The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles in W and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class W. This result is used to derive upper and lower bounds on the number of distinct minimum cycle bases. Finally, we give a polynomial-time algorithm to compute this partition. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

This purpose of this interpretive research study was to deepen our understanding of the meaning of culturally relevant physical education and health pedagogy (Ladson Billings, 1994; Halas, McRae & Carpenter, 2012) from the perspective of racialized minority women. Four female students from diverse backgrounds participated in a talking circle where they discussed their experiences in physical education and health (PEH) settings. Wilson’s (2008) idea of relational accountability, as described through Indigenous approaches to research, was used to help interrogate and interrupt systems of privilege, power and marginalization that characterize many PEH settings. The findings reveal the on-going need for culturally relevant pedagogical approaches that encourage, affirm and recognize the cultural landscapes of students. More research is needed to understand how students can be motivated to learn and grow in ways that develop their critical social consciousness regarding the social inequities that impact their PEH experiences. / October 2015

The purpose of this qualitative action research was to explore how early primary children respond to the implementation of culturally relevant oracy practices in an inclusive classroom. This study, which took place over five months in an inner city school in Western Canada, focused on children’s oracy skills following four events facilitated by an Aboriginal Elder. Data consisted of an oral assessment, transcriptions of the four events, artefacts created by the students, photographs, and the teacher’s research journal. Data analysis consisted of a comparative assessment of the student’s oral language skills and a content and discourse analysis of the transcriptions. Data analysis revealed that children respond favourably to culturally responsive oracy practices, that they are able to meet the B.C. Ministry of Education prescribed learning outcomes, and such practices adhere to the Aboriginal Enhancement Agreement (2005). / Graduate / 0727 / 0524 / winona.waldron@shaw.ca

AN ABSTRACT OF THE DISSERTATION OF SHEILA LONG, for the Doctor of Philosophy degree in CURRICULUM AND INSTRUCTION, presented on April 4, 2017, at Southern Illinois University Carbondale. TITLE: African American Males’ Achievement in Literacy at a Medium-sized School District MAJOR PROFESSOR: Dr. John McIntyre, Examination Committee Chair The purpose of this mixed methods study was to determine how culturally relevant pedagogy affects African American males’ academic achievement in literacy. The study examined the perceptions of third grade teachers and third grade African American male students about the use of culturally relevant pedagogy in their classrooms. Culturally relevant pedagogy is defined operationally as “student-centered approach to teaching in which the students' unique cultural strengths are identified and nurtured to promote student achievement and a sense of well-being about the student's cultural place in the world.” Culturally relevant pedagogy is consistent with students’ values and culture that ensures academic achievement while still meeting the expectations of the school district and state requirements. This study was a sequential explanatory mixed method study. Phase one of the study was a quantitative survey of 20 questions that was completed by 8 3rd grade teachers. A small sample size. The data was analyzed using matched pair T-Test of teachers’ perceptions of culturally responsive literacy use in the classrooms and African American males’ vocabulary. In addition to the surveys, Pre- and Post-Vocabulary Tests were collected from 47 3rd grade African American males who attend school in this predominantly white school district. Phase II of the study was a convenience sample of 9 3rd grade teachers and 19 African American males 3rd grade students. I investigated the students’ perceptions of culturally responsive pedagogy through the use of the Journeys (2013) basal series in classrooms. The data was collected and analyzed using interviews and observations. The following questions were addressed to explore the research topic: First, how does the use of culturally responsive pedagogy increase African American males’ achievement in literacy as measured by I-Ready assessment? Second, what perceptions do teachers have about the use of culturally responsive pedagogy in their classrooms? Third, what perceptions do third grade African American male students have about the use of culturally responsive pedagogy in their classrooms? The findings of the study showed that African American males’ literacy scores increased with the implementation of culturally responsive pedagogy using the Journeys’ (2013) Basal series.

The purpose of this research is to construct a comprehensive, analytic framework to clarify the construct of white ignorance and then illustrate how the framework can be applied to education research, theory and practice. To develop the framework, I consolidate and synthesize the extant literature around white ignorance, delineating a typology and conceptual vocabulary for the three core elements of the construct: 1) doxastic white ignorance, 2) active white ignorance, and 3) meta-white ignorance. Then, I show its application. First, I illustrate how researchers can use the framework to guide investigation into the ways that mostly white schools operate to reproduce and sustain white ignorance. Next, I illustrate how teachers can use the framework to combat and undermine the proliferation of white ignorance in their school and classroom. Toward that end, I develop a conception of wokeness, conceived not as the absence of ignorance but as the recognition of one’s own ignorance and the capacity to neutralize its effect on one’s judgment. Finally, I show how teacher educators can use the framework to transform the way we prepare teachers for social justice education. Ultimately, my project conceptualizes an approach called "racially responsive pedagogy," which serves to formalize a common diagnostic and pedagogical methodology between culturally responsive/sustaining pedagogies and anti-white ignorance pedagogies. In mostly nonwhite schools, white supremacist patterns of practice promote subtractive schooling and cultural erasure. In response, culturally responsive/sustaining pedagogies are warranted to reincorporate indigenous epistemologies back into the classroom. In mostly white schools, it’s the inverse. White supremacist patterns of practice promote white ignorance, which educators should work to resist and exclude. A racially responsive pedagogy elevates racial analyses, inviting educators to decode white supremacist patterns of practice, so they can activate a response and confidently advance their social justice mission regardless of the context in which they teach.

