An exploration of parent ivolvement in Response to Intervention (RTI) in Title I schools

Research demonstrates that parental involvement positively impacts student achievement and enhances targeted instruction. Notably, however, little research currently exists on how schools involve parents in Response to Intervention (RTI), a framework for implementing targeted, tiered, research-based instruction. The purpose of this study was to interview selected parents, teachers, RTI specialists, and principals in three Title I elementary schools in one school district, plus one district-level administrator, in order to examine how elementary schools currently involve parents in RTI prereferral interventions, and to understand the factors that might facilitate or challenge such parent involvement. I employed a comparative case study qualitative design with each elementary school as the main unit of analysis. I conducted individual, in-depth interviews that lasted approximately 45-60 minutes with a total of 33 participants across the three school sites, including 11 parents, 12 teachers, and six RTI specialists, three principals, and one district-level administrator. I also analyzed documents related to RTI processes that are available through websites and participants. I used Strauss and Corbin’s (1998) three-step scheme for thematic/grounded theory analysis, and Atlas.ti as the electronic tool for management and analysis. Analyses of the data revealed that personnel across the sites largely agreed on how they explain RTI to parents and notify parents of student progress. Parents mostly disagreed with these accounts, stating instead that they learn about RTI and their child’s progress by approaching teachers or their own children with questions, or by examining report cards and student work that comes home. Personnel and parents cited various challenges for involving parents in RTI. However, they all also agreed that teachers are accessible and willing to reach out to parents, and that teachers already face considerable workloads. It appears that no district- or school-wide plan guides parent involvement practices in RTI at any of the three schools. Finally, I present a discussion of findings; implications for teachers, RTI implementation leaders, and Title school leaders; study limitations; and possibilities for future research.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

Language Outcomes of the Play and Language for Autistic Youngsters (PLAY) Project Home Consultation model—An Extended Analysis

The current study is a post-hoc analysis of data from the original randomized control trial of the Play and Language for Autistic Youngsters (PLAY) Home Consultation program, a parent-mediated, DIR/Floortime based early intervention program for children with ASD (Solomon, Van Egeren, Mahone, Huber, & Zimmerman, 2014). We examined 22 children from the original RCT who received the PLAY program. Children were split into two groups (high and lower functioning) based on the ADOS module administered prior to intervention. Fifteen-minute parent-child video sessions were coded through the use of CHILDES transcription software. Child and maternal language, communicative behaviors, and communicative functions were assessed in the natural language samples both pre- and post-intervention. Results demonstrated significant improvements in both child and maternal behaviors following intervention. There was a significant increase in child verbal and non-verbal initiations and verbal responses in whole group analysis. Total number of utterances, word production, and grammatical complexity all significantly improved when viewed across the whole group of participants; however, lexical growth did not reach significance. Changes in child communicative function were especially noteworthy, and demonstrated a significant increase in social interaction and a significant decrease in non-interactive behaviors. Further, mothers demonstrated an increase in responsiveness to the child’s conversational bids, increased ability to follow the child’s lead, and a decrease in directiveness. When separated for analyses within groups, trends emerged for child and maternal variables, suggesting greater gains in use of communicative function in both high and low groups over changes in linguistic structure. Additional analysis also revealed a significant inverse relationship between maternal responsiveness and child non-interactive behaviors; as mothers became more responsive, children’s non-engagement was decreased. Such changes further suggest that changes in learned skills following PLAY parent training may result in improvements in child social interaction and language abilities.