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- Creators: School of Mathematical and Statistical Sciences
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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
Based on poor student performance in past studies, the incoherence present in the teaching of inverse functions, and teachers' own accounts of their struggles to teach this topic, it is apparent that the idea of function inverse deserves a closer look and an improved pedagogical approach. This improvement must enhance students' opportunity to construct a meaning for a function's inverse and, out of that meaning, produce ways to define a function's inverse without memorizing some procedure. This paper presents a proposed instructional sequence that promotes reflective abstraction in order to help students develop a process conception of function and further understand the meaning of a function inverse. The instructional sequence was used in a teaching experiment with three subjects and the results are presented here. The evidence presented in this paper supports the claim that the proposed instructional sequence has the potential to help students construct meanings needed for understanding function inverse. The results of this study revealed shifts in the understandings of all three subjects. I conjecture that these shifts were achieved by posing questions that promoted reflective abstraction. The questions and subsequent interactions appeared to result in all three students moving toward a process conception of function.
ContributorsFowler, Bethany (Author) / Carlson, Marilyn (Thesis advisor) / Roh, Kyeong (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2014
Description
This research compares shifts in a SuperSpec titanium nitride (TiN) kinetic inductance detector's (KID's) resonant frequency with accepted models for other KIDs. SuperSpec, which is being developed at the University of Colorado Boulder, is an on-chip spectrometer designed with a multiplexed readout with multiple KIDs that is set up for a broadband transmission of these measurements. It is useful for detecting radiation in the mm and sub mm wavelengths which is significant since absorption and reemission of photons by dust causes radiation from distant objects to reach us in infrared and far-infrared bands. In preparation for testing, our team installed stages designed previously by Paul Abers and his group into our cryostat and designed and installed other parts necessary for the cryostat to be able to test devices on the 250 mK stage. This work included the design and construction of additional parts, a new setup for the wiring in the cryostat, the assembly, testing, and installation of several stainless steel coaxial cables for the measurements through the devices, and other cryogenic and low pressure considerations. The SuperSpec KID was successfully tested on this 250 mK stage thus confirming that the new setup is functional. Our results are in agreement with existing models which suggest that the breaking of cooper pairs in the detector's superconductor which occurs in response to temperature, optical load, and readout power will decrease the resonant frequencies. A negative linear relationship in our results appears, as expected, since the parameters are varied only slightly so that a linear approximation is appropriate. We compared the rate at which the resonant frequency responded to temperature and found it to be close to the expected value.
ContributorsDiaz, Heriberto Chacon (Author) / Mauskopf, Philip (Thesis director) / McCartney, Martha (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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
This study estimates the capitalization effect of golf courses in Maricopa County using the hedonic pricing method. It draws upon a dataset of 574,989 residential transactions from 2000 to 2006 to examine how the aesthetic, non-golf benefits of golf courses capitalize across a gradient of proximity measures. The measures for amenity value extend beyond home adjacency and include considerations for homes within a range of discrete walkability buffers of golf courses. The models also distinguish between public and private golf courses as a proxy for the level of golf course access perceived by non-golfers. Unobserved spatial characteristics of the neighborhoods around golf courses are controlled for by increasing the extent of spatial fixed effects from city, to census tract, and finally to 2000 meter golf course ‘neighborhoods.’ The estimation results support two primary conclusions. First, golf course proximity is found to be highly valued for adjacent homes and homes up to 50 meters way from a course, still evident but minimal between 50 and 150 meters, and insignificant at all other distance ranges. Second, private golf courses do not command a higher proximity premia compared to public courses with the exception of homes within 25 to 50 meters of a course, indicating that the non-golf benefits of courses capitalize similarly, regardless of course type. The results of this study motivate further investigation into golf course features that signal access or add value to homes in the range of capitalization, particularly for near-adjacent homes between 50 and 150 meters thought previously not to capitalize.
ContributorsJoiner, Emily (Author) / Abbott, Joshua (Thesis director) / Smith, Kerry (Committee member) / Economics Program in CLAS (Contributor) / School of Sustainability (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This study asks the question: does gender-based discrimination exists within Arizona State University's Army Reserve Officer Training Corps (ROTC), and if so, what are the effects of such discrimination? Within this study, discrimination is defined as: the treatment or consideration of, or making a distinction in favor of or against, a person or thing based on the group, class, or category to which that person or thing belongs, rather than on individual merit. The researcher predicted that this study would show that gender-based discrimination operates within the masculine military culture of Army ROTC at ASU, resulting from women's hyper-visibility and evidenced by their lack of positive recognition and disbelief in having a voice in the program. These expectations were based on background research claiming that the token status of women in military roles causes them to be more heavily scrutinized, and they consequentially try to attain success by adapting to the masculine military culture by which they are constantly measured. For the purposes of this study, success is defined as: the attainment of wealth, favor, or eminence . This study relies on exploratory interviews and an online survey conducted with male and female Army ROTC cadets of all grade levels at Arizona State University. The interviews and survey collected demographic information and perspectives on individual experiences to establish an understanding of privilege and marginalization within the program. These results do support the prediction that women in Army ROTC at ASU face discrimination based on their unique visibility and lack of positive recognition and voice in the program. Likewise, the survey results indicate that race also has a significant impact on one's experience in Army ROTC, which is discussed later in this study in regard to needs for future research. ASU Army ROTC includes approximately 100 cadets, and approximately 30-40 of those cadets participated in this study. Additionally, the University of Arizona and the Northern Arizona University Army ROTC programs were invited to participate in this study and declined to do so, which would have offered a greater sample population. Nonetheless, the results of this research will be useful for analysis and further discussion of gender-equality in Army ROTC at Arizona State University.
