Research results from this study reveal students have difficulties understanding and using of the concepts of average rate of change and the derivative function. Students in this study held multiple approach to understand the concepts that made it difficult to develop a strong understanding of the average rate of change and derivative function. In…

The National Science Foundation identified a shortage of STEM professionals in the United States. There is a dire need to promote STEM education to secure high-paying and skilled jobs for the country's residents and the overall healthy economy. This shortage is partly due to students' low retention and persistence to graduate in STEM fields. Due…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

The purpose of this quantitative ex post facto research study is to determine if there is a difference in students' pre-calculus knowledge and mathematical skills achievement based on pre-calculus instructional conditions and gender at a community college in the Mid-Atlantic region of the United States. Three research questions were used to…

The concept of integration appears in many different scientific fields, and students' understanding of and ability to use the definite integral in applications is important to success in their STEM (science, technology, engineering, and mathematics) classes. One of the first types of application problems that students encounter is finding the…

Spatial reasoning is required for many topics in undergraduate mathematics as well as other STEM fields. In calculus specifically, there are few interventions that assess students' spatial skills and provide remediation. Haptic technology is a novel approach to spatial skills remediation due to its unfamiliarity to students and its flexibility…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

This dissertation reports on three studies about students' conceptions and learning of the idea of instantaneous rate of change. The first study investigated 25 students' conceptions of the idea of instantaneous rate of change. The second study proposes a hypothetical learning trajectory, based on the literature and results from the first study,…

Introductory calculus is mandatory for postsecondary science, technology, engineering, and mathematics (STEM) majors (Bressoud, 2015); however, many students do not persist through introductory calculus to further STEM study (Rasmussen et al., 2019). One reason for this may be that students struggle with the prior mathematical knowledge required…

The promotion of belonging, purpose, and growth mindset through subtle social psychological interventions has been shown to positively impact student outcomes (Lazowski & Hulleman, 2016; Walton & Cohen, 2007; Yeager & Walton, 2011; Yeager et al., 2016). This study explores how instructor messaging and intentional course design can…

The rise of virtual learning established e-learning as an emerging education delivery method (Jones et al., 2022). One of the barriers to virtual education was the lack of insight into the quality of students' online learning experience. For instance, without an active instructor to clarify the course content, virtual learners viewed instructional…

Students are entering postsecondary institutions without the mathematical skills needed to be successful in science, technology, engineering, and mathematics majors (STEM), leading to a shortage of qualified graduates. Consequently, institutions must identify ways to increase satisfaction and performance in mathematics. Mindset theory, with…

This study explored the lived experiences of eleven transfer students as they described their experiences in Calculus 2 at very high research land grant institutions (R1). This qualitative investigation focused on the psychological phenomenon of transition as the transfer students perceived, reflected, made sense, and understood their transition…

Research suggests learning assistant (LA) programs can be a change lever to support the institutionalization of active learning in postsecondary education. Some research suggests LAs offer unique benefits for STEM courses, independent from other change levers, but more research needs to be done to understand how LAs support active learning…

In this dissertation I explore instructors' work with instructional tasks as they plan to introduce various representations of derivatives. Drawing on the notion of "framing" from sociology, I adopt a situative lens to study calculus instructors' planning of instructional tasks. I rely on Herbst and Chazan's (2012) notion of…