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Theses/Dissertations

2018

Mathematics

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Mathematical Curves In The High School Classroom, Magdalena Zook Jan 2018

Mathematical Curves In The High School Classroom, Magdalena Zook

Masters Essays

No abstract provided.

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Optimal Delivery Of Remedial Mathematics Programs In U.S. Higher Education, Lisa Renee Loden Jan 2018

Optimal Delivery Of Remedial Mathematics Programs In U.S. Higher Education, Lisa Renee Loden

Electronic Theses and Dissertations

Remedial mathematics has been considered the roadblock to obtaining a college degree by students and educators for years. The purpose of this research is to determine the optimal time and delivery method of the three presented (fully module, module with a traditional lecture component, and fully on-line) for teaching remedial mathematics. This is accomplished by comparing pass rates. First, pass rates are compared to determine if there is a statistically significant difference between pass rates in the two models for teaching remedial mathematics (pre-requisite and co-requisite). Next, pass rates are compared to determine if there is a statistically significant difference …

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Lenstra-Hurwitz Cliques In Real Quadratic Fields, Daniel S. Lopez Jan 2018

Lenstra-Hurwitz Cliques In Real Quadratic Fields, Daniel S. Lopez

Master's Theses

Let $K$ be a number field and let $\OO_K$ denote its ring of integers. We can define a graph whose vertices are the elements of $\OO_K$ such that an edge exists between two algebraic integers if their difference is in the units $\OO_K^{\times}$. Lenstra showed that the existence of a sufficiently large clique (complete subgraph) will imply that the ring $\OO_K$ is Euclidean with respect to the field norm. A recent generalization of this work tells us that if we draw more edges in the graph, then a sufficiently large clique will imply the weaker (but still very interesting) conclusion …

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Perceptions Of Faculty Using Mymathlab In Traditional, In-Seat Math Classes, Kathleen Gromilovitz Jan 2018

Perceptions Of Faculty Using Mymathlab In Traditional, In-Seat Math Classes, Kathleen Gromilovitz

Walden Dissertations and Doctoral Studies

MyMathLab, an online interactive and educational system by Pearson Publisher, was implemented in 2 lower-level, traditional in-seat algebra courses to provide supplemental, instructional support to students in the fall of 2015 at the college under study. After the first year of use, no significant change in student success was reported, although more students passed intermediate algebra without first taking elementary algebra. The problem addressed in this study was that student results suggested there might be benefits to using MyMathLab that should be investigated. Knowles' theory of andragogy was used in this qualitative case study to gather perceptions of 7 2016-2017 …

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Relationships Of Gender On Mathematics Achievement In High Achieving Military-Connected Children, Randi Kay Rose Dalton Jan 2018

Relationships Of Gender On Mathematics Achievement In High Achieving Military-Connected Children, Randi Kay Rose Dalton

Walden Dissertations and Doctoral Studies

The purpose of this quantitative correlational study was to describe the relationship between gender and grade level to mathematics achievement for high achieving military-connected students in Grades 3 through 9 who attended American public schools between 2012 and 2016. The theoretical framework was based on Sax's research on gender differences in learning. The research questions were: if there was a statistically significant difference between the percentage of military-connected students scoring in the top 2 quartiles (at or above the national average) for normal curve equivalent (NCE) mathematics scores on the Terra Nova Third Edition (TNTE) using gender as a predictor; …

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Group Rings, Christopher Wrenn Jan 2018

Group Rings, Christopher Wrenn

Masters Essays

No abstract provided.

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Analyzing The Probabilistic Spread Of A Virus On Various Networks, Teagan Decusatis Jan 2018

Analyzing The Probabilistic Spread Of A Virus On Various Networks, Teagan Decusatis

Senior Projects Spring 2018

In this project we model the spread of a virus on networks as a probabilistic process. We assume the virus breaks out at one vertex on a network and then spreads to neighboring vertices in each time step with a certain probability. Our objective is to find probability distributions that describe the uncertain number of infected vertices at a given time step. The networks we consider are paths, cycles, star graphs, complete graphs, and broom graphs. Through the use of Markov chains and Jordan Normal Form we analyze the probability distribution of these graphs, characterizing the transition matrix for each …

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Assessment For Feedback And Achievement Growth For Middle School Math Students, Katie Jo Pemberton Jan 2018

Assessment For Feedback And Achievement Growth For Middle School Math Students, Katie Jo Pemberton

Walden Dissertations and Doctoral Studies

Inconsistent math assessment practices do not accurately represent and communicate student mathematics achievement. Because of inconsistencies in assessment practices, local middle school mathematics teachers in an urban school district in the northwestern United States piloted the use of multiple formative assessments. The purpose of this study was to compare mathematics achievement, growth, and course percentage grades for students who have multiple formative assessment attempts compared to students who are not provided multiple assessment attempts. Theoretical foundations originated from Black and Wiliam, supporting the use of formative assessment for a positive impact on student learning. A quantitative, ex post facto quasi-experimental …

