraduate mathematics. The experiment demonstrated that it was possible to integrate DVC with computer applications/graphics software to represent algebraic, geometric, and numeric concepts.…

The implementation of the program used in this study, TPIXIE, was predicated on the assumption that acquiring the skill to diagnose student errors was important for teacher trainees. The TPIXIE system (part of the PIXIE family of intelligent tutoring systems) was designed to present users with a series of task-student-answer pairs (where the…

Programs for computer-assisted instruction (CAI) which were developed at Stanford University from 1963-70 are described, and prospects for CAI in the 1970's are considered briefly. The programs include ones in arithmetic, logic, and reading for elementary grades and in basic Russian and remedial algebra for college students. Of these, the logic…