Matching Items (627)
Description
Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.
ContributorsHalani, Aviva (Author) / Roh, Kyeong Hah (Thesis advisor) / Fishel, Susanna (Committee member) / Saldanha, Luis (Committee member) / Thompson, Patrick (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis and discuss the implications of these uses for interpreting and leveraging results to produce empirically tested learning trajectories. From my summary and analysis I develop two recommendations for the cognitive researchers developing empirically supported learning trajectories. (1) A researcher should frame his/her work, and analyze others’ work, within the researcher’s image of a broadly coherent trajectory for student learning and (2) that the field should work towards a common understanding for the meaning of a hypothetical learning trajectory.
In Paper 2 I argue that prior research in online learning has tested the impact of online courses on measures such as student retention rates, satisfaction scores, and GPA but that research is needed to describe the meanings students construct for mathematical ideas researchers have identified as critical to their success in future math courses and other STEM fields. This paper discusses the need for a new focus in studying online mathematics learning and calls for cognitive researchers to begin developing a productive methodology for examining the meanings students construct while engaged in online lessons.
Paper 3 describes the online Precalculus course intervention we designed around measurement imagery and quantitative reasoning as themes that unite topics across units. I report results relative to the meanings students developed for exponential functions and related ideas (such as percent change and growth factors) while working through lessons in the intervention. I provide a conceptual analysis guiding its design and discuss pre-test and pre-interview results, post-test and post-interview results, and observations from student behaviors while interacting with lessons. I demonstrate that the targeted meanings can be productive for students, show common unproductive meanings students possess as they enter Precalculus, highlight challenges and opportunities in teaching and learning in the online environment, and discuss needed adaptations to the intervention and future research opportunities informed by my results.
In Paper 2 I argue that prior research in online learning has tested the impact of online courses on measures such as student retention rates, satisfaction scores, and GPA but that research is needed to describe the meanings students construct for mathematical ideas researchers have identified as critical to their success in future math courses and other STEM fields. This paper discusses the need for a new focus in studying online mathematics learning and calls for cognitive researchers to begin developing a productive methodology for examining the meanings students construct while engaged in online lessons.
Paper 3 describes the online Precalculus course intervention we designed around measurement imagery and quantitative reasoning as themes that unite topics across units. I report results relative to the meanings students developed for exponential functions and related ideas (such as percent change and growth factors) while working through lessons in the intervention. I provide a conceptual analysis guiding its design and discuss pre-test and pre-interview results, post-test and post-interview results, and observations from student behaviors while interacting with lessons. I demonstrate that the targeted meanings can be productive for students, show common unproductive meanings students possess as they enter Precalculus, highlight challenges and opportunities in teaching and learning in the online environment, and discuss needed adaptations to the intervention and future research opportunities informed by my results.
ContributorsO'Bryan, Alan Eugene (Author) / Carlson, Marilyn P (Thesis advisor) / Thompson, Patrick W (Committee member) / Milner, Fabio (Committee member) / Roh, Kyeong Hah (Committee member) / Tallman, Michael (Committee member) / Arizona State University (Publisher)
Created2018
Description
The current trend of interconnected devices, or the internet of things (IOT) has led to the popularization of single board computers (SBC). This is primarily due to their form-factor and low price. This has led to unique networks of devices that can have unstable network connections and minimal processing power. Many parallel program- ming libraries are intended for use in high performance computing (HPC) clusters. Unlike the IOT environment described, HPC clusters will in general look to obtain very consistent network speeds and topologies. There are a significant number of software choices that make up what is referred to as the HPC stack or parallel processing stack. My thesis focused on building an HPC stack that would run on the SCB computer name the Raspberry Pi. The intention in making this Raspberry Pi cluster is to research performance of MPI implementations in an IOT environment, which had an impact on the design choices of the cluster. This thesis is a compilation of my research efforts in creating this cluster as well as an evaluation of the software that was chosen to create the parallel processing stack.
