Browsing by Subject "mathematics"
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Item A hemodynamic modelling of the blood circulationShrestha, Maha LaxmiItem A Self-regulated Learning Intervention for Developmental Mathematics Students at a Community College: Effects of Study Journals on Achievement and Study Habits(2014-03-04) Travis, Jennifer LynnSelf-regulated learners continually monitor and adjust the learning process through a recursive loop of forethought, learning enactment, and reflection. The literature review for this study used a systematic approach with defined criteria to evaluate the effects of self-regulated learning interventions for college students. The review revealed a shortage of rigorous achievement-based research in authentic settings. This study evaluated a study-journaling intervention for developmental mathematics students at a large urban community college. Two weekly study journal worksheets were designed, based on self-regulated learning theory. In each of nine pairs of intact classes, one class was randomly assigned to the treatment (study journal) condition and the other to control. The mixed methods research design had two strands: a confirmatory strand that evaluated the intervention?s effect, and an exploratory strand that sought information about the students? study habits. The statistical analysis had two phases: propensity score matching to strategically trim the groups so they had similar distributions of starting characteristics, and logistic regression to estimate the intervention?s effect on binary variables representing course success and final exam success. Departing students were counted among the unsuccessful. Due to implementation shortcomings, the original sample (117 treatment, 140 control) was replaced by a modified sample (60 treatment, 77 control). Propensity score matching trimmed this sample further (54 treatment, 54 control). Control students experienced significantly higher course success rates and slightly higher final exam success rates. Treatment students were significantly more likely to leave the class than control students (odds ratio 2.94). However, qualitative data from focus groups and surveys indicated the study journals may have positively affected study habits. Taken together, the qualitative and quantitative results suggest the intervention increased students? awareness of study habit inadequacies and time constraints. This position was supported by qualitative analysis of the study journal entries. This study shows that study journals have potential to improve achievement. However, caution is advised, as the journals may also influence students to leave the class due to increased awareness of problems. Research recommendations include combining study journals with training, feedback or peer support; and collecting subsequent-semester data and data on students? reasons for departure.Item A Study of Conceptual and Mathematical Knowledge in Introductory Mechanics Courses(2013-09-09) Van Dyke, Michael DavidMuch of current physics education research involves the use of the Force Concept Inventory, commonly referred to as the FCI. The FCI is a conceptual inventory examination used to study student comprehension and learning of introductory mechanics. These studies often focus on comparisons between increases in performance on pre-course and post-course FCI results for two statistically significant samples; one using a traditional course structure or teaching method and the other using different techniques. This study contains a complete statistical analysis of the FCI in order to determine its validity as a metric for measuring course success and student learning within the context of introductory mechanics courses. All the data is from students enrolled in one particular variety of Physics 218 at Texas A&M University during the Fall 2011 semester. In particular, the analysis is done for a single statistically significant sample in order to more closely examine the relationships between the FCI, mathematics skills, and student performance. It is shown that the FCI is not a valid metric for measuring student learning within an introductory physics course and that incoming mathematics skills play a critical role in student performance.Item Alternative Versus Traditionally Certified Teachers: First Year and Preservice Elementary Mathematics Teachers(2014-04-16) Maxwell, Jonathan GThe purpose of this study was to examine differences between first year and preservice elementary mathematics teachers by certification route. First, the instructional practices of 90 first year elementary mathematics teachers were analyzed. Secondly, nine elementary mathematics teachers were interviewed concerning instructional practices. Finally, weighted effect sizes were compared to determine if differences existed between route to certification and correct responses to the mathematics portion of the Early Childhood-6^(th) grade Texas Examinations of Educator Standards (TExES) for every person who took the assessment during the year 2012. First year elementary mathematics teachers (n=90) were given an online survey about instructional practices with questions covering the topics of Assessment Use, Performance Procedures, Communicative Understanding, Making Connections and Active Learning. The survey came from the Survey of Instructional Practices, Teacher Survey for Grades K-8. The first year teachers were grouped by their route to certification. The groups were Traditional-University Based, Alternative-University Based, Alternative-Non-University Based, and Post Baccalaureate. MANOVA was utilized to determine if there were statistical differences between the responses to the five question groups along with calculating the effect sizes. The data in the study demonstrated that there was little to no difference between the uses of instructional strategies in the elementary mathematics classroom of first year teachers, no matter their route to certification. A cross-case study involving first year elementary mathematics teachers was then conducted. The findings of this study also showed that in a small sample, the teachers who were alternatively certified employed the use of manipulatives more often than the teachers who were traditionally certified and were also more knowledgeable as to why different strategies were important to use in the mathematics classroom when compared to their traditionally certified counterparts. Data from all participants who attempted the mathematics portions of the Texas Examinations of Educator Standards Generalist Early Childhood ? 