The development of numeracy in England and Slovenia

The Third International Mathematics and Science Study (TIMSS) placed Slovene 9 year olds significantly above the international mean in mathematics and English 9 year olds significantly below. As the project to be described here shows, however, such findings can mask finer differences in numerical abilities and problem-solving which qualitative analysis can reveal. While performance in arithmetic tasks of English 6 year olds was superior to Slovene pre-schoolers of the same age, at 7 years Slovene pupils had caught up and between 8 and 11 years forged ahead. By contrast, Slovene pupils were not quite so successful at problem-solving tasks in comparison with the English sample. Possible improvements, in the first place, might be obtained by a careful synthesis of curricula and instructional strategies but is this too simple a solution? A major goal of this paper will be to provide insight into the limitations of large-scale international studies and research methodologies as well as advocate qualitative approaches which, if not challenging such studies certainly complement and enrich them by setting out to answer another set of research questions. This paper also raises important questions about cultural differences which influence the aims and philosophy of education both directly and indirectly.     

The promises of moral foundations theory

In this article I examine whether Moral Foundations Theory can fulfil the promises that Haidt claims for the theory: that it will help in developing new approaches to moral education and to the moral conflicts that divide our diverse society. I argue that, first, the model that Haidt suggests for understanding the plurality of moralities—a shared foundation underlying diverse moralities—does not help to overcome conflicts. A better understanding of the nature and background of moral conflicts can lead to a more respectful attitude towards people with conflicting views, but need not contribute to ending conflicts. Second, I show that pervasive moral conflicts should be dealt with on the level of politics. They require a morality of compromising. Third, I examine why this approach does not seem to work in the USA.     

当代美学的本体论承诺

审美活动对于人的生命本身所具有的责任问题 ,不仅关系到它的现实有效性 ,也是美学存在的一个必要依据。审美承诺有两种历史形式 ,知识论承诺与伦理学承诺。审美承诺既不是知识论的启蒙 ,也不同于伦理学的教化 ,它是一种对人的感性存在的直接澄明。     

Computational estimation for numeracy

The importance of computational estimation is generally acknowledged. The widespread introduction of the hand-held calculator greatly increases its significance, particularly as a means of teaching number sense.The reason for its failure to be taught is traced to the multiplicity of methods used in estimation. Some agreed procedures are therefore suggested. These procedures have been developed in an unusual situation but are appropriate elsewhere. Detailed suggestions are made for estimating sums, differences, means, products, quotients and percentages.     

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

Abstract This paper describes a limited longitudinal study of young children's 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 educational needs, as well as representing a broad range of achievements levels based on standards assessment tasks. Whilst this paper focuses upon the performance of English pupils, reference is also made to the larger European sample which involved children from Flemish‐speaking Belgium, Germany, Greece, Slovenia and the Netherlands. Results showed that children's total scores at around the mid‐point of reception year were indeed predictive of later achievement at the end of KS1 though the combined scores over three testing cycles which extended to the mid‐point of Year 1, were more so. Discriminant analysis confirmed that a combination of a counting sub‐test (one seemed sufficient) and a sub‐test focusing on understanding of relations in shape, size, order or quantity (a different one at each testing cycle), together with the general number knowledge sub‐test was best predictive of final SAT levels. Comparison with the international data set suggested a different trajectory for English pupils, with more of a bias towards arithmetic sub‐tests than their European counterparts who start school later. Moreover, the pattern of dependence of scores on age in which no advantage was found in including any national differences was especially interesting. These findings are discussed within the context of different school start ages and traditions of preparation for formal schooling. Perhaps what emerged most strongly is the need for young English pupils to maintain a broad and balanced early mathematics curriculum, which places appropriate emphasis on practical problem solving.     

The promises of educational technology: A reassessment

The claims made for educational technology have not always been realized. Many programmes in education based on media and technology have produced useful documentation and supportive research; others have failed. The current, comprehensive definition of educational technology is a helpful key to understanding how a problem-solving orientation is necessary to approach teaching/learning designs. The process of educational technology begins with an analysis of the problem, rather than with the medium as a solution. Examples of appropriate applications come from open universities and primary schools where distance, time, insufficient personnel, and inadequate facilities have led to a search for alternative means for teaching and learning. Less successful programmes tended to have confused goals and an emphasis on one medium. They also lacked: support services, staff training, quality software and a system focus. The threads which run through the more successful programmes are described. The lessons learned from fifty years of media and technology development in education and training are discussed with an eye toward the future. It is clear that educational technology as a problem-solving process will lead the field into the twenty-first century.     

The pitfalls and promises of special education practice.

It is imperative that special education enable children with disabilities to achieve at high levels. Problems of equity and pedagogical validity have hindered our efforts thus far, and many children of minority cultures are far overrepresented in classrooms for students with learning disabilities and mild mental retardation. Studies have shown the importance of culturally and linguistically inclusive programs and of heterogenous groupings, as well as more effective diagnostic, remedial, and assessment practices. This article discussed a model and basic principles for such techniques to ensure that the educational outcomes of all children are improved.     

Access to numeracy: a case study

More and more pupils with learning difficulties are being taught in mainstream settings but how inclusive is the teaching they experience? In this illustrative case study, Ruth Germain, a teacher in a mainstream primary school, looks at how Paul, a pupil with Down's syndrome, is supported during 'dedicated numeracy time'. She examines the relationships between whole-class, group and individual teaching; the nature of the support Paul receives; and his educational and behavioural responses. The article closes with a call for further research into the implications for teaching and learning of the inclusion of pupils with learning difficulties in mainstream contexts.     

