In introductory math courses such as precalculus, students often have difficulty with assignments that require explanations or synthesizing knowledge. When students receive low scores on such assignments, instructors often wish to help students understand the material they struggled with. A common strategy is to allow the students to revise and…

Homework completion and self-regulatory ability have both been extensively studied to examine their impact on learning achievement. Moreover, the reciprocal nature of how these two qualities affect one another is also an area of research. While evidence shows that voluntary completion of assigned homework predicts self-regulation in students, a…

Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned…

In this study, we use Class Preparation Worksheets (CPWs) as pre-class reading assignments for a Calculus I course. We describe the implementation and data collection as well as a qualitative and quantitative analysis. Then, we discuss the implications for student engagement with course materials, a student-and-instructor feedback loop, impacts on…

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…

Although modeling is an integral process in applied mathematics, students rarely encounter modeling opportunities in their calculus courses. We introduce a laboratory experience as a starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients…

A summative portfolio is a project completed at the end of the semester that gives a student an opportunity to look at a course as a whole. This study investigates whether collegiate mathematics students gain a deeper understanding of course material through the portfolio project, via an analysis of the students' work, and a survey of students'…

We present an analysis on the differential effects of incentivizing homework in an introductory mathematics course at the United States Military Academy. We found that including homework as part of a student's overall course average (incentive) led to a significantly higher performance (achievement) on homework assignments. However, doing homework…

We explored the effectiveness of a flipped active learning pedagogy in a liberal arts mathematics course without video or interactive preparation. In both control and active learning classes, students were required to respond to a reading before class and take a quiz after class. During the active learning class, students worked together in groups…

The use of writing to learn mathematics at the university-level is a pedagogical tool that has been gaining momentum. The setting of this study is a second-year differential equations class where written assignments have been incorporated into the course. By analyzing survey results and students' written work, we examine the extent to which…

This paper describes an innovative way of randomly collecting handwritten homework in calculus classes with approximately 50 students using a standard deck of cards, which does not place an excessive burden on faculty with regard to grading. In addition to the increased awareness students develop in structuring a mathematical solution, the…

This paper describes and assesses the implementation of online homework in a first-semester calculus course. Comparing sections of the course before implementation to those after, we find statistically significant improvements in retention rates, measures of student engagement, and participation on homework. We do not, however, find statistically…

In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

Providing audio files in lieu of written remarks on graded assignments is arguably a more effective means of feedback, allowing students to better process and understand the critique and improve their future work. With emerging technologies and software, this audio feedback alternative to the traditional paradigm of providing written comments…

This paper examines various issues surrounding the use of writing in the teaching and learning of mathematics using the voice and experiences of a licensed High School teacher instructing introductory college mathematics as a graduate teaching assistant. In general, we detail the journey taken by this teacher to explore the push for writing by…