Browsing by Subject "Mathematics"
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Item A college approach to fractals in middle school(Texas Tech University, 2005-08) Duke, Billy J.; Dwyer, Jerry F.The algebra and geometry of complex numbers were presented to eighth and ninth grade mathematics classes. The purpose of the presentations was to determine if this college level mathematics would have an influence on the algebra and geometry skills of the K-12 students. Pre and post surveys were employed. Results showed an increase in both student mathematics skills and student interest in the ninth grade class. In the eighth grade class there was not a significant improvement. It may be conjectured that ninth grade students benefit from this kind of intervention, but that the average eighth grade student does not have the mathematical skills required to handle the college level material.Item A college approach to fractals in middle school(2005-08) Duke, Billy J.; Dwyer, Jerry F.; Wilhelm, Jennifer A.The algebra and geometry of complex numbers were presented to eighth and ninth grade mathematics classes. The purpose of the presentations was to determine if this college level mathematics would have an influence on the algebra and geometry skills of the K-12 students. Pre and post surveys were employed. Results showed an increase in both student mathematics skills and student interest in the ninth grade class. In the eighth grade class there was not a significant improvement. It may be conjectured that ninth grade students benefit from this kind of intervention, but that the average eighth grade student does not have the mathematical skills required to handle the college level material.Item A comparative study of the dedekind cut and the nested interval idea: with applications(Texas Tech University, 1952-05) Carpenter, Ila MaeNot availableItem A graduate pedagogy course for mathematics teaching assistants(Texas Tech University, 2005-05) Froman, Jason D.; Harris, Gary; Dwyer, Jerry F.; Surles, JamesWe will describe a three semester-hour graduate level mathematics course which focuses on issues related to the teaching of mathematics at the college level and is taken by all new graduate students entering our program as graduate teaching assistants. We attempt to assess the overall impact of this course on students’ beliefs and practice related to the teaching of mathematics at the undergraduate level. We will do this by analysing survey data and information obtained from student records, student course evaluations, and interviews with students, faculty members, and administrators involved with the course from its inception in the fall of 2000 through the fall of 2004.Item A graduate pedagogy course for mathematics teaching assistants(2005-05) Froman, Jason D.; Harris, Gary; Dwyer, Jerry F.; Surles, JamesWe will describe a three semester-hour graduate level mathematics course which focuses on issues related to the teaching of mathematics at the college level and is taken by all new graduate students entering our program as graduate teaching assistants. We attempt to assess the overall impact of this course on students’ beliefs and practice related to the teaching of mathematics at the undergraduate level. We will do this by analysing survey data and information obtained from student records, student course evaluations, and interviews with students, faculty members, and administrators involved with the course from its inception in the fall of 2000 through the fall of 2004.Item A study of abelian groups: a thesis in mathematics(Texas Tech University, 1955-05) Caskey, John HermonNOT AVAILABLEItem Algebraic criteria for quadric surfaces(Texas Tech University, 1959-08) Turner, Verdell JNot availableItem Analysis of success rates in developmental mathematics(Texas Tech University, 1995-12) Pepin, Stephanie D.Math-0302, Intermediate Algebra, is a developmental mathematics course offered at Texas Tech University. The purpose of this course is to provide students an opportunity for remediation of those skills necessary for successful completion of college level mathematics. The effectiveness of this course has become a priority of the University due to increasing enrollment and reenrollment of students in this course. This analysis was developed to investigate the relationship between student success rates in Math-0302 and success rates in college level mathematics courses, specifically, Math-1320, College Algebra, and Math-1330, Introductory Mathematical Analysis. A crucial question being asked on college campuses concerns the need for developmental mathematics at the university level. Chapter II presents background information concerning Math-0302 enrollment figures, placement criteria, and course accountability to justify this need. At Texas Tech University, current figures indicate an increasing trend in student enrollment in Math-0302. This increase can be perceived as a continuing need for developmental mathematics courses. Placement criteria and course accountability are established to determine effects, if any, these factors have on enrollment In Math-0302, Intermediate Algebra.Item Applications of orthogonal functions to two-dimensional potential problems(Texas Tech University, 1959-08) Jordan, Donald