This research study examined inclusive teaching practices, class policies, and course structures in active learning Calculus classes. Analyzing interview data, along with focus group discussions and classroom observations, obtained from 23 students and 4 instructors, themes were extracted through open-coding methodology, employing scholarly…

High-impact practices include many options to help increase student learning, and project-based learning (PBL) is one such method. In this study, we look at the effect of PBL activities embedded in the content for introductory level mathematics and statistics courses across a semester. A pre-test and post-test are used to measure student learning,…

In this dissertation, I report results from a study that investigated the impact of students' engagement in a series of tasks in an introductory proof course that was designed to stimulate their learning of reading strategies to support their comprehension of mathematics proofs. Specifically, I investigated the impact of the design of five…

Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…

The focus of this dissertation is on students' thinking regarding the function concept in the context of abstract algebra, focusing on the properties of well- and everywhere-definedness. This dissertation follows a three-paper format, where each paper has a different yet related focus. In the first paper, I analyze (non-)examples found in…

In spring 2018, an inquiry-oriented differential equations course was offered at the Lebanese American University. This paper highlights students' comprehension of some qualitative aspects of differential equations, namely their understanding of the equations and their solutions. It also explores the students' success in moving between the…

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…

Poor mathematics preparation severely restricts students' future educational and occupational choices. This paper explores the extent to which differences were observed in the pedagogical practices of those teaching college introductory college math at a community college and at a four-year college. Although college math instructors generally may…

The recent push toward active learning -- engaging students in the learning process -- is meant to benefit students. Yet there is still much to learn about students' perceptions of this phenomenon. We share results from an interview study of students' perceptions of features of two active learning models institutionalized at a large…

Many students who enroll in a first course in linear algebra major in STEM disciplines other than mathematics. Teachers who serve such students may find it difficult to provide authentic problems from these broader areas that ignite students' interest in linear algebra. In this paper, we highlight an interdisciplinary learning activity that…

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of…

Given the importance of the ability to use variables flexibly in Calculus and students' difficulties related to various uses of variables, this study examined how variables are treated in calculus class. Data for this study came from graduate teaching assistants' (TAs') classroom teaching, which plays a crucial role in undergraduate students'…

Many educators and professional organizations recommend Quantitative Reasoning as the best entrylevel postsecondary mathematics course for non-STEM majors. However, novice and veteran instructors who have no prior experience in teaching a QR course often express their ignorance of the content to choose for this course, the instruction to offer…

From an APOS (Action-Process-Object-Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the…

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced…