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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 describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet vector calculus, calculus on manifolds, linear algebra, and differential equations all rest upon the idea of functions of two (or more) variables. This dissertation contributes to understanding productive ways of thinking that can support students in thinking about functions of two or more variables as they describe complex systems with multiple variables interacting. This dissertation focuses on modeling the way of thinking of four students who participated in a specific instructional sequence designed to explore the limits of their ways of thinking and in turn, develop a robust model that could explain, describe, and predict students' actions relative to specific tasks. The data was collected using a teaching experiment methodology, and the tasks within the teaching experiment leveraged quantitative reasoning and covariation as foundations of students developing a coherent understanding of two-variable functions and their rates of change. The findings of this study indicated that I could characterize students' ways of thinking about two-variable functions by focusing on their use of novice and/or expert shape thinking, and the students' ways of thinking about rate of change by focusing on their quantitative reasoning. The findings suggested that quantitative and covariational reasoning were foundational to a student's ability to generalize their understanding of a single-variable function to two or more variables, and their conception of rate of change to rate of change at a point in space. These results created a need to better understand how experts in the field, such as mathematicians and mathematics educators, thinking about multivariable functions and their rates of change.
ContributorsWeber, Eric David (Author) / Thompson, Patrick (Thesis advisor) / Middleton, James (Committee member) / Carlson, Marilyn (Committee member) / Saldanha, Luis (Committee member) / Milner, Fabio (Committee member) / Van de Sande, Carla (Committee member) / Arizona State University (Publisher)
Created2012
Description
There have been a number of studies that have examined students’ difficulties in understanding the idea of logarithm and the effectiveness of non-traditional interventions. However, there have been few studies that have examined the understandings students develop and need to develop when completing conceptually oriented logarithmic lessons. In this document, I present the three papers of my dissertation study. The first paper examines two students’ development of concepts foundational to the idea of logarithm. This paper discusses two essential understandings that were revealed to be problematic and essential for students’ development of productive meanings for exponents, logarithms and logarithmic properties. The findings of this study informed my later work to support students in understanding logarithms, their properties and logarithmic functions. The second paper examines two students’ development of the idea of logarithm. This paper describes the reasoning abilities two students exhibited as they engaged with tasks designed to foster their construction of more productive meanings for the idea of logarithm. The findings of this study provide novel insights for supporting students in understanding the idea of logarithm meaningfully. Finally, the third paper begins with an examination of the historical development of the idea of logarithm. I then leveraged the insights of this literature review and the first two papers to perform a conceptual analysis of what is involved in learning and understanding the idea of logarithm. The literature review and conceptual analysis contributes novel and useful information for curriculum developers, instructors, and other researchers studying student learning of this idea.
ContributorsKuper Flores, Emily Ginamarie (Author) / Carlson, Marilyn (Thesis advisor) / Thompson, Patrick (Committee member) / Milner, Fabio (Committee member) / Zazkis, Dov (Committee member) / Czocher, Jennifer (Committee member) / Arizona State University (Publisher)
Created2018
Description
The concept of distribution is one of the core ideas of probability theory and inferential statistics, if not the core idea. Many introductory statistics textbooks pay lip service to stochastic/random processes but how do students think about these processes? This study sought to explore what understandings of stochastic process students develop as they work through materials intended to support them in constructing the long-run behavior meaning for distribution.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
ContributorsHatfield, Neil (Author) / Thompson, Patrick (Thesis advisor) / Carlson, Marilyn (Committee member) / Middleton, James (Committee member) / Lehrer, Richard (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2019
Model Based Automatic and Robust Spike Sorting for Large Volumes of Multi-channel Extracellular Data
Description
Spike sorting is a critical step for single-unit-based analysis of neural activities extracellularly and simultaneously recorded using multi-channel electrodes. When dealing with recordings from very large numbers of neurons, existing methods, which are mostly semiautomatic in nature, become inadequate.
This dissertation aims at automating the spike sorting process. A high performance, automatic and computationally efficient spike detection and clustering system, namely, the M-Sorter2 is presented. The M-Sorter2 employs the modified multiscale correlation of wavelet coefficients (MCWC) for neural spike detection. At the center of the proposed M-Sorter2 are two automatic spike clustering methods. They share a common hierarchical agglomerative modeling (HAM) model search procedure to strategically form a sequence of mixture models, and a new model selection criterion called difference of model evidence (DoME) to automatically determine the number of clusters. The M-Sorter2 employs two methods differing by how they perform clustering to infer model parameters: one uses robust variational Bayes (RVB) and the other uses robust Expectation-Maximization (REM) for Student’s 𝑡-mixture modeling. The M-Sorter2 is thus a significantly improved approach to sorting as an automatic procedure.
M-Sorter2 was evaluated and benchmarked with popular algorithms using simulated, artificial and real data with truth that are openly available to researchers. Simulated datasets with known statistical distributions were first used to illustrate how the clustering algorithms, namely REMHAM and RVBHAM, provide robust clustering results under commonly experienced performance degrading conditions, such as random initialization of parameters, high dimensionality of data, low signal-to-noise ratio (SNR), ambiguous clusters, and asymmetry in cluster sizes. For the artificial dataset from single-channel recordings, the proposed sorter outperformed Wave_Clus, Plexon’s Offline Sorter and Klusta in most of the comparison cases. For the real dataset from multi-channel electrodes, tetrodes and polytrodes, the proposed sorter outperformed all comparison algorithms in terms of false positive and false negative rates. The software package presented in this dissertation is available for open access.
This dissertation aims at automating the spike sorting process. A high performance, automatic and computationally efficient spike detection and clustering system, namely, the M-Sorter2 is presented. The M-Sorter2 employs the modified multiscale correlation of wavelet coefficients (MCWC) for neural spike detection. At the center of the proposed M-Sorter2 are two automatic spike clustering methods. They share a common hierarchical agglomerative modeling (HAM) model search procedure to strategically form a sequence of mixture models, and a new model selection criterion called difference of model evidence (DoME) to automatically determine the number of clusters. The M-Sorter2 employs two methods differing by how they perform clustering to infer model parameters: one uses robust variational Bayes (RVB) and the other uses robust Expectation-Maximization (REM) for Student’s 𝑡-mixture modeling. The M-Sorter2 is thus a significantly improved approach to sorting as an automatic procedure.
M-Sorter2 was evaluated and benchmarked with popular algorithms using simulated, artificial and real data with truth that are openly available to researchers. Simulated datasets with known statistical distributions were first used to illustrate how the clustering algorithms, namely REMHAM and RVBHAM, provide robust clustering results under commonly experienced performance degrading conditions, such as random initialization of parameters, high dimensionality of data, low signal-to-noise ratio (SNR), ambiguous clusters, and asymmetry in cluster sizes. For the artificial dataset from single-channel recordings, the proposed sorter outperformed Wave_Clus, Plexon’s Offline Sorter and Klusta in most of the comparison cases. For the real dataset from multi-channel electrodes, tetrodes and polytrodes, the proposed sorter outperformed all comparison algorithms in terms of false positive and false negative rates. The software package presented in this dissertation is available for open access.
ContributorsMa, Weichao (Author) / Si, Jennie (Thesis advisor) / Papandreou-Suppappola, Antonia (Committee member) / He, Jingrui (Committee member) / Helms Tillery, Stephen (Committee member) / Arizona State University (Publisher)
Created2019
Description
This paper will be exploring a marketing plan for a Kpop Fan artist, Jennifer Lee. Kpop is a genre of music originating from South Korea that provides a whole-package entertainment. Fan artists are producers who create produce for the consumption and purchase of other Kpop fans. The paper will consider segmentation and the products and platforms that best target them in order to maximize revenue. A survey was performed with a sample size of 314 participants to find out consumer behavior and preference as well as producer situation. Consumers come from both the United States and abroad. Customers come directly and almost exclusively from followers. Therefore, increasing the number of followers on Instagram is essential to increasing revenue. Jennifer has time, resource, and ability constraints, while the market has limited potential. The conclusion is that Jennifer should become more organized as a business. To grow her following, she should cater more towards the most popular fandoms (BTS), make art tutorials, consider collaborations, and better inform followers of her products/services available for purchase. The social media platforms key to marketing Jennifer's products are Instagram and Twitter. Other platforms to be used to increase exposure are Tumblr, Amino Apps, DeviantArt, Reddit, and YouTube. She must also declutter all of these virtual storefronts of unnecessary content to varying degrees in order to build ease of access and a trustworthy brand image. The best platforms for transaction is a personal store, RedBubble (a website that allows users to sell a variety of products with their uploaded images printed onto them), Patreon, and in-person at conventions.
