Dissertations / Theses on the topic 'Students – Rating of – Mathematical models'

Thesis (Ph. D.)--Illinois State University, 2001.
Title from title page screen, viewed March 30, 2006. Dissertation Committee: Graham A. Jones, James Cottrill (co-chairs), Linnea Sennott. Includes bibliographical references (leaves 107-111) and abstract. Also available in print.

Approved for public release; distribution is unlimited
The purpose of this thesis is to provide a workbook to accompany the current textbook, A First Course in Mathematical Modeling. The workbook will offer basic reviews of each lesson followed by detailed examples of how to work each model. Topics covered include difference equations, systems of difference equations, Lanchester equations, graphical analysis, proportionality, geometric similarity, model fitting, Monte Carlo simulation, and probabilistic and deterministic behaviors. The thesis will also provide a modeling toolkit for the DA student upon graduation. The toolkit will present graduates simple instructions and multiple modeling templates they can take with them upon graduation and use to solve real-world modeling problems in the field. Templates in the toolkit cover decision theory, discrete dynamic systems, expected value, Lanchester models, and two-person games.
Outstanding Thesis

The attainment of high grades on the Victorian Certificate of Education (VCE) is critical to the future study and employment prospects of many Australian adolescents. Thus it is important to understand the factors that contribute to performance in the VCE. The aims of this study were twofold: the main aim was to test competing models of academic performance, subsuming a range of situational and dispositional variables based on a) self-efficacy theory, b) target and purpose goals, c) cognitive skills and self-regulatory strategies, and d) positive psychology. These models were each tested in terms of English performance and mathematics performance as these units contribute proportionally the most to overall VCE scores. In order to study whether pressures peculiar to the VCE impact on performance, the competing models were tested in a sample of Victorian students prior to the VCE (year 10) and then during the VCE (year 11). A preliminary study was conducted in order to develop and test four scales required for use in the major study, using an independent sample of 302 year nine students. The results indicated that these new scales were psychometrically reliable and valid. Three-hundred and seven Australian students participated in the year 10 and 11 study. These students were successively asked to provide their final years 9, 10 and 11 English and mathematics grades at times one, three and five and to complete a series of questionnaires at times two and four. Results of the year 10 study indicated that models based on self-efficacy theory were the best predictors of both English and mathematics performance, with high past grades, high self-efficacy and low anxiety contributing most to performance. While the year 10 self-efficacy models, target goal models, positive psychology models, self-regulatory models and cognitive skill based models were each robust in the sample in year 11, a substantial increase in explained variance was observed from year 10 to year 11 in the purpose goal models. Results indicated that students’ mastery goals and their performance-approach goals became substantially more predictive in the VCE than they were prior to the VCE. This result can be taken to suggest that these students responded in very instrumental ways to the pressures, and importance, of their VCE. An integrated model based on a combination of the variables from the competing models was also tested in the VCE. Results showed that these models were comparable, both in English and mathematics, to the self-efficacy models, but explained less variance than the purpose goal models. Thus in terms of parsimony the integrated models were not preferred. The implications of these results in terms of teaching practices and school counseling practices are discussed. It is recommended that students be encouraged to maintain a positive outlook in relation to their schoolwork and that they be encouraged to set their VCE goals in terms of a combination of self-referenced (mastery) and other-referenced (performance-approach) goals.

Planning and optimization of TV advertising space in the area of the Czech media market requires a knowledge of features of the problem and systems that are able to suggest the best results from data taken from measurement of TV audience, which is complex and demands special capacity. These results should be obtained (calculated) by using mathematical optimization models. Results depend on the objectives of company. The content of this thesis is to create and implement mathematical models, which serve to solve practical problems about planning advertising space and commercial blocks. The work deals with the characteristics of the television media market, audience measurement, the factors that influence the ratings, as well as an examination of other indicators that are necessary for the planning and optimization of TV advertising. Besides familiarizing the reader with the operations of buying advertising space, this paper`s goal is to demonstrate newly created mathematical models that are applicable to the work of TV channels, media agencies or other companies, which deal with the optimization of the television media market.

