Selectivity nomographs for classical filters

Nomographs for determining the filter order of classical filters based on selectivity requirements are presented. The selectivities for a variety of standard classical filters are summarized in equation form and the general selectivity nomograph is constructed. The selectivity equations are then converted into nomograph form by applying the relationship between the transfer function and the response slope. Design examples are presented to demonstrate the usefulness of the selectivity nomographs. These nomographs can be used to gauge filter performance and combined with optimization techniques can yield superior classical filter designs.     

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.     

Playful structure: a novel image of early years pedagogy for primary school classrooms

Playful structure is a new pedagogic image representing a more balanced and integrated perspective on early years pedagogy, aiming to blend apparent dichotomies and contradictions and to sustain and evolve play-based practice beyond Year 1. Playful structure invites teachers and children to initiate and maintain a degree of playfulness in the child’s whole learning experience, even when the learning intentions demand a supportive structure. Thus, playfulness becomes characteristic of the interaction between adult and the child and not just characteristic of child-initiated versus adult-initiated activities, or of play-time versus task-time. The paper is based on intensive observations and interviews with teachers in Northern Ireland who participated in a play-based and informal curriculum. This paper explains how playful structure rests on complementary processes of infusion of structure into play-based activities and infusion of playfulness into more structured activities, illustrated by cameos. ‘Infusion’ suggests the subtle blending process that allows apparent dichotomies and contradictions to be resolved in practice.     

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.