Education Commons^™

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 …

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Theses

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

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 …

A Mathematical Model Of Pancreatic Cancer Growth And Response To Treatment, Allison Cruikshank

Honors Theses

Pancreatic cancer is one of the leading causes of death due to cancer in the United States. Analyzing the effects of radiation is extremely valuable in determining when a patient is allowed surgical resection, which is, presently, the only potentially curative treatment for pancreatic cancer. This study examines pancreatic tumor growth and shrinkage to predict tumor response and change of resectability for pancreatic cancer patients undergoing radiation therapy. This is done using ordinary differential equations as a mathematical model. Mathematical models have increasingly been applied to various biological systems/processes to analyze the principles involved. In our project, a population dynamical …

Content Validity Of A Mathematics Placement Test For A Gifted High School, Hannah R. Anderson

Publications & Research

The Content Validity of a mathematics placement test at a Science, Technology, Engineering, and Mathematics (STEM) gifted residential high school is examined. Data were collected from internal and external mathematics subject matter experts (SMEs) using a card- sorting task and were analyzed using Multidimensional Scaling (MDS) and Hierarchical Cluster Analysis (HCA). Results demonstrate some congruence between the two configurations, suggesting marginal evidence of Content Validity.

Teacher Beliefs About Providing Instruction For Gifted Students In Inclusive Mathematics Classrooms, Carrie Lynn Kizuka

Walden Dissertations and Doctoral Studies

Kindergarten - Grade 12 (K-12) students identified as gifted in mathematics in the United States are not being appropriately challenged. Teachers are the most important school-related factor that contributes to student success; however, researchers have not explored the experiences of teachers who work with gifted students in inclusive mathematics classrooms. The purpose of this qualitative, transcendental phenomenological study was to explore the lived experiences of K-12 teachers who provide instruction for gifted students in inclusive mathematics classrooms. Bandura's social cognitive theory framed the study. Interview data were collected from 12 teachers who provide mathematics instruction for gifted students in inclusive …

Differentiated Instruction For 1st Grade Advanced Learners In Mathematics, Patricia Cawley

Dissertations, Masters Theses, Capstones, and Culminating Projects

Differentiated instruction is student-aware teaching, in which the students not only develop content mastery, but also take ownership of their learning. This study examined the results differentiated instruction in mathematics had on advanced learners perceived competence, persistence, and intrinsic motivation. Differentiation was implemented in a classroom through various activities that challenged student thinking. Students enrolled in a first grade class in an all girl school setting served as study participants. Data were collected on a total of 21 students in the class, but analysis focused on a subgroup. Results indicated that the participants’ interest and engagement in math varied student …

The Value Of Problem Posing In Developing Creatively Gifted Mathematicians, Eric L. Mann

Faculty Presentations

The task of problem posing is often overlooked as a means to develop creatively gifted mathematicians. Silver (1997) suggested that problem posing was an instructional tactic used worldwide to develop creativity in mathematicians. More specifically, Silver advocated that deliberate instructional tactics had to be employed to precipitate creative solutions. Problem posing is often correlated with the aesthetic nature of mathematics.

In this cutting-edge session, participants’ objective is to learn about the value of problem posing through a brief presentation and have an opportunity to generate their own mathematical problem solving tasks given a mathematical concept. The intent is to encourage …

An Exploration Of The Factors That Motivate Black And Latino Students To Engage In Stem (Science, Technology, Engineering And Mathematics), Adrienne Coleman

Adrienne Coleman

No abstract provided.

What’S Art Got To Do With Math?, Eric L. Mann

Faculty Publications

No abstract provided.

Specialized Science High Schools: Exploring Contributions Of The Model To Adolescent Talent Development Specialized Science, Christopher G. Kolar, Tracy L. Cross, Rena F. Subotnik, Paula Olszewski-Kubilius

Christopher G. Kolar

As the field of gifted education shifts much of its focus to domain-specific talent development, specialized science high schools are taking their place on the stage. Back in 1981,Bloom and Sosniak argued persuasively that talent development cannot take place exclusively in schools. They stressed that schools were not prepared to offer the required levels of expert teaching, time, and effort. Yet, specialized science high schools, by design, are staffed with teachers with advanced degrees, offer relatively flexible schedules, interested peers,reasonable access to appropriate technology, and connections with research institutions to provide apprenticeships for the most motivated and interested students.

The Impact Of Smart Board Technology On Growth In Mathematics Achievement Of Gifted Learners, Patricia Ann Riska

Doctoral Dissertations and Projects

This study examined whether SMART Board technology increased growth in mathematics performance of fourth grade gifted students. Gifted students in North Carolina were studied to determine if the use of SMART Board technology during mathematics instruction impacted their growth on standardized state tests. The sample consisted of 175 students from six elementary schools with similar populations. Three of the schools used SMART Boards during mathematics instruction, and three schools did not use SMART Board technology. All students were taught the mathematics curriculum according to the North Carolina Standard Course of Study. The instrument for evaluating growth was the state End-of-Grade …

Stem Talent: Moving Beyond Traditional Boundaries, Stephanie Pace Marshall

Publications & Research

The future well-being, prosperity and sustainability of our nation, the global community and our planet resides in igniting and nurturing decidedly different STEM minds that can advance both the new STEM frontier and the human future.

Hungary And The United States: A Comparison Of Gifted Education, Julianna Connelly Stockton

Mathematics Faculty Publications

There is a lot that can be learned about a country based on the programs and provisions it has for mathematically talented students. While it is difficult to identify a single U.S. "program" or "approach" for gifted education, in general the trend is to put mathematically talented students through the standard mathematics sequence, just starting at an earlier age. In Hungary, on the other hand, the focus is on enrichment over acceleration. This paper explores how some very different historical, cultural, and political forces have shaped these two countries’ different approaches to educating mathematically talented students.

Specialized Science High Schools: Exploring Contributions Of The Model To Adolescent Talent Development Specialized Science, Christopher G. Kolar, Tracy L. Cross, Rena F. Subotnik, Paula Olszewski-Kubilius

Publications & Research

As the field of gifted education shifts much of its focus to domain-specific talent development, specialized science high schools are taking their place on the stage. Back in 1981,Bloom and Sosniak argued persuasively that talent development cannot take place exclusively in schools. They stressed that schools were not prepared to offer the required levels of expert teaching, time, and effort. Yet, specialized science high schools, by design, are staffed with teachers with advanced degrees, offer relatively flexible schedules, interested peers,reasonable access to appropriate technology, and connections with research institutions to provide apprenticeships for the most motivated and interested students.

Pattern And Mathematics: Math Enrichment Activities For Gifted Fourth, Fifth And Sixth Grade Children, Janet K. Zuber

All Graduate Projects

The purpose of this project is to provide assistance to the elementary math teacher in meeting the needs of the student gifted in the area of math. A collection of activities is provided to use with gifted intermediate students and should serve as an example of the type of activities appropriate for the gifted student. These activities would be most appropriately used with gifted students in grades four through six. The activities would be of greatest benefit if students were grouped in a homogeneous manner with one teacher taking responsibility for their math needs, Homogeneous grouping would allow for faster-paced …