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Assessing Reading And Mathematics Achievement Of Students With Disabilities In A Suburban Middle School, Terri Melissa Toomer Jan 2018

Assessing Reading And Mathematics Achievement Of Students With Disabilities In A Suburban Middle School, Terri Melissa Toomer

Theses and Dissertations

Co-teaching classrooms consist of general and special education teachers working together to benefit students with disabilities (SWDs). Many parents and teachers believe the content knowledge provided by general educators in the regular education setting, combined with the instructional service delivery model (SDM) expertise of special educators, will result in the greatest academic growth for SWDs. However, it is not known if SWDs served in one SDM progress at a faster rate than SWDs served in another SWD. Therefore, the focus of this study was to compare the reading and mathematics achievement of male and female middle school SDWs in two …

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Sports Analytics With Computer Vision, Colby T. Jeffries Jan 2018

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

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Differences In Spatial Visualization Ability And Vividness Of Spatial Imagery Between People With And Without Aphantasia, Anita Crowder Jan 2018

Differences In Spatial Visualization Ability And Vividness Of Spatial Imagery Between People With And Without Aphantasia, Anita Crowder

Theses and Dissertations

Mathematics education researchers have examined the relationship between visualization and mathematics for decades (e.g., Arcavi, 2003; Bishop, 1991; Duval, 1999; Fennema & Tartre, 1985; Presmeg, 1986). Studies have linked spatial visualization ability, such as measured in mental rotation tasks, directly to mathematics self-efficacy (Pajares & Kranzler, 1995; Weckbacher & Okamoto, 2014), which in turn influences mathematics achievement (Casey, Nuttall, & Pezaris, 1997). With the important role that spatial visualization plays in learning mathematics, the recent identification of congenital aphantasia (Zeman, Dewar, & Della Sala, 2015), which is the lack of mental imagery ability, has raised new questions for mathematics education …

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“From School Of Crisis To Distinguished”: How One School Continues To Defeat The Odds, Ben Crawford Jan 2018

“From School Of Crisis To Distinguished”: How One School Continues To Defeat The Odds, Ben Crawford

Theses and Dissertations--Science, Technology, Engineering, and Mathematics (STEM) Education

Despite conditions that would work against a small rural school in an impoverish area of rural Kentucky, Fairway Elementary School has managed to excel in its accountability measures. This study used a mixed-methods approach with data collected through interviews and MAP student growth scores in reading and mathematics. Five themes emerged from the qualitative data regarding school success: (1) a well-organized intervention system, (2) a focus on and overall enjoyment of the discipline of mathematics, (3) involvement of parents in school functions, (4) transparency of needs and organization of resources, and (5) an overall school culture that is competitive, impactful, …

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Applied Temperament, Geoffrey D. Hershberger Jan 2018

Applied Temperament, Geoffrey D. Hershberger

Theses and Dissertations--Music

The following document was created in order to promote intonation consensus in ensembles and to better facilitate learning in educational settings. Non-keyboard instruments provide musicians an opportunity to make nearly infinitesimal adjustments to pitch while performing; this creates difficulties for students and challenges even the most seasoned professionals. Non-keyboard musicians struggle their whole lives to play in tune, and even when one knows exactly where they want to place a pitch, technical difficulties can foul any musician's performance. When performing solo, the musician must choose a tuning system that is suitable for the music being performed, and attempt to realize …

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Crime Around The World: Using Mathematical Modeling Techniques To Model Aggregated Worldwide Crime Rates, Kelly M. Steurer Jan 2018

Crime Around The World: Using Mathematical Modeling Techniques To Model Aggregated Worldwide Crime Rates, Kelly M. Steurer

Senior Independent Study Theses

This aim of this study was to determine what affects aggregate crime rates around the world. This thesis used Mathematical Modeling techniques to build generalized linear models for homicide rates and burglary and housebreaking rates using the following predictive factors: economic indicators, education rates, government quality indicators, ethno-linguistic fractionalization, GDP per capita and its growth, drug consumption rates, and age and gender ratios. We used a series of factor selection techniques including linear and stepwise regressions, principal component analysis, and regression analysis to select factors to use to build final models of homicide and burglary and housebreaking.

