Dissertations / Theses on the topic 'Algebra - Intermediate'

Thesis (D.A.)--Illinois State University, 1988.
Title from title page screen, viewed Oct. 13, 2004. Dissertation Committee: Kenneth A. Retzer (chair), Lynn H. Brown, John A. Dossey, Lotus D. Hershberger, Albert D. Otto, Walter D. Pierce. Includes bibliographical references (leaves 97-102) and abstract. Also available in print.

Thesis (D.A.)--Illinois State University, 1985.
Title from title page screen, viewed June 30, 2005. Dissertation Committee: John Dossey (chair), Lawrence Eggan, Lotus Hershberger, Larry Kennedy, Albert Otto, Thomas Shilgalis. Includes bibliographical references (leaves 72-75) and abstract. Also available in print.

In Guyana, South America, the Ministry of Education seeks to provide universal, inclusive education that prepares its citizens to take their productive places in society and to creatively solve complex, real-world problems. However, with frequent national assessments that are used to place students in high school, college or into jobs, teachers resort to using familiar strategies such as lecture, recitation and test drilling. Despite their efforts, over 56% of students are failing the Grade 6 assessments, 43% failing 10th grade Mathematics and over 60% failing college algebra courses. Such performance has been linked to students’ lower academic self-concept and their negative attitudes toward mathematics aggravated by an autocratic culture that continues to view the teacher as sole authority. Subjectivist instructional strategies integrate constructivism and affect by providing a learning experience that gives children more autonomy as they solve contextually relevant algebraic problems. In a quasi-experimental study involving a treatment and control group of eighth grade students at a high school in Guyana, a modified version of the Mathematics Value Inventory was used to measure students’ attitudes towards mathematics before and after the 10-week treatment. Scores on the final examination were used to determine achievement in algebra. Forty seven students in the treatment group were guided in exploring and discovering concepts for themselves. Formal definitions were delayed until after the students experimented with relatable scenarios. Forty two students in the control group were taught using multiple opportunities to practice. Analysis was done using General Linear Models to determine the variance in achievement and attitude scores accounted for by the instructional strategies while controlling for sex, challenge index, and, pretreatment scores for attitude and achievement. The challenge index was developed to identify outside influences on students’ performance such as: travel time; whether living at home; number in household; sleepiness; noisiness; and, resource availability. Results were not all as expected but some interesting relationships surfaced between the challenges, attitudes towards mathematics and achievement scores. Ultimately it was determined that the environment in which students had to study and the challenges they faced outweighed the small gains in attitude changes for the treatment group.

Graphics calculators have become an integral part of many introductory college mathematics courses. There has been little research to show the effects of introducing technology, along with an emphasis on the interrelationships of the numeric, symbolic, graphical, and verbal forms of functions, for courses that are traditionally considered pre-college mathematics. The major purpose of this study was to determine if changes in mathematics anxiety and attitudes occurred in Intermediate Algebra classes and to determine whether these changes were dependent on age, gender of student, and experience of instructor. The relationship between beginning levels of math anxiety and successful completion of the class were also examined.All sections of Intermediate Algebra taught at Grand Valley State University during the Winter semester of 1995 participated in the study. The first week of class, 479 students completed the initial survey. The final week of class, 264 of those students completed the survey again. In addition to gender and age of student, the survey instrumentcontained questions from seven of the Fennema-Sherman Mathematics Attitudes Scales. Each scale contained 12 questions, answered on a five point Likert type scale. High scores on the questionnaire indicated a positive attitude. Students in four sections were asked open ended questions every other week. At the end of the semester, instructors were given a questionnaire to determine their perceptions of how student's attitudes and anxieties changed.MANOVA for repeated measures using SPSS was used to perform the analyses with respect to age, gender, and teacher experience, over time. Faculty responses indicated they thought attitudes and levels of math anxiety improved over the semester. Although most groups did show some improvement, no significant change occurred. The only statistically significant differences detected were in math anxiety by gender and a combination of math anxiety and attitude by age. Females had higher levels of math anxiety (N = 166, initial M = 29.96, final M = 30.80) than males (N =.98, initial M = 33.87, final M = 34.79)and while older students appeared more math anxious, they also reflected a more positive attitude about mathematics.
Department of Educational Leadership

Coteaching strategies have been implemented in many of the inclusion math classrooms in an attempt to improve the achievement of students. Math achievement continues to be a concern as reported by the National Mathematics Advisory Council in 2007. Educators and previous research reported that coteaching does not improve student achievement. The purpose of this study and the research question was designed to investigate, determine, and examine if coteaching has an impact on regular education students' achievement on an algebra assessment in the eighth grade. This concurrent mixed methods design used test data from a convenience sample of 70 eighth grade students and 6 math coteachers from a small rural middle school in a southern U.S state. The students were divided into a cotaught class (experimental) and a noncotaught class (control group). The teachers' perception and implementation of the coteaching model within the inclusive classroom was determined through interviews using a semi-structured interview guide. Students' achievement was measured based on math scores on a Basic Skills Algebra Assessment given at the beginning and end of 12 weeks. A two-way analysis of variance (ANOVA) was conducted to assess if differences exist on algebra achievement scores by group (control vs. treatment) and time (pretest vs. posttest). The results of the post hoc analysis, consisting of two independent sample t tests and two dependent sample t tests, revealed that significant mean differences did in fact exist on algebra achievement scores for only the experimental group suggesting that scores increased from pre to posttest. The interview data indicated that the teachers' perception of student learning was greater in the cotaught classroom. Evidence is provided to coteachers and administrators in support of implementing the coteaching model. It supports a change in students' attitudes and perceptions of other's differences as well as their ability to learn mathematics.

