Orange County Public Schools

A dominating set \(D\) of \(V\) is called a pitchfork dominating set if every vertex in it dominates at least \(j\) vertices and at most \(k\) vertices of \(V-D\), for any non-negative integers \(j\) and \(k\). The pitchfork domination number of \(G\), denoted by \(\gamma_{pf} (G)\) is the minimum cardinality over all pitchfork dominating sets in \(G\). In this paper, the pitchfork domination when \(j=1\) and \(k=2\) are applied to the corona of some graphs: \(G \circ C_m\), \(G \circ K_{1,n}\), \(G \circ K_{p,q}\), \(G \circ B_{2,k}\) and \(G \circ F_{2,k}\). In relation to getting new results of the corona of the mentioned graphs, we also generate results of pitchfork domination number of \(P_2+\overline{K}_n\), \(K_1 + K_{p,q}\), \(B_{2,k}\), \(F_{2,k}\) and \(K_1 + F_{2,k}\).

Abstract Many students struggle to acquire adequate reading comprehension and writing skills. Although word recognition and spelling are needed to fully actualize these skills, the oral language aspects of reading and writing can be taught and practiced without text. Oral storytelling is good for all students, but it may be essential for students with code‐related disabilities and students with limited proficiency in the mainstream academic language of U.S. schools. The purpose of this article is to offer oral storytelling as a versatile classroom‐based approach for advancing diverse students' reading and writing skills, as well as facilitating their social–emotional development. Based on an extensive theoretical and empirical literature, we propose seven strategies teachers can implement to infuse oral storytelling in their classrooms.

This study has a didactic purpose to help applied investigators and practitioners to understand the roles of observed categorical data (OCD) in structural equation modelling (SEM) and the appropriate ways of analysing such data under SPSS AMOS. To that end, the study reviews types of OCD (nominal, ordinal, dichotomous and polytomous) and their incorporation into SEM under AMOS to play different roles. The study presents two applications from the health and retirement study where Bayesian statistical inference is used to analyse one set of OCD variables serving as endogenous variables with/without groups created by another OCD variable. Besides, the study demonstrates the typical ways of summarising, reporting and interpreting the results from Bayesian statistics, and compares AMOS with several other SEM programmes (Mplus, R lavaan, Stata and SAS PROC CALIS) on handling OCD. The study concludes with summaries of the findings for its intended audience.

The Behavior Assessment Battery (BAB) for Children Who Stutter is a self-report test investigating the affective, behavioral and cognitive correlates of stuttering. Its sub-tests gauge a school-age child who stutters’ (CWS) level of anxiety and speech disruption in particular speech situations (SSC-ER: Speech Situation Checklist – Emotional Reaction and SSC-SD: Speech Situation Checklist – Speech Disruption), the use of coping behaviors (BCL: Behavior Checklist) and how a child thinks about his/her speech (CAT: Communication Attitude Test). Cross-cultural research with the BAB has pointed to its usefulness as a differential diagnostic tool and that the tests’ items lead to treatment targets. This type of multidimensional assessment instrument for children who stutter was previously unavailable in Poland, but its publication is now underway. This article presents the results of normative and psychometric testing related to the adaptation of the Polish version of the BAB.

Abstract Making causal inferences from a quasi‐experiment is difficult. Sensitivity analysis approaches to address hidden selection bias thus have gained popularity. This study serves as an introduction to a simple but practical form of sensitivity analysis using Monte Carlo simulation procedures. We examine estimated treatment effects for a school‐based support intervention designed to address student strengths and needs in academic and nonacademic areas by leveraging partnerships with community agencies. Middle school (Grades 6–8) statewide standardized test scores in mathematics and English language arts (ELA) were examined for students in a large urban district who participated in City Connects during elementary school. Results showed that the estimated treatment effects in both subjects were reduced slightly with the inclusion of U, a hypothesized unobserved binary variable. However, simulated effects fell within one‐sided 90% confidence intervals for original treatment effects, suggesting only a mild sensitivity to hidden bias. Moreover, almost identical estimated treatment effects were observed when the magnitude of the mathematical difference between each pair of the conditional probabilities of U given the treatment indicator Z was the same.

The purpose of this article is to report on the findings of a mixed-mode study that examined the effect of mentoring on 20 doctoral students and 21 mentors in the National Urban Special Education Leadership Initiative (NUSELI), a federally funded urban special education leadership doctoral program. Each doctoral student was provided a school-based leader with a doctorate to serve as his or her mentor. The mentors received training from the NUSELI director, served as a member of the student's dissertation committee, and provided access to opportunities in the school district. Mentor and mentee reports on the mentoring experience are presented.

We investigated instruction of independent creation of picture activity schedules (PASs) and how four middle school students with intellectual disability used them to complete tasks independently. A withdrawal design (A-BC-B-A-B) was used to evaluate whether the intervention had an effect on the dependent variable and to test for generalization to a community setting in a pre/post format. After instruction on the PAS, participants learned to self-manage a strategy that served as a reminder for the tasks they needed to complete. All participants exhibited increased abilities to complete a sequence of three or five tasks following verbal directions when using the PAS as compared with the conditions where no PAS was utilized. In addition, these results generalized to the community setting of a mall food court. Our findings have implications for enhancing the independent functioning of individuals with intellectual disability and reducing reliance on others, with the potential for greater levels of self-determination.

The purpose of this laboratory activity is to compare the average speed of a toy car or cart to the final speed of the same cart at the end of an inclined plane.

The purpose of the laboratory activity is to determine the average speed of a toy car moving with constant speed, and to compare the average speed to the final speed of the car.

Using one of the aluminum frames, wrap a long piece of wire around the frame. The number of turns wrapped around the frame should be between five and ten. Set the aluminum frame more than two feet from any ferromagnetic material. This includes metal parts of table, chair, your “power” supply and your ammeter. A small hand compass may be used to investigate the proposed site for the aluminum frame.