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Predictive Relationships Of Teacher Efficacy, Geometry Knowledge For Teaching, And The Cognitive Levels Of Teacher Practice On Student Achievement., Paul Klein

Electronic Theses and Dissertations

This study explored the predictive relationships of teacher efficacy, teacher knowledge, and teacher practices with student achievement. More specifically, secondary mathematics teachers' efficacy beliefs, geometry knowledge for teaching, and the cognitive complexity of the teachers' classroom practices were examined for 72 teachers in both urban and rural districts across Kentucky, along with the student achievement data of their students. Teacher and student data were obtained from the NSF-funded Geometry Assessment for Secondary Teachers (GAST) project, which administered geometry teacher knowledge assessments at the beginning and end of the school year, and collected cognitive complexity data from lessons through three classroom …

Integer Compositions, Gray Code, And The Fibonacci Sequence, Linus Lindroos

Electronic Theses and Dissertations

In this thesis I show the relation of binary and Gray Code to integer compositions and the Fibonacci sequence through the use of analytic combinatorics, Zeckendorf's Theorem, and generating functions.

Global Domination Stable Graphs, Elizabeth Marie Harris

Electronic Theses and Dissertations

A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.

Relations Among Brief Measures Of Mathematics, Reading, And Processing Speed: A Construct Validity Study, Jennifer Leigh Maynard

Electronic Theses and Dissertations

Emphasis on regular mathematics skill assessment, intervention, and progress monitoring under the RTImodel has created a need for the development of assessment instruments that are psychometrically sound, reliable, universal, and brief. Important factors to consider when developing or selecting assessments for the school environment include what skills are assessed; mathematics curriculums typically include computation and applications as separate skills taught in sequence. It is also important to consider what additional factors may potentially influence performance on such tests due to the nature of test administration and characteristics of the test items. The current study investigated the construct validity of established, …

Effects Of Departmental And Institutional Policies On Developmental Mathematics Students, Garth B. Johnson

Electronic Theses and Dissertations

Arkansas Department of Higher Education data show that approximately 75% of Arkansas community college students are required to take at least one developmental education class (Arkansas Higher Education Coordinating Board, 2012, p. 7.2). This is significantly higher than the approximately 30% average (Provasnik & Planty, 2008, p. 11) of community college students across the US. Developmental mathematics is the most commonly needed subject within Arkansas, with over 40% of community college students enrolling in at least one developmental mathematics course (Arkansas Higher Education Coordinating Board, 2012, p. 7.3). Despite being common, few institutions that teach Developmental Education perform and then …

Analysis Of The Family Of Generalized Cumulative Sum Type Control Charts, Wenmin Wang

Electronic Theses and Dissertations

As an aid to the practitioners, various Phase II quality control charts have been developed to monitor for a change in the parameters of the distribution of a quality measurement. In this project, the family of generalized cumulative sum type charts was studied. An equivalent chart version that requires fewer parameters was given. Some useful integral equations were derived for determining the run length distribution of the lower and upper one-sided charts. The Markov chain methods were also given. The parameters unknown version was presented and the performance analysis was studied for the chart for monitoring for a change in …

Precovering Dgc-Complexes, Jonathan G. Crosby

Electronic Theses and Dissertations

In this thesis we prove that with the hypotheses that dg e C is injectively resolving and that the class C is closed under arbitrary direct limits we have that the following are equivalent to dgC being covering: Every complex of C-modules is in dg e C and every exact complex of C-modules is in e C.

Compact Filters And The Arzelá-Ascoli Theorem, Nathan Denton Farmer

Electronic Theses and Dissertations

The Arzelà-Ascoli Theorem gives conditions for a set to be compact in a function space, and is a useful theorem for existence proofs in many different mathematical contexts. The most natural structure for Arzelà-Ascoli type theorems is the continuous convergence - which is not necessarily topological even if the underlying base spaces are. Compact filters, on the other hand, are the logical extension of compact sets to filters with similar compactness-type properties. Compact filters have proved to be a useful tool in optimization and analysis. This thesis will show conditions for a filter to be compact on a function space, …

The Diver's Distance, Aristide Zezouma Sanou

Electronic Theses and Dissertations

The visual assessment of clustering tendency (VAT) method, which was developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband uses a reordering of the rows and columns of a dissimilarity matrix; it then displays the ordered dissimilarity matrix (ODM) as a 2D gray-level image called an ordered dissimilarity image (ODI). Al- though successful in determining potential clustering structure of various data sets, the technique offers room for improvement. In this thesis, we propose a new proximity measure called the diver's distance which is defined based on concepts in graph theory. We then theoretically study the diver's distance …

The Praxis I Math Study Guide Questions And The Praxis I Math Skills Test Questions: A Statistical Study, Mary Elaine Wilkins

