Current Search: UWF Theses and Dissertations (x) » Mathematics (x)
VIEW ALL ITEMS
(1 - 5 of 5)
- Title
- Constructions of Ramanujan graphs from classes of regular graphs.
- Author
- Beach, Ross Joseph
- Abstract/Description
-
In this paper, we are going to show the existence of Ramanujan graphs among different classes of graphs. The main areas of research surrounding these graphs consider their classification and existence for different degrees and orders. The focus of this body of work is to observe different classes of graphs, and to see if they fit the definition of Ramanujan graph under certain conditions. First, we examine whether all strongly regular graphs are Ramanujan. Then, different restrictions are...
Show moreIn this paper, we are going to show the existence of Ramanujan graphs among different classes of graphs. The main areas of research surrounding these graphs consider their classification and existence for different degrees and orders. The focus of this body of work is to observe different classes of graphs, and to see if they fit the definition of Ramanujan graph under certain conditions. First, we examine whether all strongly regular graphs are Ramanujan. Then, different restrictions are placed on the parameters of strongly regular graphs, and we explore whether those yield Ramanujan graphs. Some other results related to graph factors and some special graphs are observed as well.
Show less - Identifier
- 1298600893, WFE0000787
- Format
- Document (PDF)
- Title
- Exploring elementary student motivationlevels within gamified digital mathematics instructional programs.
- Author
- Hoover, Jennifer Lauren
- Abstract/Description
-
Some approaches to teaching mathematics have led to decreased student motivation. Gamification is an application of game elements within nongame settings. While gamification may increase motivation in other contexts, its effective use in digital mathematics instruction to motivate elementary students is undetermined. Based on the constructs of self-determination theory (i.e., autonomy, relatedness/recognition, competence/self-efficacy), intrinsic and extrinsic motivation were the two...
Show moreSome approaches to teaching mathematics have led to decreased student motivation. Gamification is an application of game elements within nongame settings. While gamification may increase motivation in other contexts, its effective use in digital mathematics instruction to motivate elementary students is undetermined. Based on the constructs of self-determination theory (i.e., autonomy, relatedness/recognition, competence/self-efficacy), intrinsic and extrinsic motivation were the two determinants used to develop research questions and frame the study. The purpose of this qualitative study was to identify how intrinsic and extrinsic motivators embedded within gamified digital mathematics instructional programs contribute to motivation levels of third- through fifth-grade students at an elementary school located in central Texas. A target research sample that consisted of 38 participants was identified which then produced a data producing sample of 20 participants. Semi-scripted phenomenological interviews were conducted. Data were analyzed by each research question to identify the degree to which gamified components, across nine different subtypes (interest/enjoyment, perceived competence, effort/importance, perceived choice, value/usefulness, intrinsic motivation, external regulation, introjected regulation, and identified regulation), impacted student motivation. This study concluded that students reported the highest motivation levels with a combination of intrinsic and extrinsic gamified motivators. Data suggested that a lack of autonomy established by mandatory participation in digital mathematics instructional programs positively impact motivation. Future research could address the impact of gamification upon levels of motivation by age or grade level and how levels of motivation change over time.
Show less - Identifier
- 1129016349, WFE0000658
- Format
- Document (PDF)
- Title
- Meshless space-time method to solve two-dimensional wave equation.
- Author
- Mahaguruge, Niranjan Warnakulasooriya
- Abstract/Description
-
Meshless methods utilizing Radial Basis Functions(RBF) have been widely used to find numerical solutions for Partial Differential Equations(PDEs). Unlike the other numerical methods, meshless algorithms are significantly simpler to implement as they do not require a mesh in the simulation domain. Rolland L. Hardy, an Iowa State geodesist, was the first to study using RBF for scattered data interpolations in the early 1970s. He introduced his Multiquadric(MQ) RBF, which has been used to obtain...
Show moreMeshless methods utilizing Radial Basis Functions(RBF) have been widely used to find numerical solutions for Partial Differential Equations(PDEs). Unlike the other numerical methods, meshless algorithms are significantly simpler to implement as they do not require a mesh in the simulation domain. Rolland L. Hardy, an Iowa State geodesist, was the first to study using RBF for scattered data interpolations in the early 1970s. He introduced his Multiquadric(MQ) RBF, which has been used to obtain numerical solutions for various types of RBF interpolation problems. In addition to that, E. J. Kansa, in the very early 1990s, made the first attempt to extend RBF interpolation to obtain solutions for PDEs. In this thesis, we propose a numerical scheme, which has been based on Kansa's method, to solve time-dependent PDEs. In contrast to already existing methods for solving time-dependent PDEs, our model treats the time variable the same as a spatial variable. However, the accuracy of the RBF numerical methods highly depends on the shape parameter, c, which is associated with the RBF. The value of the c that guarantees the highest accuracy is problem dependent and it is called as the optimal value of c. Even with the optimal value of c, it is not possible to achieve a significantly high accuracy compared to existing methods. In order to enhance the level of accuracy, we introduce \Ghost Points" into the computational domain. While traditional RBF based numerical methods place the centers exclusively inside the computational domain, the ghost point approach expands the region of the centers inside and outside the computational domain. Our numerical results suggest that the accuracy of the numerical results has been significantly increased by the ghost points.
