## Research Statement

When I first began taking advanced mathematics courses, I often felt frustrated. At the time, it seemed like abstract algebra and real analysis had nothing to do with teaching high school mathematics. Now, as a mathematics instructor and curriculum developer, I feel that I benefit from this knowledge of advanced mathematics on a daily basis. Therefore, my overarching goal is to better understand how advanced mathematics courses can better support mathematics teachers’ practices. By doing this, I may be able to determine if it is worthwhile for teachers to take advanced mathematics courses, and if so, what specifically about these courses is useful for teachers.

My research lies in the intersection of teacher education and research in undergraduate mathematics. The focus of my dissertation is the relationship between teacher knowledge of real analysis and teaching practices. The practical pedagogical implications of my research may help structure content and methods courses to unpack the useful knowledge teachers learn in advanced mathematics courses such as real analysis, abstract algebra, number theory, and geometry.

I have been fortunate to have had the opportunity to conduct meaningful research with motivated faculty and colleagues. This research has included the use of both qualitative and quantitative research methods using a variety of software such as Atlas.ti, SAS, R, and STATA. My successful history conducting research at North Carolina State University has been a product of being immersed in a collaborative environment. I believe that innovative and groundbreaking research is most likely to occur when such collaboration occurs.

During my time at North Carolina State University, I was able to serve as a research assistant on two major funded projects: Mathematics and Pedagogy - Training for Implementation of High School Common Core Standards for Mathematics (MAP-TICCS) and Fraction Activities and Assessments for Conceptual Teaching (FAACT). Although each project had a distinct focus, serving as a research assistant for both MAP-TICCS and FAACT has been crucial to my development as a researcher. For both projects, I was afforded the opportunity to carry a out literature review, collect and analyze data, write for publication, and present results at conferences. These invaluable experiences have prepared me to conduct research at the highest level.

MAP-TICCS was a United States Department of Education funded project designed to provide professional development for high school mathematics teachers to deepen their understanding of mathematics which is foundational to and addressed in the Common Core State Standards in Mathematics. As a research assistant for this project, I had the opportunity to observe teachers using a research-based protocol, record field notes, conduct focus groups, transcribe video recordings, and analysis the data using quantitative and qualitative methods. My work on this project provided me with the skills and motivation to further study teacher knowledge.

FAACT is a current National Science Foundation funded project with the goal to study and support the development of conceptual understanding of fractions by students with learning disabilities. Although this appears to diverge from my overarching goal of studying teacher knowledge of advanced mathematics, this research has direct implications for my teaching. I currently teach courses in Calculus for Elementary Education, where elementary education majors study connections between calculus concepts and elementary mathematics. By researching how elementary school students reason about fractions, I can help my students better make these connections, such as viewing ratio as rate of change.

In addition to these funded projects, I have conducted independent research on both the teaching and learning of undergraduate mathematics as well as teacher education. For my master’s thesis, I investigated how studying cryptography can help students make connections to various subjects, such as linear algebra, abstract algebra, number theory, and discrete mathematics. My current work is focused on studying how advanced mathematics, specifically real analysis, can help teachers be more effective in the classroom. Since teachers are often required to take a course in real analysis, it is essential that the mathematics they are learning can be connected to the mathematics that they teach.

My future research agenda has two primary goals. First, I intend to continue research on the relationship between teacher knowledge of real analysis and teaching practices. Since one of the greatest factors for a mathematics teacher’s success in the classroom is their knowledge of mathematics, it is essential that they are able to apply the ideas they learn in courses such as real analysis, abstract algebra, number theory, and geometry to their teaching. The results from this work may inform the design of courses that bridge the gap between knowledge of advanced mathematics and teaching high school mathematics.