Recognition of complex events in consumer uploaded Internet videos, captured under real-world settings, has emerged as a challenging area of research across both computer vision and multimedia community. In this dissertation, we present a systematic decomposition of complex events into hierarchical components and make an in-depth analysis of how existing research are being used to cater to various levels of this hierarchy and identify three key stages where we make novel contributions, keeping complex events in focus. These are listed as follows: (a) Extraction of novel semi-global features -- firstly, we introduce a Lie-algebra based representation of dominant camera motion present while capturing videos and show how this can be used as a complementary feature for video analysis. Secondly, we propose compact clip level descriptors of a video based on covariance of appearance and motion features which we further use in a sparse coding framework to recognize realistic actions and gestures. (b) Construction of intermediate representations -- We propose an efficient probabilistic representation from low-level features computed from videos, based on Maximum Likelihood Estimates which demonstrates state of the art performance in large scale visual concept detection, and finally, (c) Modeling temporal interactions between intermediate concepts -- Using block Hankel matrices and harmonic analysis of slowly evolving Linear Dynamical Systems, we propose two new discriminative feature spaces for complex event recognition and demonstrate significantly improved recognition rates over previously proposed approaches.
Ph.D.
Doctorate
Electrical Engineering and Computing
Engineering and Computer Science
Computer Engineering

This study outlines the development and initial validation of an abbreviated instrument intended to measure motivation for mathematics of university students in developmental algebra courses. I look across many of the predominant theories on motivation with the aim of representing several of these theories as latent constructs in a single instrument that is short enough to be administered in a reasonable amount of time, but inclusive enough that it could incorporate subscales representing multiple distinct latent factors. This study answers a call by researchers expressing a need to investigate relationships between disparate theories on motivation and is a response to recent studies that have used several subscales from many published instruments in whole or in part as lengthy combined instruments to measure motivation across theories. The practice of utilizing many separate instruments to measure across theoretical frameworks may be unwieldy leading to validity concerns based on response processes, and the practice of taking individual items from separate instruments may potentially be incomplete leading to validity concerns based on the internal structure of the instrument and underrepresentation of the intended construct. To answer these concerns and develop a tool for future research, I conducted a three phase study. Phase one of this study asked experts in motivation to comment on and pick the best items from a pool of 122 items sourced from several popular previously published instruments that contained factors associated with self-determination, self-efficacy, achievement goals, and expectancy-value. The commentary by experts gave insight into item alignment with theory, and all items with at least 40% endorsement by experts proceeded to phase two. In phase two, cognitive interviews of students and instructors provided insight into the cognitive processes employed in responding to the 53 items endorsed in phase one. Two researchers coded these qualitative interview data with a grounded theory approach and quantified the data using intra-respondent matrices. Effect sizes of each code provided evidence of content validity of preferred items, and concerns over social dynamics, misrepresentation of factors associated with poor wording, and the use of words like “very much” that forced students to quantify their cognitive processes provided evidence against non-preferred items. During phase three I administered an instrument containing the surviving 34 items from phase two to 186 participants from twelve developmental algebra courses. Concerns over the broadness of the domain of mathematics led to the removal of self-efficacy and task-value items, and concerns over the abbreviated nature of the instrument led to the removal of items associated with extrinsic motivation. Concerns over the multilevel nature of achievement structured items led to their removal. Thus an exploratory and confirmatory factor analyses of the remaining 16 items representing intrinsic motivation, mastery orientations, performance orientations, and expectancy led to a four factor model that discriminated along theoretical lines and was a good fit for the data. A regression of achievement on the four latent factors from this model revealed expectancy to be the only significant predictor of achievement. With gender included as a moderating variable, performance and expectancy were both significant indicators of achievement for females, but expectancy was the only significant indicator for males. The latent factors from the instrument developed for this study had strong bivariate correlations to subscales from previously published instruments that represented similar constructs. Several sources provided evidence of content validity. Qualitative data provided evidence in the form of commentary from experts and cognitive interview data from students and instructors. A structural equation model provided evidence of validity based on relationships to other variables. For this model the dependent variable achievement was regressed upon the latent motivation variables with gender included as a moderating variable. Exploratory and confirmatory factor analyses provided validity evidence based on the internal structure. Validity based on consequences and response processes was controlled by using an anonymous process where participation was blind to instructors and researchers, and the administration of an abbreviated measure in a familiar paper and pencil face-to-face format reduced construct irrelevant variance. This process produced a four factor 16 item Motivation for Mathematics Abbreviated Instrument measuring intrinsic motivation, mastery orientation, performance orientation, and expectancy while accumulating validity evidence for three out of five sources of validity. The result of this inquiry was a psychometric instrument that may be used by researchers, practitioners, and grant writers who desire a tool to measure motivation for mathematics across several of the predominant theories on motivation.

