Evidence-based mathematics interventions are critical for supporting students with mathematics difficulties. In research and practice, collecting implementation fidelity is important for ensuring that all the core components of the intervention are implemented as designed. Historically, implementation fidelity has been defined as multi-faceted…

Geometry processing holds a foundational position within the realm of computer graphics, with advancements in this field regularly published at SIGGRAPH annually. The journey from writing the paper to implementing the algorithms is a meticulous and error-prone process, demanding significant dedication and attention to detail. Authors frequently…

This study addresses a significant gap in educational research by employing statistical methods to measure the sequencing of different components and content topics in textbooks. It is well-documented that the structure and sequencing features of textbooks play a crucial role in enhancing students' learning. However, existing literature has…

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…

Teachers' ability to elicit and use evidence of student thinking during instruction is critical in high-quality mathematics instruction. The practice of anticipating students' mathematics supports teachers in noticing and being prepared to respond to student thinking during in-the-moment instruction. To date, most research on anticipating has…

Teaching that attends to and builds on students' resources and treats students as capable mathematical sense makers has been referred to as responsive teaching. A body of research reports teachers' tendency to overlook students' mathematical thinking when their answer is correct and to correct it procedurally when students make a mistake. This…

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…

Understanding fractions, especially their magnitude, is essential for success in mathematics. Unfortunately, fractions are one of the most challenging mathematics concepts to teach and learn. Several studies have examined preservice teacher (PST) knowledge of fractions, but very few studies have looked for ways to improve this knowledge. This…

Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits…

This multiple case study dissertation aimed to examine one of the domains of pedagogical content knowledge, knowledge of content and students, between different types of elementary coaches and between coach and their respective collaborating teachers. It also investigated the impact a coaches' background experiences have on the dynamic between…

Mathematics is the language and foundation for the science, engineering, and technological fields that define and enhance our lives in the 21st century. Proficiency in math requires problem solving, logical reasoning, and critical thinking skills that are essential to success in college, the workplace, and everyday life. Unfortunately, math has…

Calculus has long been known as a "gateway course" to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional…

This dissertation investigates how early career teachers' orientations of students and their mathematical activity, as surfaced their experience in a simulation, can reveal when their well-intentioned decisions might negatively impact traditionally underserved students. Three early career teachers engaged in two online simulations where they could…

In this qualitative multiple-case study, three teachers' understanding of holistic education philosophy was explored through their enacted instructional practices in mathematics classrooms in a holistic school in India. Drawing upon the ethnographic methodology, the data collected include interviews and conversations, classroom observations, and…

The purpose of this quantitative, quasi-experimental, nonequivalent comparison-group design was to determine if "How to Learn Math: for Students" (Boaler, 2018) had a statistically significant influence on eighth-grade students' mathematical anxiety and mathematical achievement. Participants included eighth-grade students (n = 28) in a…