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…

Team-Based Learning (TBL) uses a flipped classroom model and involves students working collaboratively in small groups, with peer assessments to promote group accountability. We implemented TBL in Calculus I in both large (N [tilde] 150) and small (N [tilde] 35) class settings. We investigated the impact of this form of instruction over two…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

GeoGebra mathematical software is the best alternative way of teaching and learning calculus in the 21st century by exploration and visualization. This software opposes the traditional teaching and learning method, or solution only approaches and make the teaching and learning process more active in the classroom which goes with the constructive…

This paper presents a "virtual reality" based lesson for a common Calculus topic, including a description of how the lecture was implemented in both a virtual reality and an augmented reality hardware system. This lesson was delivered to a number of calculus classes and we describe the student response to the lesson via a quiz and a…

Ordinary Differential Equations I, is one of the core courses for science and engineering majors. Practical problem solving in science and engineering programs require proficiency in mathematics. Improving student performance and retention in mathematics classes requires inventive approaches. At the University of Central Florida (UCF) the…

Collaborative learning is well-established as a method to improve student learning and retention in engineering classrooms. One problem with collaborative learning is difficulty maximizing engagement of all students during group activities. We tested a change in implementation of collaborative problem solving sessions (Workshops) in a first-year…

Within the undergraduate mathematics curriculum, the topic of simple least-squares linear regression is often first encountered in multi-variable calculus where the line of best fit is obtained by using partial derivatives to find the slope and y-intercept of the line that minimizes the residual sum of squares. A markedly different approach from…

Background: Substantial research has been conducted focusing on student outcomes in mathematics courses in order to better understand the ways in which these outcomes depend on the underlying instructional methodologies found in the courses. From 2009 to 2014, the Mathematical Association of America (MAA) studied Calculus I instruction in United…

Despite the overwhelming amount of research on students' interpretations of rates of change in real-world physical science contexts, similar studies in real-world economic contexts are sparse. Contributing towards addressing this gap in knowledge, this study reports on how 12 pairs of business calculus students interpreted marginal change…

Active learning techniques, such as peer instruction and group work, have been gaining a lot of traction in universities. Taking a natural next step in re-evaluating current practices, many institutions recently started experimenting student-centred group exams. In order to assess the feasibility and effectiveness of collaborative assessments, we…

This study embarks on the question in the title with the construct of epistemological status, which pertains to the solver's satisfaction with the way and the degree to which their solution had fulfilled their intellectual and psychological needs in a particular problem situation. The construct is used to hypothesize that a solver's decision to…

Research has demonstrated the positive impact of active learning on students' learning outcomes, particularly in science, technology, engineering and mathematics (STEM) fields. However, few studies have explored the impact of active learning via problem-based collaborative games in large mathematics classes in the context of Asian tertiary…

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…

The authors present findings from a recently completed census survey of all mathematics departments in the United States that offer a graduate degree in mathematics. The authors report the viewpoints of departments about characteristics shown to support students' success as well as the extent to which these characteristics are being implemented in…