Digital Commons Network^™

The Effects Of Problem-Based Learning On Mathematics Motivation In A Flipped Classroom Instructional Environment, Joshua David Harrison

Theses and Dissertations

In response to decreasing motivation in high school math classrooms, teachers are transforming classrooms with various instructional techniques. Traditional math instruction relies on direct instruction and memorization of content, processes, and skills. Teachers are transitioning to more constructivist student-led approaches. Utilizing multiple instructional designs provides teachers more opportunities to access the major components of the ARCS Model: attention, relevance, confidence, and satisfaction.

Therefore, the purpose of this action research was examining problem-based learning in a flipped classroom instructional environment and measuring its effect on students’ motivation and achievement in Algebra 2. The study addressed the following research questions: 1) What …

Impacts Of Technology-Enhanced Dual Enrollment Mathematics Course On Rural High School Students’ Intentions Of Going To College, Nicolae Bordieanu

Theses and Dissertations

The purpose of this concurrent mixed methods action research study was to investigate the impact of new technology-enhanced Dual Enrollment (DE) math courses on students’ perception of college courses, the influence the technology-enhanced DE had on students’ intention of going to college, and the students' perception of the technology-enhanced DE math course. Examining student experiences in a technology-enhanced DE course informed all stakeholders as to what degree DE influenced students’ perception of college. The DE experience influenced students' postsecondary plans. The innovation of this action research study was the technology-enhanced DE math course. Software used to practice computational skills, conduct …

Incremental, Spaced Repetition And Studymate Flashcards: The Impact On College Student Memorization Of Measurement Conversion Standards, Patricia A. Bromer

Theses and Dissertations

The purpose of this action research was to evaluate the impact of and student perception of incremental, spaced repetition of StudyMate electronic flashcard use on memorization of measurement conversion standards for an online Mathematics in Health Sciences course. Online college classes require more self-direction and usually do not allow for partner or group work. These characteristics of online classes may hinder students’ ability to memorize crucial information, increasing their cognitive load and leading to feelings of inadequacy. This mixed methods study assessed the impact of incremental, spaced repetition of StudyMate flashcard use on college math students’ memorization of measurement conversion …

An Examination Of Attachment And Aspirations In Diverse Rural Youth: The Role Of Peers And Teachers, Gresi Bonomo Irdam

Theses and Dissertations

This dissertation consists of three studies that examined diverse rural youths’ educational and rural aspirations. These studies have the potential to inform rural communities, educators, and parents by providing novel understandings of how peers and teachers in mathematics and science classrooms influence diverse rural youths’ rural attachment, and aspirations (i.e., educational, rural residential, community, and proximity). Thus, the purpose of this dissertation was to investigate rural teachers and their diverse students from White, African American, Hispanic, and Native American backgrounds. In particular, the studies within this dissertation examine how teachers’ social connectedness to their rural communities relates to their teacher …

Mindset, Stereotype Threat, And The Fear Of Failure: Why Female Students Leave A Secondary High Honors Mathematics Pathway, Annabelle Merg

Theses and Dissertations

The disproportionate attrition of female students in STEM is well documented in higher education but less well understood at the secondary level. In a large, public high school in an affluent, highly educated city, the high honors mathematics pathway is the only math pathway that has not yet achieved gender parity, an implication for future educational and economic equity. Female students leave this pathway at significantly higher rates than male students, especially during and immediately after the first course. Through an explanatory, mixed methods approach, this study found that these female students are not less well prepared than their male …

Motivation In Online Course Design: Action Research Using A Self-Determination Theory-Based Mathematics Unit To Improve Students’ Autonomy, Competence, And Relatedness, Emily Rose Shank

Theses and Dissertations

Strong mathematics achievement is lacking in the United States, with motivation waning especially among mathematics and online students. Online mathematics students, in particular, struggle with self-regulation and self-efficacy (Kim, 2012; Sun & Rueda, 2012). Ryan and Deci (2017), in their well-established and empirical self-determination theory, contended that satisfying the psychological needs of autonomy (involving self-regulation), competence (involving self-efficacy), and relatedness (involving a sense of belonging) creates a suitable environment for integrated extrinsic and intrinsic motivation to thrive. The purpose of this action research was to create and implement a self-determination theory-based online unit on factoring polynomials for mathematics students at …

Personalized Geometry Instruction: A Mixed Methods Action Research Study Implementing An Adaptive Web-Based Learning Environment To Support High School Students’ Geometry Problemsolving Skills, Catherine D. Jordan

Theses and Dissertations

The purpose of this action research study was to evaluate the implementation of an adaptive web-based learning environment to personalize geometry instruction and practice for high school students at a private school in North Carolina. This study was guided by the following three research questions: (1) How and to what extent does implementing personalized geometry instruction and practice through an adaptive web-based learning environment affect high school students’ knowledge of geometry? (2) How does using personalized geometry instruction and practice through an adaptive web-based learning environment affect students’ motivation to learn geometry as well as their mathematics self-efficacy, anxiety, and …

