修正Bernstein算子的导数及其加权光滑性刻画

Della Vecchia等引进一种修正的Bernstein算子,它可以用来逼近端点具有奇性的函数。文章利用加权光滑模ω2φλ（ f,t） w和加权K 泛函K2φλ（ f,t2） w ,建立了该算子的导数与其目标函数的光滑性之间的等价关系,所得结论对权函数的参数a,b无上界限制,只要求a, b ＞0。     

Talking in class: a study of socio‐economic difference in the primary school classroom

In this paper, I consider the relationship between socio‐economic background and the school experience of two groups of children. I seek to establish whether or not there are identifiable differences in the language of primary school children living in two demographically contrasting geographical areas and, if there are differences, how these differences might impact upon a child's capacity to access learning. In investigating these relationships, I conducted semi‐structured interviews with the two groups using the work of Bernstein as a starting point. I found that while the children in the first school, located in a largely less affluent area of Bristol, appeared to lack confidence, extended vocabulary and often clarity in their speech, the children in the second school, located in a middle class, affluent area of the city appeared articulate, self‐ confident and in possession of a varied and extended vocabulary. While it is not appropriate to generalise from this small scale study, these findings raise questions about the language children experience from an early age both in the home environment and at school and suggest that there is a significant part for schools to play in ensuring that they are not excluding some groups of children from participation.     

‘Epistemic chaos’: the recontextualisation of undergraduate curriculum design and pedagogic practice in a new university business school

This paper is based on a qualitative case study of undergraduate curriculum design and pedagogic practice in the new University Business School (UBS). Data were collected using semi-structured interviews with 24 academics from across a range of business sub-disciplines together with an extensive documentary review of materials relating to two undergraduate degree programmes. The case study found that the UBS curriculum had become recontextualised as a ‘business project’ in which programmes were constructed as ‘products’ for the higher education market. The associated pedagogy was largely confined to behaviourist problem–solution routines based on narrow projections of the ‘real world’ of business. This paper contends that UBS undergraduate programmes were designed in a generic mode in response to the material and discursive influences of marketisation. As a consequence, ‘epistemic chaos’ had arisen in which knowledge and pedagogy had become fragmented and amorphous.     

The position of dance in physical education

Dance has been a part of the physical education (PE) curriculum in several countries for a long time. In spite of this, studies demonstrate that the position of dance in the subject of PE is contested and that little time is devoted to dance. The overall aim of this article is to examine the position of dance as a pedagogical discourse in Swedish steering documents over time. The empirical material consists of five Swedish curricula for PE over a period of 50 years (1962–2011). Discourse analysis is used to identify organised systems of meaning, including privileged and prioritised values. Our theoretical frame of reference draws on Bernstein's concept of codes. Three different knowledge areas within dance are found in the text material: ‘dance as cultural preserver’, ‘dance as bodily exercise’ and ‘dance as expression’. Three pedagogical discourses emerge from these knowledge areas: an identity formation discourse, a public health discourse and an aesthetic discourse. The identity formation discourse in earlier curricula focuses on the perpetuation of Swedish and Nordic cultural traditions, while in later curricula, it emphasises the construction of a broader multicultural identity formation related to the understanding of different cultures. The public health discourse constitutes a prioritised understanding of dance as physical training related to a healthy lifestyle. The aesthetic discourse, which has the weakest position over time, represents the valuing of embodied experiences and feelings expressed through movements. This discourse is closely linked to the construction of gender. Over time, a new performance code came to surpass the former competence code in the steering documents. The performance code positions dance in PE as mainly a physical activity with little artistic or aesthetic value. The pedagogical discourse of dance remains within a highly disciplinary framework of social control.     

Recognising and revealing knowers: an enhanced Bernsteinian analysis of masonic recruitment and apprenticeship

The increasing opening of French freemasonry to lower social classes raises the question of how individuals from different social backgrounds can be assimilated into the practice of context‐independent ways of speaking and writing. I address these issues by, first, describing a selection by existing members based on the dispositions already possessed by noviciates; a replacement of social hierarchies by a masonic hierarchy; and a cumulative experience for members. Using one dimension of Legitimation Code Theory, I redescribe this process of selection and apprenticeship as being one of recognising and revealing knowers. That is to say, it focuses less on specialist knowledge than on knowers. Finally, I argue that analogical reasoning and tacit pedagogy are central to the issue of how a socially diverse population is integrated within freemasonry. This form of apprenticeship enables members who may not be oriented towards abstraction to learn to engage in the manipulation of context‐independent meanings.     

Time past: impacts of ICT on the pedagogic discourse in the Interactive project

The ‘pedagogic discourse’ can describe the power relations and fields of influence within schools. This article extends the approach to include ICT-mediated learning in schools by considering evidence from the InterActive project, undertaken by the University of Bristol, England, in 2000–04. The article also considers how the pedagogic discourse can complement post-Vygotskian sociocultural models of learning. ICT is presented as a ‘recontextualising field’ that exerts influence by weakening the classification and framing of the discourse. Successful uses of ICT tend to favour ‘invisible’ pedagogies: collaborative modes of active working with shared competences, in lessons containing elements of ‘discovery’. Tensions can arise if the dominant discourse is a ‘visible’ pedagogy that favours individual performance, with the teacher as the voice of authority and controller of the discourse. These tensions can lead to ICT being marginalised or discredited by teachers or lead to new modalities of pedagogy.     

A new algorithm for designing developable Bézier surfaces

A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper. Project supported by the National Basic Research Program (973) of China (No. 2004CB719400), the National Natural Science Foundation of China (Nos. 60373033 and 60333010) and the National Natural Science Foundation for Innovative Research Groups (No. 60021201), China     

A new fractional rational Bézier curve

Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of fractional Bernstein bases. Moreover, some basic properties were dicussed and a theorem connected to Poisson curves was obtained. Some examples in this paper were given by the visual results. Project supported by the National Natural Science Foundation of China (Grant No. 10271074)     

Mapping the development of a new MA programme in higher education: comparing privately held perceptions of a public endeavour

After spending a year working on the development of a new online Master’s programme in higher education, members of the development team were interviewed to reveal their thoughts about the nature of the programme. The dialogue of each interview was summarised as a concept map. Analysis of the resulting maps included a modified Bernsteinian analysis of the focus of the concepts included in terms of their semantic gravity (i.e. closeness to context) and the degree of resonance with the underpinning regulative discourse of the programme. Data highlight a number of potential issues for programme delivery that centre around the use of appropriate language to manage student expectations in relation to the process of learning and the emotional responses this can stimulate, as well as the tensions that can be foregrounded between the demands of teaching and research within a university environment.