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#Blackgirlmathmagic: A Mixed Methods Study Examining African American Girls In Standardized Mathematicstesting, Rakeema Thomas Toussaint

LSU Doctoral Dissertations

Black women have been making successful strides in mathematics for decades; however, they continue to be underrepresented in mathematics and other STEM fields. According to Young et al. (2017), Black girls and women perform lower in mathematics than all other racial gender groups except for Black males. Considering the stakes for Black girls and women in mathematics, this study sought to address this group's challenges early in their secondary education experiences, focusing on standardized testing.

The purpose of this explanatory-sequential mixed-methods study was to determine how different mathematics item types impacted the performance of African American girls, especially multiple-select multiple-choice …

Mathematics Course For Elementary Teachers In An Alternate Certification Pathway, Rachael Cramer Williams

LSU Master's Theses

In the current alternate certification program for elementary teachers at McNeese State University, students receive course work from only one of the elementary mathematics methods courses required in the traditional certification program. To assure that candidates in the alternate path learn all the math they need, I have created a course that combines the most important concepts from the two courses in one. In this thesis I will describe how the new course was designed, present an outline of the course, detail the content at the unit level and provide a template for the final exam.

Investigating Curriculum Use And Its Impact On Teachers And Their Practice, Tiah B. Alphonso

LSU Doctoral Dissertations

This study provided insights into how upper elementary teachers from three southern school districts used standards based curriculum materials and the resulting changes in their beliefs, knowledge, and practice. Additionally, this study sought to identify whether the following four factors were predictors of change in teacher practice: coherence of the professional development program, opportunities to collaborate, years of teaching experience, and curriculum use. The participating school districts were selected through purposeful sampling with districts being chosen largely based on a strong commitment to implementing Eureka Math in their schools. For comparison purposes, a contrast school district was also included in …

Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher

LSU Doctoral Dissertations

Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work …

Writing In The Geometry Classroom, Amy Lynn Rome

LSU Master's Theses

This study sought a time-efficient way to implement writing in ninth-grade Geometry. Students wrote responses to five expository writing prompts spread out over the spring semester of the 2014-2015 school year. Students’ first attempts were graded and returned to them along with feedback in the form of a teacher-written exemplar. Students rewrote assignments to improve their grades. All first and second attempts were collected and evaluated. We found that students were more successful after seeing the exemplar. Moreover, on assignments occurring later in the semester, more students were able to score in the top categories of the writing assignments on …

Metacognition And Its Effect On Learning High School Calculus, Bonnie Sue Bergstresser

LSU Master's Theses

The following paper discusses the effect of metacognitive training sessions on students’ calculus retention. Students in two high school classes participated. The students in both classes were then given lessons on a chapter without metacognitive training and lessons on a subsequent chapter with training in a set of metacognitive skills. After the latter chapter students scored higher on a post-test and expressed desire to incorporate the skills they learned into their other classes.

Exploring Student Perseverance In Problem Solving, Angelique Renee (Treadway) Duncker

LSU Master's Theses

ABSTRACT Many high school Geometry students lack the perseverance required to complete complex and time-consuming problems. This project tests the hypothesis that if students were provided with a means of organizing their problem solving work they will be less apt to quit when faced with complex and time-consuming mathematical problems. This study involved students enrolled in 10th grade Geometry and 10th grade Honors Geometry in two similar high schools. After trying unsuccessfully to implement methods adapted from an engineering workshop, I designed a graphic organizer that was simple to use and acceptable to the students. Ultimately, I did not detect …

Determining Impact: Using Formative Evaluation In A Professional Development Program For Teachers Of Mathematics And Science, Tiah B. Alphonso

LSU Master's Theses

The purpose of this study was to evaluate a professional development (PD) program for middle and high school teachers of mathematics and science which is funded by a $5 million National Science Foundation grant. The evaluation was internal and formative in nature and took place in two separate phases. The focus of the evaluation was not only on program improvement but also to extend the body of existing knowledge in the area of teacher professional development. Both the needs of project stakeholders and the findings of previous research in the areas of professional development and program evaluation were drawn on …

The Relationship Between Music And Visual Arts Formal Study And Academic Achievement On The Eighth-Grade Louisiana Educational Assessment Program (Leap) Test, Richard Allen Baker Jr.

