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Description
This thesis attempts to answer the question ‘What changes in understanding occur as a student develops their way of understanding similarity using geometric transformations and what teacher interventions contribute to these changes in understanding?’ Similarity is a topic taught in school geometry usually alongside the related topic Congruence. The Common Core State Standards for Mathematics, upon which many states have based their state level educational standards, recommend teachers leverage transformational geometry to explain congruence and similarity using geometric transformations. "However, there is a lack of research studies regarding how transformational geometry can be taught as a productive way of understanding similarities and what challenges students might encounter when learning similarities via transformational geometry approaches." This study aims to further the efforts of teachers who are trying to develop their students’ transformational understandings of similarity.
This study was conducted as exploratory teaching interviews in Spring 2023 at a large public university. The student was an undergraduate student who had not previously taken a transformational geometry-based Euclidean geometry at the university. I, as a teacher-researcher, designed a set of tasks for the exploratory teaching interviews, and implemented them over the course of 5 weeks. I, as a researcher, also analyzed the data to create a model for the student's understanding of similarity. Specifically, I was interested in sorting the ways of understanding expressed by the student into the categories pictorial, measurement-based, and transformational. By analyzing the videos from the interviews and tracking the students’ understandings from moment to moment, I was able to see a shift in her understanding toward a transformational understanding. Thus her way of understanding similarity using geometric transformations was strengthened and I was able to pinpoint key shifts in understanding that contribute to the strengthening of this understanding.
Notably, the student developed a notion of dilation as coming from a single centerpoint, negotiated definitions from each way of understanding until eventually settling on a definition rooted in transformations, and applied similarity to an unfamiliar context using both her intuition about similarity and the definition she created. The implications of this being that a somewhat advanced understanding dilation is productive for understanding similarity using geometric transformations, and that to develop a student's way of understanding similarity using geometric transformations there must be a practical need for this created by tasks the student engages with.
ContributorsCombs, Nicole (Author) / Roh, Kyeong Hah (Thesis director) / Zandieh, Michelle (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2023-12
Description
Our thesis revolved around the Maryvale community and was centered by a Photovoice project that was a Youth Participatory Action Research method. Being a project led by the youth we continued their stories and expanded off of the topics that we discussed in our photovoice meetings. In our thesis podcast we discussed the expectation and reality of moving to a new country, the colorism our community as well as other communities face, and the health disparities that are present within underrepresented communities. We were able to expand on these topics and tie it back to the conversations we had with each other four years prior to doing our podcast and how little or how much these topics have changed and evolved.
ContributorsRuiz, Wendy (Author) / Elizalde, Manuel (Co-author) / Medina Rios, Kimberly (Co-author) / Reed, Lauren (Thesis director) / Mullady, Allison (Committee member) / Barrett, The Honors College (Contributor) / School of Politics and Global Studies (Contributor) / Department of Management and Entrepreneurship (Contributor)
Created2023-05
DescriptionWritten reviews and rankings of fifteen shows that played in the West End during the 2023 season.
ContributorsLewis, Cheyenne (Author) / Hunt, Kristin (Thesis director) / Peavey, Katie (Committee member) / Barrett, The Honors College (Contributor) / School of Politics and Global Studies (Contributor) / School of Music, Dance and Theatre (Contributor)
Created2023-12
Description
One common problem that occurs to students during breaks is the retrogression of knowledge due to lack of practice. This problem occurs for students at all levels of education but is especially harmful to students who are taking sequential classes such as Calculus for Engineers I and Calculus for Engineers II where the retention of topics taught in Calculus for Engineers I are required for students to succeed. One solution to this problem is the Keep in School Shape (KiSS) program. The KiSS program is a very efficient and easily accessible program that allows students to stay warmed up and ready to go when they start a sequential course by having daily review material during academic breaks.
During an academic break, students who are signed up for the KiSS program are sent a link through text message or email every day that allows them to access a multiple choice review problem. The review problem that they are given is a problem that presents material from the previous course that will be needed in the upcoming course. At the beginning of the review, students have the option to choose between a Level 1 or a Level 2 problem, where a Level 2 problem is related to its Level 1 counterpart but slightly more difficult. Before the students are permitted to solve the problem, they must first use a five point scale that indicates their confidence in their ability to solve the problem. After they complete either the Level 1 or Level 2 daily problem, those that got it wrong have the option to view a hint and try again or view a solution. The students that got the Level 1 daily problem right are also allowed to view the solution but will be permitted to go onto the next level right away whereas the students that got the Level 1 problem incorrect will need to try a similar problem before being able to move onto Level 2. For students who chose to do the Level 2 problem and were not very confident, they were given the option to solve a level 1 problem instead. Students who chose level 2 and got it wrong are given the options to view a hint and try again or simply view the solution before moving on to flashcard versions of the daily problems. Students who get the Level 2 problem correct are also given the option to continue practicing using the flashcards if they choose to.
Once a week, there is also a trivia day where students have the choice to complete solely a mathematical trivia question or complete both the trivia question along with a daily review problem. This feature allows students to take a day off from doing mathematics if they choose, but still stay engaged by doing a related activity.
Through this program, there is a lot to learn about whether doing Level 1 problems can help students improve their understanding of a concept enough to correctly solve a Level 2 problem. There are many factors to consider such as which question the student chose to answer first, student confidence, and student perseverance. Through the Summer Break 2023 KiSS program, there was data collected for every student answer for each day they accessed the daily KiSS activity. This thesis presents an analysis of the data showing how having two levels of problems is beneficial for students and the correlation between students’ results in Level 1 problems and Level 2 problems for students who chose to attempt both problems.
