Definitions are fundamental to any mathematics classroom. We consider how definitions are presented in textbooks and instructors' lecture notes, and whether students are positioned to gain a full understanding of new terms. Four textbooks, covering precalculus, calculus, and analysis, as well as three professors' Calculus I lecture notes are…

While proof is often presented to mathematics undergraduates as a well-defined mathematical object, the proofs students encounter in different pedagogical contexts may bear salient differences. In this paper we draw on the work of Dawkins and Weber (2017) to explore variations in norms and values underlying a proof across different pedagogical…

This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

In this paper, we examine the benefits of employing an inverted or "flipped" class design in a Transition-to-Proof course for second-year mathematics majors. The issues concomitant with such courses, particularly student acquisition of "sociomathematical norms" and self-regulated learning strategies, are discussed along with…

Lectures have been widely criticized as a method of teaching, but remain a standard component of most university mathematics courses. Does this necessarily harm students' education? This critical review contends that many arguments against lecturing are misconceived, at least when applied to mathematics. The effectiveness of lectures in carrying…

The purpose of this study was to determine if course format significantly impacted student learning and course completion rates in an introductory statistics course taught at Harford Community College. In addition to the traditional lecture format, the College offers an online, and a hybrid (blend of traditional and online) version of this class.…

According to "Standards of Excellence in Teaching Mathematics in Australian Schools," excellent teachers of mathematics need to create "an environment that maximises students' learning opportunities"; so that they can encourage self-directed learning, "model mathematical thinking and reasoning," and provide…

One prohibitory component to graduation rates in college is the lack of student success in college algebra. The current national passing rate of college students enrolled in college algebra is approximately 40 percent. Lack of success in college algebra creating higher enrollments in remediation courses for students has also been linked to…

It has been reported that the students' level of mathematics when entering university has changed in recent years. A surprising number of students struggle with mathematics or have a mathematics anxiety. Although this was widely reported within the UK, there was some uncertainty if colleagues in other countries were experiencing the same…

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based "transition to proof" courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as…

Students in this study were enrolled in either an Introductory Algebra or Intermediate Algebra class taught through computer-mediated instruction or lecture. In the first year of the study, students were asked what they believed helped them learn mathematics in the instructional format in which they were enrolled. They were also asked what they…

This article describes a study of learning when students used interactive spreadsheet-based computer tutorials in a mathematical literacy course. It foregrounds theories relating to the role of computer technology (and specifically spreadsheets) as a mediator for learning of mathematics. It outlines the application of quantitative methods…