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- All Subjects: Education
- Creators: School of Mathematical and Statistical Sciences
Description
This paper considers what factors influence student interest, motivation, and continued engagement. Studies show anticipated extrinsic rewards for activity participation have been shown to reduce intrinsic value for that activity. This might suggest that grade point average (GPA) has a similar effect on academic interests. Further, when incentives such as scholarships, internships, and careers are GPA-oriented, students must adopt performance goals in courses to guarantee success. However, performance goals have not been shown to correlated with continued interest in a topic. Current literature proposes that student involvement in extracurricular activities, focused study groups, and mentored research are crucial to student success. Further, students may express either a fixed or growth mindset, which influences their approach to challenges and opportunities for growth. The purpose of this study was to collect individual cases of students' experiences in college. The interview method was chosen to collect complex information that could not be gathered from standard surveys. To accomplish this, questions were developed based on content areas related to education and motivation theory. The content areas included activities and meaning, motivation, vision, and personal development. The developed interview method relied on broad questions that would be followed by specific "probing" questions. We hypothesize that this would result in participant-led discussions and unique narratives from the participant. Initial findings suggest that some of the questions were effective in eliciting detailed responses, though results were dependent on the interviewer. From the interviews we find that students value their group involvements, leadership opportunities, and relationships with mentors, which parallels results found in other studies.
ContributorsAbrams, Sara (Author) / Hartwell, Lee (Thesis director) / Correa, Kevin (Committee member) / Department of Psychology (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
Description
We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost ci > 0 to the individual performing task i. We examine this process on complete graphs, bipartite graphs, and the integers, answering questions about the relationship between communication, defection rates and the division of labor. Assuming the division of labor is ideal when exactly half of the colony is performing each task, we nd that on some bipartite graphs and the integers it can eventually be made arbitrarily close to optimal if defection rates are sufficiently small. On complete graphs the fraction of individuals performing each task is also closest to one half when there is no defection, but is bounded by a constant dependent on the relative costs of each task.
ContributorsArcuri, Alesandro Antonio (Author) / Lanchier, Nicolas (Thesis director) / Kang, Yun (Committee member) / Fewell, Jennifer (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
A thorough understanding of the key concepts of logic is critical for student success. Logic is often not explicitly taught as its own subject in modern curriculums, which results in misconceptions among students as to what comprises logical reasoning. In addition, current standardized testing schemes often promote teaching styles which emphasize students' abilities to memorize set problem-solving methods over their capacities to reason abstractly and creatively. These phenomena, in tandem with halting progress in United States education compared to other developed nations, suggest that implementing logic courses into public schools and universities can better prepare students for professional careers and beyond. In particular, logic is essential for mathematics students as they transition from calculation-based courses to theoretical, proof-based classes. Many students find this adjustment difficult, and existing university-level courses which emphasize the technical aspects of symbolic logic do not fully bridge the gap between these two different approaches to mathematics. As a step towards resolving this problem, this project proposes a logic course which integrates historical, technical, and interdisciplinary investigations to present logic as a robust and meaningful subject warranting independent study. This course is designed with mathematics students in mind, with particular stresses on different formulations of deductively valid proof schemes. Additionally, this class can either be taught before existing logic classes in an effort to gradually expose students to logic over an extended period of time, or it can replace current logic courses as a more holistic introduction to the subject. The first section of the course investigates historical developments in studies of argumentation and logic throughout different civilizations; specifically, the works of ancient China, ancient India, ancient Greece, medieval Europe, and modernity are investigated. Along the way, several important themes are highlighted within appropriate historical contexts; these are often presented in an ad hoc way in courses emphasizing technical features of symbolic logic. After the motivations for modern symbolic logic are established, the key technical features of symbolic logic are presented, including: logical connectives, truth tables, logical equivalence, derivations, predicates, and quantifiers. Potential obstacles in students' understandings of these ideas are anticipated, and resolution methods are proposed. Finally, examples of how ideas of symbolic logic are manifested in many modern disciplines are presented. In particular, key concepts in game theory, computer science, biology, grammar, and mathematics are reformulated in the context of symbolic logic. By combining the three perspectives of historical context, technical aspects, and practical applications of symbolic logic, this course will ideally make logic a more meaningful and accessible subject for students.
ContributorsRyba, Austin (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
DescriptionThis project examines the television industry today, especially the field of educational programs. It includes the detailed implementation of one such show, a 30-minute demonstration of life skills, split into 3 segments. The pilot episode is also included.
ContributorsKesting, Amanda Jean (Author) / Alvarez, Melanie (Thesis director) / Snyder, Brian (Committee member) / Glaser, Ann (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Walter Cronkite School of Journalism and Mass Communication (Contributor)
Created2013-05
Description
Serge Galams voting systems and public debate models are used to model voting behaviors of two competing opinions in democratic societies. Galam assumes that individuals in the population are independently in favor of one opinion with a fixed probability p, making the initial number of that type of opinion a binomial random variable. This analysis revisits Galams models from the point of view of the hypergeometric random variable by assuming the initial number of individuals in favor of an opinion is a fixed deterministic number. This assumption is more realistic, especially when analyzing small populations. Evolution of the models is based on majority rules, with a bias introduced when there is a tie. For the hier- archical voting system model, in order to derive the probability that opinion +1 would win, the analysis was done by reversing time and assuming that an individual in favor of opinion +1 wins. Then, working backwards we counted the number of configurations at the next lowest level that could induce each possible configuration at the level above, and continued this process until reaching the bottom level, i.e., the initial population. Using this method, we were able to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion, for any group size greater than or equal to three. For the public debate model, we counted the total number of individuals in favor of opinion +1 at each time step and used this variable to define a random walk. Then, we used first-step analysis to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion for group sizes of three. The spatial public debate model evolves based on the proportional rule. For the spatial model, the most natural graphical representation to construct the process results in a model that is not mathematically tractable. Thus, we defined a different graphical representation that is mathematically equivalent to the first graphical representation, but in this model it is possible to define a dual process that is mathematically tractable. Using this graphical representation we prove clustering in 1D and 2D and coexistence in higher dimensions following the same approach as for the voter model interacting particle system.