ContributorsO'Meara, Braedon Richard (Author) / Meuth, Ryan (Thesis director) / Dasgupta, Partha (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This thesis discusses three recent optimization problems that seek to reduce disease spread on arbitrary graphs by deleting edges, and it discusses three approximation algorithms developed for these problems. Important definitions are presented including the Linear Threshold and Triggering Set models and the set function properties of submodularity and monotonicity. Also, important results regarding the Linear Threshold model and computation of the influence function are presented along with proof sketches. The three main problems are formally presented, and NP-hardness results along with proof sketches are presented where applicable. The first problem seeks to reduce spread of infection over the Linear Threshold process by making use of an efficient tree data structure. The second problem seeks to reduce the spread of infection over the Linear Threshold process while preserving the PageRank distribution of the input graph. The third problem seeks to minimize the spectral radius of the input graph. The algorithms designed for these problems are described in writing and with pseudocode, and their approximation bounds are stated along with time complexities. Discussion of these algorithms considers how these algorithms could see real-world use. Challenges and the ways in which these algorithms do or do not overcome them are noted. Two related works, one which presents an edge-deletion disease spread reduction problem over a deterministic threshold process and the other which considers a graph modification problem aimed at minimizing worst-case disease spread, are compared with the three main works to provide interesting perspectives. Furthermore, a new problem is proposed that could avoid some issues faced by the three main problems described, and directions for future work are suggested.
ContributorsStanton, Andrew Warren (Author) / Richa, Andrea (Thesis director) / Czygrinow, Andrzej (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Construction is a defining characteristic of geometry classes. In a traditional classroom, teachers and students use physical tools (i.e. a compass and straight-edge) in their constructions. However, with modern technology, construction is possible through the use of digital applications such as GeoGebra and Geometer’s SketchPad.
Many other studies have researched the benefits of digital manipulatives and digital environments through student completion of tasks and testing. This study intends to research students’ use of the digital tools and manipulatives, along with the students’ interactions with the digital environment. To this end, I conducted exploratory teaching experiments with two calculus I students.
In the exploratory teaching experiments, students were introduced to a GeoGebra application developed by Fischer (2019), which includes instructional videos and corresponding quizzes, as well as exercises and interactive notepads, where students could use digital tools to construct line segments and circles (corresponding to the physical straight-edge and compass). The application built up the students’ foundational knowledge, culminating in the construction and verbal proof of Euclid’s Elements, Proposition 1 (Euclid, 1733).
The central findings of this thesis are the students’ interactions with the digital environment, with observed changes in their conceptions of radii and circles, and in their use of tools. The students were observed to have conceptions of radii as a process, a geometric shape, and a geometric object. I observed the students’ conceptions of a circle change from a geometric shape to a geometric object, and with that change, observed the students’ use of tools change from a measuring focus to a property focus.
I report a summary of the students’ work and classify their reasoning and actions into the above categories, and an analysis of how the digital environment impacts the students’ conceptions. I also briefly discuss the impact of the findings on pedagogy and future research.
Many other studies have researched the benefits of digital manipulatives and digital environments through student completion of tasks and testing. This study intends to research students’ use of the digital tools and manipulatives, along with the students’ interactions with the digital environment. To this end, I conducted exploratory teaching experiments with two calculus I students.
In the exploratory teaching experiments, students were introduced to a GeoGebra application developed by Fischer (2019), which includes instructional videos and corresponding quizzes, as well as exercises and interactive notepads, where students could use digital tools to construct line segments and circles (corresponding to the physical straight-edge and compass). The application built up the students’ foundational knowledge, culminating in the construction and verbal proof of Euclid’s Elements, Proposition 1 (Euclid, 1733).
The central findings of this thesis are the students’ interactions with the digital environment, with observed changes in their conceptions of radii and circles, and in their use of tools. The students were observed to have conceptions of radii as a process, a geometric shape, and a geometric object. I observed the students’ conceptions of a circle change from a geometric shape to a geometric object, and with that change, observed the students’ use of tools change from a measuring focus to a property focus.
I report a summary of the students’ work and classify their reasoning and actions into the above categories, and an analysis of how the digital environment impacts the students’ conceptions. I also briefly discuss the impact of the findings on pedagogy and future research.