6^(th) grade in 2012 were collected from the Texas Education Agency and were analyzed in two ways using the grouping variable of route to certification. First each question was treated as an independent study and analyzed by calculating the variance of the average proportion and then calculating the weighted effect size. For each question, the weighted effect sizes were compared using analog to the analysis of variance. The weighted effect sizes from the data from the Texas Education Agency on the 2012 mathematics portion of the Texas Examinations of Educator Standards, Generalists Early Childhood ? 6^(th) grade pointed out that preservice elementary mathematics teachers from alternative routes were outperformed by their traditionally certified colleagues in the areas of Mathematical Instruction, Number Concepts and Operations, Patterns and Algebra, Geometry and Measurement, Probability and Statistics, and Mathematical Processes.Item Applications of full rank factorization to solving matrix equations(1992-12) Sykes, Jeffery D.; Mathematics.In the study of matrices, we are always searching for tools which allow us to simplify our investigations. Because full rank factorizations exist for all matrices and their properties often help to simplify arguments, their uses are abundant. There exist many matrix equations for which solutions are otherwise quite difficult to find. Full rank factorizations and generalized inverses allow us to easily find solutions to many such equations. Their properties can also be used to study the diagonalization of non-square matrices and to develop conditions under which matrices are simultaneously diagonalizable. Finally, the full rank factorization can be used to derive canonical forms and other factorizations such as the singular value decomposition.Item Curriculum-Based Measurement as an Intervention: A Literature Review and Meta-Analysis(2014-04-29) Williams, Cara DeMarisA two-article dissertation format is provided. The first article is a literature review of Curriculum-based measurement (CBM) as an intervention and has three purposes: a) describe foundational components of CBM; b) explain CBM as an intervention versus an outcome measure; and c) examine connections between CBM and RtI. The second article, a meta-analytic study, addresses CBM in mathematics (CBMM) as an intervention and examines specific outcomes for students in grades K-12, including those in general education and special education, when detailed feedback was utilized, and when detailed feedback was not incorporated. The three research questions include: (a) What are the effects of implementing CBM-M as an intervention when digits correct are assessed for computation and concepts and applications? (b) What are the effects of CBM-M as an intervention when problems correct are assessed for computation and concepts and applications? and (c) What are the effects on overall mathematics achievement when CBM-M as an intervention is implemented? Upon completion of the meta-analysis, results indicated that when digits correct are assessed for computation, all students had a higher statistically significant effect when detailed feedback was utilized. More specifically, students in general education experience higher effects when detailed feedback is used, while students in special education benefit from CBM with or without detailed feedback. No studies were found for addressing concepts and applications with digits correct. When addressing problems correct for computation, all students had the most statistically significant benefit when detailed feedback was incorporated, yet students in general education had the most benefit. Much more data is needed in the area of problems correct for concepts and applications. From the data gathered, small non-statistically significant effects were found for all students without the inclusion of detailed feedback, yet a negative non-statistically significant effect was found for students in special education. Not enough data was found to assess the use of detailed feedback. In terms of overall mathematical achievement, data was only found for the inclusion of detailed feedback. Results indicated that students in general education achieve small statistically significant effects, while students in special education did not show an effect at all. Overall, using detailed feedback produced higher statistically significant effects for students in both general and special education. Most research has been conducted in the area of computation for grades 3-6. Much more research is needed in the areas of concepts and applications, overall mathematical achievement, and at the secondary grade levels. Both articles, the literature review and meta-analytic study, are discussed separately.Item Empowering and Facilitating Student Learning: An Investigation of Culturally Relevant Pedagogy for High-school Mathematics Instruction(2013-11-25) Hubert, Tarcia LashaImplementing culturally relevant pedagogy (CRP) in a mathematics classroom is often recommended by researchers as a strategy for improving mathematical achievement among underrepresented students. This study explores the