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This dissertation is focused on developing efficient numerical methods and theoretical analysis for solving various inverse problems that arise in the fields of mathematics, physics, engineering, and beyond. We propose in this dissertation a unified framework with two stages to solve severely ill-posed and highly nonlinear inverse problems. In the first stage, we derive a system of partial differential equations by introducing a new variable and truncating the Fourier series of the solution to the governing equation. In the second stage, we solve the system derived in the first stage using the quasi-reversibility method, the Carleman contraction mapping method, and the convexification method. The obtained solutions of this stage directly yield the desired solutions to the inverse problems. An important contribution of the dissertation is that we will rigorously and numerically prove the efficiency of this framework, including its global convergence to the true solution. The analytic proofs are based on some Carleman estimates, and the numerical proofs are provided by successfully testing our methods with highly noisy simulated data and experimental data provided by US Army Research Laboratory engineers.
The term “kindergarten readiness” lacks a formal definition. This study was done to understand the perceptions of preschool and kindergarten teachers concerning typically developing students on day 60 of kindergarten. Focus groups were used to determine particular skills that a kindergartener should exhibit by that point in school in order to be successful during that year. Both groups of teachers were knowledgeable about the developmental continuum kindergartners should follow in order to achieve needed skills. A second finding was that kindergarten teachers scored students lower than preschool teachers on the anticipated ability of their students to achieve a skill. All teachers considered some skills were introduced prematurely. Kindergarten readiness can be described as skills that students should exhibit on day 60 of kindergarten in order to be successful. These include having control of their emotions, and understanding the emotions of others and what may cause them. Students on day 60 of kindergarten should also understand how to behave in familiar environments and when routines and procedures did not change. Further, they should be able to discriminate the sound that an alliteration and rhyme make but may not be able to explain the reason for the alliteration or rhyme.
Safety, often understood as freedom from unacceptable loss, and reliability, the capacity to accomplish particular outcomes repeatedly through operational sensitivity, are compelling performance objectives for high-risk organizations. If either is absent, people, organizations, and their external environments are potentially at unnecessary risk. Focused on continuous performance improvement, debriefs are team meetings that are often implemented to enable safe, reliable outcomes in these settings through post-incident discussion. Historically, research has presumed debriefs to support the capacity of teams to pursue the twin objectives of safety and reliability simultaneously without contradiction. However, this theoretical assumption has never been assessed according to how a team’s discourse in debriefs constitutes safety and reliability as distinct outcomes. This research adopts Craig and Tracy’s (2021) grounded practical theory methodology to analyze talk in post-competition debriefs among stock car racing pit crews. Analysis framed debrief participants’ talk according to problem and technical levels of grounded practical reconstruction, suggesting a central dilemma that constrains pit crews’ efforts for safety and reliability in these meetings, namely a contradiction among performance expectations for regulatory adherence and for boundary pushing. Results also feature several discursive techniques that pit crews employ during debriefs in response to this dilemma. A model of dilemmatic talk in debriefs situates these outcomes in the context of fragility, an implicit value of this complex, dynamic work environment made explicit.
The term “kindergarten readiness” lacks a formal definition. This study was done to understand the perceptions of preschool and kindergarten teachers concerning typically developing students on day 60 of kindergarten. Focus groups were used to determine particular skills that a kindergartener should exhibit by that point in school in order to be successful during that year. Both groups of teachers were knowledgeable about the developmental continuum kindergartners should follow in order to achieve needed skills. A second finding was that kindergarten teachers scored students lower than preschool teachers on the anticipated ability of their students to achieve a skill. All teachers considered some skills were introduced prematurely. Kindergarten readiness can be described as skills that students should exhibit on day 60 of kindergarten in order to be successful. These include having control of their emotions, and understanding the emotions of others and what may cause them. Students on day 60 of kindergarten should also understand how to behave in familiar environments and when routines and procedures did not change. Further, they should be able to discriminate the sound that an alliteration and rhyme make but may not be able to explain the reason for the alliteration or rhyme.
