On orthogonal polynomials

A study is made of the orthogonal polynomials on certain curves in the complex plane. Necessary and sufficient conditions for a set of polynomials to be orthogonal on the curves are obtained in terms of symmetric matrices. The relations of the symmetric matrices to Toeplitz matrices and innerwise matrices are shown.     

Contributions of Emergent Literacy Skills to Name Writing, Letter Writing, and Spelling in Preschool Children

The purpose of this study was to examine which emergent literacy skills contribute to preschool children's emergent writing (name-writing, letter-writing, and spelling) skills. Emergent reading and writing tasks were administered to 296 preschool children aged 4-5 years. Print knowledge and letter-writing skills made positive contributions to name writing; whereas alphabet knowledge, print knowledge, and name writing made positive contributions to letter writing. Both name-writing and letter-writing skills made significant contributions to the prediction of spelling after controlling for age, parental education, print knowledge, phonological awareness, and letter-name and letter-sound knowledge; however, only letter-writing abilities made a significant unique contribution to the prediction of spelling when both letter-writing and name-writing skills were considered together. Name writing reflects knowledge of some letters rather than a broader knowledge of letters that may be needed to support early spelling. Children's letter-writing skills may be a better indicator of children's emergent literacy and developing spelling skills than are their name-writing skills at the end of the preschool year. Spelling is a developmentally complex skill beginning in preschool and includes letter writing and blending skills, print knowledge, and letter-name and letter-sound knowledge.     

Profiles of emergent literacy skills among preschool children who are at risk for academic difficulties

The purpose of this study was to explore patterns of within-group variability in the emergent literacy skills of preschoolers who are at risk for academic difficulties. We used the person-centered approach of cluster analysis to identify profiles of emergent literacy skills, taking into account both oral language and code-related skills. Participants were 492 preschoolers (aged 42-60 months) enrolled in needs-based programs. In the fall of the academic year, children were administered eight measures of emergent literacy: four oral language measures (i.e., expressive and receptive grammar, expressive and receptive vocabulary) and four code-related measures (i.e., print concepts, alphabet knowledge, name writing, and rhyme). Controlling for age, hierarchical-agglomerative and K-means cluster analysis procedures were employed. Five psychometrically sound profiles emerged: highest emergent literacy (prevalence = 14%); three profiles with average oral language and differential code-related abilities (16%, 24%; 23%); and lowest oral language with broad code-related weaknesses (23%). Profiles were then compared on midyear teacher ratings of emergent literacy as well as end-of-kindergarten literacy performance; results provided convergent evidence of predictive validity. This study highlights the considerable heterogeneity of emergent literacy abilities within an “at-risk” group. The resulting profiles have theoretical and practical relevance when examining both concurrent relationships between oral language and code-related skills as well as longitudinal relationships between early patterns of performance and later reading achievement.     

From Scribbles to Scrabble: Preschool Children's Developing Knowledge of Written Language

The purpose of this study was to concurrently examine the development of written language across different writing tasks and to investigate how writing features develop in preschool children. Emergent written language knowledge of 372 preschoolers was assessed using numerous writing tasks. The findings from this study indicate that children demonstrate knowledge about writing before beginning school and receiving formal instruction. There was clear evidence to support the claim that universal writing features develop before language-specific features. Children as young as 3 years possess knowledge regarding universal and language-specific writing features. Preschoolers appear to progress along a continuum from scribbling to conventional spelling. Although this progression is sequential, children’s writing proficiency is task dependent. Implications of these findings on writing development are discussed.     

Israel Moiseevich Gelfand (1913–2009)

In this homage to the late I M Gelfand, we try to give an overview of some of his contributions to the theories of Banach algebras in general and C*-algebras in particular, and briefly elaborate on the celebrated Gelfand-Naimark-Segal construction which gives a way of passing from positivity-preserving linear functionals to representations on Hilbert space.     

Young children's learning and transfer of biological information from picture books to real animals

Preschool children (N = 104) read a book that described and illustrated color camouflage in animals (frogs and lizards). Children were then asked to indicate and explain which of 2 novel animals would be more likely to fall prey to a predatory bird. In Experiment 1, 3- and 4-year-olds were tested with pictures depicting animals in camouflage and noncamouflage settings; in Experiment 2, 4-year-olds were tested with real animals. The results show that by 4 years of age, children can learn new biological facts from a picture book. Of particular importance, transfer from books to real animals was found. These findings point to the importance that early book exposure can play in framing and increasing children's knowledge about the world.     

Predicting First Grade Reading Performance from Kindergarten Response to Tier 1 Instruction

Many schools are beginning to implement multi-tier response to intervention (RTI) models for the prevention of reading difficulties and to assist in the identification of students with learning disabilities (LD). The present study was part of our larger ongoing longitudinal RTI investigation within the Florida Learning Disabilities Center grant. This study used a longitudinal correlational design, conducted in 7 ethnically and socio-economically diverse schools. We observed reading instruction in 20 classrooms, examined response rates to kindergarten Tier 1 instruction, and predicted students' first grade reading performance based upon kindergarten growth and end of year reading performance (n = 203). Teachers followed an explicit core reading program and overall, classroom instruction was rated as effective. Results indicate that controlling for students' end of kindergarten reading, their growth across kindergarten on a variety of language and literacy measures suppressed predictions of first grade performance. Specifically, the steeper the students' trajectory to a satisfactory outcome, the less likely they were to demonstrate good performance in first grade. Implications for future research and RTI implementation are discussed.