Biplanar Crossing Numbers Of Bipartite Graphs, Sydney Miyasaki

Senior Theses

The goal of this thesis is to compute upper and lower bounds on the biplanar crossing numbers of complete bipartite graphs. The concept of a biplanar crossing number was first introduced by Owens (Owens 1971) as an optimization problem in circuit design. To prove upper bounds, we follow a method used by Czabarka et. al. (Czabarka et. al. 2006), in which they start from an optimal drawing of a small bipartite graph and use it to generate drawings of larger bipartite graphs. We explore several possibilities for computing lower bounds. One is using Ramsey theory, via the Bipartite Ramsey Number …

Evaluating The Use Of Writing Prompts & Graphic Organizers In Middle School Mathematics: Action Research To Improve Mathematical Achievement And Students’ Attitudes With Authentic Assessments, Kyla Candee Steppler

Theses and Dissertations

The purpose of this action research was to evaluate the impact of writing prompts and graphic organizers on Mona school’s 7th and 8th grade students’ mathematical academic achievement and their attitudes towards the authentic application of mathematics. Two research questions guided the study: (1) How and to what extent, do writing prompts and graphic organizers impact 7th and 8th grade students’ mathematical achievement and attitudes towards mathematics? (2) What were the 7th and 8th grade students’ perceptions about the implementation of authentic writing prompts and graphic organizers in a mathematics course at Mona school? This action research followed a convergent …

Math Workshop And Its Impact On Higher-Level Thinking Skills, Elizabeth Ross

Theses and Dissertations

This paper addresses the problem of students not using problem solving and critical thinking skills in high school mathematics classes. It describes an action research project that looked at the impact of Math Workshop on higher-level thinking skills, number of attempts to demonstrate proficiency, and students’ feelings/attitudes about mathematics in a high school Algebra II setting. In a small high school, 20 students enrolled in an Algebra II course were selected to complete a pre-test, post-test and tasks framed by Math Workshop. A triangulated mixed-methods design was used to compare quantitative and qualitative data to answer the research questions. Descriptive …

Making Elearning Engaging: The Effect Of Technology Strategies On Student Engagement And Content Knowledge Development In A Secondary Mathematics Digital Classroom, Allison Knapp

Theses and Dissertations

This action research study employed a mixed-methods design to examine the effect of technology strategies on secondary students’ engagement and development of geometry content knowledge in an eLearning setting. Seeking to understand student preferences of the technology tools, this two-week study was conducted during a geometry unit on quadrilaterals and employed the following technology tools: student response systems (SRS), computer-assisted instruction (CAI), gamification, and teacher-made screencasts. Quantitative data was collected on student engagement, the usefulness of the technology, and student self-efficacy through a Likert-scale survey after each day of using technology. Qualitative data were collected through purposeful interviews with students …

A Foundation For Understanding The Neurocognitive Processes That Underlie Mathematics Performance In Children, Christopher Anzalone

Theses and Dissertations

The current study investigated the prognostic utility of resting state EEG coherence in the prediction of standardized mathematics scores. Quantitative EEG analyses were performed for 60 school-aged children (ages 7 to 12 years) with and without math learning disabilities (MLD). Analyses assessing intrahemispheric coherence at rest were performed across the entire sample and several coherence networks were extracted.

Specifically, networks that included Brodmann area 40 (BA 40) -- a region of the brain heavily involved in the cognitive processes responsible for mathematics performance (Anderson, Betts, Ferris, & Fincham, 2011; Cohen, Dehaene, Chochon, Lehericy, & Naccache, 2000; Kroger, Nystrom, Cohen, & …

Feminist-Infused Participatory Action Research To Promote Female Students’ Self- Efficacy In Mathematics, Nicole Hreno

Theses and Dissertations

Prompted by the manifestations of decreased levels of mathematical self-efficacy among the female students in my district, the purpose of this study was to investigate the source of self-efficacy development that was most influential among our female students and engage in praxis to combat these gender inequities. Grounded in critical feminist theory, I engaged six teacher-researchers in participatory action research through qualitative methodologies. Using questionnaires to examine the worldviews of our female students, the emergent study was guided by these voices which were previously silenced. The interventions employed were a direct result of the females’ expressed mathematical experiences, leading us …

Developing Specialized Content Knowledge For Equitable Practice In Mathematics: Exploring A Constructivist Approach To Preservice Teacher Education, Jane Rector Wilkes

Theses and Dissertations

A successful teacher education program prepares preservice teachers to provide high quality mathematics education for all students. In order to effectively address the needs of diverse and historically underserved groups of students, future teachers need to have a deep understanding of both basic content knowledge and pedagogical content knowledge. The purpose of this study was to examine ways to support preservice teachers in improving procedural and conceptual content mastery, as well as the specialized content knowledge that they will need in order to feel empowered to teach their future students.