FNot availableItem Approaches to the Use of Geometry in Architecture: A study of the works of Andrea Palladio, Frank Lloyd Wright, and Frank Gehry(2010-01-16) Srinivasan, UrmilaGeometry deals with form, shape, and measurement and is a part of mathematics where visual thought is dominant. Both design and construction in architecture deal with visualization, and architects constantly employ geometry. Today, with the advent of computer software, architects can visualize forms that go beyond our everyday experience. Some architects claim that the complex forms of their works have correlations with non-Euclidean geometry, but the space we experience is still Euclidean. Given this context, I have explored possible correlations that might exist between mathematical concepts of geometry and the employment of geometry in architectural design from a historic perspective. The main focus will be to describe the two phenomena historically, and then investigate any connections that might emerge from the discussion. While discussing the way geometry has been approached in architecture, I have focused on the Renaissance, Modern, and Post-modern phases as they have a distinct style and expression. Andrea Palladio, Frank Lloyd Wright, and Frank Gehry's works will be case studies for the Renaissance, Modern, and Post-modern phases respectively. One of the important conclusions of this study is that architects use geometry in a more subconscious and intuitive manner while designing. Certain approaches to geometry can be determined by the way an architect deals with form and space. From the discussions of the works of Palladio, Wright, and Gehry, it can be concluded that from a two-dimensional simple approach to form and space in architecture, there has been a development of thinking about complex forms three dimensionally. Similarly, in mathematics, geometry has developed from a two-dimensional and abstract description of our surroundings to something that can capture the complex and specific nature of a phenomena. It is also shown that architects rarely come up with new concepts of geometry. Significant developments in geometry have always been in the domain of mathematics. Hence, most correlations between geometry in architecture and geometry in mathematics develop much later than the introduction of those concepts of geometry in mathematics. It is also found that the use of Euclidean geometry persists in architecture and that later concepts like non-Euclidean geometry cannot be used in an instrumental manner in architecture.Item Approximate Solutions to the Allen-Cahn Equation Using the Finite Difference Method(Texas A&M International University, 2016-06-13) Villarreal, Jamil Malik; Lin, RunchangSeeking a deeper understanding of the world has been a driving factor in Applied Mathematics. From counting and measuring physical objects to developing equations and ratios that resemble patterns in nature, mathematics is used to interpret and explain the intricate structures that we observe everyday. The field of Applied Mathematics almost always involves setting up and then solving, or approximating solutions to, at least one partial differential equation that takes the physical and mathematical properties into consideration. This is the process of creating mathematical models. For this thesis, we will investigate approximate solutions to the Allen-Cahn equation whose analytic solution is still unknown due to the nonlinearities of the problem as well as its sensitivity to certain constants as we shall see. The numerical schemes involved in these approximations are obtained from the finite difference method.Item Bilingual teachers reflecting on mathematics teaching : what they notice about engaging children in problem solving(2013-05) Maldonado, Luz Angélica; Empson, Susan B.Teachers are being asked to engage in ambitious mathematics teaching in order to reform children's mathematics learning, and it has proven to be challenging. Unraveling the challenges requires understanding the in-the-moment decisions that teachers make while teaching mathematics. The focus of this study is to understand teacher noticing, the ways in which teachers identify, reason about and make decisions in the situations that occur when engaging English language learners in problem solving. Specifically, I used the construct of professional noticing of children's mathematical thinking (Jacobs, Lamb, & Philipp, 2010) to investigate what three bilingual teachers notice as they participate in a teacher study group to analyze and reflect on their experiences in weekly problem solving small groups. What teachers noticed reflected attention to situations in which they struggled to understand children's mathematical thinking and attempts to direct students towards correct problem solving. Teachers' decisions and struggles in engaging children in problem solving also revealed a focus on the role of preparing English language learners be successful for standardized testing. However, looking at student's work in the teacher study group began to help teachers focus on children's mathematical thinking. Implications on continued understanding of teacher noticing, effective mathematics professional development and developing understanding