Motivados pelos resultados do artigo [BBFK11], nosso trabalho começa analisando, no caso da álgebra de Lie afim sl(n;C), a possibilidade de se obter módulos de Verma J-imaginários, via representações análogas às feitas por Cox em [Cox05]. Inicialmente consideramos, por simplicidade, n = 2 e, só então, analisamos o caso geral. Depois, de modo análogo, estudamos os artigos [CF04] e [CF05] com o intuito de obter módulos J-intermediários de Wakimoto. Finalmente imbutimos, no caso n = 2, uma ação de álgebra de Virasoro nos módulos imaginários de Wakimoto, utilizando-nos do resultado exposto em [EFK98], em que tal problema é abordado para o caso dos módulos de Verma. Desta forma, obtemos equações análogas às de Knizhnik-Zamolodchikov (equações KZ) para os módulos imaginários de Wakimoto.
Following the results of [BBFK11], our work starts analyzing (for bsl(n;C)) if we can obtain J-imaginary Verma modules using similar representations used by Cox in [Cox05]. We did it for n = 2 and after, for the general case. The next step was the study of J-intermediate Wakimoto modules, following the ideas of [CF04] and [CF05]. To finish, for affine sl(2;C), we defined an action of Virasoro algebra on the imaginary Wakimoto modules following [EFK98] and we obtained an analogue of the KZ-equations for imaginary Wakimoto modules.

The study explored the relationship between student academic performance in an exit-level, developmental mathematics course and subsequent academic performance in a college-level mathematics course. Using an ex post facto research design, the study focused specifically on the influence of three sets of factors: (a) demographic characteristics, (b) "stopping-out," and (c) the developmental course. The criterion variables were college-level performance, defined in terms of the student's course grade, and college-level persistence, defined in terms of whether or not the student officially withdrew from the course. A convenience sample of 824 community college students who had completed both the exit-level developmental mathematics course and the entry-level college course during a three-year period from fall 1989 to summer 1992 was used for the data set; the students in the set were shown to be similar to several populations of developmental students. Discriminant function analysis indicated that the data supported the hypotheses. The discriminant function was calibrated on 364 cases randomly selected from the data set; the remainder of the cases were used to cross-validate the results. Cross-validated correct classification rates of 76.74% for academic success and 81.09% for persistence were obtained. The major conclusions of the study were: (1) Developmental course performance is a significant discriminator of college-level mathematics performance and persistence. (2) The length of time a student allows to pass between exiting the developmental course and entering the college-level course is a negatively related discriminator of both college-level performance and persistence. (3) Student age is a positively related discriminator of college-level mathematics performance. (4) The number of attempts at the developmental course is a negatively related discriminator of persistence. (5) African American completers of developmental mathematics appear to be more likely to withdraw from entry-level college mathematics than developmental completers in other ethnic groups. (6) Poor performance in exit-level developmental mathematics greatly increases the risk of failure or attrition for students in entry-level college mathematics. The implications of these results and those of several post hoc analyses were discussed in terms of their theoretical and applied contributions, the limitations of the study were detailed, and suggestions made for future research.
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La validation des systèmes critiques réalistes nécessite d'être capable de modéliser et de vérifier formellement des données complexes, du parallélisme asynchrone, et du temps-réel simultanément. Des langages de haut-niveau, comme ceux qui héritent des fondations théoriques des algèbres de processus, ont une syntaxe concise et une grande expressivité pour représenter ces aspects. Cependant, ils disposent de peu d'outils logiciels permettant d'appliquer des algorithmes efficaces du model-checking. Néanmoins, de tels outils existent pour des modèles graphiques, de niveau plus bas, tels que les automates temporisés (par exemple UPPAAL) et les réseaux de Petri temporisés (par exemple TINA). Les modèles intermédiaires sont un moyen pour combler le fossé qui sépare les langages des modèles graphiques. Par exemple, NTIF (New Technology Intermediate Format) a été proposé pour représenter des processus séquentiels non temporisés qui manipulent des données complexes. Dans cette thèse, nous proposons un nouveau modèle nommé ATLANTIF, qui enrichit NTIF de constructions temps-réel et de compositions parallèles de processus séquentiels. Leur synchronisation est exprimée d'une manière simple et intuitive par la nouvelle notion de synchroniseur. Nous montrons qu'ATLANTIF est capable d'exprimer les constructions principales des langages de haut niveau. Nous présentons aussi des traducteurs d'ATLANTIF vers des automates temporisés (pour la vérification avec UPPAAL) et vers des réseaux de Petri temporisés (pour la vérification avec TINA). Ainsi, ATLANTIF étend la classe des systèmes qui peuvent en pratique être vérifiés formellement, ce que nous illustrons par un exemple.