Research attention on word of mouth (WOM) communication is growing in necessity and popularity as recent studies continue to confirm that WOM has a significant effect on consumer and organisational decision-making and buying behaviour. Much of the theory generated from this field of communications research has been based on product purchase situations that take place in the United States. More recent developments in the stream of research have begun to address WOM in service contexts and also driven a need to test the reliability of previous works in other countries and cultures. The research problem of this thesis emerged from such needs to further develop WOM theory and is defined by two key statements: (i) How does perceived source credibility and the content (message) of personal communication shape and determine the nature of a WOM system? (ii) What likely influence does culture have on a WOM system? The WOM system conceptualised within this thesis refers to a network of actors in which, personal, verbal, face to face communication occurs. It also refers to the nature of the information exchanged and how these messages determine which actors within the system participate. Addressing the need for further research into service-based contexts, the industry of export education was identified as an ideal environment in which to investigate the problem. In particular, international students (current and potential) were interviewed and surveyed on how WOM is used to gather information to make a decision on where to study. A predictive model of referral source selection is developed as the significant contribution to theory resulting from the qualitative and quantitative research employed in the methodology. The qualitative research was exploratory in nature and designed to understand the decision-making process international students went through before making a choice on their study destination. In depth interviews confirmed that WOM was used frequently throughout this process and identified the important pieces of information sought after by students and which sources the students consulted to obtain the information. International students are concerned about the international recognition of a university, teaching styles, tuition fees, graduate prospects and how compatible the lifestyle of the host country is for them amongst many issues. They consult a variety of personal sources including family, friends, alumni, university agents and even their school teachers. The main quantitative study in this thesis surveyed 420 university students from China and Malaysia and was designed to provide theory verification for the WOM system and explore potential impacts of culture on this system. Firstly, four common WOM themes were identified from all of the content exchanged through WOM between students and their referral sources. These themes are grouped as; informational messages, comparative messages, personal perspectives and guidance messages. The WOM system was then depicted as a predictive model of referral source selection based on which WOM themes are exchanged between actors. As consumers progress through a structured decision-making process, their information requirements (WOM themes) change and so do the sources selected to deliver the information. Secondly, important differences in WOM behaviour emerged between the Chinese and Malaysian samples. Although students from both countries are equally influenced by personal sources of communication, Malaysians considered alumni friends and parent/family sources to be more influential than the Chinese. Whereas the Chinese preferred talking with school teachers and close friends to help in their decisions. These findings added credible evidence of national culture effects to the predictive model of source selection. The thesis concludes by addressing limitations in the research - largely, that the study failed to produce evidence of cultural value dimensions impacting on the WOM system. The Chinese cultural value framework employed was well justified as an appropriate measure however, there were no equivalent measurements of Malaysian cultural values and the study was conducted on a limited convenience sample, making results difficult to generalise through Chinese and Malaysian populations. Further research was then suggested to address these limitations.

Understanding base-ten numbers is one of the most important mathematics topics taught in the primary school, and yet also one of the most difficult to teach and to learn. Research shows that many children have inaccurate or faulty number conceptions, and use rote-learned procedures with little regard for quantities represented by mathematical symbols. Base-ten blocks are widely used to teach place-value concepts, but children often do not perceive the links between numbers, symbols, and models. Software has also been suggested as a means of improving children's development of these links but there is little research on its efficacy. Sixteen Queensland Year 3 students worked cooperatively with the researcher for 10 daily sessions, in 4 groups of 4 students of either high or low mathematical achievement level, on tasks introducing the hundreds place. Two groups used physical base-ten blocks and two used place-value software incorporating electronic base-ten blocks. Individual interviews assessed participants' place-value understanding before and after teaching sessions. Data sources were videotapes of interviews and teaching sessions, field notes, workbooks, and software audit trails, analysed using a grounded theory method. There was little difference evident in learning by students using either physical or electronic blocks. Many errors related to the "face-value" construct, counting and handling errors, and a lack of knowledge of base-ten rules were evident. Several students trusted the counting of blocks to reveal number relationships. The study failed to confirm several reported schemes describing children's conceptual structures for multidigit numbers. Many participants demonstrated a preference for grouping or counting approaches, but not stable mental models characterising their thinking about numbers generally. The independent-place construct is proposed to explain evidence in both the study and the literature that shows students making single-dimensional associations between a place, a set of number words, and a digit, rather than taking account of groups of 10. Feedback received in the two conditions differed greatly. Electronic feedback was more positive and accurate than feedback from blocks, and reduced the need for human-based feedback. Primary teachers are urged to monitor students' use of base-ten blocks closely, and to challenge faulty number conceptions by asking appropriate questions.

by Kwok Yiu Keung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.
Includes bibliographical references (leaves 102-109).
ACKNOWLEDGMENTS --- p.i
ABSTRACT --- p.iii
LISTS OF FIGURES --- p.vii
LISTS OF TABLES --- p.viii
Chapter Chapter 1: --- INTRODUCTION --- p.1
Chapter Chapter 2: --- LITERATURE REVIEW --- p.3
Need for and Relevance of Research on Proposed Topic --- p.3
Significance of this Research --- p.3
Different Views of Sales Performance --- p.4
Situation Approach --- p.5
Attitudinal Approach --- p.6
Modeled Instruction Approach --- p.7
Antecedents and Consequences of Salesperson's Sales Performance --- p.8
Antecedents of Sales Performance --- p.9
Consequences of Sales Performance --- p.13
Antecedents and Consequences of Sales Performance --- p.23
Summary --- p.26
Chapter Chapter 3: --- THE PROPOSED MODEL AND RESEARCH HYPOTHESES --- p.27
A Model of Sales Performance of Salesperson --- p.27
Conceptualization and Hypotheses --- p.30
Summary --- p.38
Chapter Chapter 4: --- RESEARCH METHODOLOGY --- p.39
Measurement Scales --- p.39
Data Collection --- p.41
Reliability --- p.43
Analysis of the Model --- p.45
Structural Equation Modeling --- p.45
The Measurement Model --- p.45
Model Notations --- p.49
Summary --- p.50
Chapter Chapter 5: --- RESULTS FROM THE ANALYSIS --- p.51
Scale Analysis --- p.51
Reliability --- p.56
Structural Equation Modeling --- p.57
Full Model Evaluation --- p.57
Reduced Model Evaluation --- p.59
Summary --- p.65
Chapter Chapter 6: --- DISCUSSION AND CONCLUSION --- p.66
Major Findings --- p.66
Sales Performance and Its Antecedents --- p.66
Sales Performance and Its Consequences --- p.68
Contributions of the Research --- p.69
Conceptual Contribution --- p.69
Managerial Contribution --- p.69
Limitations --- p.75
Directions for Future Research --- p.75
Extension of the Conceptual Model --- p.75
Sample Quality --- p.76
Methodology and Measurement --- p.77
APPENDIX 1: Cross Cultural Translation --- p.78
APPENDIX 2: English and Chinese Versions of Questionnaire --- p.86
APPENDIX 3: Companies Participated in the Survey --- p.100
APPENDIX 4: Description of Sample --- p.101
REFERENCES --- p.102

The aim of this thesis was to investigate the use of effect sizes to report the results of statistical credit rating models in a more practical way. Rating systems in the form of statistical probability models like logistic regression models are used to forecast the behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers. Therefore, model results were reported in terms of statistical significance as well as business language (practical significance), which business experts can understand and interpret. In this thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into standardised and measurable units, which can be reported practically. These effect sizes indicated strength of correlations between variables, contribution of variables to the odds of defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability between high and low risk customers.
Statistics
M. Sc. (Statistics)