of mathematics teaching to English Language learners are discussed.Item Comparing silence with verbal & non-verbal music and irrelevant speech in mathematics assessment(2012-08) Yonnone, Patrick M.; Crawford, Richard H.; Seepersad, CarolynThis study looks at the effects of silence as compared to two different types of music and one type of irrelevant speech to analyze the effects on an assessment of 4 categories of mathematical questions. The hypothesis tested was that students would perform best when subject to no distraction (silence), followed closely by non-verbal music (dubstep), while verbal music (Rap) and irrelevant self-speech (repeating the word ‘za’) would result in a decrease in performance. The hypothesis was not found to be statistically significant, but a general trend supporting the hypothesis was present and found to be consistent with similar research.Item Continua which are G-like for multiple graphs G(2005-05) Peterson, Kimberly R.; Lewis, Ira W.; Byerly, Robert E.In this thesis, different types of continua and the relationshiops between them will be considered.Item DIFFERENCES IN DEVELOPMENTAL EDUCATION ENROLLMENT AND PERFORMANCE AT TEXAS 4-YEAR UNIVERSITIES: A MULTIYEAR, STATEWIDE STUDY(2017-03-21) Priesmeyer, Kimberly; Slate, John R.; Moore, George W.; Lunenburg, Frederick C.Purpose The purpose of this journal-ready dissertation was to analyze the numbers and percentages of students enrolled in developmental education in reading, mathematics, and writing at 4-year universities in Texas from the 2002-2003 through the 2009-2010 academic years. In addition, students who were enrolled in developmental education in reading, mathematics, and writing and who then completed a college-level course were analyzed. Specifically, the differences from the 2002-2003 to the 2009-2010 academic years were examined. The multiple academic years analyzed determined which trends were present in numbers and percentages of developmental education students in reading, mathematics, and writing at 4-year universities in Texas. Method A longitudinal, exploratory investigation was used herein (Johnson, 2001). Archival data were downloaded and analyzed from the Texas Higher Education Board Interactive Accountability System in each of the three empirical studies in this journal-ready dissertation. Specifically, archival data were obtained for the 2002-2003 through the 2009-2010 academic years for the numbers and percentages of students enrolled in developmental education in reading, mathematics, and writing at Texas 4-year universities. Findings Statistically significant differences were present in all academic years for students enrolled in developmental education in reading. Numbers and percentages of students enrolled decreased, and students who completed a college-level course in reading increased. Statistically significant differences were present for numbers of students enrolled in developmental education in mathematics and for percentages of students who completed a college-level course in mathematics. Both the numbers of students enrolled and the percentages of students who completed a college-level course in mathematics increased. However, a statistically significant difference was not present for percentages of students enrolled in developmental education in mathematics. Statistically significant differences were present for percentages of students enrolled in developmental education in writing and for percentages of students who completed a college-level course in writing. The percentages of students enrolled decreased and the percentages of students who completed a college-level course in writing increased. However, a statistically significant difference was not present for numbers of students enrolled in developmental education in writing. The numbers of students remained nearly the same over the years of the study.Item Differences in Teacher and Student Characteristics by Accountability Ratings: A Texas Statewide Multiyear Study(2017-05-09) Moreno, Samson A.; Slate, John R.; Martinez-Garcia, CynthiaPurpose Four purposes were present in this journal-ready dissertation. The first purpose was to examine the degree to which the percentage of beginning teachers in traditionally configured elementary, middle, and secondary Texas schools differed as a function of two distinction designations (i.e., Academic Achievement in Reading/English Language Arts and Academic Achievement in Mathematics). The second purpose was to determine the extent to which differences were present in student ethnic/racial enrollment as a function of two distinction designations for traditionally configured elementary, middle, and secondary Texas schools. The third purpose was to ascertain whether trends were present in the percentage of beginning teachers and student ethnic/racial enrollment with respect to distinction designations in reading and in mathematics. The final purpose was to determine the degree to which prior trends established by Martinez-Garcia and Slate (2010, 2012a, 2012b), Moreno and Slate (2015), and Lopez and Slate (2014) were commensurate with the 2011-2012 through the 2014-2015 school years that were examined in this study. Method A non-experimental causal-comparative research design was