ContributorsTaylor, Nicole Robyn (Co-author) / Lanchier, Nicolas (Co-author, Thesis director) / Smith, Hal (Committee member) / Hurlbert, Glenn (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology, I devised an interview method, which I structured using multiple phases of pre-planned support. With these interviews, I gathered information about two main aspects about students' thinking: how students think when attempting to reason covariationally and which of the identified ways of thinking are most propitious for the development of an understanding of covariational reasoning. I will discuss how, based on interview data, one of the five identified ways of thinking about covariational reasoning is highly propitious, while the other four are somewhat less propitious.
ContributorsWhitmire, Benjamin James (Author) / Thompson, Patrick (Thesis director) / Musgrave, Stacy (Committee member) / Moore, Kevin C. (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor)
Created2014-05
Description
Cryptocurrencies have become one of the most fascinating forms of currency and economics due to their fluctuating values and lack of centralization. This project attempts to use machine learning methods to effectively model in-sample data for Bitcoin and Ethereum using rule induction methods. The dataset is cleaned by removing entries with missing data. The new column is created to measure price difference to create a more accurate analysis on the change in price. Eight relevant variables are selected using cross validation: the total number of bitcoins, the total size of the blockchains, the hash rate, mining difficulty, revenue from mining, transaction fees, the cost of transactions and the estimated transaction volume. The in-sample data is modeled using a simple tree fit, first with one variable and then with eight. Using all eight variables, the in-sample model and data have a correlation of 0.6822657. The in-sample model is improved by first applying bootstrap aggregation (also known as bagging) to fit 400 decision trees to the in-sample data using one variable. Then the random forests technique is applied to the data using all eight variables. This results in a correlation between the model and data of 9.9443413. The random forests technique is then applied to an Ethereum dataset, resulting in a correlation of 9.6904798. Finally, an out-of-sample model is created for Bitcoin and Ethereum using random forests, with a benchmark correlation of 0.03 for financial data. The correlation between the training model and the testing data for Bitcoin was 0.06957639, while for Ethereum the correlation was -0.171125. In conclusion, it is confirmed that cryptocurrencies can have accurate in-sample models by applying the random forests method to a dataset. However, out-of-sample modeling is more difficult, but in some cases better than typical forms of financial data. It should also be noted that cryptocurrency data has similar properties to other related financial datasets, realizing future potential for system modeling for cryptocurrency within the financial world.
ContributorsBrowning, Jacob Christian (Author) / Meuth, Ryan (Thesis director) / Jones, Donald (Committee member) / McCulloch, Robert (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Grade inflation in modern universities across the United States has been documented since the 1960's and shows no signs of disappearing soon. Responses to this trend have ranged from mild worry to excessive panic. However, is the concern justified? How significant are the effects, if any, of grade inflation on students? Specifically, does grade inflation on the aggregate level have any effect on how much an individual will learn from their courses? This is precisely the question my project hoped to address. Grade inflation in U.S. colleges has played a central role in student-teacher relationships and the way university classrooms run. Through teacher interviews, student surveys, and a literature review, this paper investigates the nuanced effects grade inflation is having on student motivation and learning. The hypothesis is that the easier it is for a student to obtain their desired grade, the less they will end up engaging in and learning from a given course. Major findings of the literature include: grade inflation has robbed grades of their signaling power, grade inflation has helped create students are too grade-oriented, student evaluations of teaching have prompted higher grades, higher expectations for high grades induce greater study times, and open dialogue can help reverse grade inflation trends. The student surveys and faculty interviews agreed with much of the literature and found that professors believe grade inflation is real but do not believe its effects are significant, students admit to being primarily motivated by grades, and students find grades critically important to their future. The paper concludes that grade inflation is not as detrimental to student outcomes as ardent critics argue and offers practical ways to address it.
ContributorsGregory, Austin Scott (Author) / Ruediger, Stefan (Thesis director) / Goegan, Brian (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
We study two models of a competitive game in which players continuously receive points and wager them in one-on-one battles. In each model the loser of a battle has their points reset, while the points the winner receives is what sets the two models apart. In the knockout model the winner receives no new points, while in the winner-takes-all model the points that the loser had are added to the winner's total. Recurrence properties are assessed for both models: the knockout model is recurrent except for the all-zero state, and the winner-takes-all model is transient, but retains some aspect of recurrence. In addition, we study the population-level allocation of points; for the winner-takes-all model we show explicitly that the proportion of individuals having any number j of points, j=0,1,... approaches a stationary distribution that can be computed recursively. Graphs of numerical simulations are included to exemplify the results proved.
ContributorsVanKirk, Maxwell Joshua (Author) / Lanchier, Nicolas (Thesis director) / Foxall, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2016-12