1,721,482 research outputs found
Understanding subtraction through enhanced communication
No full textThis chapter forms part of an edited book which is a culmination of a 3-year international study investigating creative communication in primary mathematics. Using interviews, observations and video the researchers studied and developed strategies for promoting mathematical understanding among 5-11 year olds. These were then tried and tested in the other project countries. The findings reported in this chapter were highly encouraging as they demonstrated such an approach broadened both teachers' and pupils' understandings of subtraction. Moreover, in using examples from the UK in particular, the European teachers were encouraged to focus on mathematical processes rather than product. The original research bid was subject to rigorous scrutiny, the project was evaluated by 2 European academics and the book proposal refereed by a panel of teachers and academics. Cockburn wrote this chapter and edited the book
Hyperbolic monopoles, JNR data and spectral curves
Full text linkA large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data
Equal in diversity: reflections on Primary Teachers' Learning
No full textAbstract: An unexpected observation made during an international study exploring mathematical misconceptions in primary schools (Cockburn and Littler, 2008) was that there was a large commonality in what was observed even though, in discussion, we noted that there remarkable differences in the way the teachers taught and had been trained. For example the equals sign, together with arithmetic algorithms and structural properties, gave rise to misconceptions (Parslow-Williams and Cockburn, 2008) which, in some cases, extended well beyond the primary years of schooling (Marchini and Cockburn, 2008). Closer examination of the data revealed that, although many of the misconceptions may have originated in the earliest years of schooling, frequently they did not become manifest for several years. As we will demonstrate, in spite of the many differences in culture, language and experience, it was striking that the teachers in Italy and England discussed similar implications for their future practice
Teaching practices revealed through arithmetic misconceptions
No full textAbstract. The aim of our research was to investigate whether primary school pupils (7-11 year olds) can distinguish between simple arithmetic errors and misconceptions. Data from a specifically designed task are presented. We demonstrate the importance of teachers’ practice in the development of pupils’ reflexive thinking
Flexible mental computation: What about accuracy?
No full textFlexibility in strategy choice in mental computation is considered to be a component of number sense. This paper reports on an investigation into cognitive, metacognitive, and affective factors that support both flexibility and accuracy in mental addition and subtraction in Year 3 students. While some factors appeared to be essential for flexibility, additional factors were necessary for accurate employment of strategies. Further, there were qualitative differences between the mental strategies employed by the students who were accurate and those who were inaccurate
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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