Ray Godfrey

Early Mathematics Development and Later Achievement: Further Evidence

There is a growing international recognition of the importance of the early years of schooling as well as an interest being shown in the relationship of early education to later achievement. This article focuses on a cohort of English pupils who have been tracked through primary school during the first five years of the new National Numeracy Strategy. It reports a limited longitudinal study of young children’s early mathematical development, initially within three testing cycles: at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-ofage). These cycles were located within the broader context of progress through to the end of Key Stage 1 (at seven years) and Key Stage 2 (at eleven years) on the basis of national standardised assessment tests (SATs). Results showed that children who bring into school early mathematical knowledge do appear to be advantaged in terms of their mathematical progress through primary school. Numerical attainment increases in importance across the primary years and practical problem solving remains an important element of this. This finding is significant given the current emphasis on numerical calculation in the English curriculum. It is concluded that without active intervention, it is likely that children with little mathematical knowledge at the beginning of formal schooling will remain low achievers throughout their primary years and, probably, beyond.

Children’s early numeracy in England, Finland and People’s Republic of China

This research investigated the similarities and differences between countries in young children’s early numeracy skills related to age, culture, and gender. The participants were five‐year‐old children from Beijing (People’s Republic of China), England, and Finland. The rationale for the cross‐cultural comparison originates from research results with older children showing that Asian children outperform children from America or Europe, and from the lack of such information concerning younger children. The results showed that in all locations older children performed better than the younger children. Cultural differences were found: young children from Beijing outperformed those from England and Finland in overall early numeracy performance, as well as in sub‐tests for understanding of quantities and relations (i.e. relational skills), and counting skills. Finnish children had better scores than English children in the whole early numeracy scale and in the relational scale. The results are discussed in relation to culture, instruction in preschools, and learning support at home, as well as the effects of language characteristics. The culture’s appreciation of and approach to mathematics learning in early childhood is a plausible explanation for the cross‐cultural differences found in this study.

The development of children's early numeracy through key stage 1

This paper describes a limited longitudinal study of young childrens early numeracy development within three testing cycles, at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-of-age), located within the broader context of progress through to Key Stage 1 SAT results (at seven years). Assessment was carried out using the Utrecht Early Mathematical Competence Test (Van Luit et al., 1994). This comprised eight sub-topics, five items in each, including comparison, classification, correspondence, seriation, counting, calculation and real-life number problem solving. Broadly, one set of sub-tests related to understanding of relations in shape, size, quantity and order, whilst a second set of sub-tests related to basic arithmetic. Three hundred pupils were selected from twenty-one schools, large and small, from rural and urban areas, with high and low concentrations of children eligible for free school meals and/or with special ...

The Development of Early Numeracy in Europe

This article describes a limited longitudinal European study of young children’s early numeracy development within three testing cycles, onaverage, at the mid-point and towards the end of their fifth to sixth year and again at the mid-point of their sixth to seventh year. Assessment was carried out using the Utrecht Early Numeracy Test (ENT) (Van Luit, Van de Rijt and Pennings, 1994). The multilevel modelling method of analysis used for the study provided an extension of multiple regression to incorporate the hierarchical structure of the data collected, with boys and girls of different social-economic status, nested within different institutions within different countries. The results showed that the ENT was a useful tool for international comparison. The finding that differences between countrieswere negligible was surprising bearing in mind that the English pupils werein formal schooling throughout the testing cycle, the Belgian, German, Greek and Dutch children from the mid-point, and the Slovene children, not at all.

How Do They Manage? An Investigation of Early Childhood Leadership

Early childhood (EC) leadership literature indicates few theoretically based studies identifying and testing different models and characteristics of leadership. Objectives were thus to identify, describe and analyse what leadership meant to key EC participants; to consider roles, responsibilities and characteristics; to investigate core components; to capture practice and judge how it was understood and enacted. A case-study approach used 12 sites and multiple data-gathering methods: questionnaires; interviews; and in-depth ‘day in the life’ video vignettes. Participants described their organizations as hierarchical in structure and traditional in strategic decision-making, yet collaborative in culture and operational functioning. Variation in leadership, management and administration patterns across settings indicated multiple leadership roles in diverse EC settings. Principal components analysis revealed that those with postgraduate qualifications favoured ‘leaders as guides’; those with professional heritages other than teaching leaned towards ‘leaders as strategists’; those with NVQ qualifications tended towards ‘leaders as motivators’; those with postgraduate qualifications also valued ‘leaders as business oriented’. New models of leadership are thus worthy of consideration. Leaders acknowledged difficulty in standing back and reflecting, recognizing an essential aspect of leadership was ongoing thinking and decision-making, inaccessible unless they ‘talked-aloud’ whilst engaging in professional practice. This suggests a need to increase self-understanding and alternative routes to problem-solving.

Excluding primary school children: the outcomes six years on

This article reports and discusses a study which followed up, through case records, 726 children excluded permanently, indefinitely or for fixed–term periods in 1993/4 in 10 LEAs. The outcomes at secondary level in 1998/9 were found to be moderately poor with the problems intensifying for half the sample. Forty six per cent had further primary school exclusions and 36 per cent received exclusions in their secondary education. Looked–after children and those with special educational needs fared worse and achieved less. Case studies showed the kinds of commitment and support that can work even with very difficult cases.

Explaining high attainment in faith schools: the impact of Religious Education and other examinations on pupils’ GCSE points scores

Faith schools are popular with parents and feature towards the top of the annual tables of school performance in England based on the government’s preferred measures of school outcomes. Academic studies suggest that although the observed differentials between the faith and non‐faith sectors at the end of Key Stage 4 are partly explicable in demographic and similar terms, they do nonetheless represent a real phenomenon. There is little research into the causes of this. The simplest hypothesis is that pupils attending faith schools take more examinations, thus boosting their average points scores. The possible additional courses are, by inference, in Religious Education. This study examines the hypothesis and finds it wanting as an adequate explanation. Further areas of research are suggested.

ASSESSING EARLY MATHEMATICAL DEVELOPMENT

The work discussed here is part of an international study involving Dutch, Belgian, German, Greek, Finnish and Slovenian as well as English children aged between 52 and 98 months. The project is coordinated by the University of Utrecht and employs the Utrecht Early Mathematical Competence Test. The full international data set is currently being analysed. This paper reports only the analysis of the English data, together with some international data already in the public domain. The data are interrogated to throw light upon (a) the comparison between England and other countries, (b) the relationship between age and mathematical attainment in the English sample, (c) differences between boys and girls and (d) the relationship between attainment in Piagetian tasks and more arithmetical tasks.