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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
For as long as humans have been working, they have been looking for ways to get that work done better, faster, and more efficient. Over the course of human history, mankind has created innumerable spectacular inventions, all with the goal of making the economy and daily life more efficient. Today, innovations and technological advancements are happening at a pace like never seen before, and technology like automation and artificial intelligence are poised to once again fundamentally alter the way people live and work in society. Whether society is prepared or not, robots are coming to replace human labor, and they are coming fast. In many areas artificial intelligence has disrupted entire industries of the economy. As people continue to make advancements in artificial intelligence, more industries will be disturbed, more jobs will be lost, and entirely new industries and professions will be created in their wake. The future of the economy and society will be determined by how humans adapt to the rapid innovations that are taking place every single day. In this paper I will examine the extent to which automation will take the place of human labor in the future, project the potential effect of automation to future unemployment, and what individuals and society will need to do to adapt to keep pace with rapidly advancing technology. I will also look at the history of automation in the economy. For centuries humans have been advancing technology to make their everyday work more productive and efficient, and for centuries this has forced humans to adapt to the modern technology through things like training and education. The thesis will additionally examine the ways in which the U.S. education system will have to adapt to meet the demands of the advancing economy, and how job retraining programs must be modernized to prepare workers for the changing economy.
ContributorsCunningham, Reed P. (Author) / DeSerpa, Allan (Thesis director) / Haglin, Brett (Committee member) / School of International Letters and Cultures (Contributor) / Department of Finance (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The purpose of this paper is to understand how companies are finding high potential employees and if they are leaving top talent behind in their approach. Eugene Burke stated in 2014 that 55% of employees that are labeled as a High Potential Employee will turn over and move companies. Burke (2014) also states that the average high potential employee tenure is five years. The Corporate Leadership Council says that on average, 27% of a company's development budget is spent on its high potential program (CEB 2017). For a midsize company, the high potential development budget is almost a million dollars for only a handful of employees, only to see half of the investment walking out the door to another company . Furthermore, the Corporate Leadership Council said that a study done in 2005 revealed that 50% of high potential employees had significant problems within their job (Kotlyar and Karkowsky 2014). Are time and resources are being given to the wrong employees and the right employees are being overlooked? This paper exams how companies traditionally select high potential employees and where companies are potentially omitting employees who would be better suited for the program. This paper proposes that how a company discovers their top talent will correlate to the number of turnovers or struggles that a high potential employee has on their job. Future research direction and practical considerations are also presented in this paper.
ContributorsHarrison, Carrie (Author) / Mizzi, Philip (Thesis director) / Ruediger, Stefan (Committee member) / Department of Management and Entrepreneurship (Contributor) / School of Sustainability (Contributor) / Department of Supply Chain Management (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
In which industry that has ever been profit generating, does a firm profit from their failure? The United States has a mass incarceration problem. With 25% of the world prison population residing in the US, spending on detention costs the US government $80 billion annually. Over 50% of the individuals incarcerated in America are of black or Latino descent. This massive growth in the incarcerated population of America began in the 1970s and with the passive support of American citizens has created an industry whose players profit from the detention of people. Currently, the privately run detention facilities in the United States hold 7% of state prisoners, 18% of federal prisoners, and nearly 75% of ICE's undocumented detainee population. The detention of people for profit is an idea rooted in the same profit motive that allowed the institution of slavery to flourish. However even after the 13th Amendment abolished slavery in the U.S., the oppressive forces behind slave-era economics have been perpetuated through legislation and policies that continued the stratification of society and reinforcement of the social order. With the help of corporate lobbyists, political action committees, and organizations such as the American Legislative Exchange Council, the corporate shareholders of private prisons, such as CoreCivic and The GEO Group, are able to directly align their profit-driven interests with those of federal and state legislators. By the incorporation of legislation and policy into state and federal law, the shareholders of private prisons are able to directly affect legislation as well as their own potential for profit. The justification for the usage of private prisons is thought to be seen in the price savings and flexibility that it provides for federal and state governments. However, due to the law enforcement contractor's exemption from public record laws, there is no clear evidence of where the cost savings occur, or even if there are cost savings at all. Is it ethical for a for-profit-prison corporation to be responsible for the care, security, and rehabilitation of an individual, when if they fail to rehabilitate the individual, it will add to the number of inmates under their control? The measure of a prison's failure to rehabilitate an inmate is considered the recidivism rate, and is affected when an inmate leaves a detention facility, commits another crime, then is arrested. This profit motive is causing our society to incarcerate increasing numbers of people in private prisons. For-profit prisons financially benefit from long-term incarceration and recidivism. The passive investments from public and private employees and institutions through investment corporations are the legs that allow the private prison industry to stand. Twenty-nine investment firms, such as The Vanguard Group and Fidelity Investments, own nearly two-thirds of the two largest players in the private prison industry. This includes the passive investments by public institutions such as the Arizona State University Foundation's $600 million endowment fund as well as the $500 million directly invested into CoreCivic and GEO Group from the University of Texas/ Texas A&M Investment Management Company. The goal of abolishing private prisons will require years of litigation against the giants of the industry as well as the governmental entities supporting them. However, we can start today by demanding divestiture by our school and similar institutions as well continuing to share the knowledge of the oppressive forces associated with the detention of individuals for profit.
