Matching Items (29)
Filtering by
- All Subjects: Education
- Creators: School of Mathematical and Statistical Sciences
- Status: Published
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
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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
The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use of the inverse fast Fourier transform algorithm. By minimizing the error of the PRM approximation at the sampled Fourier modes, the PRM can also be used to improve on initial edge location estimates. Numerical examples show that using the PRM to improve on initial edge location estimates and then taking of the PRM approximation of the integer frequency Fourier coefficients is a viable way to reconstruct the underlying function in one dimension. In particular, the PRM is shown to converge more quickly and to be more robust than current resampling techniques used in MRI, and is particularly amenable to highly irregular sampling patterns.
ContributorsGutierrez, Alexander Jay (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Viswanathan, Adityavikram (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
The objective of the research presented here was to validate the use of kinetic models for the analysis of the dynamic behavior of a contrast agent in tumor tissue and evaluate the utility of such models in determining kinetic properties - in particular perfusion and molecular binding uptake associated with tissue hypoxia - of the imaged tissue, from concentration data acquired with dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) procedure. Data from two separate DCE-MRI experiments, performed in the past, using a standard contrast agent and a hypoxia-binding agent respectively, were analyzed. The results of the analysis demonstrated that the models used may provide novel characterization of the tumor tissue properties. Future research will work to further characterize the physical significance of the estimated parameters, particularly to provide quantitative oxygenation data for the imaged tissue.
ContributorsMartin, Jonathan Michael (Author) / Kodibagkar, Vikram (Thesis director) / Rege, Kaushal (Committee member) / Barrett, The Honors College (Contributor) / Chemical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-12
Description
In applications such as Magnetic Resonance Imaging (MRI), data are acquired as Fourier samples. Since the underlying images are only piecewise smooth, standard recon- struction techniques will yield the Gibbs phenomenon, which can lead to misdiagnosis. Although filtering will reduce the oscillations at jump locations, it can often have the adverse effect of blurring at these critical junctures, which can also lead to misdiagno- sis. Incorporating prior information into reconstruction methods can help reconstruct a sharper solution. For example, compressed sensing (CS) algorithms exploit the expected sparsity of some features of the image. In this thesis, we develop a method to exploit the sparsity in the edges of the underlying image. We design a convex optimization problem that exploits this sparsity to provide an approximation of the underlying image. Our method successfully reduces the Gibbs phenomenon with only minimal "blurring" at the discontinuities. In addition, we see a high rate of convergence in smooth regions.
ContributorsWasserman, Gabriel Kanter (Author) / Gelb, Anne (Thesis director) / Cochran, Doug (Committee member) / Archibald, Rick (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
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
Smart contrast agents allow for noninvasive study of specific events or tissue conditions inside of a patient's body using Magnetic Resonance Imaging (MRI). This research aims to develop and characterize novel smart contrast agents for MRI that respond to temperature changes in tissue microenvironments. Transmission Electron Microscopy, Nuclear Magnetic Resonance, and cell culture growth assays were used to characterize the physical, magnetic, and cytotoxic properties of candidate nanoprobes. The nanoprobes displayed thermosensitve MR properties with decreasing relaxivity with temperature. Future work will be focused on generating and characterizing photo-active analogues of the nanoprobes that could be used for both treatment of tissues and assessment of therapy.
ContributorsHussain, Khateeb Hyder (Author) / Kodibagkar, Vikram (Thesis director) / Stabenfeldt, Sarah (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05