used in this study. Archival quantitative data were obtained and analyzed from the Texas Academic Performance Reports for the 2012-2013 through the 2015-2016 school years. Only data from traditionally configured public elementary, middle, and high schools were analyzed. Inferential statistical procedures were calculated to determine the degree to which the percentages of beginning teachers and student ethnicity/race enrollment percentages differed between two distinction designations (i.e., Academic Achievement in Reading/English Language Arts and Academic Achievement in Mathematics). Findings Statistically significant differences were present in the percentage of beginning teachers between the two different distinction designations. Higher percentages of beginning teachers were present in schools that did not meet the two distinction designations than in schools that did meet the two distinction designations. With respect to student enrollment percentages by ethnicity/race, higher percentages of Asian students and lower percentages of Black students, Hispanic students, and White students were present at schools that met the two distinction designations. Results from this study were congruent with much of the recent empirical literature. Implications for policy and recommendations for research were provided.Item Differences in the college-readiness rates of English Language Learners by gender, economic status, and ethnicity/race: A Texas statewide, multiyear investigation(2017-09-25) Resilla, Clare Amparito; Slate, John R.Purpose The purpose of this journal-ready dissertation was to determine the degree to which differences were present in reading, mathematics, and both subjects college-readiness for English Language Learners who were enrolled in Texas high schools. In the first investigation, the extent to which English Language Learner boys differ in their college-readiness from English Language Learner girls was addressed. In the second study, the degree to which college-readiness differed by the economic status of English Language Learners was ascertained. Finally, in the third investigation, the extent to which college-readiness differed by the ethnicity/race of English Language Learners was determined. In each of these three empirical investigations, eight years of Texas statewide public school data were analyzed. Through this multiyear analysis, the degree to which trends were present in college-readiness of English Language Learners as a function of their gender, economic status, and ethnicity/race was determined. Method A non-experimental, causal-comparative research design (Creswell, 2009) was used in this study. Analyzed were archival data from the Texas Education Agency Public Education Information Management System for the 2004-2005 through the 2010-2011 school years. Independent variables were gender, economic status, and the ethnicity/race of Texas English Language Learners and the dependent variables were the reading, mathematics, and both subjects college-readiness performance. Findings With respect to gender, English Language Learner girls outperformed English Language Learner boys in reading college-readiness and in both subjects college-readiness, whereas English Language Learner boys outperformed English Language Learner girls in mathematics college-readiness. Regarding economic status, English Language Learners who were economically disadvantaged had lower college-readiness in reading, mathematics, and in both subjects than English Language Learners who were not economically disadvantaged. Concerning ethnicity/race, Asian English Language Learner had higher college-readiness in all three areas than did White, Hispanic, and Black English Language Learners. Of note was that no White English Language Learners in Texas were college-ready in any of the three areas in any of the 7 school years and that low percentages of English Language Learners were college-ready. Results were consistent across the 7 years of school data that were analyzed. Implications for policy and recommendations for research were provided.Item Effects of explicit, strategic teacher directed instruction with iPad application practice on the multiplication fact performance of 5th grade students with learning disabilities(2014-05) Ok, Min Wook; Bryant, Diane PedrottyIt is critical that students develop computational skills with basic facts to attain more advanced mathematical skills (e.g., algebra and fractions). A limited ability in accuracy and fluency with basic facts by students with learning disabilities (LD) who have Individualized Education Program (IEP) goals in mathematics can hinder their performance with more advanced mathematical skills. Thus, it is imperative to provide effective instruction to help students with LD to improve their basic fact skills. Explicit, strategic instruction has been highly recommended as an effective method for helping students with LD to improve basic fact skills. In addition, recent studies reported tablet computers such as iPads have potential for teaching basic fact skills. Thus, the purpose of this study was to investigate the effects of explicit, strategic teacher-directed instruction with iPad application practice on the multiplication fact performance