effect of CRP on the mathematical achievement of underrepresented students by: 1) conducting a meta- synthesis in order to determine the effects that have been found in prior culturally relevant mathematics studies; 2) contributing to the literature on the effect by engaging high school students in a 10-day culturally relevant mathematics intervention and measuring their mathematical achievement by a pre- and post- assessment; and 3) determining students? perspectives of culturally relevant mathematics instruction by interviewing five students that participated in the culturally relevant intervention. The results of investigating CRP revealed that it has positive impacts for all students participating. Not only did CRP improve mathematics achievement among all students, but CRP also increased students?: 1) engagement in the learning process; 2) life-skills; 3) habits of learning; 4) general knowledge; 5) community advocacy; 6) attitudes; 7) and interests in mathematics. Also, the students in the study had positive perspectives of CRP and preferred CRP over traditional mathematics instruction. Broader impacts of the results from this study are also provided.Item Evaluating the effectiveness of doing mathematics warm-up problems with an agricultural context on improving mathematics performance(Texas A&M University, 2007-04-25) Jasek, Mary HelenThe purpose of this study was to evaluate one instructional activity that could be used by agricultural science teachers to improve math performance of students, grades 7- 12. The treatment group (11 schools, 218 students) used math warm-up problems that coincided with topics covered in Agriscience 101, while the control group (13 schools, 170 students) did not use contextual warm-up problems. Both groups were tested with a 30-item word problem exam. Students and teachers in each group were asked questions regarding demographics. Students and teachers in the treatment group were also asked questions related to their perceptions of the activity and TAKS-related materials. The results of the study showed no statistically significant difference in the performance of the groups. The scores for schools in the treatment group had a mean of 18.95 (SD 4.33), while the scores for schools in the control group had a mean of 20.14 (SD 2.35). Hispanic students in the treatment group outperformed all other subgroups in both experimental groups. A majority of students in the treatment group perceived the difficulty level of the warm-up problems as "neutral" (42.2%) or "easy" (29.9%) and did not enjoy doing the warm-up problems (71.8%). Over 40% of the students in the treatment group believed that the warm-up problems were "absolutely" (4.9%) or "probably" (36.8%) beneficial for improving their math skills. Teachers in the treatment group perceived their students' attitudes about doing the warm-up problems as favorable (40%) or indifferent (40%) and all perceived the warm-up problems as being "very beneficial" (33.3%) or "beneficial" (66.6%). Furthermore, teachers were almost unanimous in expressing their desire for more TAKS-related materials based on an agricultural context. In summary, this study showed that the warm-up problems activity did not significantly improve math performance overall, but seemed to have some benefits for Hispanic students.Item EXPLORING THE DEVELOPMENT OF MATHEMATICS PATTERNING SKILLS AND CONCEPTS IN YOUNG CHILDREN WHO EXPERIENCE INTEGRATED MUSIC AND MATH LESSONS(2012-04-19) Wade, Carolyn; Andrews, Nicole; Copley, Juanita; Edgar, Teresa; Watson, MargaretWade, Carolyn. “Exploring the Development of Mathematics Patterning Skills and Concepts in Young Children Who Experience Integrated Music and Math Lessons” Unpublished Doctor of Education Dissertation, University of Houston, August 2011. Abstract Research touting the positive effects of music instruction on mathematical ability is abundant. Specifically, studies have shown a causal link between listening to music and spatial temporal reasoning (Rauscher, 1994), receiving music lessons and spatial-task performance (Hetland, 2000), and music instruction and spatial cognitive abilities (Costa-Giomi, 1999). This growing body of research presents a platform upon which future studies may stand. While studies have shown the positive effects of music education on mathematics ability for students of varying ages, the result of early mathematics and music education is beneficial (Bryant-Jones, Shimmins, &Vega, 2000). In addition, many studies focus solely on the effect of music on spatial-temporal reasoning or spatial task performance. Therefore, the proposed study explores how mathematics patterning skills and concepts develop when pre-kindergarteners experience mathematics and music lessons. Since both mathematics and music present pattern generation within their learning outcomes and standards, this connection will be part of the proposed exploration. Support for combining separate disciplines comes not only from Rauscher’s studies, but also from national organizations such as NAEYC, NCTM, and MENC that promote integrated and developmentally appropriate curriculum. The research question for the study was: How are mathematics patterning skills and concepts developed when young children experience integrated mathematics and music lessons? The participants were 11 pre-kindergarteners, aged four and five, who enrolled in pre-kindergarten at a private preschool in a suburb of a major metropolitan city. The children were taught 8, 20 minute mathematics and music lessons for two weeks. Using qualitative methods, data was collected using four “windows of observation” (adapted from Clements and Sarama, 2009) and provided a comprehensive analysis of pre-kindergarteners’ patterning abilities. These four windows included: performance tasks from thePerformance Task- Pattern Path Assessment, focused observation, video-taping, and