Electronic Theses and Dissertations

In 2001, No Child Left Behind introduced the highly qualifiedstatus for k-12 teachers, which mandatedthe successfulscores on a series of high-stakestest; within this series is the Pre-Professional Skills Test (PPST) orPRAXISI. The PPSTmeasures basic k-12 skills for reading, writing, and mathematics.The mathematics sub-test is a national concern because some American high school students may graduate with basic math skills deficits that may prohibit their performance on the PPST. One approach to understanding this national concern is to explore the PPST preparation materials. This study focused on the numbers and operations, Algebra, Geometry and measurement, and data analysis and probability categories …

Examination Of An Online College Mathematics Course: Correlation Between Learning Styles And Student Achievement, Bridget Steele

Electronic Theses and Dissertations

The purpose of this study was to determine if there was a significant relationship between learning styles and student learning outcomes in an online college mathematics course. Specifically, the study was guided by two research questions focused on (a) the extent to which learning styles had a predictive relationship with student achievement in an online college mathematics course and (b) the extent to which various learning styles among mathematics students in online versus face-to-face courses predicted mathematics achievement. The population for this study consisted of the 779 college mathematics and algebra (CMA) students who were enrolled in a private multimedia …

Mathematic Strategies For Teaching Problem Solving: The Influence Of Teaching Mathematical Problem Solving Strategies On Students' Attitudes In Middle School, Kelly Lynn Klingler

Electronic Theses and Dissertations

The purpose of this action research study was to observe the influence of teaching mathematical problem solving strategies on students’ attitudes in middle school. The goal was to teach five problem solving strategies: Drawing Pictures, Making a Chart or Table, Looking for a Pattern, Working Backwards, and Guess and Check, and have students reflect upon the process. I believed that my students would use these problem solving strategies as supportive tools for solving mathematical word problems. A relationship from the Mathematics Attitudes survey scores on students’ attitudes towards problem solving in mathematics was found. Students took the Mathematics Attitudes survey …

Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak

Electronic Theses and Dissertations

The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups …

Neuropsychological Predictors Of Math Calculation And Reasoning In School-Aged Children, Dana Schneider

Electronic Theses and Dissertations

After multiple reviews of the literature, which documented that multiple cognitive processes may be involved in mathematics ability and disability, Geary (1993) proposed a model that included three subtypes of math disability: Semantic, Procedural, and Visuospatial. A review of the extant literature produced three studies that examined Geary's three subtypes, which provided some support for Geary's model. Given the paucity of research examining Geary's subtypes of math disability, this study aimed to add to the literature by exploring the presence of these three subtypes in a sample of school-aged children. The sample consisted of 60 participants (30 males, 30 females) …

Cayley-Dickson Loops, Jenya Kirshtein

Electronic Theses and Dissertations

In this dissertation we study the Cayley-Dickson loops, multiplicative structures arising from the standard Cayley-Dickson doubling process. More precisely, the Cayley-Dickson loop Q_n is the multiplicative closure of basic elements of the algebra constructed by n applications of the doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). Starting at the octonions, Cayley-Dickson algebras and loops become nonassociative, which presents a significant challenge in their study.

We begin by describing basic properties of the Cayley–Dickson loops Q_n. We establish or recall elementary facts about Q_n, e.g., inverses, …

The Effects Of Journaling And Vocabulary Strategies On Elementary Students' Attitudes Towards Mathematical Performance, Renee Marie Janzen

Electronic Theses and Dissertations

In an attempt to examine the effects of journaling and vocabulary strategies on elementary students’ attitudes towards mathematical performance, I embedded reflective journaling and vocabulary strategies into my fourth grade mathematics curriculum. The mathematics content focused on whole number place value, multiplication, and division. My study revealed the positive effects these interventions can have on elementary students’ attitudes towards mathematics.

Enriching Students With Developmental Delays In An Early Childhood Classroom Using Ipads With Mathematics Applications, Selma Powell

Electronic Theses and Dissertations

Laws and legislation related to early childhood and special education have shaped the field and impacted the need for early intervention services, but the outcomes of those services both academically and socially at the forefront. Children with developmental delays today are eligible for school services beginning at birth across the country, the new challenging is determining the impact of services on the social and academic outcomes. Many children with developmental delays are served in inclusive early intervention classrooms. A need for developmentally appropriate quality mathematics instruction exists to prepare students to meet the demands of a global economy; students must …

Equal Or Not? An Exploration Of Eighth-Grade Students' Experience Of Algebra, Janice L. Reyes

Electronic Theses and Dissertations

Over the past two decades, a considerable amount of algebra instruction nationwide has shifted from high school to middle school. In Georgia, all eighth-grade students have been required to take a course that is equivalent to about 80 percent of a traditional Algebra 1 course. The purpose of this qualitative study was to explore how a selected group of eighth-grade students in a suburban Georgia middle school experience algebra within the eighth grade mathematics curriculum. A qualitative research design was used to investigate students’ perceptions of algebra, the strategies employed by teachers to teach algebra, students’ difficulties with algebra, and …