Tinto’s (1993) Theory of Individual Departure from Institutions of Higher Education conceptualized the decision making process students navigate when committing to institutions of higher education and persisting to graduation. Transfer students are gaining the attention of administrators and policy-makers because of the high level of transfer activity in higher education. Many of these students face a uniquely difficult transition when moving from one institutional environment to another. The phenomenon, known as transfer shock, is the overall integration and adaptation difficultly that transfer students face (Hills, 1965). Since previous institution cumulative grade point average (GPA) is a criterion used in transfer admissions decisions, it was studied. Six-year graduation totals were also observed in the study because they indicates student commitment to their institution and goals toward graduation. The purpose of this study was to examine Ball State University entering transfer students and how to predict post-transfer GPA and six-year graduation based on previous institution cumulative grade point average, age, sex, previous institution type, and BSU college. Regression analysis was used to make predictive models for post-transfer GPA and six-year graduation using the observed variables (i.e., previous institution cumulative GPA, age, sex, previous institution type, and BSU college). The sample consisted of 1,857 entering transfer students at Ball State University, a state-assisted, residential university with high research activity in Muncie, Indiana. Previous institution cumulative GPA averaged 2.994 while the average post-transfer GPA was 1.681. Nearly 60% of the sample achieved six-year graduation. The results of the revised model for predicting post-transfer GPA found only previous institution cumulative GPA, age, previous institution type, and whether or not the student was in CAST to be statistically significant predictors. The model used to predict six-year graduation found previous institution type, age, sex, previous institution type, and three of the BSU colleges (CAST, CCIM, and TC) to be statistically significant predictors. When applied to the data, the six-year graduation prediction model correctly predicted six-year graduation at a rate of 79.6% and had an overall correct prediction percentage of 63.6% of the time. Suggestions for practice and recommendations for future research were included.
Department of Educational Studies

This study examines how mathematical modeling activities within a collaborative group impact students' `value creation' through mathematics. Creating `value' in this study means to apply one's knowledge in a way that benefits the individual and society, and the notion of `value' was adopted from Makiguchi's theory of `value creation' (1930/1989). With a unified framework of Makiguchi's theory of `value', mathematical disposition, and identity, the study identified three aspects of value-beauty, gains, and social good-using observable evidence of mathematical disposition, identity, and sense of community. Sixty students who enrolled in a college algebra course participated in the study. The results showed significant changes in students' mathematics dispositions after engaging in the modeling activities. Analyses of students' written responses and interview data demonstrated that the modeling tasks associated with students' personal data and social interactions within a group contributed to students' developing their identity as doers of mathematics and creating social value. The instructional model aimed to balance the cognitive aspect and the affective skills of learning mathematics in a way that would allow students to connect mathematical concepts to their personal lives and social lives. As a result of the analysis of this study, there emerged a holistic view of the classroom as it reflects the Makiguchi's educational philosophy. Lastly, implications of this study for research and teaching are discussed.

This study uses a discourse analysis from the perspectives of James Paul Gee (2005; 1999) in order to establish a socio-situated view of why grade 10 students often experience difficulties in representing mathematical word problems into appropriate equations and expressions that enable a solution to the problems. A discursive methodology was used to throw light on the difficulties that students experience that was different from the perspectives adopted previously, viz. from a view of the structure of the problems, from a pedagogic point of view and a cognitive understanding. An initial case study in one school in which four students were selected revealed that a master model existed that students were enacting when doing and talking about their experiences with word problems, viz. that word problems are obfuscatory. This master model rendered the students relatively mathematically helpless within a Discourse of school mathematics word problems. In order to more fully understand these findings an extended study was set up in which the methodology and analytic framework were refined. This extended study saw four students at each of three different sites selected to participate. The findings of this extended study were that the students enacting a situated Discourse model were more enabled within the Discourse of school mathematics word problems, whilst those enacting a deficit Discourse model were either peripheral or outside of that Discourse. This study contributes in that the constructs for the phenomena and the analytic tools within the context of school mathematics needed to be pioneered, adapted and refined over a period of time to address aspects particular to school mathematics. This resulted in a view from a socio-situated perspective which saw a shift in seeing what students do with the problem to what students do in the social setting associated with the problem. From this shift in focus came a new understanding of student difficulties with word problems that gave rise to a sub-Discourse within the Discourse surrounding school mathematics word problems, and students finding themselves in this sub-Discourse becoming marginalised through enacting a deficit Discourse model because they are unable to ascribe to the success model, or situated Discourse model.

