Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read and discuss mathematics critically, reach a consensus on correctness and clarity as a group, and verbalize what…

This article includes a case study describing our innovative teaching technique of assigning reading journals in a first semester calculus course (Calculus I), as well as an exposition about and recommendations arising from our subsequent experiences implementing similar methods in Junior and Senior mathematics courses. In the primary case study…

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

An important step to achieving a sustainable department culture that encourages innovation in teaching is the alleviation of the isolation that teaching faculty experience. Decreasing this isolation should be accomplished in a manner that respects all instructors' classroom practices while simultaneously exposing faculty to new ideas. In this…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in…

This paper describes an activity using a dog treat ball to introduce systems of first-order differential equations. Beads are placed in the first of two hemispherical chambers of a food-dispensing dog toy. As the ball is turned, students track the number of beads in the first chamber, the second chamber, and the exterior of the ball. Students…

We share our experience and lessons learned from using Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) modeling scenarios in our Differential Equations I class at Middle Tennessee State University. Specific projects with Python codes are presented. Discussions are brought forth on how to…

In this work, we studied the use of open education resources (OER) in the form of online modules combined with an open textbook as it relates to student performance and perceptions in a Linear Algebra course. In this approach, we compared student performance and perceptions from three sections of this intermediate level mathematics course. One was…

Math courses graded on homework, tests, and a final examination can result in students putting together enough partial credit to pass the class without gaining a reasonable mastery of the course content. Mastery-based testing can help to address this by allowing the instructor to align course grades with mastery of the learning objectives for the…

This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this…

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…