ContributorsXu, Everest Christine (Author) / Eaton, Kathryn (Thesis director) / Ingram-Waters, Mary (Committee member) / Department of Marketing (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The advertising agency, in its variety of forms, is one of the most powerful forces in the modern world. Its products are seen globally through various multimedia outlets and they strongly impact culture and economy. Since its conception in 1843 by Volney Palmer, the advertising agency has evolved into the recognizable—and unrecognizable—firms scattered around the world today. In the United States alone, there are roughly 13.4 thousand agencies, many of which also have branches in other countries. The evolution of the modern advertising agency coincided with, and even preceded, some of the major inflection points in history. Understanding how and why changes in advertising agencies affected these inflection points provides a glimpse of understanding into the relationship between advertising, business, and societal values.
In the pages ahead we will explore the future of the advertising industry. We will analyze our research to uncover the underlying trends pointing towards what is to come and work to apply those explanations to our understanding of advertising in the future.
In the pages ahead we will explore the future of the advertising industry. We will analyze our research to uncover the underlying trends pointing towards what is to come and work to apply those explanations to our understanding of advertising in the future.
ContributorsHarris, Chase (Co-author) / Potthoff, Zachary (Co-author) / Gray, Nancy (Thesis director) / Samper, Adriana (Committee member) / Department of Information Systems (Contributor) / Department of Marketing (Contributor) / Herberger Institute for Design and the Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The goal of our project was to determine how to create the most marketable hockey team. To do this, consumer needs, team psychology, and financing were all researched and evaluated. With this information, a business plan was designed around the next NHL expansion team. Two surveys, one for marketing distributed to the general public, and one for team psychology distributed to current and former hockey players were created and sent out, while data for the financing aspect was collected by comparing data from other NHL teams and franchises from different sports. In terms of financials, this comes in lower than average ticket prices, a nice and expensive stadium, the ideal city to generate capital, and sufficient money spent on advertising. Our ticket prices of $140 is based on having a low enough price to generate lots of demand while high enough to make a profit. The $600 million stadium (which will be fully funded) will surely draw a significant crowd. Choosing Seattle as a city is the most ideal to meet these goals and lastly, in meeting with an NHL GM, we determined $4 million in yearly advertising costs as sufficient in creating the most marketable team. Throughout this whole process, we remained data focus. We focused on data from a customized marketing survey, organizational structures, salary cap, and attendance. What our marketing survey results showed us is that our potential fans wanted three characteristics in a hockey team: speed, intensity, and scoring. In looking at organizational structures teams that exemplified these characteristics had a heavy emphasis on development and scouting. So we built our organizational tree around those two ideals. We hired GM Mike Futa, a current director of player personnel for the L.A. Kings, and Head Coach Adam Oates, a current skills development coach for top players to bring those ideals to fruition. In constructing our team we replicated the rules set forth for the Vegas Knights' expansion draft and hypothesized a likely protected list based off of last years lists. As a result we were able to construct a team that statistically out performed the Vegas Knights draft numbers by double, in goals, assists, and points, while also beating them in PIM. Based off of these numbers and an analysis of how goals translate into game attendance we are confident that we have constructed a team that has the highest potential for marketability. For the team psychology area, when creating a roster and scouting players, some of our main findings were that it is important to pursue players who get along well with their teammates and coaching staff, are aggressive, are leaders on the team, and are vocal players who communicate effectively. We also recommended avoiding players who significantly portrayed any "pet-peeve" traits, with the most emphasis placed on "disrespectful toward teammates," and the least emphasis placed on "over-aggression." By following all of these recommendations, we believe the most marketable hockey team possible can be created.
