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Uncovering Transformative Experiences: A Case Study Of The Transformations Made By One Teacher In A Mathematics Professional Development Program, Rachelle Myler Orsak

Theses and Dissertations

Effective professional development is vital for improving mathematics teaching (National Council of Teachers of Mathematics [NCTM], 2007), so studying effective professional development programs is important to the field of mathematics education. This case study presents findings on one teacher, Rebecca, and her experiences in a five-semester mathematics professional development for elementary teachers. The participants in this professional development engaged in collaborative problem solving of challenging mathematical tasks over extended periods of time. I used qualitative research methods based on grounded theory methodology (Charmaz, 2006) to analyze Rebecca's entrance and exit surveys, video data of Rebecca's individual interviews, and video data …

Responsiveness Of Elementary-Aged Students, With And Without Specific Learning Disabilities, To Interventions For Mathematics Calculation, Masanori Ota

Theses and Dissertations

The Response to Intervention (RtI) model is an identification model for Specific Learning Disability (SLD), one of the 13 disability categories identified under the Individual with Disabilities Education Act (IDEA) of 2004. The RtI model has been proposed as an alternative model to the discrepancy model (e.g., intelligence quotient-achievement discrepancy model). In the RtI model, students’ responsiveness (e.g., levels of performance and slopes of progress) yields their eligibility for special education. However, to date, research that examined the validity of the RtI model (e.g., examination of intervention responsiveness with students with academic deficits) has been limited in the area of …

A Comparison Of Academic Achievement And Retention Of Community College Students In College Algebra After Completion Of Traditional Or Technology-Based Instruction, Jennifer Ferrill Seal

Theses and Dissertations

This study was designed to compare the success rates in College Algebra between two groups of students attending a Mississippi community college. Eighty students enrolled in a College Algebra course were taught using traditional instructional techniques, and 70 students received technology-enhanced instruction. This study considered the effects of grade scores on a mathematics-achievement pretest and posttest, student attitudes toward mathematics, time-on-task while using technology during mathematics study, mathematics subscores on the American College Test, and withdrawal rates. Data collected for this study were derived from the official transcripts of students enrolled in spring 2007 College Algebra classes of a Mississippi …

A Comparison Of Traditional Instruction And Standards-Based Instruction On Seventh-Grade Mathematics Achievement, Manika Deshawn Kemp

Theses and Dissertations

The purpose of this study was to determine if method of instruction, standards-based or traditional, had an impact on student mathematics achievement. More specifically, this study sought to determine if students taught using the JBHM Achievement Connections® standards-based method of instruction would show higher academic gain than students taught using a traditional method of instruction through the use of Mathematics: Applications and Connections, Course 2® in seventh-grade. The research design was a quasi-experimental design, with 65 students participating. Group A received a traditional method of instruction through the use of Mathematics: Applications and Connections, Course 2 and Group B received …

Improving A Second Grade Student's Number Sense: An Instructional Intervention, Elizabeth Leigh Mathews

Theses and Dissertations

The purpose of this qualitative case study was to help a second grade student, who struggled with mathematics but excelled in reading, to develop a conceptual understanding of number sense, using a teacher researcher-created intervention. The five-step, one-on-one intervention included the following: (1) use trade books to build mathematical knowledge and vocabulary (2) teacher modeling of concepts, (3) guided practice with manipulatives, (4) review using games and a ?Fact Pack?, and (5) journal writing to explain concepts. The Early Mathematics Assessment-3 (TEMA-3) was used as a pre- and post-test assessment the student?s mathematical knowledge. Other data included transcriptions of audio …

One Problem, Two Contexts, Danielle L. Gigger

Theses and Dissertations

In this study, a group of students were presented with two mathematically isomorphic problems but in radically different contexts. Analysis of their thinking and reasoning as they worked to solve and explain each problem demonstrates that the thinking and reasoning that emerged in each problem responded to clear purposes that the problems elicited in these students. The first problem was posed in a context that relied on experience and intuition rather than a formal mathematical description. The second problem was posed in a formal, set-theoretic context. While the analysis offered here reveals similarities in the students' final reasoning in the …

Evaluation Of The Effects Of A Curriculum-Based Math Intervention Package With Elementary School-Age Students In A Summer Academic Clinic, Nicholas E. Hoda

Theses and Dissertations

The purpose of this study was to empirically evaluate the effects of the Math to Mastery intervention package versus the effects of immediate corrective feedback with elementary school students who were performing at least one year below grade level in mathematics. Students were participants in a one-month summer academic clinic for remediation of reading, writing, and mathematics deficits held at a university in the southeastern United States. A combined-series multiple baseline design across participants was used to evaluate the effects of both interventions for gains in fluency as measured by digits correct per minute on one minute curriculum-based measurement probes. …

Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing

Theses and Dissertations

I inquire about second graders' capabilities of developing solution strategies and the original variety of strategies they bring forth while solving a combination problem. Based on analysis of the data presented in this paper, students developed five different general strategies. After analyzing what the second grade students were capable of developing, we can conclude that young children are capable of developing powerful systematic strategies grounded in their personal experiences. This research shows that even when the teacher does not foster personal agency, children will still exercise agency. The social interactions in the classroom helped students learn to propose mathematical ideas, …

On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell

Theses and Dissertations

In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.

The Experiences Of A Rural Mississippi Mathematics Teacher: A Case Study, John Hamilton Lamb

Theses and Dissertations

This study investigates my experiences as a rural Mississippi secondary mathematics teacher. The culture surrounding accountability testing and rural education as well as student perceptions of my mathematics instruction and classroom management were investigated. With recent educational legislation such as the No Child Left Behind Act of 2001, teachers and students are experiencing education differently than teachers and students of the past. Through this basic interpretive case study, I sought to increase the limited research surrounding student perceptions of rural mathematics instruction and accountability testing and to provide a descriptive image of teaching in this rural school. The students, administrators, …

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses?, Matthew M. Webb

Theses and Dissertations

Lesson study is a form of professional development for teachers adopted in recent years from Japan. Introducing lesson study to U.S. teachers and researchers has been the focus of most of the literature on this subject. Much of the literature outlines how lesson study works and describes its essential features. One of the features of lesson study is anticipating student responses, also known as anticipating student thinking. Anticipating student responses is passingly described in lesson study literature. This research was conducted to understand what it means to anticipate student responses for preservice mathematics teachers in a lesson study group. Lesson …

Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff

Theses and Dissertations

The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …

Reasoning About Motion: A Case Study, Tiffini Lynn Glaze

Theses and Dissertations

Several dance and industrial design students were given the opportunity to attend a non-traditional mathematics course. The nature of this course prompted student interaction and expected collaboration. My research focuses on one dance student, Sara, who did not consider herself a strong mathematics student, but who understood physical motion very well. This paper explores the evolution of Sara's representations for physical motion in a given task, and discusses her reasoning for keeping or dismissing various parts of her representations during the course of this task. I examine first how Sara learns mathematics with understanding in this task, and second how …

Bounding The Number Of Graphs Containing Very Long Induced Paths, Steven Kay Butler

Theses and Dissertations

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.

In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.

In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as …