Although significant research has been conducted on opportunity gaps between White and racially minoritized students, the percentage of minority students has reached 53% of the United States K-12 public schools (NCES, 2022). While the percentage of minority students now constitute the majority of public schools, the teacher workforce and school leadership remains majority White. As such, there is a need for additional investigations examining the role of culturally responsive classroom and school leadership practices in public schools. In particular, in the research, less is known about African American males and their culturally responsive school leadership practices. Thus, this study uses autoethnography to explore the experiences of a Black male school leader and the role of culturally responsive school leadership (CRSL) and conscientization in promoting effective school practices. As a member of a minority group, the school leader had relevant life and educational experiences of struggles and triumphs that impacted his leadership practices. These practices included but are not limited to fostering empathy, care, relevance, and rigor, which impacted the overall school climate and achievement. With the use of these practices that are grounded in CRSL, this urban school outperformed schools in the neighboring district. In sum, the findings suggest that there remains a need for more investigations on the role of CRSL in promoting urban school success.
Although significant research has been conducted on opportunity gaps between White and racially minoritized students, the percentage of minority students has reached 53% of the United States K-12 public schools (NCES, 2022). While the percentage of minority students now constitute the majority of public schools, the teacher workforce and school leadership remains majority White. As such, there is a need for additional investigations examining the role of culturally responsive classroom and school leadership practices in public schools. In particular, in the research, less is known about African American males and their culturally responsive school leadership practices. Thus, this study uses autoethnography to explore the experiences of a Black male school leader and the role of culturally responsive school leadership (CRSL) and conscientization in promoting effective school practices. As a member of a minority group, the school leader had relevant life and educational experiences of struggles and triumphs that impacted his leadership practices. These practices included but are not limited to fostering empathy, care, relevance, and rigor, which impacted the overall school climate and achievement. With the use of these practices that are grounded in CRSL, this urban school outperformed schools in the neighboring district. In sum, the findings suggest that there remains a need for more investigations on the role of CRSL in promoting urban school success.
As student demographics continue to evolve in higher education, the intersection of college-going generation status and U.S. immigrant-generation status needs to be considered; particularly, how these bi/polycultural experiences may play a role in the experience of belonging in college. This qualitative, phenomenological research study aimed to explore the lived experiences of four-year university students identifying as first-generation in college (FGC) and second-generation immigrants (SGI) in the U.S., with a focus on sense of belonging experiences at this identity intersection. Ten in-depth, semi-structured interviews with FGC-SGI students at an institution in the Southeastern U.S. were conducted to highlight identity and belonging narratives. Findings revealed that FGC-SGI students more readily engaged in identity disclosure with peers who shared at least one identity, and experienced implicit pressures to succeed due to their identities. Findings also revealed that FGC-SGI students sought out peers with similar identity characteristics to feel belonging, and that belonging played a critical role in how they viewed both their identities and their abilities to succeed in college. Thus, understanding FGC-SGI students' lived experiences may assist equity-minded higher education professionals with framing and creating settings that purposefully engage with this population to promote a positive, inclusive college experience, aiding in persistence and success.
The teaching practices of African American teachers are rooted in their personal and racialized experiences and have implications for teacher preparation programs and teacher scholarship. While research is abundant on how the teaching practices of Black male teachers positively impact student outcomes, the formation of their teaching practices is not as explicit in the existing literature. Employing critical race theory theoretical framework, this study explored how Black male teachers in the South's racialized and gendered experiences impact their teaching practices. The following research questions guided this qualitative study: 1) What are the racialized and gendered experiences of Black male teachers in the South; 2) What are the teaching practices of Black male teachers in the South?; and 3) How do the racialized and gendered experiences of Black male teachers in the South impact their teaching practices? A thematic analysis of participant interviews and archival documents revealed themes that add to the existing literature on how Black male teachers racialized and gendered experiences impact their teaching practices. Recommendations are provided for school and district leaders, professional development staff, teacher preparation programs, and other educational stakeholders.
This phenomenological qualitative study, serves to fill a gap in the research surrounding how the multiplicities of identities inform the instructional practices and racial identity of self-identified antiracist educators by answering the following questions: “How do intersections of identity shape the way teachers view themselves in the classroom?” and “How do the varied intersections of white identity inform teacher experiences, philosophical and pedagogical paradigms, and instructional practice amongst self-identified antiracist educators?” Using interpretive phenomenological analysis and employing the theoretical frameworks of critical whiteness (Roediger, 1994), critical whiteness feminism, and double-imagery (Seidl & Hancock, 2011), the following themes were identified as relevant to forming white teachers’ critical consciousness (Freire, 2018), thus supporting an antiracist pedagogical paradigm: gender, religion, proximity to people of color, and education. These intersections in turn shifted their pedagogical paradigm to a student-centered humanizing paradigm, centering student identity, culture, voice, and choice through rigorous and relevant instructional practices.
