The purpose of this research was to investigate students' mathematical understandings of fraction division with an ethnomathematics/STEM framework. A small group teaching study (Cobb et al., 2003) was conducted using design research methodology to examine how students interacted with the curriculum. The researcher served as interventionist and…

Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…

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…

The learning of basic facts, or the sums and products of numbers 0-10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts.…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

Studies of discourse are prevalent in mathematics education, as are investigations on facilitating change in instructional practices that impact student attitudes toward mathematics. However, the literature has not sufficiently addressed the operationalization of the commognitive framework in the context of Calculus I, nor considered the…

For students to be successful in future mathematics classes, mathematics teachers must be able to help students decipher content in Algebra I, the foundation of higher mathematics. Research on vocabulary in the math classroom shows there are multiple ways to represent vocabulary and reading comprehension. The research question, which focused on…

This qualitative, multiple case study provided comprehensive descriptions of the conceptual difficulties and learning experiences of in-service teachers as they improved their ability to effectively model fraction division with pictorial diagrams. Video data were collected on eight teachers as they individually progressed through a professional…

Through instructional tasks, teachers can present content in ways that require students to apply critical thinking, problem-solving, and other cognitive skills. The purpose of this mixed methods collective case study was to determine how teacher-assigned instructional tasks in mathematics impact students' learning of mathematical concepts. In this…

In 2 experiments, I studied the effects of an Equivalence Based Instruction (EBI) math intervention on the emergence of untaught selection responses and abstraction to production responses. In Experiment I, using a multiple baseline design, I implemented the EBI intervention among a group of 17 first grade participants with varying levels of math…

This quasi-experimental design study aimed to examine how exposure to supporting productive struggle teaching practice impacts students' conceptual understanding, procedural fluency, and strategic competence when solving high-demanding quadratic functions problem solving tasks. Results suggested that students in the supporting productive struggle…

This study used a constructivism theoretical framework to focus on a group of elementary mathematics teachers and their lived experiences after the introduction of new mathematical content standards through the lens of the Mathematical Teacher's Specialized Knowledge Model. After the introduction of new mathematics content standards, many…

While some might say that mathematics is neutral, free from political and social bias, social justice concerns can be found in the day-to-day actions of teachers in mathematics classrooms. Teaching mathematics for social justice requires teachers to gain knowledge of the world and systems of oppression as well as current efforts to both address…

In this study, I examined the ways in which teachers' facilitation techniques are associated with students' mathematical thinking. The teachers' beliefs and students' perception about mathematics discussions were also examined in order to determine whether or not the connection of the teachers' facilitation techniques with students' thinking were…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…