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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
ContributorsDaval, Charles (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-26
Description
Biological organisms are made up of cells containing numerous interconnected biochemical processes. Diseases occur when normal functionality of these processes is disrupted, manifesting as disease symptoms. Thus, understanding these biochemical processes and their interrelationships is a primary task in biomedical research and a prerequisite for activities including diagnosing diseases and drug development. Scientists studying these interconnected processes have identified various pathways involved in drug metabolism, diseases, and signal transduction, etc. High-throughput technologies, new algorithms and speed improvements over the last decade have resulted in deeper knowledge about biological systems, leading to more refined pathways. Such pathways tend to be large and complex, making it difficult for an individual to remember all aspects. Thus, computer models are needed to represent and analyze them. The refinement activity itself requires reasoning with a pathway model by posing queries against it and comparing the results against the real biological system. Many existing models focus on structural and/or factoid questions, relying on surface-level information. These are generally not the kind of questions that a biologist may ask someone to test their understanding of biological processes. Examples of questions requiring understanding of biological processes are available in introductory college level biology text books. Such questions serve as a model for the question answering system developed in this thesis. Thus, the main goal of this thesis is to develop a system that allows the encoding of knowledge about biological pathways to answer questions demonstrating understanding of the pathways. To that end, a language is developed to specify a pathway and pose questions against it. Some existing tools are modified and used to accomplish this goal. The utility of the framework developed in this thesis is illustrated with applications in the biological domain. Finally, the question answering system is used in real world applications by extracting pathway knowledge from text and answering questions related to drug development.
ContributorsAnwar, Saadat (Author) / Baral, Chitta (Thesis advisor) / Inoue, Katsumi (Committee member) / Chen, Yi (Committee member) / Davulcu, Hasan (Committee member) / Lee, Joohyung (Committee member) / Arizona State University (Publisher)
Created2014
DescriptionThe purpose of this project is to explore the influence of folk music in guitar compositions by Manuel Ponce from 1923 to 1932. It focuses on his Tres canciones populares mexicanas and Tropico and Rumba.
ContributorsGarcia Santos, Arnoldo (Author) / Koonce, Frank (Thesis advisor) / Rogers, Rodney (Committee member) / Rotaru, Catalin (Committee member) / Arizona State University (Publisher)
Created2014
Description
Modeling dynamic systems is an interesting problem in Knowledge Representation (KR) due to their usefulness in reasoning about real-world environments. In order to effectively do this, a number of different formalisms have been considered ranging from low-level languages, such as Answer Set Programming (ASP), to high-level action languages, such as C+ and BC. These languages show a lot of promise over many traditional approaches as they allow a developer to automate many tasks which require reasoning within dynamic environments in a succinct and elaboration tolerant manner. However, despite their strengths, they are still insufficient for modeling many systems, especially those of non-trivial scale or that require the ability to cope with exceptions which occur during execution, such as unexpected events or unintended consequences to actions which have been performed. In order to address these challenges, a theoretical framework is created which focuses on improving the feasibility of applying KR techniques to such problems. The framework is centered on the action language BC+, which integrates many of the strengths of existing KR formalisms, and provides the ability to perform efficient reasoning in an incremental fashion while handling exceptions which occur during execution. The result is a developer friendly formalism suitable for performing reasoning in an online environment. Finally, the newly enhanced Cplus2ASP 2 is introduced, which provides a number of improvements over the original version. These improvements include implementing BC+ among several additional languages, providing enhanced developer support, and exhibiting a significant performance increase over its predecessors and similar systems.
ContributorsBabb, Joseph (Author) / Lee, Joohyung (Thesis advisor) / Lee, Yann-Hang (Committee member) / Baral, Chitta (Committee member) / Arizona State University (Publisher)
Created2014
Description
Due to government initiatives, education in the classroom has focused on high stakes test scores measuring student achievement on basic skills. The purpose of this action research study was to augment fourth grade students' knowledge of basic content by teaching greater meaning and depth of understanding--to teach critical thinking using Socratic circles. Using a constructivist approach, a comprehensive plan was designed and implemented that included an age-appropriate platform for argument and inquiry, a process that required critical thinking skills, and allowed the intellectual standards for critical thinking to be developed and measured. Ten students representing the academic levels of the whole class were selected and participated in seven Socratic circles. Over a period of 15 weeks, a mixed methods approach was employed to determine how students were able to apply the intellectual standards to reasoning during Socratic circles, how this innovation provoked participation in student-centered dialogue, and how Socratic circles improved students' evaluation of competing ideas during their reasoned discourse. Results suggested that Comprehensive Socratic Circles increased participation in reasoned discourse. Students' ability to evaluate competing ideas improved, and their application of the intellectual standards for critical thinking to their reasoning increased. Students also increased their use of student-centered dialogue across the sessions. These findings suggest that Socratic circles is a flexible and effective teaching strategy that fosters critical thinking in fourth graders.
