Achievement gaps in mathematics between middle and high school Black students when compared to their white peers exist in part because of access, but also because Black learners' brilliance is not recognized. Finding ways to help students, especially Black students, become successful mathematical problem solvers was a driving force behind this…

Many students arrive at colleges and universities underprepared for college-level mathematics courses. In the United States, these students are required to complete developmental mathematics courses before completing the required mathematics courses for their degrees. Students who are required to take developmental mathematics courses frequently…

In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

This study aims to explore the validity of measuring joint attention through gaze coordination in computer-supported collaborative learning (CSCL) research. Gaze coordination, aligning visual attention in social contexts, aids comprehension and communication. Many CSCL researchers use gaze coordination to gauge joint attention quantitatively.…

In this dissertation, I utilize the post-structural philosophy of Gilles Deleuze and Fe´lix Guattari as a lens for investigating the proof process. Deleuze and Guattari were both post- structural philosophers who, like many in this tradition, troubled traditional notions related to stable identities, meaning, language, and mathematics. For…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

In the spring of 2020, many colleges and universities had to move their classes online due to COVID-19. This move to the virtual environment highlighted a growing problem in higher education, being increase failure rates for online students. This study addressed two research questions: 1) To what extent does the use of short lectures and small…

To make sense of our interconnected and algorithm driven world, students increasingly need proficiency with computational thinking (CT), systems thinking (ST), and computational modeling. One aspect of computational modeling that can support students with CT, ST, and modeling is testing and debugging. Testing and debugging enables students to…

The work presented in the following chapters was undertaken with the goal of understanding and improving education in organic chemistry. Initial work, described in Chapters 1 and 2, focuses on students' ability to explain and rationalize the outcomes of organic chemistry reactions. Chapter 1 explores the relationship between assessment emphasis…

Gifted students' often go unchallenged in the classroom, and this lack of tailored instruction can lead to decreased motivation, which, in turn, influences underachievement, which is a significant concern since these children, theoretically, should be our highest achievers. This 4-week (i.e., eight instructional days) semi-randomized,…

This dissertation examines the development of combinatorial reasoning in high school students through an in-depth analysis of a problem-solving session involving the Pizza Problem. The study, part of the long-term Rutgers-Kenilworth longitudinal research project, focuses on four 11th-grade students as they explore and connect concepts related to…

As students with autism spectrum disorder (ASD) participate in the general education setting at greater rates, they are expected to meet rigorous grade-level academic standards. Students with ASD typically struggle with problem solving, higher-ordered thinking, and mathematical reasoning. When students enter middle school, mathematics becomes more…

Mathematics is traditionally taught using direct instruction, which has been found to engender negative affective responses towards the subject, including anxiety and low self-efficacy (Borko et al., 1992; Mischo & Maas, 2013). Direct instruction places authority on the instructor and involves teaching students about mathematics instead of…

To solve an unfamiliar mathematics problem, students of the subject must know more than the appropriate prerequisite content knowledge. They must also know how best to strategically apply their knowledge, how to monitor and gauge the effectiveness of their work, and how to respond (both cognitively and emotionally) to unanticipated results.…

The present study was conducted to determine how implementing computational thinking (via a proxy in AP Computer Science Principles) into a school's curriculum impacted student proficiency rates on the New York State Geometry Regents. Recent research has suggested that computational thinking is a skill that transcends specific content areas and…