LSU Doctoral Dissertations

The purpose of this study was to examine the policy implications allowing administrators to exempt a student from required arts instruction if the student obtained unsatisfactory scores on the high-stake state mandated tests in English and mathematics. This study examined English language arts and math test scores for 37,222 eighth grade students enrolled in music and/or visual arts classes and those students not enrolled in arts courses. There were more than 12,000 students who were eligible, but not enrolled in arts courses. Methodology consisted of comparing the mean scores of students receiving music and visual arts instruction with the mean …

Multimedia Mathematics Intervention For Math-Delayed Middle School Students, Lisa L. Stokes

LSU Doctoral Dissertations

The purpose of this study is to determine if the Sharpening Math Skills Lab technology-mediated mathematics instructional practices for math-delayed middle school students have positive effects on their mathematics achievement and spatial visualization ability and to gauge student engagement in learning, implementation of the principles of instructional design, and attitudes toward mathematics instruction. The results of a recent meta-analysis report a range of significantly positive to significantly negative effect sizes which establish a need for further evaluation of academic achievement utilizing technology-mediated mathematics programs at the middle school level (Slavin, Lake, & Groff, 2007). The literature (Moreno & Mayer, 2000) …

Integration Of Conceptual Mathematical Relationships Into Constant Time Delay Instruction, Bethany Ann Porter

LSU Master's Theses

There is constant debate over mathematics education in the United States. One central controversy is whether or not the current methods used to teach students mathematics are effective. Some scholars believe that students are not getting enough practice and that they are not getting a good conceptual understanding of mathematics. It has been shown that mathematics equations are rich in patterns and inter-relationships and when children understand these relationships they have higher mathematic skill levels than their peers who do not. This study examined the effectiveness of using an empirically supported, fast paced mastery oriented teaching procedure that promotes automaticity …

The Importance Of Fluent Component Skills In Mathematical Comprehension, Chisato Komatsu

LSU Master's Theses

The primary question to be addressed by the present study was whether fluency on component skills is important in the development of overall competency in mathematics. Reading fluency has served as an excellent predictor of one’s reading comprehension. However, few studies have investigated whether the fluency on component skills is essential in the development of overall competency in mathematics. In fact, there has been a push for instructional strategies to deemphasize the importance component skills. In the current study, 140 students in second- through fourth- grade classrooms from general education participated. Each student took three curriculum-based measurement probes (a single-skill …

Orientations Of Graphs Which Have Small Directed Graph Minors., Glenn Randolph Berman

LSU Historical Dissertations and Theses

Graphs are characterized by whether or not they have orientations to avoid one or more of the digraphs K&ar;3 , S&ar;3 , and P&ar;3 . K&ar;3 , S&ar;3 and P&ar;3 are created by starting with a triangle, a three point star, or a path of length three respectively, and replacing each edge with a pair of arcs in opposite directions. Conditions are described when all orientations of 3-connected and 4-connected graphs must have one or more of the above digraphs as a minor. It is shown that double wheels, and double wheels without an axle, are the only 4-connected graphs …

Densities Of 4-Ranks Of K(2) Of Rings Of Integers., Robert Burke Osburn

LSU Historical Dissertations and Theses

Conner and Hurrelbrink established a method of determining the structure of the 2-Sylow subgroup of the tame kernel K2( O ) for certain quadratic number fields. Specifically, the 4-rank for these fields was characterized in terms of positive definite binary quadratic forms. Numerical calculations led to questions concerning possible density results of the 4-rank of tame kernels. In this thesis, we succeed in giving affirmative answers to these questions.

On K-Conjugacy Classes Of Maximal Tori In Semi-Simple Algebraic Groups., Uroyoan Ramon-Emeterio Walker

LSU Historical Dissertations and Theses

An attempt was made to make this a self-contained reading. The first three chapters are intended to provide the necessary background. Chapter one develops the tools needed from Galois Cohomology. Chapter two is a brief description of involutions, and in chapter three we define the notion of (linear) algebraic group, we give some examples and discuss some of their properties. In chapter four, we discuss some variants of the classical Skolem-Noether theorem, requiring only that the subalgebra have a unique faithful representation of full degree over a separable closure. We verify that we can extend every isomorphism to the whole …

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

Linear Codes Defined From Higher -Dimensional Varieties., Gary Lynn Salazar

LSU Historical Dissertations and Theses

We establish an algebraic foundation to complement the improved geometric codes of Feng and Rao. Viewing linear codes as affine variety codes, we utilize the Feng-Rao minimum distance bound to construct codes with relatively large dimensions. We examine higher-dimensional affine hypersurfaces with properties similar to those of Hermitian curves. We determine a Grobner basis for the ideal of the variety of rational points on certain affine Fermat varieties. This result is applied to determine parameters of codes defined from Fermat surfaces.

