The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom model, there are two lecture days and two discovery-based discussion days each week. Discussions center around…

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…

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…

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.

We discuss an innovative course model used in first-year calculus courses at a large North American research university, which we refer to as the "Blended Model." We argue that our model takes the best features of lectures, flipped classrooms, and traditional recitations, and gathers them into a cohesive, robust structure that benefits…

We describe the process of adjusting the balance between computer-based learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format…

We discuss an implementation of the research-based Pathways precalculus curriculum in a large-lecture format supported by recitations, clickers, and online homework. We describe our approach to adapting the implementation of Pathways precalculus from a small class to a large lecture instructional format. We report data on student learning and…

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the…

Large lecture halls are a common feature of many undergraduate mathematics programs. However, teaching effectively in a large lecture hall can be challenging. This paper discusses the use of personal whiteboards for students as a way to make large lecture halls a more productive learning environment. I discuss the logistics of using whiteboards,…

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and…

We discuss a decade of initiatives to improve the teaching and learning of calculus at The Ohio State University. Calculus at OSU is taught in lecture/recitation format with large lectures and is tightly coordinated, so all innovations had to occur within that framework. We show how many smaller projects built upon one another to create a larger…

In this paper, we will introduce partial results from our 3-year NSF funded grant titled "Inverted and Active Learning Pedagogies (IALP) for Student Success." We will present our results comparing student achievement between inverted (flipped) classrooms and traditional lecture formats in statistics classes at Texas Lutheran University.…

We describe a case study of a problem-solving section, using the "Harkness" discussion method, of an honors multivariable calculus course. Students in the problem-solving section had equivalent outcomes on exams, reported higher ratings in self-assessments of skills, and took more math classes in the following year, compared with…

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…

The authors have completed a 2-year quasi-experimental study on the use of inquiry-based learning (IBL) in precalculus. This study included six traditional lecture-style courses and seven modified Moore method courses taught by three instructors. Both quantitative and qualitative analyses were used to investigate the attitudes and beliefs of the…