ContributorsBayham, Michael (Author) / Gomez, Alan (Thesis director) / Dacey, John (Committee member) / W.P. Carey School of Business (Contributor) / Department of Supply Chain Management (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Social-emotional learning (SEL) methods are beginning to receive global attention in primary school education, yet the dominant emphasis on implementing these curricula is in high-income, urbanized areas. Consequently, the unique features of developing and integrating such methods in middle- or low-income rural areas are unclear. Past studies suggest that students exposed to SEL programs show an increase in academic performance, improved ability to cope with stress, and better attitudes about themselves, others, and school, but these curricula are designed with an urban focus. The purpose of this study was to conduct a needs-based analysis to investigate components specific to a SEL curriculum contextualized to rural primary schools. A promising organization committed to rural educational development is Barefoot College, located in Tilonia, Rajasthan, India. In partnership with Barefoot, we designed an ethnographic study to identify and describe what teachers and school leaders consider the highest needs related to their students' social and emotional education. To do so, we interviewed 14 teachers and school leaders individually or in a focus group to explore their present understanding of “social-emotional learning” and the perception of their students’ social and emotional intelligence. Analysis of this data uncovered common themes among classroom behaviors and prevalent opportunities to address social and emotional well-being among students. These themes translated into the three overarching topics and eight sub-topics explored throughout the curriculum, and these opportunities guided the creation of the 21 modules within it. Through a design-based research methodology, we developed a 40-hour curriculum by implementing its various modules within seven Barefoot classrooms alongside continuous reiteration based on teacher feedback and participant observation. Through this process, we found that student engagement increased during contextualized SEL lessons as opposed to traditional methods. In addition, we found that teachers and students preferred and performed better with an activities-based approach. These findings suggest that rural educators must employ particular teaching strategies when addressing SEL, including localized content and an experiential-learning approach. Teachers reported that as their approach to SEL shifted, they began to unlock the potential to build self-aware, globally-minded students. This study concludes that social and emotional education cannot be treated in a generalized manner, as curriculum development is central to the teaching-learning process.
ContributorsBucker, Delaney Sue (Author) / Carrese, Susan (Thesis director) / Barab, Sasha (Committee member) / School of Life Sciences (Contributor, Contributor) / School of Civic & Economic Thought and Leadership (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
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
This document is a proposal for a research project, submitted as an Honors Thesis to Barrett, The Honors College at Arizona State University. The proposal summarizes previous findings and literature about women survivors of domestic violence who are suffering from post-traumatic stress disorder as well as outlining the design and measures of the study. At this time, the study has not been completed. However, it may be completed at a future time.
ContributorsKunst, Jessica (Author) / Hernandez Ruiz, Eugenia (Thesis director) / Belgrave, Melita (Committee member) / School of Music (Contributor) / Dean, W.P. Carey School of Business (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The purpose of this thesis is to explore how Blockchain technology can help solve problems large corporations commonly face. For example, it is a common problem for large businesses and organizations to manage sales contracts with thousands of items on them. Likewise, it can be difficult to accurately monitor complex payment histories with thousands of items on them. Another issue is the difficulty that is introduced when making periodic reconciliations based on separate recording systems. At a broader level, some organizations may hesitate to do business with new strange companies or oversea companies for the first time because they do not trust that the other organization can deliver what they promise. Such problems cost organizations a lot of money, effort, and time to solve. However, Blockchain technology, first developed in 2009, could revolutionize how the business community deals with these common problems. The shared and immutable ledger on Blockchain can help organizations to keep track on transactions, manage the contracts in a smarter way, ensure correct purchase history records, eliminate the periodically reconciliation processes, and provide visibility for real-time transactions.
ContributorsHuynh, Phu Thanh (Author) / Popova, Laura (Thesis director) / Pankaj, Sneha (Committee member) / Department of Supply Chain Management (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Osteoporosis is a medical condition that leads to decreased bone mineral density, resulting in increased fracture risk.1 Research regarding the relationship between sleep and bone mass is limited and has primarily been studied in elderly adults. While this population is most affected by osteoporosis, adolescents are the most proactive population in terms of prevention. The purpose of this study was to evaluate the relationship between sleep efficiency and serum osteocalcin in college-aged individuals as a means of osteoporosis prevention. Thirty participants ages 18-25 years (22 females, 8 males) at Arizona State University were involved in this cross-sectional study. Data were collected during one week via self-recorded sleep diaries, quantitative ActiWatch, DEXA imaging, and serum blood draws to measure the bone biomarker osteocalcin. Three participants were excluded from the study as outliers. The median (IQR) for osteocalcin measured by ELISA was 11.6 (9.7, 14.5) ng/mL. The average sleep efficiency measured by actigraphy was 88.3% ± 3.0%. Regression models of sleep efficiency and osteocalcin concentration were not statistically significant. While the addition of covariates helped explain more of the variation in serum osteocalcin concentration, the results remained insignificant. There was a trend between osteocalcin and age, suggesting that as age increases, osteocalcin decreases. This was a limited study, and further investigation regarding the relationship between sleep efficiency and osteocalcin is warranted.
ContributorsMarsh, Courtney Nicole (Author) / Whisner, Corrie (Thesis director) / Mahmood, Tara (Committee member) / School of International Letters and Cultures (Contributor) / School of Nutrition and Health Promotion (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05