ContributorsQuinn, Colin Christopher (Co-author) / Spigel, Carlos (Co-author) / Meyer, Matt (Co-author) / Eaton, John (Thesis director) / McIntosh, Daniel (Committee member) / Department of Marketing (Contributor) / Sandra Day O'Connor College of Law (Contributor) / Department of Management and Entrepreneurship (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
In recent years, companies have been expanding their business efforts on a global scale. This project explores this expansion of American-based multinational corporations (MNCs) in Ireland, and the comparison of how their culture motivation in the workplace. We did a cultural study using Hofstede and Trompenaars' cultural dimensions of the two countries then used McClelland's Needs Theory, Equity Theory, and Herzberg's Motivation-Hygiene Theory in order to create three research questions. (1) How does the manager define success for the firm as a whole and for their employees, (2) How is the definition of success reflected in the company's corporate culture (i.e. values, norms and practices), along with how cultural values, norms and practices affect the company, and (3) How do external forces (i.e. governmental factors, workplace technology, etc.) affect the workplace environment and motivation for employees? With these we hypothesized that for research question 1, we hypothesized that from our study of Hofstede's and Trompenaars' cultural frameworks, Irish employees will show a greater tendency to favor affiliation, nAff, as opposed to a need for achievement, nAch, in American employees, according to McClelland's Needs Theory. For research question 2, we predicted that motivation would be administered through style of feedback to employees and office norms, such as autonomy, flexible hours, and work-life balance. For research question 3, we hypothesized that Ireland would have an impact from external factors such as government and technology, whereas the U.S. employees would face no clear impact. We conducted eight, qualitative interviews using a questionnaire, either in person or via video conference. The interviewees were all managers in some facet and have all had some international experience. Through the analysis of the interviews, we found that the Irish employees focused on how employees are able to help or contribute to a group (nAff), instead of looking at how the contribution of a group can be used to meet individual goals (nAch). The American companies reflected Trompenaars' definition of individualism in which employees focus on collaborating in teams, as long as individual goals are met, and benchmarked collaboration as a performance measure, tying in the need for achievement, for research question one. For the second research question, we found that employees in Ireland had a focus on teamwork in the workplace and much higher respect for work-life balance. American firms, in contrast, had a greater focus on making sure employees were contributing, meeting their goals, and getting their work done. While American firms did acknowledge work-life balance and its importance, there was a priority for coming in early and/or staying late to make sure a job got done. Findings for our third question showed that government factors did impact Ireland more, due to labor laws such as required vacation days in Ireland, and that technology had less of an impact than expected, for both countries. More importantly was our finding that the companies in Ireland were greatly impacted by the decisions made by the business executives in the United States.
ContributorsSong, Jenny Jungwon (Co-author) / Brown, William (Co-author) / Arrfelt, Mathias (Thesis director) / Moore, James (Committee member) / Department of Marketing (Contributor) / Department of Management and Entrepreneurship (Contributor) / W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This paper looks at the growth of influencer marketing in application and how it has shifted the relationship between brands and consumers. Barriers to enter the space and methods of practice are discussed and analyzed to project the accessibility of obtaining influencer status. Best practices for brands and influencers are outlined based on research, and key findings are analyzed from interviewed participants that play an active role in the field. Another component of the paper includes the discussion of the significance of platform dependence regarding influencers and brands using social media channels to reach consumers. The dynamic of the relationship that exists between consumers, brands and platforms is demonstrated through a model to demonstrate the interdependence of the relationship. The final component of the paper involves the exploration of the field as an active participant through an experiment that was conducted by the researcher on behalf of the question: can anyone be an influencer? The answer to this question is explored through personal accounts on the journey during an eight month process of testing content creation and promotion to build awareness and increase engagement. The barriers to enter the space as an influencer and to collaborate with brands is addressed through the process of testing tactics and strategies on social channels, along with travel expeditions across Arizona to contribute to content creation purposed into blog articles. The findings throughout the paper are conclusive that the value of influencer marketing is increasing as more brands validate and utilize this method in their marketing efforts.
ContributorsDavis, Natalie Marie (Author) / Giles, Bret (Thesis director) / Schlacter, John (Committee member) / Department of Information Systems (Contributor) / Department of Marketing (Contributor) / Walter Cronkite School of Journalism and Mass Communication (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05