With the increasing popularity and competition in professional basketball in the past decade, data driven decision has emerged as a big competitive edge. The advent of high frequency player tracking data from SportVU has enabled a rigorous analysis of player abilities and interactions that was not possible before. The tracking data records two-dimensional x-y coordinates of 10 players on the court as well as the x-y-z coordinates of the ball at a resolution of 25 frames per second, yielding over 1 billion space-time observations over the course of a full season. This dissertation offers a collection of spatio-temporal models and player evaluation metrics that provide insight into the player interactions and their performance, hence allowing the teams to make better decisions. Conventional approaches to simulate matches have ignored that in basketball the dynamics of ball movement is very sensitive to the lineups on the court and unique identities of players on both offense and defense sides. In chapter 2, we propose the simulation infrastructure that can bridge the gap between player identity and team level network. We model the progression of a basketball match using a probabilistic graphical model. We model every touch event in a game as a sequence of transitions between discrete states. We treat the progression of a match as a graph, where each node represents the network structure of players on the court, their actions, events, etc., and edges denote possible moves in the game flow. Our results show that either changes in the team lineup or changes in the opponent team lineup significantly affects the dynamics of a match progression. Evaluation on the match data for the 2013-16 NBA season suggests that the graphical model approach is appropriate for modeling a basketball match. NBA teams value players who can ``stretch'' the floor, i.e. create space on the court by drawing their defender(s) closer to themselves. Clearly, this ability to attract defenders varies across players, and furthermore, this effect may also vary by the court location of the offensive player, and whether or not the player is the ball handler. For instance, a ball-handler near the basket attracts a defender more when compared to a non ball-handler at the 3 point line. This has a significant effect on the defensive assignment. This is particularly important because defensive assignment has become the cornerstone of all tracking data based player evaluation models. In chapter 3, we propose a new model to learn player and court location specific offensive attraction. We show that offensive players indeed have varying ability to attract the defender in different parts of the court. Using this metric, teams can evaluate players to construct a roster or lineup which maximizes spacing. We also improve upon the existing defensive matchup inference algorithm for SportVU data. While the ultimate goal of the offense is to shoot the ball, the strategy lies in creating good shot opportunities. Offensive play event detection has been a topic of research interest. Current research in this area have used a supervised learning approach to detect and classify such events. We took an unsupervised learning approach to detect these events. This has two inherent benefits: first, there is no need for pretagged data to learn identifying these events which is a lobor intensive and error prone task; second, an unsupervised approach allows us to detect events that has not been tagged yet i.e. novel events. We use a HMM based approach to detect these events at any point in the time during a possession by specifying the functional form of the prior distribution on the player movement data. We test our framework on detecting ball screen, post up, and drive. However, it can be easily extended to events like isolation or a new event that has certain distinct defensive matchup or player movement feature compared to a non event. This is the topic for chapter 4. Accurate estimation of the offensive and the defensive abilities of players in the NBA plays a crucial role in player selection and ranking. A typical approach to estimate players' defensive and offensive abilities is to learn the defensive assignment for each shot and then use a random effects model to estimate the offensive and defensive abilities for each player. The scalar estimate from the random effects model can then be used to rank player. In this approach, a shot has a binary outcome, either it is made or it is a miss. This approach is not able to take advantage of the “quality” of the shot trajectory. In chapter 5, we propose a new method for ranking players that infers the quality of a shot trajectory using a deep recurrent neural network, and then uses this quality measure in a random effects model to rank players taking defensive matchup into account. We show that the quality information significantly improves the player ranking. We also show that including the quality of shots increases the separation between the learned random effect coefficients, and thus, allows for a better differentiation of player abilities. Further, we show that we are able to infer changes in the player's ability on a game-by-game basis when using a trajectory based model. A shot based model does not have enough information to detect changes in player's ability on a game-by-game basis. A good defensive player prevents its opponent from making a shot, attempting a good shot, making an easy pass, or scoring events, eventually leading to wasted shot clock time. The salient feature here is that a good defender prevents events. Consequently, event driven metrics, such as box scores, cannot measure defensive abilities. Conventional wisdom in basketball is that ``pesky'' defenders continuously maintain a close distance to the ball handler. A closely guarded offensive player is less likely to take or make a shot, less likely to pass, and more likely to lose the ball. In chapter 6, we introduce Defensive Efficiency Rating (DER), a new statistic that measures the defensive effectiveness of a player. DER is the effective distance a defender maintains with the ball handler during an interaction where we control for the identity and wingspan of the the defender, the shot efficiency of the ball handler, and the zone on the court. DER allows us to quantify the quality of defensive interaction without being limited by the occurrence of discrete and infrequent events like shots and rebounds. We show that the ranking from this statistic naturally picks out defenders known to perform well in particular zones.