I also plan to continue to research issues in undergraduate mathematics education. Since one of my career goals is to effectively teach undergraduate mathematics to all students, I intend for my research to directly influence my teaching practices. Additionally, I hope to share these results with my colleagues so that we can continue to improve teaching throughout the mathematics department. In order to initiate this research agenda, I plan to immediately seek support for funding at the university, local, state, and national levels. This would enable to conduct my research on a grander scale, ultimately impact a greater number of teachers and learners.

My research lies in the intersection of teacher education and research in undergraduate mathematics. The focus of my dissertation is the relationship between teacher knowledge of real analysis and teaching practices. The practical pedagogical implications of my research may help structure content and methods courses to unpack the useful knowledge teachers learn in advanced mathematics courses such as real analysis, abstract algebra, number theory, and geometry.

I have been fortunate to have had the opportunity to conduct meaningful research with motivated faculty and colleagues. This research has included the use of both qualitative and quantitative research methods using a variety of software such as Atlas.ti, SAS, R, and STATA. My successful history conducting research at North Carolina State University has been a product of being immersed in a collaborative environment. I believe that innovative and groundbreaking research is most likely to occur when such collaboration occurs.

During my time at North Carolina State University, I was able to serve as a research assistant on two major funded projects: Mathematics and Pedagogy - Training for Implementation of High School Common Core Standards for Mathematics (MAP-TICCS) and Fraction Activities and Assessments for Conceptual Teaching (FAACT). Although each project had a distinct focus, serving as a research assistant for both MAP-TICCS and FAACT has been crucial to my development as a researcher. For both projects, I was afforded the opportunity to carry a out literature review, collect and analyze data, write for publication, and present results at conferences. These invaluable experiences have prepared me to conduct research at the highest level.

MAP-TICCS was a United States Department of Education funded project designed to provide professional development for high school mathematics teachers to deepen their understanding of mathematics which is foundational to and addressed in the Common Core State Standards in Mathematics. As a research assistant for this project, I had the opportunity to observe teachers using a research-based protocol, record field notes, conduct focus groups, transcribe video recordings, and analysis the data using quantitative and qualitative methods. My work on this project provided me with the skills and motivation to further study teacher knowledge.

FAACT is a current National Science Foundation funded project with the goal to study and support the development of conceptual understanding of fractions by students with learning disabilities. Although this appears to diverge from my overarching goal of studying teacher knowledge of advanced mathematics, this research has direct implications for my teaching. I currently teach courses in Calculus for Elementary Education, where elementary education majors study connections between calculus concepts and elementary mathematics. By researching how elementary school students reason about fractions, I can help my students better make these connections, such as viewing ratio as rate of change.

In addition to these funded projects, I have conducted independent research on both the teaching and learning of undergraduate mathematics as well as teacher education. For my master’s thesis, I investigated how studying cryptography can help students make connections to various subjects, such as linear algebra, abstract algebra, number theory, and discrete mathematics. My current work is focused on studying how advanced mathematics, specifically real analysis, can help teachers be more effective in the classroom. Since teachers are often required to take a course in real analysis, it is essential that the mathematics they are learning can be connected to the mathematics that they teach.

My future research agenda has two primary goals. First, I intend to continue research on the relationship between teacher knowledge of real analysis and teaching practices. Since one of the greatest factors for a mathematics teacher’s success in the classroom is their knowledge of mathematics, it is essential that they are able to apply the ideas they learn in courses such as real analysis, abstract algebra, number theory, and geometry to their teaching. The results from this work may inform the design of courses that bridge the gap between knowledge of advanced mathematics and teaching high school mathematics.

I also plan to continue to research issues in undergraduate mathematics education. Since one of my career goals is to effectively teach undergraduate mathematics to all students, I intend for my research to directly influence my teaching practices. Additionally, I hope to share these results with my colleagues so that we can continue to improve teaching throughout the mathematics department. In order to initiate this research agenda, I plan to immediately seek support for funding at the university, local, state, and national levels. This would enable to conduct my research on a grander scale, ultimately impact a greater number of teachers and learners.

DiversityStatement.pdf |