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The Rsa Cryptosystem, Rodrigo Iglesias Jan 2018

The Rsa Cryptosystem, Rodrigo Iglesias

Williams Honors College, Honors Research Projects

This paper intends to present an overview of the RSA cryptosystem. Cryptosystems are mathematical algorithms that disguise information so that only the people for whom the information is intended can read it. The invention of the RSA cryptosystem in 1977 was a significant event in the history of cryptosystems. We will describe in detail how the RSA cryptosystem works and then illustrate the process with a realistic example using fictional characters. In addition, we will discuss how cryptosystems worked prior to the invention of RSA and the advantage of using RSA over any of the previous cryptosystems. This will help …

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An Algorithm To Determine All Odd Primitive Abundant Numbers With D Prime Divisors, Jacob Liddy Jan 2018

An Algorithm To Determine All Odd Primitive Abundant Numbers With D Prime Divisors, Jacob Liddy

Williams Honors College, Honors Research Projects

An abundant number is said to be primitive if none of its proper divisors are abundant. Dickson proved that for an arbitrary positive integer d there exists only finitely many odd primitive abundant numbers having exactly d prime divisors. In this paper we describe a fast algorithm that finds all primitive odd numbers with d unique prime divisors. We use this algorithm to find all the number of odd primitive abundant numbers with 6 unique Divisors. We use this algorithm to prove that an odd weird number must have at least 6 prime divisors.

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Logic -> Proof -> Rest, Maxwell Taylor Jan 2018

Logic -> Proof -> Rest, Maxwell Taylor

Senior Independent Study Theses

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

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Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal Jan 2018

Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal

Senior Independent Study Theses

The International Monetary Fund (IMF) calculates the voting power of a country by dividing the total of one member's votes by the total of all members' votes. This method of calculating the power of a state judges power as voting weight. However, voting weights are the total number of votes a country has in an institution, while voting power is the influence a country has on a policy decision. A better approach to calculate this voting power within an institution is by using voting power indices. However, literature only calculates the winning power, while voting power is defined as the …

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Teacher Perceptions Of Professional Learning Communities' Impact On Math Critical Thinking Pedagogy, Elizabeth Ann Daly Jan 2018

Teacher Perceptions Of Professional Learning Communities' Impact On Math Critical Thinking Pedagogy, Elizabeth Ann Daly

Walden Dissertations and Doctoral Studies

U.S. educational leaders struggle with declining mathematics achievement among students as compared to other countries. The problem for this study was low standardized mathematics scores in one district in a major city in the Southwestern United States. The purpose of this sequential explanatory mixed method project study was to analyze the effectiveness of professional learning communities (PLCs) on the mathematics critical thinking pedagogy among teachers in 2 elementary schools. The conceptual framework focused on work by Olivier, Hipp, Huffman, and Hord on the efficacy of PLCs for improving teacher pedagogy. Research questions addressed in this study were designed to explore …

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Elementary Teachers' Affective Relationship With Mathematics And Its Influence On Mathematics Instruction, Kelly Kreitzer Sutton Jan 2018

Elementary Teachers' Affective Relationship With Mathematics And Its Influence On Mathematics Instruction, Kelly Kreitzer Sutton

Walden Dissertations and Doctoral Studies

In a South Carolina school district, approximately 45% of 3rd-5th grade students performed poorly on the state mathematics test. K-5 teachers attended district training to improve mathematics instruction and content mastery, but the training omitted teachers' affective domain in teaching. Teachers' affective relationships with mathematics (ARM) affects content delivery, instructional decisions, and teachers' confidence levels and motivation. The purpose of this sequential mixed methods study was to investigate whether teachers' years of experience, grade levels taught, or past mathematics experiences influenced K-5 teachers' ARM, as measured by the ARM survey, and to explore teachers' perceptions of their ARM in instruction. …

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A Qualitative Case Study Of Mathematics Teachers' Formative Assessment Feedback, Ryan Rathje Jan 2018

A Qualitative Case Study Of Mathematics Teachers' Formative Assessment Feedback, Ryan Rathje

Walden Dissertations and Doctoral Studies

Formative assessment is supported by research as a process to enhance student learning. A vital aspect in the process is the role of feedback which, based on its use, can support or hinder student learning. The problem addressed in this study was based on the concern of a high school administrator that teachers in the school were not using formative feedback in a manner that supported student learning. The purpose of this instrumental qualitative case study was to explore and understand the assessment and feedback practices of mathematics teachers in a private high school setting. The conceptual framework for this …

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Descriptions Of Differentiated Instruction In Mathematics In A Title 1 School District, Sheril Bulley-Simpson Jan 2018

Descriptions Of Differentiated Instruction In Mathematics In A Title 1 School District, Sheril Bulley-Simpson

Walden Dissertations and Doctoral Studies

In an urban Title 1 school district, the average number of Grade 3-5 students who scored proficient or advanced on the state standardized assessment was 37.3% below Grade 3-5 students countywide and 19.4% below Grade 3-5 students statewide. Low mathematics scores may indicate a gap in practice that affects student achievement. The purpose of this descriptive case study was to examine teachers' descriptions of instructional strategies implemented to mediate instruction for students who struggle in mathematics. This study was based on the conceptual framework of Tomlinson's differentiated instruction (DI), a means of accommodating the varied ways that students learn. The …

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Ancient Cultures + High School Algebra = A Diverse Mathematical Approach, Laryssa Byndas Jan 2018

Ancient Cultures + High School Algebra = A Diverse Mathematical Approach, Laryssa Byndas

Masters Essays

No abstract provided.