Homflypt Skein Modules., Jianyuan Zhong

LSU Historical Dissertations and Theses

Let k be a subring of the field of rational functions in x, v, s which contains x+/-1, v+/-1, s+/-1. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) x --1L+ -- xL -- = (s -- s--1 )L0; (2) L with a positive twist = (xv--1)L; (3) L ⊔ O = u-u-1 s-s-1L where O is the unknot. We give two bases for the relative Homflypt skein module of …

Sociomathematical Norms Of Elementary School Classrooms: Crossnational Perspectives On The *Reform Of Mathematics Teaching., Jeongsuk Pang

LSU Historical Dissertations and Theses

Mathematics education reform in the United States has marshaled large-scale support for instructional innovation, and enlisted the participation and allegiance of large numbers of mathematics teachers. However, there is concern that many teachers have not grasped the full implications of the reform ideals. This study explored the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals by comparing and contrasting two reform-oriented classrooms. This study was an exploratory, qualitative, comparative case study using constant comparative analysis. Seven mathematics lessons were video-taped from each class, and intensive interviews conducted with the two teachers. …

Developing Students' Understanding Of Similar Figures: A Perceptual Approach., Danny Ray Mcnabb

LSU Historical Dissertations and Theses

Children encounter and recognize similar figures in their everyday experiences with such things as basketballs, soccer balls, tennis balls, ping-pong balls; or a candy bar that comes in various sizes of the same shape. Yet their school experience with the mathematics of similarity generally does not build on these perceptual intuitions. Traditional mathematics curricula bypass students' visual intuitions and their quantitative understandings, proceeding directly to set piece problems solved by formal algebraic methods. The result for many students is that the topic of similarity contributes to their evolving view of mathematics as a domain of complex procedural methods divorced from …

Classically Unstable Approximations For Linear Evolution Equations And Applications., Yu Zhuang

LSU Historical Dissertations and Theses

Temporal discretization methods for evolutionary differential equations that factorize the resolvent into a product of easily computable operators have great numerical appeal. For instance, the alternating direction implicit (ADI) method of Peaceman-Rachford for 2-D parabolic problems greatly reduces the simulation time when compared with the Crank-Nicolson scheme. However, just like many other factorized approximation methods that exhibit numerical stability, the ADI method is known to satisfy only the Von Neumann stability condition, a necessary condition that is usually surmised as sufficient in practical cases as pointed out by Lax and Richtmyer. Intensive efforts have been directed to understand the Von …

On Some Optimal Control Problems For The Centroaffine Geometry On The Plane., Angel L. Cruz Delgado

LSU Historical Dissertations and Theses

A certain parametrization of substantial planar curves yields a centroaffine arclength s and a centroaffine curvature ks that remain invariant under GL(2, R ) motions. In Chapter 4 we search for those substantial curves with predetermined position and velocity at the initial and terminal points, which minimize the total square curvature 0T k2s 2ds as k varies over all square summable functions on each interval [0, T]. These curves are called centroaffine elastic curves. Thinking of the curvature k as a control, we pose our problem as an optimal control problem over the Lie group GL(2, R ) with fixed …

A Canonical Description Of The Plancherel Measure For A General Two-Step Free Nilpotent Lie Group., Chin-Te Chu

LSU Historical Dissertations and Theses

In this work on g=Fn,2 , free 2-step nilpotent Lie algebra on n generators, we use the group of automorphisms to give a basis-free description of the Fourier Inversion Formula, thereby generalizing and strengthening an example discussed by Corwin & Greenleaf. In the Introduction we discuss Example 4.3.14 in Corwin & Greenleaf's book. It demonstrates how different bases of F3,2 lead to different inversion formulas. But the third "more" invariant formula describes Plancherel measure on a support expressed in terms of rotations, dilations, and translations. Actually it is not canonical since it still depends on choices of bases for F3,2 …

