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,…

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 I discuss my experience in using the inverted classroom structure to teach a proof-based, upper level Advanced Calculus course. The structure of the inverted classroom model allows students to begin learning the new mathematics prior to the class meeting. By front-loading learning of new concepts, students can use valuable class time…

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

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…

To further understand student thinking in the context of combinatorial enumeration, we examine student work on a problem involving set partitions. In this context, we note some key features of the multiplication principle that were often not attended to by students. We also share a productive way of thinking that emerged for several students who…

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.…

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

In this paper we present a short tutorial on creating mini-videos using two platforms--PCs and tablets such as iPads--and software packages that work with these devices. Specifically, we describe the step-by-step process of creating and editing videos using a Wacom Intuos pen-tablet plus Camtasia software on a PC platform and using the software…

Advances in learning theory call us to examine ways to get students more actively engaged both inside and outside of the classroom. This report offers suggestions for encouraging and increasing student reading, writing, and collaborative development in a real analysis course.

In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…

Common arguments for integrating the arts into mathematics courses include the arts fostering student creativity, improving academic achievement, and encouraging transfer between subjects. Research supporting these arguments is limited and carries layered complexities--such as what constitutes creativity and transfer, and whether they can be…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

In this paper I will share my experience with flipping a math content course for pre-service elementary teachers. The flipped class format involves students receiving instruction outside the classroom through readings and/or video lectures and working on "homework" inside the classroom. I will share strategies for creating lessons for my…

The increased use of videos in mathematics courses means that direct instruction, traditionally part of class lectures, now often occurs outside of the classroom. Although students come to class with some baseline level of understanding, instructors lose opportunities to assess students' understanding of content as it is seen for the first time.…