ContributorsSakauye, Noelle Marie (Author) / Roh, Kyeong Hah (Thesis director) / Zandieh, Michelle (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
In the last few years, billion-dollar companies like Yahoo and Equifax have had data breaches causing millions of people’s personal information to be leaked online. Other billion-dollar companies like Google and Facebook have gotten in trouble for abusing people’s personal information for financial gain as well. In this new age of technology where everything is being digitalized and stored online, people all over the world are concerned about what is happening to their personal information and how they can trust it is being kept safe. This paper describes, first, the importance of protecting user data, second, one easy tool that companies and developers can use to help ensure that their user’s information (credit card information specifically) is kept safe, how to implement that tool, and finally, future work and research that needs to be done. The solution I propose is a software tool that will keep credit card data secured. It is only a small step towards achieving a completely secure data anonymized system, but when implemented correctly, it can reduce the risk of credit card data from being exposed to the public. The software tool is a script that can scan every viable file in any given system, server, or other file-structured Linux system and detect if there any visible credit card numbers that should be hidden.
ContributorsPappas, Alexander (Author) / Zhao, Ming (Thesis director) / Kuznetsov, Eugene (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Political polarization is the coalescence of political parties -- and the individuals of which parties are composed -- around opposing ends of the ideological spectrum. Political parties in the United States have always been divided, however, in recent years this division has only intensified. Recently, polarization has also wound its way to the Supreme Court and the nomination processes of justices to the Court. This paper examines how prevalent polarization in the Supreme Court nomination process has become by looking specifically at the failed nomination of Judge Merrick Garland and the confirmations of now-Justices Neil Gorsuch and Brett Kavanaugh. This is accomplished by comparing the ideologies and qualifications of the three most recent nominees to those of previous nominees, as well as analysing the ideological composition of the Senate at the times of the individual nominations.
ContributorsJoss, Jacob (Author) / Hoekstra, Valerie (Thesis director) / Critchlow, Donald (Committee member) / Computer Science and Engineering Program (Contributor) / School of Politics and Global Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The original version of Helix, the one I pitched when first deciding to make a video game
for my thesis, is an action-platformer, with the intent of metroidvania-style progression
and an interconnected world map.
The current version of Helix is a turn based role-playing game, with the intent of roguelike
gameplay and a dark fantasy theme. We will first be exploring the challenges that came
with programming my own game - not quite from scratch, but also without a prebuilt
engine - then transition into game design and how Helix has evolved from its original form
to what we see today.
for my thesis, is an action-platformer, with the intent of metroidvania-style progression
and an interconnected world map.
The current version of Helix is a turn based role-playing game, with the intent of roguelike
gameplay and a dark fantasy theme. We will first be exploring the challenges that came
with programming my own game - not quite from scratch, but also without a prebuilt
engine - then transition into game design and how Helix has evolved from its original form
to what we see today.
ContributorsDiscipulo, Isaiah K (Author) / Meuth, Ryan (Thesis director) / Kobayashi, Yoshihiro (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
RecyclePlus is an iOS mobile application that allows users to be knowledgeable in the realms of sustainability. It gives encourages users to be environmental responsible by providing them access to recycling information. In particular, it allows users to search up certain materials and learn about its recyclability and how to properly dispose of the material. Some searches will show locations of facilities near users that collect certain materials and dispose of the materials properly. This is a full stack software project that explores open source software and APIs, UI/UX design, and iOS development.
ContributorsTran, Nikki (Author) / Ganesh, Tirupalavanam (Thesis director) / Meuth, Ryan (Committee member) / Watts College of Public Service & Community Solut (Contributor) / Department of Information Systems (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
At present, the vast majority of human subjects with neurological disease are still diagnosed through in-person assessments and qualitative analysis of patient data. In this paper, we propose to use Topological Data Analysis (TDA) together with machine learning tools to automate the process of Parkinson’s disease classification and severity assessment. An automated, stable, and accurate method to evaluate Parkinson’s would be significant in streamlining diagnoses of patients and providing families more time for corrective measures. We propose a methodology which incorporates TDA into analyzing Parkinson’s disease postural shifts data through the representation of persistence images. Studying the topology of a system has proven to be invariant to small changes in data and has been shown to perform well in discrimination tasks. The contributions of the paper are twofold. We propose a method to 1) classify healthy patients from those afflicted by disease and 2) diagnose the severity of disease. We explore the use of the proposed method in an application involving a Parkinson’s disease dataset comprised of healthy-elderly, healthy-young and Parkinson’s disease patients.
ContributorsRahman, Farhan Nadir (Co-author) / Nawar, Afra (Co-author) / Turaga, Pavan (Thesis director) / Krishnamurthi, Narayanan (Committee member) / Electrical Engineering Program (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05