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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 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
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
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
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
Engineering is a multidisciplinary field with a variety of applications. However, since there are so many disciplines of engineering, it is often challenging to find the discipline that best suits an individual interested in engineering. Not knowing which area of engineering most aligns to one’s interests is challenging when deciding on a major and a career. With the development of the Engineering Interest Quiz (EIQ), the goal was to help individuals find the field of engineering that is most similar to their interests. Initially, an Engineering Faculty Survey (EFS) was created to gather information from engineering faculty at Arizona State University (ASU) and to determine keywords that describe each field of engineering. With this list of keywords, the EIQ was developed. Data from the EIQ compared the engineering students’ top three results for the best engineering discipline for them with their current engineering major of study. The data analysis showed that 70% of the respondents had their major listed as one of the top three results they were given and 30% of the respondents did not have their major listed. Of that 70%, 64% had their current major listed as the highest or tied for the highest percentage and 36% had their major listed as the second or third highest percentage. Furthermore, the EIQ data was compared between genders. Only 33% of the male students had their current major listed as their highest percentage, but 55% had their major as one of their top three results. Women had higher percentages with 63% listing their current major as their highest percentage and 81% listing it in the top three of their final results.
ContributorsWagner, Avery Rose (Co-author) / Lucca, Claudia (Co-author) / Taylor, David (Thesis director) / Miller, Cindy (Committee member) / Chemical Engineering Program (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
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