In this dissertation a study will be made of university performance in the Science Faculty of the University of Natal, Durban. In particular, we will develop models that can be used to predict the success rate of a student based on his or her matriculation results. These models will prove useful for selecting students to universities. They may also be used to assist sponsors, bursars and donors in allocating funds to deserving students. In addition, these models may be used to identify students who might experience difficulties in their studies at university.
Thesis (M.Sc.)-University of Natal, Durban, 1994.

Indiana University-Purdue University Indianapolis (IUPUI)
Background: Recent literature on medical professionalism claims that self-awareness and the ability to reflect upon one’s experiences is a critical component of professionalism; however there is a paucity of empirical evidence to support this claim. This study employed a mixed methods approach to explore the utility of reflective writing and self- and peer assessments in explaining professionalism lapses among medical students. Methods: A retrospective case-control study was conducted using students from Indiana University School of Medicine (IUSM) who had been disciplined for unprofessional behavior between 2006-2013 (case group; n=70). A randomly selected control group (n=230) was used for comparison. Reflective ability was assessed using a validated rubric to score students’ professionalism journals. Mean reflection scores and assessment scores were compared using t-tests. Logistic regression analysis was used to determine the impact of reflection scores and self- and peer assessment scores on the likelihood of having been disciplined for unprofessional behavior. Subsequent qualitative analysis further explored when and how students learned professionalism during their clinical experiences. Results: The study found that students in the case group exhibited lower reflective ability than control students. Furthermore, reflective ability was a significant factor in explaining the odds that a student had been cited for professionalism lapses. There were no differences in self-assessment scores between the two groups, but students in the case group had significantly lower peer assessment scores than control students. Peer assessment scores also had the greatest influence on the odds that a student had been cited for professionalism deficiencies during medical school. Qualitative analysis revealed that students learn professionalism from role models who demonstrated altruism and respect (or lack thereof). Conclusions: These findings suggest that students should be provided with guidance and feedback on their reflective writing to promote higher levels of reflection, which may reduce the number of students who are cited for professionalism lapses. These findings also indicate that peer assessments can be used to provide students with insightful feedback regarding their professional development. Finally, role models have a strong influence on students’ professional development, and therefore must be cognizant of the implicit messages their behaviors convey.