of 5th grade students with LD. A single-case, multiple probe design across participants was applied for this study. Four 5th grade students with LD who had IEP goals in mathematics received fifteen 1:1 intervention sessions in multiplication facts (×4s and ×8s). Digits correct per minute in daily probes, use of a doubling strategy in strategy usage tests, and perspectives of students toward the intervention were measured. Results showed that all students improved their performance with multiplication fact proficiency; one student achieved the mastery level while the three other students approached mastery. All students also maintained the intervention gains, two weeks following the intervention. Additional findings showed that students increased their use of the doubling strategy to solve facts and were able to answer facts automatically following the intervention. Social validity interviews revealed that the intervention was viewed favorably by all students by their expression of positive perspectives toward using the doubling strategy and an iPad application to practice.Item Effects of rephrasing word problems on sixth-grade ESL and native English-speaking students' mathematics performance and attitudes(Texas Tech University, 1998-12) Tan, JiangOne hundred and four sixth-grade students, 52 native English-speaking and 52 English as a Second Language (ESL) students, participated in this experimental study. The purpose of the study was to investigate the effects of native language and rephrasing of mathematics word-problems on their performance on mathematics word-problem solving and attitude toward mathematical tasks. It was predicted that rephrasing mathematics wordproblems, by replacing low-frequency vocabularies and restructuring complex sentences to make the problems easy to understand, would positively affect students' performance on the problems and change their attitude toward mathematical tasks. It was also predicted that the enhancing effects of rephrasing of word-problems would be more profound among ESL students than native-English-speaking students. The enhancing effect of rephrasing, as predicted, was evidenced in the study in which students working with the revised version of the mathematics word-problems outperformed those who working with the original version of problems drawn from mathematics textbooks. As revealed in the result of the study, the native Englishspeaking students performed better than the ESL students on the mathematics test. Not supported by the study, however, the interaction effect between native language and rephrasing of word-problems that rephrasing should have had a stronger effect on ESL students than it did for the native English-speaking students. Opposite to the prediction, native English-speaking students working with the revised version of the test performed significantly better than control group students working with the original version. Although ESL students working with the revised version of the test had better score than those working on the original version, they did not perform significantly better than the other group. The pattern of the difference was explained in terms of anguage proficiency of Englishspeaking and ESL students. It was postulated that the rephrasing of the word-problems did not reduce the language difficulty level that was appropriate to some ESL students, especially those who were at the beginning level of a ESL program, but rephrasing benefited native English speaking students who had problems understanding original mathematics word-problems. This explanation implies that extra attention should be given to students' language proficiency in future research.Item Engaging elementary students in active learning through engineering : methods, observations and outcomes(2014-08) Pearce, Logan Anthony; Petrosino, Anthony J. (Anthony Joseph), 1961-; Barufaldi, JamesEngineering as a pedagogical tool for teaching content and driving student intellectual development is often confined to secondary school grades – middle and high school students. The goal of this work is to explore the feasibility of incorporating engineering, in the form of engineering design challenges, into elementary grade levels. The hypothesis is that engineering design challenges can be made to be age appropriate for elementary students, specifically 1st grade students, without sacrificing elements which make them effective pedagogical tools. This hypothesis was tested through the designing of an engineering design challenge for 1st grade students, which was then taught to a group of elementary students, whose responses were analyzed for desired outcomes indicating effectiveness. The design challenge was demonstrated to be engaging, effective, and feasible for the group of elementary students participating in the research. Students were observed to display engineering habits of mind, an understanding of cause and effect, systems thinking, and a basic understanding of science content through participation in the design challenge. Aspects of the design challenge which were not effective or age appropriate are discussed in this work, and recommendations for further modification of the design challenge to better accommodate elementary students is given.