Relevant market on multisided online platforms in the view of the European Commission and doctrine Abstract The master thesis deals with the issue of defining the relevant market in relation to multilateral platforms. In its first part, it analyzes in detail the leading theories regarding a definition of a multisided platform is its typology. The conclusions of these analyzes then form the basis of the second part, which is the core of the work. There are described leading methods of defining the relevant market, problems with their application to multisided platforms and doctrinal proposals on how to modify these methods. This core part first deals with the dilemma of defining one market encompassing both sides of a platform or separate markets for each side of the platform and then it focuses on the issue of implementation of the SSNIP test. The individual decisions of the Commission are confronted with the comprehensive conclusions of the doctrine within the individual analyzes, and the compliance of the Commission's approach in the given decision with the doctrine is assessed here. Keywords: multisided platforms, relevant market, SSNIP test

This mixed methods study sought to uncover the needs of culturally diverse students in the online learning environment. Several of the unexplored factors that may contribute to high attrition rate among online undergraduate students, were also analyzed. The study examined how the variables of prior educational experience, age, gender, ethnicity, country of birth, and first or native language spoken contributed to success in online classes. The research also explored how institutional support contributed to the success of online learners. Through the use of survey data collection and interviews, the results of this study indicated that culturally diverse learners reported three skills that are essential to their success in online learning environments: time management, self-directedness, and computer or technical skills. Students also indicated that institutional and instructor support are vital to their success in online classes. Although all variables examined were not significant predictors to the success of online learners, the results of this study provide insight into the needs of culturally diverse learners. These findings may be helpful to educators and policymakers when planning for or designing online courses for culturally diverse learners. These findings may also aid in reducing the high attrition rate of culturally diverse learners in online environments by encouraging more readiness assessments for students enrolling in online courses to determine their level of readiness for online learning. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection

The growing population of Latino students in the United States requires a focus on culturally relevant practices for teaching Latino students. The purpose of this study was to investigate music educators’ Latino cultural knowledge and their use of that knowledge for teaching Latino students. Ladson-Billings’ (1995b) theory of culturally relevant pedagogy frames this study. Three questions guided this study. First, what cultural knowledge do music educators hold about Latino students and the communities in which they teach? Second, how do music educators use cultural knowledge to inform their pedagogical practice with Latino students? Finally, what specific culturally relevant pedagogical practices are enacted by music educators for teaching Latino students? To address the research questions, I interviewed three music teachers and observed their teaching practices. Interviews with a sample of the teachers’ Latino students also informed the study. I utilized elements of portraiture to present the data through vignettes followed by discussions and personal reflections. An analysis of the data through the lens of culturally relevant pedagogy revealed numerous methods that music educators frequently used when teaching Latino students. After I categorized those methods and aligned them with current research on core instructional practices, a list emerged of 12 culturally relevant core instructional practices that facilitate learning for Latino students. Based on the findings of this study, I recommend that teachers take an asset-based approach when working with Latino students and families, understand and make distinctions between Latino cultures, find ways to communicate effectively with Latino students and families, implement Latino language and culture into class curriculum, and enact characteristics of caring for Latino students. In addition, teacher education programs may benefit from developing courses in culturally relevant pedagogy specifically for working with Latino students.

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<p>This dissertation is premised on using an asset-based framework to investigate how engineering educators provide culturally relevant engineering education to Nigerian students at the undergraduate level. Its research questions are as follows: <i>How do engineering educators provide culturally relevant teaching to Nigerian students? What can we learn about culturally relevant teaching in engineering education from a comparative study of institutions and educators in the Nigerian context? What are the affordances, challenges, and recommendations</i><i>?</i> This dissertation leverages the socio-psychological teacher conceptions of “knowledge,” “social relations,” and the “self” and “others” described by Gloria Ladson Billings’ culturally relevant pedagogy (CRP) framework. Schools located in all six of Nigeria’s geopolitical zones and participants fluent in her three major spoken languages are represented in the study. The analyzed data for this study include surveys, in-person and virtual classroom observations, teacher reflection journals, classroom artifacts, school policy documents, and semi-structured interviews with 37 engineering faculty members, 2 provosts, 5 engineering college deans, and 2 students. The findings reveal a strong penchant for <b>analogies and proverbs as analogical bridges</b> that engineering instructors in this context used when traditional experiments, classroom demonstrations, or available educational resources failed. Nuances of culturally-relevant teacher conceptions include: <u>using proverbs to build cognitive reasoning in Nigerian engineering classrooms; visual and auditory cues as a type of formative feedback; analogies as a pedagogical form; advocating for active and authentic learning through tutorials; leveraging the communal nature of the culture in the classroom; colonial antecedents responsible for certain school policies; manifestations of Ladson-Billings’ conceptions in this context; and peculiarities of the three CRP criteria in this context.</u> The dissertation concludes with implications of the study for culturally relevant engineering education and useful recommendations for instructors looking for culturally relevant ways of supporting students of Nigerian origins in their engineering classrooms.</p>