Theory and Applications of Correspondences

Throughout this paper, we will examine correspondences, also known as set-valued functions. A definition of correspondences and their graphs are given. Properties of correspondences including continuity, optimization, and existence of fixed points are considered. Examples are considered demonstrating these properties. Applications in the field of Economics are introduced. Specifically the optimization of consumer utility is examined through examples

Surviving the COVID-19 Pandemic with a Wolf Pack and the Marco Polo App

This narrative nonfiction essay explores the ways in which a group of academic mothers used Marco Polo, a video instant messaging app, to remain tethered to each other and to their work during the COVID-19 pandemic. The mothers, who are a combination of millennial and Gen Xers with children aged two to twenty-three, hail from a range of academic disciplines (e.g., theatre, education, environmental science, community health, counseling, psychology, and hospitality administration). We were all well into our careers and accustomed to grappling with the myriad ways in which the things we were raised to believe—that we could do anything we put our minds to and could definitely be mothers and career women—sometimes still felt like a pipe dream. And then COVID-19 came barreling into our lives, laying waste to all the usual coping and time management strategies upon which we typically rely. Since mid-March, we have exchanged an average of between fifty and seventy-five Marco Polo messages per day and have covered a wide range of topics—from spice storage methods, to preferred Cheeto shapes, to teaching our children to do long division while attending Zoom meetings, and to watching our male colleagues soar in terms of research productivity while we struggle to find five minutes of uninterrupted time to respond to an email. The essay offers some speculative ideas as to the role Marco Polo played in a larger story about connections between adult women during challenging times

Speaking the language of integration: a case study of South Boulevard Foreign Language Academic Immersion Magnet

Racial segregation and an achievement gap persist despite the promises of Brown vs. Board of Education (1954). In Baton Rouge, Louisiana, public schools are 83% Black, while nearly one-third of all children attend private schools which are 86% White. South Boulevard (SB) Foreign Language Academic Immersion Magnet Elementary is a counterexample because it has achieved integration and academic achievement well above district and state averages on high stakes tests. This research explores the culture of SB’s immersion magnet program in relation to its success as an integrated public school with high student achievement and explores the factors that motivated a diverse set of parents to choose public education over private education. This one-year ethnographic case study of SB is based on document analysis, interviews, and participant observation. In-depth interviews were conducted with 53 students, parents, school faculty, district administrators, and school board members. Using purposeful sampling, participants were selected who represented diverse backgrounds and perspectives. On-site participant observation (including classes, recess, lunch, PTO activities and meetings, and school board meetings) was conducted for one academic semester and follow-up observations the following semester. The data were broken down into units of meaning that served as themes that were first subjected to a systematic content analysis and then the constant comparative method. SB’s achievement of integration and academic achievement is a counternarrative to dominant narratives that focus on the achievement gap and deficit models of minority culture. The primary explanation for SB’s success is the unique culture created by the immersion curriculum. SB has a culture of academic rigor in which teachers have high expectations of all students. The second language creates a new culture of power that equalizes cultural and linguistic differences that may privilege or marginalize students elsewhere. SB has a culture of multiplicity that values diverse perspectives and includes a unique immersion subculture in which all students are equal participants. SB has a culture of community characterized by trusting relationships between members of the school community that emerge out of commitment to the immersion curriculum rather than geographical boundaries

Maximizing the effect of visual feedback for pronunciation instruction: A comparative analysis of three approaches

Visual feedback, in which learners visually analyze acoustic speech characteristics, has been shown to significantly improve pronunciation, but extant research has varied widely with respect to the target feature, length of the intervention, and type of intervention. This study presents a comparative analysis of three methods of visual feedback for L2 segmental pronunciation instruction. These methods, all focused on training voice onset time for English-speaking learners of Spanish, differed in duration of instruction (i.e., short and long) and the nature of each intervention (i.e., phonemes presented simultaneously or sequentially). Results show that while all forms of visual feedback significantly improve L2 Spanish pronunciation, evidenced by a reduction in voice onset time, the greatest improvement was found following both longer treatments and a sequential approach. Theoretical and pedagogical implications are discussed

Visual Feedback and Second Language Segmental Production: the Generalizability of Pronunciation Gains