Show less - Date Issued
- 2020, 2020
- Identifier
- 1202266955, WFE0000720
- Format
- Document (PDF)
- Title
- Predicting middle-achieving students' achievement in eighth-grade algebra 1.
- Author
- Jacobson, Jennifer Swann
- Abstract/Description
-
Eighth-grade students who are placed into Algebra 1 but fail end-of-course exams may experience lowered grade point averages (GPAs) and loss of motivation for math or avoid taking advanced mathematics courses in high school. Middle-achieving students present challenges in terms of mathematics placement. Self-efficacy theory and locus of control theory suggest the noncognitive traits mathematics self-efficacy (MSE) and academic locus of control (ALOC) are associated with mathematics...
Show moreEighth-grade students who are placed into Algebra 1 but fail end-of-course exams may experience lowered grade point averages (GPAs) and loss of motivation for math or avoid taking advanced mathematics courses in high school. Middle-achieving students present challenges in terms of mathematics placement. Self-efficacy theory and locus of control theory suggest the noncognitive traits mathematics self-efficacy (MSE) and academic locus of control (ALOC) are associated with mathematics achievement and could predict achievement in eighth-grade algebra. The purpose of this quantitative correlational study was to examine whether MSE, ALOC, and prior-year State of Texas Assessments of Academic Readiness (STAAR) mathematics score predict achievement in eighth-grade algebra among middle-achieving students in South Texas more accurately than prior-year STAAR mathematics scores alone. The sample included 111 eighth-grade algebra students in a large suburban school district in South Texas, whose scores on the previous year's STAAR mathematics exam fell between the 25th and 75th percentiles. MSE predicted meeting grade-level standards (R 2 = .229), performance category (R 2 = .327), and percent score on the NEISD Algebra 1 Benchmark exam (R 2 = .317). ALOC was not associated with achievement on the NEISD Algebra 1 Benchmark exam. These results suggest that predictions of achievement in eighth-grade algebra for middle-achieving students were improved with the addition of measures of MSE, but not ALOC. Suggestions for future research include developing a mathematics locus of control instrument and broader studies exploring the relationship between MSE and achievement in eighth-grade Algebra 1.
Show less - Date Issued
- 2021, 2021
- Identifier
- 1293881341, WFE0000763
- Format
- Document (PDF)
- Title
- Relating student perceptions of parent attitudes to student motivation for learning mathematics.
- Author
- Schamber, Wendy Diane
- Abstract/Description
-
In response to declining national academic rankings, the United States developed a set of common standards (Common Core State Standards Initiative [CCSSI], 2015; Neuman & Roskos, 2013); however, success requires student effort. In that respect, the purpose of this study was to explore the relationship between student perceptions of parent attitudes toward student ability and effort following implementation of the Common Core Standards for Mathematics (CCSSM) and student motivation for...
Show moreIn response to declining national academic rankings, the United States developed a set of common standards (Common Core State Standards Initiative [CCSSI], 2015; Neuman & Roskos, 2013); however, success requires student effort. In that respect, the purpose of this study was to explore the relationship between student perceptions of parent attitudes toward student ability and effort following implementation of the Common Core Standards for Mathematics (CCSSM) and student motivation for learning mathematics. The construct of perception evident in Weiner's attribution theory of interpersonal motivation indicates individuals attribute motivation to factors they perceive to be real (Weiner, 2000). Student perceptions of parent attitudes can influence student motivation. This study utilized a quantitative cross-sectional design with survey methodology to gather data online from middle school students in a district that implemented the CCSSM. The study used 122 participants for an alpha of .05, power of .80, and medium effect size. The study utilized Pearson's r and Spearman r along with simple linear regression and multiple regression analyses to describe the relationship between the variables. Results indicate that student perceptions of parent attitudes toward student ability have a greater influence on student motivation than student perceptions of parent attitudes toward student effort. Student perceptions of parent attitudes toward both student ability and student effort are more positive than student perceptions of their own ability and effort, consistent with Weiner's (2000) social component of motivation. The study implies possible changes to policy and practice that would increase parent communication and involvement in a child's education.
Show less - Identifier
- 1129599806, WFE0000673
- Format
- Document (PDF)
