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Two-Stage Least Squares Estimation in a Spatial Lag Model under a Complete Bipartite Network
Full text linkThis paper considers a spatial lag model with a complete bipartite network weighting matrix which is important in network theory. We show that two-stage least squares is equivalent to ordinary least squares and both estimators are inconsistent for the cross-section data case. This result has also been derived for the spatial lag model with an equal weight matrix by Kelejian and Prucha (2002). We also show that the fixed effects two-stage least squares estimator is consistent in case we have panel data and the spatial lag model includes time fixed effects. This is different from the result for an equal weight matrix derived by Kelejian, Prucha and Yuzefovich (2006)
Parent Engagement and Preschooler Development in Suriname: Unveiling Patterns, Predictors, and Outcomes through Latent Class Analysis
Full text linkDespite the fact that different aspects of parent engagement with preschool aged children have a significant impact on children’s social and cognitive development, this area of research is still emerging in global majority contexts, such as the Caribbean. This study identified parenting engagement patterns in a Surinamese sample and examined the relationship between parent engagement patterns and child social and cognitive development. Propositions within sociocultural theory, parenting and literacy models, and the developmental niche model guided the formulation of research questions and hypotheses. A sample of 1765 mothers/caregivers of 3- and 4-year-olds interviewed in the UNICEF Multiple Indicators Cluster Surveys (MICS) were included in the study. A latent class analysis was used to identify parent engagement patterns, predictors of engagement patterns and associations between parent engagement patterns, and children’s social and literacy skills. Four parent engagement patterns were identified for both mothers and fathers marked by low, high, and moderate social and literacy activities. Significant predictors of mother’s class memberships were the number of children’s books in the home, child age, and maternal education level whereas significant predictors of father’s class membership were child age, wealth index, and maternal education level. Maternal engagement patterns significantly predicted children identifying at least 10 letters of the alphabet, reading words, recognizing numbers, and following directions. Paternal engagement patterns significantly predicted children identifying at least 10 letters of the alphabet, reading words, recognizing numbers, and following directions. Findings are discussed in terms of their meaning for the development of family intervention and prevention programs for families in Caribbean cultural contexts. Keywords: Parenting patterns, Parent engagement, Suriname, Caribbean, Social Development, Cognitive development, Literacy Materials, Preschool, Latent Class Analysi
Linking the Mathematics Identities of Learners, Teachers, and Educators
No full textIn this three-paper dissertation, I present three studies focused on mathematics identity. The three studies complement one another as each seeks to expand our knowledge of mathematics identity through conceptualizations of mathematics learner identity, mathematics teacher identity, and mathematics educator identity. Given that each paper is intended to be submitted individually to a mathematics education research journal, I share below the three unique abstracts that conform to the formatting requirements of the specific mathematics education research journal that I have targeted for each paper. Abstract for Paper One: Despite consistent efforts for change in mathematics education aligned with ambitious and equitable teaching practices, many preservice teachers continue to enroll in teacher-preparation programs having learned mathematics in traditional, teacher- centered ways. If mathematics teacher educators are to support preservice teachers in breaking the cycle of teaching in the traditional ways that they themselves were taught, a greater understanding of how the mathematics learner identities and mathematics teacher identities of preservice teachers interrelate is needed. In this paper, we contribute a conceptual distinction of between identities and within identities to explore the interrelated nature of preservice elementary teachers’ mathematics learner identities and mathematics teacher identities in the context of a problem solving focused mathematics content course. We collected data from 21 preservice elementary teachers who were in their first year enrolled at a university and deductively analyzed their self-reported experiences in the problem-solving focused mathematics content course. We share our findings of several ways that the mathematics learner identities and mathematics teacher identities interrelated in this study. Ultimately, we suggest that these findings support progress toward supporting preservice elementary teachers to take up ambitious and equitable teaching practices. Abstract for Paper Two: In the context of a preparing elementary teachers to teach mathematics, this qualitative multiple case study documents the self-told first-person identity stories of three preservice elementary teachers. Three contributions are made in this paper: (a) first, the documentation of a novel attempt to elicit self-told first-person identity stories including findings for the effectiveness of this attempt; (b) second, findings of the ways that preservice elementary teachers’ mathematics identities developed throughout their field placement based on their identity stories; and (c) third, findings of the ways that preservice elementary teachers’ mathematics identities co-developed throughout their field placement based on their identity stories. Abstract for Paper Three: Conceptualizations of mathematics teacher identity and mathematics-related teacher identity are helpful for understanding how mathematics teachers shape mathematics learner identities from within a mathematics classroom. However, I draw on Wenger’s (1998) theory of identity in communities of practice to suggest that these constructs are not sufficient for understanding the boundaries and peripheries of a mathematics community