ContributorsCleveland, Julie (Author) / Rotheram-Fuller, Erin (Thesis advisor) / Dinn-You Liou, Daniel (Committee member) / Lansdowne, Kimberly (Committee member) / Arizona State University (Publisher)
Created2015
ContributorsKotronakis, Dimitris (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-01
Description
Image Understanding is a long-established discipline in computer vision, which encompasses a body of advanced image processing techniques, that are used to locate (“where”), characterize and recognize (“what”) objects, regions, and their attributes in the image. However, the notion of “understanding” (and the goal of artificial intelligent machines) goes beyond factual recall of the recognized components and includes reasoning and thinking beyond what can be seen (or perceived). Understanding is often evaluated by asking questions of increasing difficulty. Thus, the expected functionalities of an intelligent Image Understanding system can be expressed in terms of the functionalities that are required to answer questions about an image. Answering questions about images require primarily three components: Image Understanding, question (natural language) understanding, and reasoning based on knowledge. Any question, asking beyond what can be directly seen, requires modeling of commonsense (or background/ontological/factual) knowledge and reasoning.
Knowledge and reasoning have seen scarce use in image understanding applications. In this thesis, we demonstrate the utilities of incorporating background knowledge and using explicit reasoning in image understanding applications. We first present a comprehensive survey of the previous work that utilized background knowledge and reasoning in understanding images. This survey outlines the limited use of commonsense knowledge in high-level applications. We then present a set of vision and reasoning-based methods to solve several applications and show that these approaches benefit in terms of accuracy and interpretability from the explicit use of knowledge and reasoning. We propose novel knowledge representations of image, knowledge acquisition methods, and a new implementation of an efficient probabilistic logical reasoning engine that can utilize publicly available commonsense knowledge to solve applications such as visual question answering, image puzzles. Additionally, we identify the need for new datasets that explicitly require external commonsense knowledge to solve. We propose the new task of Image Riddles, which requires a combination of vision, and reasoning based on ontological knowledge; and we collect a sufficiently large dataset to serve as an ideal testbed for vision and reasoning research. Lastly, we propose end-to-end deep architectures that can combine vision, knowledge and reasoning modules together and achieve large performance boosts over state-of-the-art methods.
Knowledge and reasoning have seen scarce use in image understanding applications. In this thesis, we demonstrate the utilities of incorporating background knowledge and using explicit reasoning in image understanding applications. We first present a comprehensive survey of the previous work that utilized background knowledge and reasoning in understanding images. This survey outlines the limited use of commonsense knowledge in high-level applications. We then present a set of vision and reasoning-based methods to solve several applications and show that these approaches benefit in terms of accuracy and interpretability from the explicit use of knowledge and reasoning. We propose novel knowledge representations of image, knowledge acquisition methods, and a new implementation of an efficient probabilistic logical reasoning engine that can utilize publicly available commonsense knowledge to solve applications such as visual question answering, image puzzles. Additionally, we identify the need for new datasets that explicitly require external commonsense knowledge to solve. We propose the new task of Image Riddles, which requires a combination of vision, and reasoning based on ontological knowledge; and we collect a sufficiently large dataset to serve as an ideal testbed for vision and reasoning research. Lastly, we propose end-to-end deep architectures that can combine vision, knowledge and reasoning modules together and achieve large performance boosts over state-of-the-art methods.
ContributorsAditya, Somak (Author) / Baral, Chitta (Thesis advisor) / Yang, Yezhou (Thesis advisor) / Aloimonos, Yiannis (Committee member) / Lee, Joohyung (Committee member) / Li, Baoxin (Committee member) / Arizona State University (Publisher)
Created2018
Description
After surveying the literature on the normativity of logic, the paper answers that logic is normative for reasoning and rationality. The paper then goes on to discuss whether this constitutes a new problem in issues in normativity, and the paper affirms that it does. Finally, the paper concludes by explaining that the logic as model view can address this new problem.
ContributorsCadenas, Haggeo (Author) / Pinillos, Angel (Thesis advisor) / Creath, Richard (Committee member) / Kobes, Bernard (Committee member) / nair, shyam (Committee member) / Arizona State University (Publisher)
Created2017
ContributorsDavin, Colin (Performer) / ASU Library. Music Library (Publisher)
Created2018-10-05