This case study examines how online mathematics homework impacts student learning, attitude, and efficacy in a college Calculus I class. This research is important because it provides data on student perceptions for how to effectively implement online homework. Participants for this study completed homework using a blend of online and paper…

Several publishing companies now offer competing brands of online homework (OHW) software. Students rarely have a voice in choosing their required course materials, even though, ultimately, they will be asked to use and pay for these systems. In this study, Calculus I students each tested three different OHW systems. The students were then asked…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

This article describes a framework of Standards-Based Grading suitable for use in a variety of mathematics courses. We detail our experience adapting this framework to various courses, ranging from Pre-calculus to Differential Equations, at four different institutions, including both small liberal arts colleges and large universities, and in class…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…

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…

Introductory and remedial courses in college mathematics often serve as a gateway to student success. However, these university courses have seen little innovation despite historically low success rates. We sought to address deficits of the traditional lecture model and enhance student learning in an introductory college algebra course through the…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

The flipped classroom model interchanges the roles of in-class and out-of-class time to allow students more time to engage with cognitively demanding tasks when expert help from their instructor is more available. An extensive body of literature supports the effectiveness of this model. In contrast, I present a case study of a less-successful…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

In this paper, we tell a story of iterative design and continual improvement of an asynchronous technological resource, pencasts, to support development of students' modeling skills while studying at home. Our students were typically engineering majors, enrolled in differential equations as a prerequisite for their subsequent engineering courses.…

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 article shares an example of a course in Combinatorics, taught at Adelphi University in Fall 2012, designed with a primary goal of engaging students in pursuing mathematics as mathematicians do. The course went beyond usual applications of inquiry-based learning in that students were also charged with the responsibility of posing the…

This assessment study examined one potential instructional method for improving student learning in Calculus for majors, flipped learning, in comparison with traditional lecture-based instruction. Results suggest that participation in flipped learning substantially improved growth in achievement over the semester, final exam grades, and final…