of practice. I conceptualize mathematics educators as those individuals who participate in a mathematics community of practice from the edges of the community and are neither mathematics students nor professional mathematics teachers. I conducted a systematic literature review of mathematics educator identity research to understand who may be considered a mathematics educator, how mathematics educators participate in mathematics communities of practice, and how mathematics educators may influence mathematics learner identities. I found empirical evidence of administrators, community members, counselors, grandparents, parents, and teachers of students with special needs participating as mathematics educators. In addition to this, I found five ways that mathematics educators participated in mathematics communities of practice with some evidence of their influence on mathematics learner identities: (1) through the funds of knowledge they brought to a community of practice (2) through the different roles they played within schools, beyond teaching mathematics (3) by collaborating, or not collaborating, with other members within a community of practice to support learners (4) through the expectations of achievement that they communicated to learners and (5) through the languages they used to communicate within their community of practice
TOO MUCH OR NOT ENOUGH. THE PERCEPTIONS AND PRACTICES OF SINGLE MOTHERS OF COLOR AND SCHOOL INVOLVEMENT
Full text linkABSTRACT Family involvement varies based on family structure, creating challenges for single mothers of color in engaging with schools. These mothers, particularly in urban settings, often require specific supports to facilitate participation in their children’s education. Understanding their barriers is crucial for fostering inclusive family involvement practices. Many marginalized women\u27s experiences remain unheard, making it essential to address this gap and develop strategies that better support their engagement. This study examines how district and school-level efforts impact family involvement for single mothers of color, particularly in urban schools. This qualitative study explores the experiences of four single mothers—two of Latina heritage and two of African American descent—whose children attend four different schools in a large urban district in Central New York. Data were collected through semi-structured and focus group interviews, participant observations, and family video recordings. The study was framed using critical race theory, critical race parenting, and critical mothering frameworks. The research sought to answer the following questions: (a) how have the personal experiences of single mothers of color shaped their perceptions of education as they raise their own school-aged children? And (b) in what ways do single mothers of color experience and navigate the challenges of parenting their school-aged children? Deductive coding methods identified key themes: barriers to engagement, communication preferences, desire for collaboration, and socioeconomic impact. Findings indicate that schools often overlook the specific needs of single mothers of color, applying a one-size-fits-all approach that fails to foster meaningful engagement. Addressing these challenges is essential for more inclusive and effective family involvement practices
EXPLORING DIGITAL READING THROUGH PISA DATA: GLOBAL TRENDS AND RACIAL DISPARITIES
No full textIn an increasingly digital world, navigating, evaluating, and comprehending online texts is essential for academic success and lifelong learning. My dissertation explores digital reading and practice through two interconnected studies: a scoping review of digital reading research using PISA data and an empirical investigation of racial disparities in digital reading achievement among U.S. adolescents. The first study conducts a scoping literature review of peer-reviewed research (2009–2023) on digital reading within PISA studies, examining conceptualizations, methodologies, and regional variations. Using four databases (ERIC, PsycINFO, Education Source, Web of Science), the review identifies global trends in digital reading research, highlighting how scholars define and measure digital reading. Findings explored that digital reading is conceptualized as a multifaceted skill integrating ICT literacy, critical evaluation, and hypertext navigation. Variations in definitions across countries underscore digital reading\u27s complex, evolving nature as a core educational competency. The second study investigates the racial disparities in digital reading achievement among Black and White U.S. adolescents using PISA 2018 data. Grounded in QuantCrit and Digital Literacy frameworks, the study examines how socioeconomic status (SES), gender, reading motivation, metacognitive strategies, ICT access (home and school), reading self-concept, and teacher encouragement shape students\u27 digital reading achievement. My second study examines the underlying factors that influence digital reading achievement among U.S. adolescents, focusing specifically on racial differences and structural inequalities, using data from the PISA 2018 dataset with multiple regression analyses. The findings show that Black students scored lower, even when controlling for key predictors. My second study highlights the systemic barriers that limit Black students’ digital reading achievement, the disparate effects of SES, and the unequal role of motivation and teacher incentives across racial groups. The findings highlight that simply having access to technology or owning technological devices is not enough and that addressing structural inequities in digital literacy education is crucial. However, it has been revealed that students must use technology to some extent. Neither prolonged exposure to technological devices nor complete lack of access to these devices is appropriate. In conclusion, my dissertation contributes to a deeper understanding of digital reading in global education assessments and the factors that shape adolescents\u27 digital reading achievement in the United States. My dissertation highlights the need for structured digital literacy integration and equity-focused policies to close the racial gap in digital reading achievement
Geometry and Mechanical Response of Twisted Thin Tubes
