My current research interest lie in the intersection between technology enabled learning and undergraduate mathematics. I wish to assess what mechanisms of online learning are the most successful for different learners (e.g., entry-level undergraduates, pre-service teachers, and mathematics majors) and how these mechanisms will impact student attitudes, enjoyment, and long-term success in mathematics. In addition, I wish to examine how higher level mathematical concepts can be conceptualized with the aid of visual renderings and computer algorithms.
The purpose of this study was to investigate how a set of physical and digital instructional activities can serve as an example space to help further develop a concept image that is aligned with the formal concept definition for the limit of a sequence. In addition this study examined the unique affordances and constraints allowed by using either a physical or digital modality in understanding the convergence of a sequence. Results suggest that both of these activities served to help students conceptualize the arbitrary nature of the error bound, and for some students it further illustrated the relationship between an arbitrarily small error bound, the limit value, and the index of the sequence. The physical activity constrained students to think of the sequence as a finite terminating set of numbers whereas the digital activity provided additional information that student used in subsequent problem solving.
My interest in technology and learning started during my five years of professional experience in the private sector as a Senior Information Technology Trainer, where I conducted curriculum design, classroom instruction, project management, and extensive development of e-learning modules. My experiences with the real life application of learning theory lead to the development of my current research project examining the impact of using a flipped classroom technique on students’ attitudes and academic performance. For this project I independently designed and implemented a study analyzing roughly 400 students’ perceptions and experiences in a college Pre-Calculus II course. I was honored to be awarded a three-year graduate research fellowship by the National Science Foundation in recognition of the intellectual merit and broader impacts of the study. I would like to continue this line of inquiry by building a program of research in technology-enhanced learning and undergraduate math education. Preliminary analyses from my current study and the existing literature suggest that when compared to a traditional model, students in a flipped classroom show improved academic success, have positive attitudes, and report increased confidence in their abilities. Although when given a choice, many students prefer a traditional model of learning. One key research questions I am investigating is why certain students adapt more easily to online learning and why some are resistant to this format, as well as what technological structures contribute to successful academic performance in the undergraduate calculus sequence.
The EngrTEAMS: Engineering to Transform the Education of Analysis, Measurement, and Science in a Team-Based Targeted Mathematics-Science Partnership vision is to increase grade 4-8 student learning of science concepts, as well as the mathematics concepts related to data analysis and measurement, by using an engineering design based approach to teacher professional development and curricular development. My primary role on the project is a mathematical pedagogy expert and curriculum developer.
My second research assistantship in algebraic geometry served as the basis for my year-long honors thesis examining the graver complexity of complete bipartite graphs, which I presented at several national conference. In order to make some progress toward the complicated open problem of
determining a unique minimal Markov basis for a 3 × 4 × r contingency table with fixed
two-dimensional marginals, we provide and discuss in detail a number of new results for the
Graver complexities of the complete bipartite graphs K1,n and K2,n.
Research was conducted to assess three main aspects of lesbian, gay, bisexual, transgender, and ally (LGBTA) issues at the College of Saint Benedict and Saint John’s University. The first assessment analyzed the general campus climate, and showed that most students were comfortable with LGBT individuals, but had also heard high rates of anti-LGBT remarks. The second assessment was an attitude assessment, in which we examined gender differences toward gay men versus lesbian women. Results showed that men rated homosexuals more negatively than females; however, an interaction effect took place indicating that women rated lesbian more negatively and men rated gay men more negatively on the sub-scale of contact. The final assessment examined the experiences of self-identified LGBTA students’ and the effectiveness of resources. Our findings showed that students rated institutional resources as more effective than non-institutional resources, and that experiences for LGBTA students were mixed.
This research project was a joint partnership with Southwest Normal University in BeiBei China. Our research team spent six weeks in BeiBei researching finite abelian groups, and then spent six weeks together in collegeville united states researching edge colored graphs. We examined the homomorphism that preserves distances of the cuboctahedron that maps to the octahedron, and then tried to achieve a product that would build the cuboctahedron from its homomorphic image (the octahedron).