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Advanced Enrichment Topics In An Honors Geometry Course, Kayla Woods Jan 2018

Advanced Enrichment Topics In An Honors Geometry Course, Kayla Woods

Masters Essays

No abstract provided.

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Improving Mathematical Skill: The Perceptions Of Rural Minnesota Mathematics Educators, Michael Haskins Jan 2018

Improving Mathematical Skill: The Perceptions Of Rural Minnesota Mathematics Educators, Michael Haskins

All Graduate Theses, Dissertations, and Other Capstone Projects

This qualitative phenomenological study is focused on the perceptions of mathematics educators on how to improve mathematical skill in high school students. The main purpose was to describe, recognize, and interpret the lived experience that have allowed educators to achieve the best results for their students. The population for the current study was mathematics educators that were located in a rural Southwest Minnesota city with medium population. These educators were either college educators or middle and high school teachers. The measures that were used to select the participants for the study were that they must hold at least a bachelor's …

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Lagrangian Coherent Structures: A Climatological Look, Andrew Sven Mccall Jr. Jan 2018

Lagrangian Coherent Structures: A Climatological Look, Andrew Sven Mccall Jr.

UVM College of Arts and Sciences College Honors Theses

A relatively new area at the crossroads of fluid and nonlinear dynamics are objects known as Lagrangian Coherent Structures (LCSs). LCSs are mathematically classified to differentiate parts of fluid flows. They, themselves, are the most influential parts of fluids. These objects have the most influence on the fluids around them and they allow for a sense of hierarchy in an otherwise busy environment of endless variables and trajectories. While all particles of fluids have the same dynamics on an individual basis, areas of fluid are not created equal and to be able to detect which parts will be the most …

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Providing Working Memory Support To Anxious Students Using Cognitive Load Theory Compliant Instructions, Deborah Chadwick Jan 2018

Providing Working Memory Support To Anxious Students Using Cognitive Load Theory Compliant Instructions, Deborah Chadwick

University of Wollongong Thesis Collection 2017+

Learning mathematics has been identified as a significant source of anxiety for many students. This anxiety places a burden on working memory, which is additional to the cognitive load associated with the learning task. Cognitive Load Theory (CLT) has informed empirically derived design principles for instructional materials that provide optimal learning support through consideration of human cognitive architecture. Worked examples are one instructional technique proposed by CLT to reduce load on working memory and support learner engagement. The assumption in this study, in the domain of mathematics, is that task complexity and the burden on working memory while completing mathematics …

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Counseling Program Intervention For Improving African American Students’ Science, Technology, Engineering, And Mathematics Dual Enrollment Participation, Sonja L. Taylor Jan 2018

Counseling Program Intervention For Improving African American Students’ Science, Technology, Engineering, And Mathematics Dual Enrollment Participation, Sonja L. Taylor

Theses and Dissertations

African Americans are underrepresented at all points in the STEM pipeline from K-12 coursework into professional careers. The reasons for this underrepresentation are varied and reflect a myriad of contributing factors based on early academic experiences, sociocultural influences, and the effects of standardized testing. The three-fold purpose of this study was to implement a counseling program to inform nine African American study participants about the dual enrollment opportunity at their high school, to gain perspective about the factors which shaped their STEM disposition, and to determine the effect of the program on their attitudes about dual enrollment participation. The study …

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Problem-Solving In An Early Childhood Mathematics Classroom, Lockey Plyler Jan 2018

Problem-Solving In An Early Childhood Mathematics Classroom, Lockey Plyler

Theses and Dissertations

Problem-solving occurs when mathematical tasks create opportunities that provide challenges for increasing students' mathematical understanding and development. This research study determined the influence of the launch-explore-summarize/extend problem-solving framework on second-grade student performance of place value tasks. The dissertation in practice measured problem-solving success. This action research study occurred at an elementary school in Columbia, South Carolina. The teacher-researcher determined appropriate problem-solving tasks and assessed students’ academic achievement and critical thinking skills. Following a mixed methods action research design, the researcher analyzed qualitative and quantitative data to determine the significance of the problem-solving framework. The data indicated significant student growth during …

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