Based on the theoretical frameworks of two components of mathematical …

The Relationship Between Mindset And Motivation In An Alternative School Mathematics Classroom, Jo Ellen Dowdy

Theses and Dissertations

The purpose of this action research study was to determine the impact of a Khan Academy growth mindset lesson plan on the motivation of at-risk ninth grade students in a mathematics classroom. Data were collected for quantitative analysis of students’ self- reporting of perceptions pertaining to mindset beliefs before and after a mindset intervention and perceptions about motivation in the mathematics classroom. Analysis revealed there was no relationship between mindset and motivation. A minimal decrease in fixed mathematical mindset was determined after a Khan Academy mindset intervention. Increases were found in students’ beliefs in the importance of math, the usefulness …

The Impact Of Intelligent Tutoring Software On Geometry Students, Simela Oueini

Theses and Dissertations

This purpose of this paper is to deepen the understanding for a problem of practice in the mathematics educators’ classroom of low retention of information thus leading to poor mathematics achievement. The identification of the problem of practice led to a development of a research focus examining the effects of using intelligent tutoring software in the mathematics classroom and the impact it has on mathematics achievement, student motivation as it relates to self-efficacy, student engagement and attitudes towards mathematics. Using a convergent mixed methods approach (Creswell, 2012), this paper elaborates on the research questions addressing “What effects does the integration …

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 …

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 …

Relationships Between Prior Experiences, Current Teaching Contexts, And Novice Teachers' Use Of Concrete Representation For Mathematics Instruction, Elizabeth Lee Johnson

Theses and Dissertations

This case study documents the perceived influences on three novice elementary teachers’ use of concrete representations for teaching mathematics. In order to develop mathematical proficiency, students need access to a variety of representations (i.e. pictures, words, symbols, concrete materials, and real world contexts) to make sense of mathematical ideas. Three sources of data were collected: video-recorded lessons, interviews, and a focus group. Analyses indicated that although concrete representations were accessible to all three teachers, they were least used among the available representations. Verbal expression was most prominent, followed closely by abstract written symbols. Technology, which was not one of the …

On The Group Of Transvections Of Ade-Diagrams, Marvin Jones

Theses and Dissertations

In this thesis we examine symplectic spaces with forms generated by the ADEdiagrams. Specifically, we determine the generators of the group of transvections for each space under the standard basis, S, of Kⁿ (where K is a field with characteristic 0) and the hyperbolic basis, H, we get from the classification theorem of symplectic spaces. Further, we examine how the generators of these groups are related via g : G_f,S ! SL(Z)_n where g(X) = P⁻¹XP where P is the change of basis matrix for S to H.

Selected Research In Covering Systems Of The Integers And The Factorization Of Polynomials, Joshua Harrington

Theses and Dissertations

In 1960, Sierpi\'{n}ski proved that there exist infinitely many odd positive integers $k$ such that $k\cdot 2^n+1$ is composite for all positive integers $n$. Such integers are known as Sierpi\'{n}ski numbers. Letting $f(x)=ax^r+bx+c\in\mathbb{Z}[x]$, Chapter 2 of this document explores the existence of integers $k$ such that $f(k)2^n+d$ is composite for all positive integers $n$. Chapter 3 then looks into a polynomial variation of a similar question. In particular, Chapter~\ref{CH:FH} addresses the question, for what integers $d$ does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ with $f(1)\neq -d$ such that $f(x)x^n+d$ is reducible for all positive integers $n$. The last two chapters of …

Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients, Morgan Cole

Theses and Dissertations

Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some integer b greater than or equal to 2. We will investigate the size of the coefficients of the polynomial and establish a largest such bound on the coefficients that would imply that f(x) is irreducible. A result of Filaseta and Gross has established sharp bounds on the coefficients of such a polynomial in the case that b = 10. We will expand these results for b in {8, 9, ..., 20}.

Coloring Pythagorean Triples And A Problem Concerning Cyclotomic Polynomials, Daniel White

Theses and Dissertations

One may easily show that there exist $O( \log n)$-colorings of $\{1,2, \ldots, n\}$ such that no Pythagorean triple with elements $\le n$ is monochromatic. In Chapter~\ref{CH:triples}, we investigate two analogous ideas. First, we find an asymptotic bound for the number of colors required to color $\{1,2,\ldots ,n\}$ so that every Pythagorean triple with elements $\le n$ is $3$-colored. Afterwards, we examine the case where we allow a vanishing proportion of Pythagorean triples with elements $\le n$ to fail to have this property.

Unrelated, in 1908, Schur raised the question of the irreducibility over $\Q$ of polynomials of the form …

3-D Computational Investigation Of Viscoelastic Biofilms Using Gpus, Paisa Seeluangsawat

Theses and Dissertations

A biofilm is a slimy colony of bacteria and the materials they secrete, collectively called “extracellular polymeric substances (EPS)”. The EPS consists mostly of bio-polymers, which cross link into a network that behave viscoelastically under deformation. We propose a single-fluid multi-component phase field model of biofilms that captures this behavior, then use numerical simulations on GPUs to investigate the biofilm’s growth and its hydrodynamics properties.