metacognitive fieldnotes. The researcher analyzed the Performance Task Pattern Path Assessment by color coding the developmental levels of the children. The remaining three sets of recorded data were analyzed by highlighting and coding recurring themes in the data collected. Commonalities and points of interest among the data were examined and discussed according to themes generated. The researcher found that Child 1 and Child 3 showed no change from the pretest to the posttest (both easily completed the color and shape pattern tasks and Child 3 also correctly completed the rhythmic pattern tasks). Child 2, Child 4, and Child 5, did have a change from the pretest to the posttest. All three demonstrated change in the same categories. Each had a change in the “Pattern Fixer”, “Pattern Extender”, and “Pattern Unit Recognizer” sections. Child 2 also showed a change in the “Numeric Patterner” section. The researcher also found that during the music and math lessons, each of the 5 children created a color and shape pattern-ABABA and AABBAABB-and read the patterns in rhythm. Additionally, each of the children (with the exception of Child 4) created a unique pattern during the lessons. The 7 themes generated from the observation before the lessons, metacognitive fieldnotes, and video-tape recording of the lessons included, “The children have a natural interest in music”, “The Use of Instruments as Non-Musical Toys Before Music and Math Lessons”, “The Children’s Natural Interest in Music was Piqued During Music and Math Lessons”, “Non-Pattern Sounds Created by the Children”, “Pattern making with color and shape”, “Reading patterns in rhythm with one-to-one correspondence”, “Unique pattern making”.Item Optimal shape design for a layered periodic structure(Texas A&M University, 2004-09-30) Flanagan, Michael BradyA multi-layered periodic structure is investigated for optimal shape design in diffraction gratings. A periodic dielectric material is used as the scattering profile for a planar incident wave. Designing optimal profiles for scattering is a type of inverse problem. The ability to fabricate such materials on the order of the wavelength of the incoming light is key for design strategies. We compute a finite element approximation on a variational setup of the forward problem. On the inverse and optimal design problem, we discuss the stability of the designs and develop computational strategies based on a level-set evolutionary approach.Item Preservice Teachers? Content Knowledge of Function Concept within a Contextual Environment(2012-10-19) Brown, IrvingThe overarching goal of this dissertation research was to develop and measure the psychometric properties of an instrument to assess preservice teachers? content knowledge of the function concept embedded in contextual problems. This goal was accomplished through two research projects described in two central chapters. Chapter II reports on the collective case study that was used to pilot test the instrument and Chapter III details the rationale used in item selection and the psychometric properties of the new instrument. Unlike existing research studies that examine a broad range of function related topics using various forms of symbolic, tabular, and graphical representations as the basis for questions and problems, this study focused solely on function problems immersed in various real world contexts. Since this is not a common approach to measuring content knowledge of the function concept, the existing instruments in published studies were not found to be suitable for this specialized purpose. The psychometric measurements of the instrument did not suggest that the instrument was valid or reliable so more research will be required to validate the instrument. However, based on the preliminary results from testing, several potential suggestions can be made to teacher educations programs. Inferences drawn from the mathematical problem-solving cognition will aid in the development and validation of future instruments to assess preservice mathematics teachers? knowledge of how to connect their knowledge mathematical concept of function to a contextual setting.Item The Achievement Gaps and Mathematics Education: An Analysis of the U.S. Political Discourse in Light of Foucault's Governmentality(2013-08-06) Indiogine, Salvatore Enrico PaoloThe research question that I posed for this investigation is how the principles of Foucault?s governmentality can shed light on the political discourse on the achievement gaps (AGs) at the federal level. The AGs have been for some years now an actively researched phenomenon in education in the U.S. as well as in the rest of the world. Many in the education profession community, politicians, social activists, researchers and others have considered the differences in educational outcomes an indication of a grave deficiency of the educational process and even of the society at large. I began this work with a review of the educational research relevant to the above mentioned research question. Then I presented my research methodology and de- scribed how obtained my data and analyzed them both qualitatively and quantitatively. The results of the analysis were discussed in the light of federal legislation, the work of Foucault on governmentality, and the relevant literature and woven into a series of narratives. Finally, I abstracted these narratives into a model for under- standing the federal policy discourse. This model consists of an intersection of eight antitheses: (1) the rgime of discipline versus the apparatuses of security, (2) the appeal to danger versus assurances of progress or even success, (3) the acknowledgement of the association between the AGs and the ?disadvantage? of the students and the disregard and even prohibition of the equalization of school funding, (4) the desire for all students to be ?equal,? but they have to be dis-aggregated, the (5) injunction of research based instruction practices imposed by an ideology-driven reform policy, (6) we expect equal outcomes by using market forces, which are known to produce a diversity of results, (7) the teacher is a ?highly qualified? professional, but also a functionary of the government, and finally (8) the claim to honor local control and school flexibility versus the unprecedented federalization and bureaucratization of the schools, which is a mirror of the contrast between the desire to establish apparatuses of security in schools and the means to establishing them through rgimes of discipline.Item Using manipulatives and visual cues with explicit vocabulary enhancement for mathematics instruction with grade three and four low achievers in bilingual classrooms(Texas A&M University, 2004-09-30) Garcia, Edith PosadasA study was conducted to assess the effects of two instructional strategies: manipulative-based instruction and visual cues in mathematics (both enhanced by explicit vocabulary enrichment) in a small group setting with young Hispanic students who are English language learners. The duration of the study was five weeks. Sixty-four third and fourth grade students were selected for participation based on their performance with problem solving items from the four release tests for 1999-2002 mathematics Texas Assessment of Academic Skills (TAAS) for third and fourth grades. A pre-assessment composed of 10 of the 13 TAAS objectives were administered. The four pre-selected objectives on which the students scored the lowest were identified for further instruction and assessment. The student population was limited to those of the original sixty-four achieving <55% overall on the pre-assessment. Following each week of instruction, a different assessment/probe was administered, for a total of 6 probes-including the initial pretest. For instruction, students were organized into three groups: 1) manipulative based instruction, 2) visual (drawings) cue instruction, and 3) no additional mathematical instruction. The students in the three groups were of equivalent mathematical ability, and every effort was made to ensure the groups had the same number of students. Pre-posttest improvement was measured with a mixed ANOVA (repeated measures, with a grouping factor), with instructional group as the grouping factor, and the pre/post assessment of math as the repeated measure. ANOVA results included non-significant progress for either grade level. Neither of the experimental groups in grades three or four showed significant improvement between the pre and post assessment. Six sequential probes also were administered throughout the five-week study. A trend analysis for the three separate groups was conducted on the probe results to evaluate growth over time; trend analyses were conducted for each individual student and then averaged for each group. For the two experimental groups, the overall improvement at third and fourth grades was minimal. Overall, gradual improvement was noted, but the progress did not consistently occur from one week to another, and the improvement trend was not linear.Item Using Mathematics Curriculum Based Measurement as an Indicator of Student Performance on State Standards(2010-07-14) Hall, Linda D.Math skills are essential to daily life, impacting a person?s ability to function at home, work, and in the community. Although reading has been the focus in recent years, many students struggle in math. The inability to master math calculation and problem solving has contributed to the rising incidence of student failure, referrals for special education evaluations, and dropout rates. Studies have shown that curriculum based measurement (CBM) is a well-established tool for formative assessment, and could potentially be used for other purposes such as a prediction of state standards test scores, however to date there are limited validity studies between mathematics CBM and standard-based assessment. This research examined a brief assessment that reported to be aligned to national curriculum standards in order to predict student performance on state standards-based mathematics curriculum, identify students at-risk of failure, and plan instruction. Evidence was gathered on the System to Enhance Educational Performance Grade 3 Focal Mathematics Assessment Instrument (STEEP3M) as a formative, universal screener. Using a sample of 337 students and 22 instructional staff, four qualities of the STEEP3M were examined: a) internal consistency and criterion related validity (concurrent); b) screening students for a multi-tiered decision-making process; c) utility for instructional planning and intervention recommendations; and d) efficiency of administration, scoring, and reporting results which were the basis of the four research questions for this study. Several optimized solutions were generated from Receiver Operator Curve (ROC) statistical analysis; however none demonstrated that the STEEP3M maximized either sensitivity or specificity. In semi-structured interviews teachers reported that they would consider using the STEEP3M, however only as a part of a decision-making rubric along with other measures. Further, teachers indicated that lessons are developed before the school year starts, more in response to the sequence of the state standards than to students? needs. While the STEEP3M was sufficiently long enough for high-stakes or criterion-referenced decisions, this study found that the test does not provide sufficient diagnostic information for multi-tiered decision-making for intervention or instructional planning. Although practical and efficient to administer, the conclusions of this study show the test does not provide sufficient information on the content domain and does not accurately classify students in need of assistance.