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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
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 study was to create a screening tool specifically for the identification of sex trafficking victims in the medical setting through the analysis of existing human trafficking screening tool studies geared towards use in the medical setting. Screening questions from these studies were compiled and modified into a survey that was distributed to healthcare professionals through the nationwide HEAL (Health Professional Education, Advocacy, Linkage) Trafficking listserv. Each screening tool study demonstrated benefits and disadvantages that were helpful in the sampling and selection of screening tool questions. The small sample size and a lack of data on the attitudes of medical professionals on sex trafficked victims were noted as limitations to this study. Further implications for this study would include validating the screening tool questions in a medical setting to determine the sensitivity of the survey in identifying patients as possible sex trafficking victims.
ContributorsCatano, Karen Samantha (Co-author) / Byun, Jiwon (Co-author) / Roe-Sepowitz, Dominique (Thesis director) / Lee, Maurice (Committee member) / School for the Science of Health Care Delivery (Contributor) / College of Integrative Sciences and Arts (Contributor) / W.P. Carey School of Business (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
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
Description
The passage of 2007's Legal Arizona Workers Act, which required all new hires to be tested for legal employment status through the federal E-Verify database, drastically changed the employment prospects for undocumented workers in the state. Using data from the 2007-2010 American Community Survey, this paper seeks to identify the impact of this law on the labor force in Arizona, specifically regarding undocumented workers and less educated native workers. Overall, the data shows that the wage bias against undocumented immigrants doubled in the four years studied, and the wages of native workers without a high school degree saw a temporary, positive increase compared to comparable workers in other states. The law did not have an effect on the wages of native workers with a high school degree.
ContributorsSantiago, Maria Christina (Author) / Pereira, Claudiney (Thesis director) / Mendez, Jose (Committee member) / School of International Letters and Cultures (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Insects have intricate systems they depend on for survival. They live in societies where every individual plays an important role. Ants are a great example of this observation. They are known for having structurally sound societies that ensure the livelihood of the colony. The ant species analyzed for this research, Harpegnathos saltator, portrays a structured colony and serves as a useful example of levels of hierarchy. In the colony of H. saltator, one can find a queen, gamergates, workers, and male ants living underground in Southern India. Recording and analyzing egg-laying rates are important in this study because of the amount of information it provides. It is used especially when observing the relationship among the gamergates in colonies with varying colony sizes. Three different methods were used to record the egg-laying rates, each providing insight into valuable information. Results show that the smaller colonies with fewer identified gamergates do share an equal amount of egg-laying. In larger colonies, it appears that there are more active identified gamergates than others. Egg-laying duration times are smaller in colonies with fewer gamergates. It is also found that the presence of brood does not affect egg-laying rates and reproductive inhibition could be a possibility based on two of the colonies observed F65 and F21. Based on the data found, a more active colony that attempts to maintain stability by demonstrating aggression may be affecting the reproduction of gamergates. Future work that would further strengthen the research and conclusions made would involve further observation of colonies, both large and small, with varying numbers of gamergates. More observation involving behavior among gamergates and workers would also be beneficial. Mathematical modeling could also be incorporated to create equations that could determine information about colonies based on size, number of gamergates, and egg-laying rates.
ContributorsMayoral, Alejandra (Author) / Kang, Yun (Thesis director) / Liebig, Juergen (Committee member) / College of Integrative Sciences and Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12