Matching Items (992)
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
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
With the new independence of adulthood, college students are a group susceptible to adopting unsupported, if not harmful, health practices. A survey of Arizona State University undergraduate students (N=200) was conducted to evaluate supplement use, trust in information sources, and beliefs about supplement regulation. Of those who reported using supplements, college students most frequently received information from friends and family. STEM majors in fields unrelated to health who were taking a supplement were found to be less likely to receive information about the supplement from a medical practitioner than those in health fields or those in non-STEM majors (-26.9%, p=0.018). STEM majors in health-related fields were 15.0% more likely to treat colds and/or cold symptoms with research-supported methods identified from reliable sources, while non-health STEM and non-STEM majors were more likely to take unsupported cold treatments (p=0.010). Surveyed students, regardless of major, also stated they would trust a medical practitioner for supplement advice above other sources (88.0%), and the majority expressed a belief that dietary supplements are approved/regulated by the government (59.8%).
ContributorsPerez, Jacob Tanner (Author) / Hendrickson, Kirstin (Thesis director) / Lefler, Scott (Committee member) / College of Liberal Arts and Sciences (Contributor) / School of Molecular Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
ContributorsChandler, N. Kayla (Author) / Neisewander, Janet (Thesis director) / Sanabria, Federico (Committee member) / Olive, M. Foster (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2013-05
Description
I propose that norms regulate behaviors that negatively impact an individual's survival and reproduction. But because monitoring and enforcing of norms can be costly, individuals should be selective about which norms they police and under what circumstances they should do so. Two studies tested this idea by experimentally activating fitness-relevant motives and having participants answer questions about the policing of norms. The first study examined a norm prescribing respect for status and another proscribing sexual coercion. Results from Study 1 failed to support the hypotheses; activating a status-seeking motive did not have the predicted effects on policing of the respect-status norm nor did activating a mating motive have the predicted effects on policing of the respect-status norm or anti-coercion norm. Study 2 examined two new norms, one prescribing that people stay home when sick and the other proscribing people from having sex with another person's partners. Study 2 also manipulated whether self or others were the target of the policing. Study 2 failed to provide support; a disease avoidance motive failed to have effects on policing of the stay home when sick norm. Individuals in a relationship under a mating motive wanted less policing of others for violation of the mate poaching norm than those in a baseline condition, opposite of the predicted effects.
ContributorsSmith, M. Kristopher (Author) / Neuberg, L. Steven (Thesis director) / Presson, Clark (Committee member) / Hruschka, J. Daniel (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2013-05
Description
Literature in public administration emphasizes a growing dissatisfaction with government on the part of residents. Where there tends to be a lack in the literature is in terms of solutions to this problem. We would like to argue that the engagement process itself has the power to foster a profound attitudinal shift on the part of both residents and government. This paper explores the structural and cultural barriers to satisfactory public engagement both from literature and a combination of policy analysis, semi-structured interviews and participatory observation within the City of Tempe. We then provide recommendations to the City of Tempe on how to overcome these barriers and effect authentic public engagement practices. With these new suggested practices and mindsets, we provide a way that people can have the power to create their own community.
ContributorsRiffle, Morgan (Co-author) / Tchida, Celina (Co-author) / Ingram-Waters, Mary (Thesis director) / Grzanka, Patrick (Committee member) / King, Cheryl (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2013-05
Description
This thesis examines the relationship between unofficial, official, and parallel Islam in Uzbekistan following the end of the Soviet Union. Key touchstone moments in Uzbekistan during the twentieth-century show the history between unofficial and official Islam and the resulting precedents set for Muslims gathering against the government. This historical analysis shows how President Karimov and the Uzbek government view and approach Islam in the country following independence.
ContributorsTieslink, Evan (Author) / Batalden, Stephen (Thesis director) / Kefeli, Agnes (Committee member) / Saikia, Yasmin (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Politics and Global Studies (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor)
Created2013-05
Description
Through this creative project, I executed a Distracted Driving Awareness Campaign at Arizona State University to raise awareness about the dangers of distracted driving, specifically texting while driving. As an Undergraduate Student Government Senator, my priority is the safety and success of students, both in and out of the classroom. By partnering with State Farm and AT&T, we were able to raise awareness about the dangers of distracted driving and collected over 200 pledges from students to never text and drive.
ContributorsHibbs, Jordan Ashley (Author) / Miller, Clark (Thesis director) / Parmentier, Mary Jane (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Politics and Global Studies (Contributor) / Department of Psychology (Contributor) / Graduate College (Contributor)
Created2014-05
Description
Teen dating violence is a significant problem in the U.S., with approximately 1 out of 3 teens experiencing some form of dating violence. BLOOM is a not-for-profit organization created by Donna Bartos. BLOOM's educators enter high schools in Arizona and present their educational program on dating abuse prevention. BLOOM's primary goal is to educate teens on how to prevent teen dating violence and empower them with the skills leading to healthy relationships. After participants complete their educational program, a feedback card is filled out with an open-response section. This project focused on the open response section to analyze feedback cards through a process of code development, coding, and tallying. Information provided by this project could assist BLOOM in re-evaluating their curriculum, appealing to future investors, and growing their program to reach more students. With a coding system in place, BLOOM will also be able to better assess the impact they have on the participants of their program.
ContributorsHarmon, Ashley Nicole (Author) / Bodman, Denise (Thesis director) / Dumka, Larry (Committee member) / T. Denny Sanford School of Social and Family Dynamics (Contributor) / College of Liberal Arts and Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05