According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean…

Reflections are presented on the first time flipping of an introductory Ordinary Differential Equations course. Assessment results, student motivation, and student attitudes are compared between flipped and traditional learning pedagogies in this course over two terms at a small technical university in the northeast United States. Assessments and…

The percentage of college students receiving unproductive grades in introductory mathematics courses is a concern for post-secondary institutions across the country. Many factors can be targeted as potential explanations for this lack of success, yet none of these issues are more noteworthy than the fact that many students enter college…

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…

Quantitative Reasoning for Business is a two-semester sequence that serves as an alternative to elementary and intermediate algebra for first-year business students with weak mathematical preparation. Students who take the sequence have been retained at a higher rate and demonstrated a larger reduction in math anxiety than those who take the…

Metacognition as a dimension of learning ranks highest in the revised Bloom's Taxonomy of cognitive tasks. In this paper we illustrate how it can be incorporated into a repeated exercise in the mathematics classroom, through a specific case study in the context of a liberal arts mathematics course. Through the semester, students were asked weekly…

Research has shown that a significant majority of students in remedial mathematics do not remediate successfully. Such widespread failure raises the question of motivation. Some would argue that the instructor should directly compel students to commit themselves to the course and its work. This can be done by mandating attendance and/or by…

By understanding what motivates students to learn mathematics, instructors can adapt their teaching strategies to help students achieve a level of engagement conducive to learning mathematics. There is a substantial body of research on motivations and academic achievement at the elementary and high school levels, but less is known at the college…

Encouraging students to make independent discoveries is an effective way to get them excited about mathematics, and sharing their triumphant moments (their light bulb moments) helps to spread this excitement to their peers. A Mathematics for the Liberal Arts course is a perfect venue for the sharing of light bulb moments, as it helps to correct…