While a number of researchers have noted the lack of research on pronunciation instruction, relative to other aspects of language (i.e. syntax), pronunciation has been shown to be crucial for facilitating intelligible and comprehensible second language (L2) productions. Addressing the need for empirically tested pedagogical methods, the current study considers the use of a classroom-based visual feedback paradigm for the instruction of a segmental feature, namely voice onset time, which has been shown to be a distinctive marker of accent for English-dominant L2 learners of Spanish. In addition, this study examines the potential generalizability of gains made through the visual feedback paradigm, assessing whether gains made in controlled reading tasks (i.e. carrier sentences) will extend to more continuous and spontaneous speech. The results demonstrate significant improvements in voice onset time produced by participants following the visual feedback paradigm, relative to a control group. Furthermore, while the visual feedback training was limited to short, controlled utterances (i.e. carrier sentences), benefits were observed for more continuous and spontaneous speech

Current neurologic treatment and emerging therapies in CDKL5 deficiency disorder

BACKGROUND: CDKL5 deficiency disorder (CDD) is associated with refractory infantile onset epilepsy, global developmental delay, and variable features that include sleep, behavioral disturbances, and movement disorders. Current treatment is primarily symptom-based and informed by experience in caring for this population. METHODS: We describe medication and non-medication approaches to treatment of epilepsy and additional key neurologic symptoms (sleep disturbances, behavioral issues, movement disorders, and swallowing dysfunction) in a cohort of 177 individuals meeting criteria for CDD, 154 evaluated at 4 CDKL5 Centers of Excellence in the USA and 40 identified through the NIH Natural History Study of Rett and Related Disorders. RESULTS: The four most frequently prescribed anti-seizure medications were broad spectrum, prescribed in over 50% of individuals. While the goal was not to ascertain efficacy, we obtained data from 86 individuals regarding response to treatment, with 2-week response achieved in 14-48% and sustained 3-month response in 5-36%, of those with known response. Additional treatments for seizures included cannabis derivatives, tried in over one-third of individuals, and clinical trial medications. In combination with pharmacological treatment, 50% of individuals were treated with ketogenic diet for attempted seizure control. Surgical approaches included vagus nerve stimulators, functional hemispherectomy, and corpus callosotomy, but numbers were too limited to assess response. Nearly one-third of individuals received pharmacologic treatment for sleep disturbances, 13% for behavioral dysregulation and movement disorders, and 43% had gastrostomy tubes. CONCLUSIONS: Treatment for neurologic features of CDD is currently symptom-based and empiric rather than CDD-specific, though clinical trials for CDD are emerging. Epilepsy in this population is highly refractory, and no specific anti-seizure medication was associated with improved seizure control. Ketogenic diet is commonly used in patients with CDD. While behavioral interventions are commonly instituted, information on the use of medications for sleep, behavioral management, and movement disorders is sparse and would benefit from further characterization and optimization of treatment approaches. The heterogeneity in treatment approaches highlights the need for systematic review and guidelines for CDD. Additional disease-specific and disease-modifying treatments are in development

Seascape Genetics: A Coupled Oceanographic-Genetic Model Predicts Population Structure of Caribbean Corals

SummaryPopulation genetics is a powerful tool for measuring important larval connections between marine populations [1–4]. Similarly, oceanographic models based on environmental data can simulate particle movements in ocean currents and make quantitative estimates of larval connections between populations possible [5–9]. However, these two powerful approaches have remained disconnected because no general models currently provide a means of directly comparing dispersal predictions with empirical genetic data (except, see [10]). In addition, previous genetic models have considered relatively simple dispersal scenarios that are often unrealistic for marine larvae [11–15], and recent landscape genetic models have yet to be applied in a marine context [16–20]. We have developed a genetic model that uses connectivity estimates from oceanographic models to predict genetic patterns resulting from larval dispersal in a Caribbean coral. We then compare the predictions to empirical data for threatened staghorn corals. Our coupled oceanographic-genetic model predicts many of the patterns observed in this and other empirical datasets; such patterns include the isolation of the Bahamas and an east-west divergence near Puerto Rico [3, 21–23]. This new approach provides both a valuable tool for predicting genetic structure in marine populations and a means of explicitly testing these predictions with empirical data (Figure 1)

From soliciting answers to eliciting reasoning: Questioning our questions in digital math tasks

How can classroom teachers and task designers pose questions to promote students’ reasoning? The authors share a Toy Car task, developed in Desmos, then provide three design principles guiding task questions

Activist 101 Activities for Pre-Service Teachers

This Teaching Note briefly describes three activities that can easily be integrated into any teacher education course

The evolution of the WAVES database: from KWOK index to the web

pp. 105-11