The Effect Of Antecedent And Consequent Strategies On Increasing Student Homework Compliance And Academic Achievement., Donna Marie Gilbertson

LSU Historical Dissertations and Theses

The primary purpose of this investigation was to evaluate the effects of homework and alternatives to homework on student math completion, accuracy and fluency for low socioeconomic students. To examine possible causes of homework problems as well as the effect of different treatments on math fluency, this study used an idiographic protocol to systematically examine the effects of antecedent and consequential strategies on different types of homework performance problems through several phases. First, a brief experimental analysis was conducted for each student to identify whether poor homework performance was due to a swill deficit or a performance deficit. Next, an …

On Stochastic Integration For White Noise Distribution Theory., Said Kalema Ngobi

LSU Historical Dissertations and Theses

This thesis consists of two parts, each part concentrating on a different problem from the theory of Stochastic Integration. Chapter 1 contains the introduction explaining the results in this dissertation in general terms. We use the infinite dimensional space S'R endowed with the gaussian measure mu. The Hilbert space ( L2) is defined as (L2) (L2) ≡ L2( S'R , mu) and our results are based on the Gel'fand triple ( S )beta ⊂ (L2) ⊂ S* b . The necessary preliminary background in white noise analysis are well elaborated in Chapter 2. In Chapter 3 we present a generalization …

Weierstrass Pairs And Minimum Distance Of Goppa Codes., Gretchen L. Matthews

LSU Historical Dissertations and Theses

We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code that has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of certain codes defined using a linear combination of the two points. In particular, we obtain some two-point codes on a Hermitian curve that have better parameters than the one-point code on this curve with the same …

Structure And Minors In Graphs And Matroids., Galen Ellsworth Turner Iii

LSU Historical Dissertations and Theses

This dissertation establishes a number of theorems related to the structure of graphs and, more generally, matroids. In Chapter 2, we prove that a 3-connected graph G that has a triangle in which every single-edge contraction is 3-connected has a minor that uses the triangle and is isomorphic to K5 or the octahedron. We subsequently extend this result to the more general context of matroids. In Chapter 3, we specifically consider the triangle-rounded property that emerges in the results of Chapter 2. In particular, Asano, Nishizeki, and Seymour showed that whenever a 3-connected matroid M has a four-point-line-minor, and T …

On Harmonic Analysis For White Noise Distribution Theory., Aurel Iulian Stan

LSU Historical Dissertations and Theses

This thesis is composed of two parts, each part treating a different problem from the theory of Harmonic Analysis. In the first part we present an inequality in White Noise Analysis similar to the classical Heisenberg Inequality for functions in L2Rn . To do this we replace the finite dimensional space R n and its Lebesgue measure by the infinite dimensional space E' , which is the dual of a nuclear space E , and its Gaussian measure. Choosing an arbitrary element eta in E , we may define the multiplication operator Q&d5;h , which is the sum between the …

Integral Kernel Operators In The Cochran -Kuo -Sengupta Space., John Joseph Whitaker

LSU Historical Dissertations and Theses

This dissertation contains several results about integral kernel operators in white noise analysis. The results found here apply to the space of test functions and generalized functions that were constructed in the paper of Cochran, Kuo, and Sengupta, based on a sequence of numbers &cubl0;an&cubr0; infinityn=0. . We shall prove results about existence, restrictions, and extensions of integral kernel operators based on the conditions on &cubl0;an&cubr0; infinityn=0. contained in the paper of Kubo, Kuo, and Sengupta. Also, we shall prove an analytic property and growth condition of the symbol of a continuous operator in CKS space. Our results are similar …

Inequalities Between Pythagoras Numbers And Algebraic Ranks In Witt Rings Of Fields., Sidney Taylor Hawkins

LSU Historical Dissertations and Theses

This dissertation establishes new lower bounds for the algebraic ranks of certain Witt classes of quadratic forms. Let K denote a field of characteristic different from 2 and let q be a quadratic form over K. The form q is said to be algebraic when q is Witt equivalent to the trace form qL∣K of some finite algebraic field extension L∣K . When q is algebraic, the algebraic rank of q is defined to be the degree of the minimal extension L∣K whose trace form is Witt equivalent to q. It is an important, unsolved problem to find reasonable bounds …