A small randomized group design (N = 20) was used to examine a parent-implemented intervention designed to improve the spoken language skills of school-aged and adolescent boys with FXS, the leading cause of inherited intellectual disability. The intervention was implemented by speech-language pathologists who used distance video-teleconferencing to deliver the intervention. The intervention taught mothers to use a set of language facilitation strategies while interacting with their children in the context of shared story-telling. Treatment group mothers significantly improved their use of the targeted intervention strategies. Children in the treatment group increased the duration of engagement in the shared story-telling activity as well as use of utterances that maintained the topic of the story. Children also showed increases in lexical diversity, but not in grammatical complexity.

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Using a single case design, a parent-mediated spoken language intervention was delivered to three mothers and their school-aged sons with fragile X syndrome, the leading inherited cause of intellectual disability. The intervention was embedded in the context of shared story-telling using wordless picture books and targeted three empirically-derived language support strategies. All sessions were implemented via distance video-teleconferencing. Parent education sessions were followed by 12 weekly clinician coaching and feedback sessions. Data was collected weekly during independent homework and clinician observation sessions. Relative to baseline, mothers increased their use of targeted strategies and dyads increased the frequency and duration of story-related talking. Generalized effects of the intervention on lexical diversity and grammatical complexity were observed. Implications for practice are discussed.

Peak sets of a permutation record the indices of its peaks. These sets have been studied in a variety of contexts, including recent work by Billey, Burdzy, and Sagan, which enumerated permutations with prescribed peak sets. In this article, we look at a natural analogue of the peak set of a permutation, instead recording the values of the peaks. We define the "pinnacle set" of a permutation w to be the set {w(i) : i is a peak of w}. Although peak sets and pinnacle sets mark the same phenomenon, these objects differ in notable ways. In the work below, we characterize admissible pinnacle sets and study various enumerative questions related to these objects.

No previous study has examined a distance-delivered parent-implemented language intervention for young boys with fragile X syndrome. Mothers were able to increase their use of verbally responsive language. Intervention efficacy might be enhanced by incorporating an augmentative and alternative communication device for some children and a more concerted focus on increasing the frequency of child communication acts. Findings provide preliminary support for the efficacy of the distance delivery format.