Gifted Education Commons^™

Applications Of Financial Mathematics: An Analysis Of Consumer Financial Decision Making, Alyssa Betterton

Honors Theses

Students always ask, “How can this be applied to the real world?” Mortgages, car loans, and credit card bills are things that almost everyone will have to make decisions about at some point in their lives. This research discusses the many different financial choices that consumers have to make. Consumers can use this information to understand how interest rates, the length of the loan, and the initial amount being borrowed affects the amount that is paid back to the companies. The intent of this thesis is to present the mathematical theory of interest. A web-based application has been built based …

Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics, Grace Farson

Honors Theses

The study investigated how game theory can been utilized to model multipolar escalation dynamics between Russia, China, and the United States. In addition, the study focused on analyzing various parameters that affected potential conflict outcomes to further new deterrence thought in a tripolar environment.

A preliminary game theoretic model was created to model and analyze escalation dynamics. The model was built upon framework presented by Zagare and Kilgour in their work ‘Perfect Deterrence’. The model is based on assumptions and rules set prior to game play. The model was then analyzed based upon these assumptions using a form of mathematical …

Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith

Honors Theses

The realm of education was shaken by the onset of the COVID-19 pandemic in 2020. It had drastic effects on the way that courses were delivered to students, and the way that students were getting their education at the collegiate level. At the University of Nebraska – Lincoln, the pandemic dramatically changed the way that first-year mathematics courses looked for students. By Spring 2021, students had the opportunity to take their first-year math courses either in-person or virtually. This project sought to identify differences between the two methods of course delivery during the Spring 2021 semester, regarding interaction with peers …

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Theses

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle

Honors Theses

This senior project outlines potential lecture activities for a guest speaker or teacher in a high school classroom to present interesting applications of linear algebra. These applications are meant to be pertinent to things students at this age level are already learning or are interested in. The activities are designed such that the ideas of upper-level math are introduced in a very guided and non-intense way. The intent of the activities is mostly applications and interesting results rather than mathematical lecturing or instruction.

The high school level courses explored in this project are chemistry, economics, and health/physical education. For these …

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

Honors Theses

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy

Publications & Research

Mathematicians view mathematics within interesting and natural contexts. In this session, participants will engage and explore Three-Act Math Tasks; a story-telling pedagogical strategy that elicits student curiosity, collaboration, and questioning while redefining the term “real-world context” and the role that students play in the learning process. Resources will be provided

The Prominence Of Affect In Creativity: Expanding The Conception Of Creativity In Mathematical Problem Solving, Eric L. Mann, Scott A. Chamberlin, Amy K. Graefe

Faculty Publications

Constructs such as fluency, flexibility, originality, and elaboration have been accepted as integral components of creativity. In this chapter, the authors discuss affect (Leder GC, Pehkonen E, Törner G (eds), Beliefs: a hidden variable in mathematics education? Kluwer Academic Publishers, Dordrecht, 2002; McLeod DB, J Res Math Educ 25:637–647, 1994; McLeod DB, Adams VM, Affect and mathematical problem solving: a new perspective. Springer, New York, 1989) as it relates to the production of creative outcomes in mathematical problem solving episodes. The saliency of affect in creativity cannot be underestimated, as problem solvers require an appropriate state of mind in order …

Does A Co-Learner Delivery Model In Professional Development Affect Teachers’ Self-Efficacy In Teaching Mathematics, John J. Ribeiro, Denise Demagistris

Teacher Education

A mixed method study is reported examining teacher efficacy regarding professional development in mathematics instruction for two groups of teachers: in building with peers (N=17) and MAT student co-learners in the classroom (N=14). An end-of-course survey, focus group interviews and pre-post data for the Teacher Self Efficacy Scale were used to investigate:1. What is the difference in teachers’ efficacy regarding mathematics instruction based on the professional development delivery system they experienced? 2. What are teachers’ perceptions of their professional development with peers conducted onsite in district compared with professional development with peers and preservice teachers at a university setting? Descriptive …

Comparative Instructor Attitudes Toward College Level English And Mathematics Experiences For Gifted High School Students, Bruce Vickers

Masters Theses & Specialist Projects

Samples derived from a mailed questionnaire were compared. The sample represented high school, community college and university instructors of mathematics and English. The Kentucky public schools sampled were equally represented among high school, community colleges and universities. The research indicated that of those instructors sampled a very high percentage (97.7%) feel that those high school students shown to be academically gifted would benefit from a college experience before high school graduation. The attitudes of those instructors sampled indicated that multiple criteria – grades, recommendations, standardized test scores and personal interview – were considered the preferred method of selection (82.5%). The …