Learning to be teachers of adult numeracy

This paper investigates how teacher education programmes provide adequate preparation for its prospective teachers. It uses adult numeracy teacher education in the post‐compulsory education sector in England as exemplar. Using findings from two research projects on adult numeracy teacher education courses, the article investigates the applications of Bernstein's theories to teacher education, the approaches in which the diversity of prospective teachers is catered for on the course, the ways in which the recontextualization process may be incorporated into the course, the strategies to enable prospective teachers to learn to be teachers and the perception of prospective teachers regarding the weaknesses of their courses. Finally, this article mentions additional areas for research in order to gain further insight into the complex process of learning to be a teacher.     

The effects of integration and generation of immigrants on language and numeracy achievement

In many Western countries the pressure exerted on immigrants to integrate has become intense in recent years. Efforts to preserve their ethnic identity through multicultural recognition has now been replaced by the requirements of active civic participation and assimilation. Of course integration is considered important not only for the immigrant parents but also for their children. The central question in this article is whether there is a relationship between the degree of integration of the immigrant parents and the generation of their children on the one hand and the level of language and numeracy achievement of the children on the other. To answer this question we use data collected in 2008 from the Dutch COOL^5–18 cohort study. The information comes from more than 9000 immigrant and 16,000 indigenous children and their parents. The results show that as immigrant parents are better integrated and their children are of later generations, the language and numeracy skills of the children improve, though there remain large differences in achievement between different ethnic groups.     

教师组织承诺在学校管理中的地位与作用

教师组织承诺是指基于对学校办学目标和价值观的认同,教师对学校产生的一种责任心和义务感.它是教师愿意忠诚于教育事业、为学校努力做好教育教学工作的一种行为倾向.较高的教师组织承诺是达成较高学校效能的重要心理基础和必要条件.在学校管理中提高教师的组织承诺具有重大意义.     

The promise and the promises of Making in science education

Making is a rapidly emerging form of educational practice that involves the design, construction, testing, and revision of a wide variety of objects, using high and low technologies, and integrating a range of disciplines including art, science, engineering, and mathematics. It has garnered widespread interest and support in both policy and education circles because of the ways it has been shown to link science learning to creativity and investigation. Making has taken root in out-of-school settings, such as museums, science festivals, and afterschool and library programmes; and there is now growing interest from primary and secondary educators in how it might be incorporated into the classroom. Making expands on traditions associated with Technology Education and Design-Based Learning, but differs in ways that can potentially broaden participation in science and STEM learning to include learners from communities historically underrepresented in STEM fields. STEM-Rich Making is centrally organised around design and engineering practices, typically integrating digital tools and computational practices, and positions scientific and mathematical concepts and phenomena as the materials for design. This paper takes a critical view of the claims about Making as a productive form of science teaching and learning, and reviews the current research literature’s substantiation of the ways in which Making supports students’ agency, promotes active participation in science and engineering practices, and leverages learners’ cultural resources.     

Children's early numeracy in Finland and Iran

This research investigates similarities and differences in young children's early numeracy skills related to age, nationality and gender. The participants were five- to seven-year-old children from Finland and Iran. Early numeracy was investigated by using tasks measuring number-related relational skills (e.g. comparison, one-to-one correspondence) and counting skills (e.g. enumeration, number-word sequence skills). A hybrid multigroup, multiple-indicator-multiple-cause (MIMIC) approach to factorial invariance and latent mean differences between groups was used. The results showed that Finnish children had better scores in relational and counting tasks than did children in Iran. There was a gender difference in relational skills favouring girls in both countries. Younger children had weaker early numeracy skills than the older children in both countries. Comparing age groups in both countries shows a bigger difference in counting skills between young Iranian and Finnish children than between older children in both countries. The results are discussed in the context of early mathematics learning and gender equity in schooling.     

The promises and limitations of international comparative research on teacher education

This article revisits methodological perspectives on international comparative research on teacher education (TE). Benefits and problems related to comparative educational research methodology in general are discussed. Further, methodological issues associated with designing and carrying out an international comparative study on TE are addressed using a multi-level study on teacher education in Finland and Norway an as example. Towards the end of the article, the promises and limitations of international comparative research on TE are presented. Important benefits of comparative education on TE include widening the understanding of one’s own and other TE systems as well as gaining an understanding of international trends. However, uncritical use of such research may lead to decontextualised, ahistorical and standardised transfer and development of education and educational policies. The article concludes by urging researchers in the field of international comparative research on teacher education to address the questions: What is being compared? How is context addressed?     

Mental Calculation: its place in the development of numeracy

Recent curricular initiatives in the UK have been emphasising the importance of mental calculation in the achievement of improved numeracy standards. This article argues that while the emphasis on mental calculation is to be welcomed, the construct itself needs to be understood in all its complexity. This means recognising what is involved in mental calculation and, further, recognising the developmental shift from additive to multiplicative reasoning which is necessary for a mature conceptualisation of number. It is suggested that this shift is difficult to achieve because it involves reconceptualising the essential meaning of ‘a number’. Furthermore, the pedagogical practices which could possibly support children in their transition from additive to multiplicative reasoning must be more than helping children to develop an ever increasing repertoire of mental strategies.     

Learning disabilities and literacy & numeracy development

Abstract

This article provides a summary of the literature review contained in Volume Two of the DETYA Report, Mapping the Territory: Primary students with learning difficulties in literacy and numeracy. It summarizes the last three sections from the review. Section Three explores effective instructional techniques and programs in literacy and numeracy for students with learning difficulties. After that effective service delivery approaches within regular settings are examined in Section Four. Finally, issues in program evaluation and measurement of outcomes are addressed in Section Five.