Mathematical notations not only contribute to but also confound the development of the understanding of mathematical concepts (Leinhardt, Zaslavsky & Stein,1990). Inaccurate use of calculus notations is likely to have a significant influence on student conceptual understanding and student assessment scores in the Calculus 1 course. This…

The purpose of this study was to examine the psychometric properties of the Precalculus Concept Assessment (PCA), a 25-item multiple-choice instrument designed to assess student reasoning abilities and understanding of foundational calculus concepts (Carlson et al., 2010). When this study was conducted, the extant research on the PCA and the PCA…

Instructional explanations are an ubiquitous component of classroom instruction, but are relatively neglected in science education when compared to other facets of teaching and learning. The ubiquity of instructional explanations and their potential to stimulate learning in students suggests that they should garner more attention from science…

Students experience great social and academic challenges during their first semester of college and for many, the completion of required mathematics courses is one of those challenges. This study investigated the relationship of first-time college freshmen's mathematics course enrollment, gender, and high school mathematics course experience to…

The goal of learning analytics is to optimize learning and the environments in which it occurs. Since 2011, when learning analytics was defined as a separate and distinct area of academic inquiry, the literature has identified a need for research that presents evidence of effective learning analytics, as well as, learning analytics research that…

The purpose of this dissertation is to investigate the relationships between student persistence and students' attributes or perceptions of instructional pedagogies, as well as to examine whether the identified relationships are moderated by three different instructional settings. Improving student persistence in science, technology, engineer, and…

Demand is high for engineering students and educators must identify factors affecting persistence and graduation of engineers. Retention and graduation rates remain problematic for many institutions. Higher education research focuses on these two issues as many students head to engineering programs with a wide range of attributes, characteristics,…

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…

There is a need for research to explore the connections between students' self-perceptions and their goals and future engagement with mathematics. This is particularly the case when considering that student interest declines as they transition through K-12 and gender differences continue to persist in mathematics related careers. Knowing how…

This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well…

This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the…

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

A primary gateway to a career in engineering is the attainment of the bachelor of science degree in engineering. In contrast, a common barrier to becoming an engineer is failure to attain the degree. Those variables that are related to college graduation are often in place prior to college admission. The purpose of this study was to examine the…