ContributorsAllemang, Lindsey Ann (Author) / Wood, Reed (Thesis director) / Switzer, Heather (Committee member) / School of Politics and Global Studies (Contributor) / School of Social Transformation (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The objective of this paper is to provide an educational diagnostic into the technology of blockchain and its application for the supply chain. Education on the topic is important to prevent misinformation on the capabilities of blockchain. Blockchain as a new technology can be confusing to grasp given the wide possibilities it can provide. This can convolute the topic by being too broad when defined. Instead, the focus will be maintained on explaining the technical details about how and why this technology works in improving the supply chain. The scope of explanation will not be limited to the solutions, but will also detail current problems. Both public and private blockchain networks will be explained and solutions they provide in supply chains. In addition, other non-blockchain systems will be described that provide important pieces in supply chain operations that blockchain cannot provide. Blockchain when applied to the supply chain provides improved consumer transparency, management of resources, logistics, trade finance, and liquidity.
ContributorsKrukar, Joel Michael (Author) / Oke, Adegoke (Thesis director) / Duarte, Brett (Committee member) / Hahn, Richard (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The number of undergraduate students participating in short-term experiences in global health (STEGHs) abroad has increased dramatically in recent years (Eyler 2002, Drain et al. 2007). These experiences, in tandem with classroom learning, are designed to help students master skills related to global health competencies, including cultural humility and sensitivity, collaborating with community partners, and sociocultural and political awareness. Although STEGHs offer potential benefits to both students and to sending institutions, these experiences can sometimes be problematic and raise ethical challenges. As the number of students engaged in STEGHs continues to increase, it is important to better understand the impact of these programs on student learning. Current ethical and best practice guidelines for STEGHs state that programs should establish evaluation methods to solicit feedback from students both during and on completion of the program (Crump et al. 2010). However, there is currently no established method for gathering this feedback because of the many different global health competency frameworks, types and duration of programs, and different models of student engagement in such programs. Assessing the quality of a STEGH is a profoundly important and difficult question that cannot be answered as succinctly and quantitatively as classroom performance, which has more standard and established assessment metrics. The goal of this project is to identify the most appropriate and useful assessment metric(s) for determining educational quality and impact for STEGHs at ASU by comparing a typical quantitative evaluation tool (pre-post survey with brief open-ended questions) to a more in-depth qualitative method (key informant interviews). In performing my analysis I seek to examine if the latter can produce a richer narrative of student experiences to inform ongoing program evaluations. My research questions are: 1. What are the current qualitative and quantitative evaluation methods available to assess student learning during short-term experiences in global health? 2. How can current methodology for assessing student experiences with short-term experiences in global health be adapted to collect the most information from students? 3. How do student knowledge and attitudes change before and after their short-term experience in global health? Why is understanding those changes important for adapting programs? My end goal would be to use these new, optimal assessment methods for gathering student perspectives and experiences to adapt pre-departure trainings and post-experience debriefings for study abroad programs, both of which I believe will lead to more sustainable partnerships and a healthier understanding of global health work for students.
ContributorsHale, Brittany Ann (Author) / Jehn, Megan (Thesis director) / Wutich, Amber (Committee member) / School of Human Evolution and Social Change (Contributor) / School of Social Transformation (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The Super Catalan numbers are a known set of numbers which have so far eluded a combinatorial interpretation. Several weighted interpretations have appeared since their discovery, one of which was discovered by William Kuszmaul in 2017. In this paper, we connect the weighted Super Catalan structure created previously by Kuszmaul and a natural $q$-analogue of the Super Catalan numbers. We do this by creating a statistic $\sigma$ for which the $q$ Super Catalan numbers, $S_q(m,n)=\sum_X (-1)^{\mu(X)} q^{\sigma(X)}$. In doing so, we take a step towards finding a strict combinatorial interpretation for the Super Catalan numbers.
ContributorsHouse, John Douglas (Author) / Fishel, Susanna (Thesis director) / Childress, Nancy (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Genocide studies have traditionally focused on the perpetrator’s intent to eradicate a particular identity-based group, using the Holocaust as their model and point of comparison. Although some aspects of the Holocaust were undoubtedly unique, recent scholars have sought to challenge the notion that it was a singular phenomenon. Instead, they draw attention to a recurring pattern of genocidal events throughout history by shifting the focus from intent to structure. One particular branch of scholars seeks to connect the ideology and tactics of imperialism with certain genocidal events. These anti-imperialist genocide scholars concede that their model cannot account for all genocides, but still claim that it creates meaningful connections between genocides committed by Western colonialist powers and those that have occurred in a neoimperialist world order shaped according to Western interests. The latter includes genocides in postcolonial states, which these scholars believe were shaped by the scars of their colonial past, as well as genocides in which imperial hegemons assisted local perpetrators. Imperialist and former colonial powers have contributed meaningfully to all of these kinds of genocides, yet their contributions have largely been ignored due to their own influence on the creation of the current international order. Incorporating the anti-imperialist perspective into the core doctrine of genocide studies may lead to breakthroughs in areas of related policy and practice, such as prevention and accountability.
ContributorsParker, Ashleigh Mae (Author) / Thies, Cameron (Thesis director) / Sivak, Henry (Committee member) / School of Politics and Global Studies (Contributor) / School of Social Transformation (Contributor) / Department of English (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05