ContributorsWang, Ryan (Author) / Van de Sande, Carla (Thesis director) / Reiser, Mark (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2023-12
Description
There are many emerging issues in the insurance market that have become more prevalent following COVID-19. Initially the issues were within the life and health insurance sector; however, in recent years there has been a notable increase in other sectors of insurance, with property and casualty being one of them. Following 2020, 2021, and 2022 losses, many property and casualty companies had to reassess where they were at and what losses they would be willing to take on. As reserves began to grow thin and severity began to rise, insurers and reinsurers began to investigate ways to combat the rising cost of insuring their policyholders. Even though this is an issue nationwide, the recent shifts in the California insurance market will be the scope for this dissection. This deeper look into the hardening market will provide greater insight to the issue at hand, as well as potential solutions for this market and insurers alike in the upcoming years.
ContributorsHarris, Emily (Author) / Zicarelli, John (Thesis director) / Zhou, Kenneth (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2023-12
Description
Gerrymandering involves the purposeful manipulation of districts in order to gain some political advantage. Because legislators have a vested interest in continuing their tenure, they can easily hijack the redistricting process each decade for their and their political party's benefit. This threatens the cornerstone of democracy: a voter’s capability to select an elected official that accurately represents their interests. Instead, gerrymandering has legislators to choose their voters.
In recent years, the Supreme Court has heard challenges to state legislature-drawn districts, most recently in Allen v. Milligan for Alabama and Moore v. Harper for North Carolina. The highest court of the United States ruled that the two state maps were gerrymandered, and in coming to their decision, the 9 justices relied on a plethora of amicus briefs- one of which included the Markov Chain Monte Carlo method, a computational method used to find gerrymandering.
Because of how widespread gerrymandering has become on both sides of the political aisle, states have moved to create independent redistricting commissions. Qualitative research regarding the efficacy of independent commissions is present, but there is little research using the quantitative computational methods from these SCOTUS cases. As a result, my thesis will use the Markov Chain Monte Carlo method to answer if impartial redistricting commissions (like we have in Arizona) actually preclude unfair redistricting practices.
My completed project is located here:
https://dheetideliwala.github.io/honors-thesis/
ContributorsDeliwala, Dheeti (Author) / Bryan, Chris (Thesis director) / Strickland, James (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor) / School of Politics and Global Studies (Contributor)
Created2023-12
ContributorsDeliwala, Dheeti (Author) / Bryan, Chris (Thesis director) / Strickland, James (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor) / School of Politics and Global Studies (Contributor)
Created2023-12
ContributorsDeliwala, Dheeti (Author) / Bryan, Chris (Thesis director) / Strickland, James (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor) / School of Politics and Global Studies (Contributor)
Created2023-12
Description
In the United States, Black defendants are more likely to be sentenced to death than their white counterparts exclusively due to their race. There are several aspects that work to explain why this pattern is present, and this paper analyzes our current sentencing disparity through the lens of race to understand why this is the case. First, the historical context of legal racial discrimination will be explored as I discuss the legacy slavery and how the trade and ownership of Black people led to the devaluation of African Americans long after the 13th Amendment abolished the practice. This is seen from the establishment of convict leasing directly following abolition, to the development of Black Codes and Jim Crow laws, and eventually this legacy became the foundation that contributed to the targeted mass incarceration of African Americans beginning with Richard Nixon’s 1970s “war on drugs” campaign and spanning to today. Next, six important milestone Supreme Court cases relating to the evolution of capital punishment in the United States will be described. These cases include Furman v. Georgia, Gregg v. Georgia, Lockett v. Ohio, Batson v. Kentucky, and McCleskey v. Kemp. This research also presents data that illustrates the current trends in death penalty sentencing within 26 states who currently implement this punishment. The results show that there is an overwhelming amount of data in support of harsher criminal sentences and therefore a higher likelihood of Black defendants being sentenced to death in comparison to their white counterparts. Lastly, the systemic inequalities embedded within several aspects of capital trials are outlined—both in terms of juror bias against African American defendants as well as racial issues when hiring an attorney—and works to inform my argument that the death penalty should be abolished. An offender’s race should not play any role in determining the severity of their punishment, but the historic criminalization of Black people works to ensure that these groups of people are typically at a severe disadvantage when navigating the American justice system. Overall, the application of the death penalty can not be applied in a standard manner, nor can there be regulations passed in such a way to guarantee an absence of racism within our current system. Therefore, the United States should abolish this unjust, discriminatory practice.
ContributorsSasselli, Annabella (Author) / Shabazz, Rashad (Thesis director) / Corey, Susan (Committee member) / Barrett, The Honors College (Contributor) / School of Social Transformation (Contributor) / School of Politics and Global Studies (Contributor)
Created2023-12
Description
For this study, my overarching goal was to understand the possibilities of humanity’s future in space exploration. Addressing the future of space exploration not only opens doors for a multitude of discoveries but may answer questions that can be essential to our survival on Earth. This study, more specifically, aimed to determine how college students at Arizona State University, engineering and astronomy students in particular, visualize the future of space exploration, as in the future, they will become the leading experts at the forefront of all space-related developments. The method through which I have conducted this study is a short survey, consisting of a variety of questions, designed to encourage students to develop their own unique interpretations of space exploration and ultimately, its imminent future. The results ultimately demonstrated that most participants in the study believed that political obstacles were the most prevalent concern in the further development of space exploration. There also appeared to be a moderate outlook on the future success and vitality of space exploration among student scientists and engineers. From a statistical standpoint, there appeared to be no alarming difference of opinion between these two ASU student groups.
ContributorsMontano, Sebastian (Author) / Voorhees, Matthew (Thesis director) / Aganaba, Timiebi (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Earth and Space Exploration (Contributor)
Created2023-12