The main objective of this study is to develop a mathematical modeling framework for a deeper understanding of dynamics of math anxiety as a contagious process. Borrowing from theories of the spread of infectious disease, we develop two classes of mathematical models representing the spread of math anxiety in math gateway classes. The first…

This work explores the complex cognitive processes students engage in when addressing contextual tasks requiring linear and exponential models. Grounded within Piagetian constructivism and the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993, 2018), this empirical study in a clinical setting develops a Microgenetic Learning…

Number sense is a key indicator of students' future academic success. Students from low socio-economic backgrounds often come to kindergarten lacking number sense skills that other students acquire before they begin formal schooling. Small-group intervention that is focused on number sense skills is an effective way to address this foundational…

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…

With the rise in popularity of social media and e-commerce platforms, "discrete math" is at the heart of our online experiences, playing a front-end role in the recommendation of what to click, watch, or buy, or who to follow or friend, as well as a back-end role in data storage, access, and transfer. This thesis focuses on two such…

The purpose of this study was to understand children's operations on fragmenting schemes while they are engaged with three different visual models, including circle, rectangle, and length model. This study was a sequential explanatory mixed method, which included two phases that happened sequentially with the dominant use of the quantitative…

Optimization is a component critical to method development. Mathematical modeling of physical phenomena enables an efficient search for the parameters and conditions that optimize methods and systems. Here, optimization of methods in sonoelectrochemistry, electrochemical separations, electrochemical education, and assessment of diabetic status are…

This dissertation investigates the ways that natural languages evolve and what it means in the overall cultural evolution of society. Computational and modeling advances have made possible to explore large-scale text data and test hypothesis of language evolution. Similar to biological systems, natural languages are evolving systems with words as…

Contextual learning experiences using integrated STEM, agricultural sciences (AgS), and mathematical modeling (model eliciting activities [MEAs]) can be a powerful approach to engage students from urban areas in STEM literacy, career exploration, and community awareness. This three-study dissertation contributes to: (1) an innovative framework for…

This is a study of student engagement with computational labs in Calculus 2. The labs task students with using MATLAB to investigate contexts such as rocket science, disease modeling, and market economics forecasting by modifying and executing provided code, guided by questions that have students report the results of their simulations or…

We study flexible Bayesian methods that are amenable to a wide range of learning problems involving complex high dimensional data structures, with minimal tuning. We consider parametric and semiparametric Bayesian models, that are applicable to both static and dynamic data, arising from a multitude of areas such as economics, finance and…

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well…

The purpose of this study was to explore students' mathematical practices while working on modeling problems using 3 interactive computer simulations. Three fifth grade students' interactions with computer-based modeling simulation were examined to identify how children defined and prioritized and coordinated variables and parameters in…

In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…

The teaching of mathematical modeling is limited in P-12 classrooms. Little is known in regards to how to support teachers to successfully enact modeling activities. Teachers do not always appreciate the value of modeling activities in mathematics learning and often feel unprepared to implement modeling in their classrooms. Teachers often struggle…