<p>  </p> <p>The dissertation study presented here explores what higher education instructors believe about problem-solving. Beliefs about problem-solving pedagogy and the influences that change pedagogical approaches in the post-secondary realm of physics education require more robust exploration. The level of change that occurs through the day-to-day teaching cycle and the support that garners improvement are essential aspects of teaching in higher education that need robust understanding.</p> <p>Insight into higher education could illuminate the transitional experience of students between high school and college-level physics. This study explores the beliefs of Indiana college and high school educators, all of whom teach college-level physics content, and probed how those beliefs shaped higher education instructional strategies and teaching philosophies. The study was conducted using a Constructivist Grounded Theory approach.</p> <p>The findings show that physics educators in college and high school learning environments lacked support explicitly geared toward them and physics. All the educators included in the study taught college-level physics. Four of the six participants were the only ones teaching physics in their schools. Despite the isolation, all participants noted the importance of peer-to-peer learning for themselves and their students, noting interactions with exterior training opportunities (e.g., educational conferences or online educator communities). However, the most crucial source of change in their teaching beliefs and approaches that the participants noted was the feedback they received from students.</p>

Combinatorial Group Testing (CGT) is a process of identifying faulty interactions (“errors”) within a particular set of items. Error Locating Arrays (ELAs) are combinatorial designs that can be built from Covering Arrays (CAs) to not only cover all errors in a system (each involving up to a certain number of items), but to locate and identify the errors as well. In this thesis, we survey known results for CGT, as well as CAs, ELAs, and some other types of related arrays. More importantly, we give several new results. First, we give a new algorithm that can be used to test a system in which each component (factor) has two options (values), and at most two errors are present. We show that, for systems with at most two errors, our algorithm improves upon a related algorithm by Mart´ınez et al. in terms of both robustness and efficiency. Second, we give the first adaptive CGT algorithm that can identify, among a given set of k items, all faulty interactions involving up to three items. We then compare it, performance-wise, to current-best nonadaptive method that can identify faulty interactions involving up to three items. We also give the first adaptive ELA-building algorithm that can identify all faulty interactions involving up to three items when safe values are known. Both of our new algorithms are generalizations of ones previously given by Mart´ınez et al. for identifying all faulty interactions involving up to two items.

Combinatorial Group Testing (CGT) is a process of identifying faulty interactions (“errors”) within a particular set of items. Error Locating Arrays (ELAs) are combinatorial designs that can be built from Covering Arrays (CAs) to not only cover all errors in a system (each involving up to a certain number of items), but to locate and identify the errors as well. In this thesis, we survey known results for CGT, as well as CAs, ELAs, and some other types of related arrays. More importantly, we give several new results. First, we give a new algorithm that can be used to test a system in which each component (factor) has two options (values), and at most two errors are present. We show that, for systems with at most two errors, our algorithm improves upon a related algorithm by Mart´ınez et al. in terms of both robustness and efficiency. Second, we give the first adaptive CGT algorithm that can identify, among a given set of k items, all faulty interactions involving up to three items. We then compare it, performance-wise, to current-best nonadaptive method that can identify faulty interactions involving up to three items. We also give the first adaptive ELA-building algorithm that can identify all faulty interactions involving up to three items when safe values are known. Both of our new algorithms are generalizations of ones previously given by Mart´ınez et al. for identifying all faulty interactions involving up to two items.

Combinatorial Group Testing (CGT) is a process of identifying faulty interactions (“errors”) within a particular set of items. Error Locating Arrays (ELAs) are combinatorial designs that can be built from Covering Arrays (CAs) to not only cover all errors in a system (each involving up to a certain number of items), but to locate and identify the errors as well. In this thesis, we survey known results for CGT, as well as CAs, ELAs, and some other types of related arrays. More importantly, we give several new results. First, we give a new algorithm that can be used to test a system in which each component (factor) has two options (values), and at most two errors are present. We show that, for systems with at most two errors, our algorithm improves upon a related algorithm by Mart´ınez et al. in terms of both robustness and efficiency. Second, we give the first adaptive CGT algorithm that can identify, among a given set of k items, all faulty interactions involving up to three items. We then compare it, performance-wise, to current-best nonadaptive method that can identify faulty interactions involving up to three items. We also give the first adaptive ELA-building algorithm that can identify all faulty interactions involving up to three items when safe values are known. Both of our new algorithms are generalizations of ones previously given by Mart´ınez et al. for identifying all faulty interactions involving up to two items.