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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 study was to observe the effectiveness of the phenylalanyl arginine β-naphthylamide dihydrochloride inhibitor and Tween 20 when combined with an antibiotic against Escherichia. coli. As antibiotic resistance becomes more and more prevalent it is necessary to think outside the box and do more than just increase the dosage of currently prescribed antibiotics. This study attempted to combat two forms of antibiotic resistance. The first is the AcrAB efflux pump which is able to pump antibiotics out of the cell. The second is the biofilms that E. coli can form. By using an inhibitor, the pump should be unable to rid itself of an antibiotic. On the other hand, using Tween allows for biofilm formation to either be disrupted or for the biofilm to be dissolved. By combining these two chemicals with an antibiotic that the efflux pump is known to expel, low concentrations of each chemical should result in an equivalent or greater effect on bacteria compared to any one chemical in higher concentrations. To test this hypothesis a 96 well plate BEC screen test was performed. A range of antibiotics were used at various concentrations and with varying concentrations of both Tween and the inhibitor to find a starting point. Following this, Erythromycin and Ciprofloxacin were picked as the best candidates and the optimum range of the antibiotic, Tween, and inhibitor were established. Finally, all three chemicals were combined to observe the effects they had together as opposed to individually or paired together. From the results of this experiment several conclusions were made. First, the inhibitor did in fact increase the effectiveness of the antibiotic as less antibiotic was needed if the inhibitor was present. Second, Tween showed an ability to prevent recovery in the MBEC reading, showing that it has the ability to disrupt or dissolve biofilms. However, Tween also showed a noticeable decrease in effectiveness in the overall treatment. This negative interaction was unable to be compensated for when using the inhibitor and so the hypothesis was proven false as combining the three chemicals led to a less effective treatment method.
ContributorsPetrovich Flynn, Chandler James (Author) / Misra, Rajeev (Thesis director) / Bean, Heather (Committee member) / Perkins, Kim (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The inherent risk in testing drugs has been hotly debated since the government first started regulating the drug industry in the early 1900s. Who can assume the risks associated with trying new pharmaceuticals is unclear when looked at through society's lens. In the mid twentieth century, the US Food and Drug Administration (FDA) published several guidance documents encouraging researchers to exclude women from early clinical drug research. The motivation to publish those documents and the subsequent guidance documents in which the FDA and other regulatory offices established their standpoints on women in drug research may have been connected to current events at the time. The problem of whether women should be involved in drug research is a question of who can assume risk and who is responsible for disseminating what specific kinds of information. The problem tends to be framed as one that juxtaposes the health of women and fetuses and sets their health as in opposition. That opposition, coupled with the inherent uncertainty in testing drugs, provides for a complex set of issues surrounding consent and access to information.
ContributorsMeek, Caroline Jane (Author) / Maienschein, Jane (Thesis director) / Brian, Jennifer (Committee member) / School of Life Sciences (Contributor) / Sanford School of Social and Family Dynamics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
An in-depth analysis on the effects vortex generators cause to the boundary layer separation that occurs when an internal flow passes through a diffuser is presented. By understanding the effects vortex generators demonstrate on the boundary layer, they can be utilized to improve the performance and efficiencies of diffusers and other internal flow applications. An experiment was constructed to acquire physical data that could assess the change in performance of the diffusers once vortex generators were applied. The experiment consisted of pushing air through rectangular diffusers with half angles of 10, 20, and 30 degrees. A velocity distribution model was created for each diffuser without the application of vortex generators before modeling the velocity distribution with the application of vortex generators. This allowed the two results to be directly compared to one another and the improvements to be quantified. This was completed by using the velocity distribution model to find the partial mass flow rate through the outer portion of the diffuser's cross-sectional area. The analysis concluded that the vortex generators noticeably increased the performance of the diffusers. This was best seen in the performance of the 30-degree diffuser. Initially the diffuser experienced airflow velocities near zero towards the edges. This led to 0.18% of the mass flow rate occurring in the outer one-fourth portion of the cross-sectional area. With the application of vortex generators, this percentage increased to 5.7%. The 20-degree diffuser improved from 2.5% to 7.9% of the total mass flow rate in the outer portion and the 10-degree diffuser improved from 11.9% to 19.2%. These results demonstrate an increase in performance by the addition of vortex generators while allowing the possibility for further investigation on improvement through the design and configuration of these vortex generators.
ContributorsSanchez, Zachary Daniel (Author) / Takahashi, Timothy (Thesis director) / Herrmann, Marcus (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The objective of this project was to design an electrically driven centrifugal pump for the Daedalus Astronautics @ASU hybrid rocket engine (HRE). The pump design was purposefully simplified due to time, fabrication, calculation, and capability constraints, which resulted in a lower fidelity design, with the option to be improved later. The impeller, shroud, volute, shaft, motor, and ESC were the main focuses of the pump assembly, but the seals, bearings, lubrication methods, and flow path connections were considered as elements which would require future attention. The resulting pump design is intended to be used on the Daedalus Astronautics HRE test cart for design verification. In the future, trade studies and more detailed analyses should and will be performed before this pump is integrated into the Daedalus Astronautics flight-ready HRE.
ContributorsShillingburg, Ryan Carl (Author) / White, Daniel (Thesis director) / Brunacini, Lauren (Committee member) / Mechanical and Aerospace Engineering Program (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
As of 2019, 30 US states have adopted abortion-specific informed consent laws that require state health departments to develop and disseminate written informational materials to patients seeking an abortion. Abortion is the only medical procedure for which states dictate the content of informed consent counseling. State abortion counseling materials have been criticized for containing inaccurate and misleading information, but overall, informed consent laws for abortion do not often receive national attention. The objective of this project was to determine the importance of informed consent laws to achieving the larger goal of dismantling the right to abortion. I found that informed consent counseling materials in most states contain a full timeline of fetal development, along with information about the risks of abortion, the risks of childbirth, and alternatives to abortion. In addition, informed consent laws for abortion are based on model legislation called the “Women’s Right to Know Act” developed by Americans United for Life (AUL). AUL calls itself the legal architect of the pro-life movement and works to pass laws at the state level that incrementally restrict abortion access so that it gradually becomes more difficult to exercise the right to abortion established by Roe v. Wade. The “Women’s Right to Know Act” is part of a larger package of model legislation called the “Women’s Protection Project,” a cluster of laws that place restrictions on abortion providers, purportedly to protect women, but actually to decrease abortion access. “Women’s Right to Know” counseling laws do not directly deny access to abortion, but they do reinforce key ideas important to the anti-abortion movement, like the concept of fetal personhood, distrust in medical professionals, the belief that pregnant people cannot be fully autonomous individuals, and the belief that abortion is not an ordinary medical procedure and requires special government oversight. “Women’s Right to Know” laws use the language of informed consent and the purported goal of protecting women to legitimize those ideas, and in doing so, they significantly undermine the right to abortion. The threat to abortion rights posed by laws like the “Women’s Right to Know” laws indicates the need to reevaluate and strengthen our ethical defense of the right to abortion.
ContributorsVenkatraman, Richa (Author) / Maienschein, Jane (Thesis director) / Brian, Jennifer (Thesis director) / Abboud, Carolina (Committee member) / Historical, Philosophical & Religious Studies (Contributor) / School of Life Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05