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…

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…

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…

This holistic, mixed-methods action research case study aimed to determine the influence of professional development on participants' mathematical teaching practices and how the changes influenced students' opportunities for discourse. In this two-year study, participants engaged in two professional development phases and implemented new…

Harmful and inaccurate narratives about the nature of mathematics, and about the mathematical incapability of historically marginalized groups, are pervasive and longstanding. The persistence of these narratives, and their documented negative impacts in school, the discipline, and beyond, have led some scholars to conclude that there is something…

The topic of this research study is mastery learning, an educational theory that began with the work of John Carrol in 1963. The core principle of this theory is that all students can achieve uniform learning outcomes, but it will take some students longer than others to reach the same performance goals. The problem that this research study…

Education has always been and will continue to be the key that unlocks doors of opportunity and success for all. Our national test scores, over the last several decades, reveal that a majority of America's students are failing to meet academic benchmarks and standards, thus limiting the possibilities for opportunity. Mathematics, in particular,…

In this participatory action research (PAR) study, I sought to understand how teachers implemented equitable and culturally responsive academic discourse to support African American students during mathematics instruction. Working with a group of teachers in a co-practitioner researcher (CPR) group, I examined to how teachers effectively planned…

Rising numbers of English learners (ELs) being placed in general education high school mathematics classrooms with underprepared teachers is an increasing concern in U.S. public schools. Despite its importance, there has been little research on how to best support high school mathematics teachers in their attempt to teach both the highly…

Modeling with mathematics (MP4) is a mathematical practice standard that can be used to engage students in mathematical content standards as well as additional mathematical practice standards. Research has shown the benefits of mathematical modeling (e.g., Aguirre et al., 2019; Cirillo et al., 2016a), but also the challenges teachers can face…

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…

In recent years, a group of teacher educators has developed a method of teacher education that incorporates practices that provide guidance about how to teach along with a principled vision of teaching that supports teachers to use the practices with judgement. Sometimes termed "core practices-focused teacher education" (Forzani, 2014,…

Through a social constructivist lens, this study looked at how paraprofessionals understand mathematics instructional content and associated pedagogical skills and explore an organization's current involvement of support staff in schools' mathematical classrooms. The setting for this bounded case study was two elementary schools contained in one…