We developed various retention programs to support first-year engineering students who start behind their cohort in terms of the Calculus sequence. We focused on increasing the persistence of these students via counseling along with opportunities for students to regain cohort status. Although the retention program evolved, we retained enough of…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…

This dissertation consists of a literature review and two empirical studies that focus on the forethought phase of self-regulated learning. The overall goal was to provide a more thorough understanding of the processes students engage in prior to initiating their academic tasks. This dissertation is composed of five chapters. Chapter One…

In the field of physics education research, numerous studies have been dedicated to investigating the relationship between gender identity and physics learning. However, these studies have predominantly employed binary gender measurement methods, which may limit the range of research questions that can be explored and impede the discovery of…

Despite the standardization of calculus education as a Calculus and Analytic Geometry course after the 1950s, curriculum updates have been slow to penetrate the undergraduate mathematics classroom practice, taking decades to manifest. Common struggles with the teaching and learning of calculus, such as relying on a procedural understanding of…

In online STEM courses, self-regulated learning (SRL) serves a critical role in academic success because students are required to monitor and regulate their learning processes. Yet, relatively little research has investigated which and to what extent do SRL strategies contribute to students' online learning experiences. In this paper, with a lens…

Learning centers offer academic resources to postsecondary students to aid in their success. Despite deep work examining the efficiency of these learning centers, the field still does not know enough about students' experiences with these learning centers' resources. By understanding the mechanisms and experiences of students as they learn about,…

Assembly Bill 1705 (AB 1705) seeks to strengthen students' completion of the first STEM Calculus course for Science, Technology, Engineering, and Math (STEM) programs across the California Community Colleges. The law sets new standards for students' placement and first math enrollment to ensure STEM students begin in transfer-level coursework that…

Problem-solving is the essence of mathematics and is the main goal in learning mathematics. Many students did not have good problem-solving skills based on the field observations. The problems grew up because the students were not used to solving the problems and the problem-solving stages. They did not include issues with high complexity, such as…

Though the curriculum reform movement that began in 1989 has had a significant impact on calculus pedagogy and content (Windham, 2008), the question remains to what extent reform-based calculus textbooks reflect these reforms. This paper explores this question by analyzing the mathematical content and pedagogical approach of the chapter on…

This study focuses on the analysis of certain performance predictors for calculus I. We collected data from 717 students from 2013 through 2018 at a southeastern university in the United States to explore any correlation between course times (particularly very early versus the rest) and student performance in this specific course, along with a…

Greater flexibility with procedures is known to be associated with greater conceptual knowledge of mathematics and vice versa. In parallel, a student's emotional relationship to mathematics -- i.e. their 'affect' -- is known to influence how they learn and perform in mathematics. For example, a confident student may engage more fully with…

This research explores the use of guided notes in a post-secondary calculus course and the extent to which use enhanced students' success in a first year calculus course. Guided notes have been previously shown to be perceived as helpful to learning by students, and one study showed that the use of guided notes improved pass rates in a first year…

Methods of teaching differential equations (DE) have long focused on rote analytic solution methods that align poorly with more industry-relevant numerical and computational methods. Engineering and mathematics educators agree that there is a need to shape DE curricula to reflect the mathematical practices of the disciplines whose students take…