Full text linkNature provides many examples of thin sheets and shells, from flower petals to graphene sheets. Such materials can exhibit complex deformations such as creases, folds and wrinkles, particularly in thin, flexible structures like cylindrical shells and ribbons. Here we investigate the geometric transformation and mechanical response of a twisted thin tube, which is made from a thin polymer sheet. In Chapter 2, an interesting locking behavior was found in a thin cylindrical shell. After an initial compression, the shell can be twisted with little resistance until it reaches a “locking angle”, which coincides with the appearance of an ordered wrinkle pattern. We construct a simple geometric model to predict the morphology of the shell and the locking angle under different compression. We also perform “force-controlled” experiments by applying a small tension to the shell as well as twisting it in the Rheometer, in excellent agreement with our model. Our results establish a route to a tunable locking material—a system with an interval where it is freely deformable, and where the endpoints of this interval can be changed continuously over a wide range. Chapter 3 shows how the boundary conditions affect the geometric structures of a twisted cylinder and how pre-creasing alters the behavior of a twisted crimped tube. By applying two creases to the tube prior to twist, we observe the formation of an ordered structure composed of repeating triangular facets oriented at varying angles. We then measure the exerted torque during the twist and analyze how the structural evolution depends on parameters such as material thickness and the twist angle. Our findings show that, similar to twisted ribbons, pre-creased toothpaste tubes exhibit a approximately linear increase in torque and, under certain conditions, develop a creased helicoid structure. Furthermore, we explore how the length of pre-creases influences the extent of triangular facet region as the twist angle increases. This study provides insights into controlling the buckling of thin shells, offering a potential pathway for designing ordered structures in soft materials. In Chapter 4, we consider another promising research direction in this system. By measuring the normal force exerted on a cylindrical shell subjected to cyclic compressions, we investigate the mechanical response of a thin crumpled shell under different loading protocols, revealing memory effects in crumpled sheets. In addition to the force-verses-compression measurements, we analyze acoustic signals and images captured during the experiment to track the evolution of folds and ridges, providing other ways of observing memory formation. Our findings highlight intriguing memory effects in a cylindrical sheet under cyclic compression or twist, contributing to a deeper understanding of memory in materials. Our study highlights the rich mechanical behaviors that emerge in thin cylindrical shells under twisting and compression, from locking transitions to ordered facet formation and memory effects. By combining experimental observations with theoretical modeling, we provide new insights into how geometric and mechanical constraints govern ordered patterns in thin sheets. These findings not only advance our understanding of buckling patterns and memory formation in soft materials but also suggest potential applications in designing tunable metamaterials
Disputing narratives and promoting visibility: The communicative actions of Northeastern Afro-Brazilian women organizations on Instagram
No full textIn this study, I examine the communicative digital actions by a network of Black feminist organizations from Brazil’s Northeast on social media. Specifically, I analyze their Instagram activities as a fundamental form of political expression by Northeastern Black women in Brazil through modes of public feminist pedagogy on social media. To do so, I adopted the principles of critical technocultural discourse analysis (CTDA) to conduct a qualitative analysis of the social media archives shared on the public Instagram pages of eight Black feminist organizations affiliated with the Northeast Black Women’s Network in Brazil. This analysis is complemented by in-depth semi-structured interviews with members of five different organizations who have maintained the Instagram pages of their respective organizations. In the findings, I analyze their Instagram practices under two overarching themes: Disputing Narratives on Instagram and Connective Visibilities on Instagram. These overarching themes discuss how the organizations engage in discursive communicative practices that have potential to promote increased visibility to counter-hegemonic narratives about Afro-Brazilian women from Brazil\u27s Northeast. I thus elaborate on the significance of their communicative practices on a platform substantially shaped by gendered and raced economies of visibility that tend to shape and constrain what gets to be seen and valued online
ENCIRCLING CHAINS AROUND 4- AND 6-CLUSTERS IN FULLERENES
Full text linkFullerenes are purely carbon molecules which can be represented by a 3-regular planar graph consisting of only hexagonal and (exactly 12) pentagonal faces. Since carbon atoms have valence 4 but our graphs are trivalent we need to double the edges in a perfect matching to bring the valence up to 4. The edges in a perfect matching form a Kekulé structure and the hexagonal faces bound by three Kekulé edges are called benzene rings. A maximal independent set of benzene rings for a given Kekulé structure is called a Clar set, and the maximum possible size of a Clar set over all Kekulé structures is the Clar number of the fullerene. A perfect Kekulé structure can be extended through isolated regions, called clusters, which contain the pentagons in a way the creates a chain decomposition. These chain decompositions can be used to help find the Clar number for a given fullerene through the idea of the Clar deficit. In this paper we will look to extend the notion of chains to a new type of chain called an encircling chain. Then, we will look to answer if encircling chains around larger clusters improves the Clar deficit. We will answer this question for the case of 4-clusters. Then, for the case of 6-clusters we will look at examples that get us closer to this answer