2.11. Necessary conditions for interpolation by entire functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41580/1/10958_2005_Article_BF01221572.pd

Activity theory, complexity and sports coaching: An epistemology for a discipline

The aim of this article is two-fold. Firstly, it is to advance the case for Activity Theory (AT) as a credible and alternative lens to view and research sports coaching. Secondly, it is to position this assertion within the wider debate about the epistemology of coaching. Following a framing introduction, a more comprehensive review of the development and current conceptualisation of AT is given. Here, AT’s evolution through three distinct phases and related theorists, namely Vygotsky, Leont’ev and Engeström, is initially traced. This gives way to a more detailed explanation of AT’s principal conceptual components, including ‘object’, ‘subject’, ‘tools’ (mediating artefacts), ‘rules’, a ‘community’ and a ‘division of labour’. An example is then presented from empirical work illustrating how AT can be used as a means to research sports coaching. The penultimate section locates such thinking within coaching’s current ‘epistemological debate; arguing that the coaching ‘self’ is not an autonomous individual, but a relative part of social and cultural arrangements. Finally, a conclusion summarises the main points made, particularly in terms in presenting the grounding constructivist epistemology of AT as a potential way forward for sports coaching

The Depth and Dynamics of Context: Tracing the Sources and Channels of Engagement and Disengagement in Students' Response to Literature

In this article, we analyze one coauthor's 12th-grade English class, focusing on a small group of students who interpreted the character of Gertrude in Hamlet through a body biography, a life-sized human outline that students filled with words and images that represented their understanding of the character. We analyze the body biography production as a function of the social context of activity and then analyze the processes of composition involved in their production. Analysis of the data reveals that (a) the students exhibited different degrees of commitment to and involvement in the group task, (b) the degree of equity in productivity and social relations varied within the group in accordance with these different degrees of engagement, and (c) the inequity in social relations and contributions to the group product belied the degree to which the final interpretive product met the teacher's assessment criteria. We conclude with a reconsideration of the notion of engagement that includes attention to both the immediate social relations within the classroom and the histories of engagement that students bring to class.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Competences of Mathematics Teachers in Diagnosing Teaching Situations and Offering Feedback to Students:Specificity, Consistency and Reification of Pedagogical and Mathematical Discourses

In the study we report in this chapter, we investigate the competences of mathematics pre- and in-service teachers in diagnosing situations pertaining to mathematics teaching and in offering feedback to the students at the heart of said situations. To this aim we deploy a research design that involves engaging teachers with situation-specific tasks in which we invite participants to: solve a mathematical problem; examine a (fictional yet research-informed) solution proposed by a student in class and a (fictional yet research-informed) teacher response to the student; and, describe the approach they themselves would adopt in this classroom situation. Participants were 23 mathematics graduates enrolled in a post-graduate mathematics education programme, many already in-service teachers. They responded to a task that involved debating the identification of a tangent line at an inflection point of a cubic function through resorting to the formal definition of tangency or the function graph. Analysis of their written responses to the task revealed a great variation in the participants’ diagnosing and addressing of teaching issues – in this case involving the role of visualisation in mathematical reasoning. We describe this variation in terms of a typology of four interrelated characteristics that emerged from the data analysis: consistency between stated beliefs/knowledge and intended practice, specificity of the response to the given classroom situation, reification of pedagogical discourses, and reification of mathematical discourses. We propose that deploying the theoretical construct of these characteristics in tandem with our situation-specific task design can contribute towards the identification – as well as reflection upon and development – of mathematics teachers’ diagnostic competences in teacher education and professional development programmes

Project management between will and representation

This article challenges some deep-rooted assumptions of project management. Inspired by the work of the German philosopher, Arthur Schopenhauer, it calls for looking at projects through two complementary lenses: one that accounts for cognitive and representational aspects and one that accounts for material and volitional aspects. Understanding the many ways in which these aspects transpire and interact in projects sheds new light on project organizations, as imperfect and fragile representations that chase a shifting nexus of intractable human, social, technical, and material processes. This, in turn, can bring about a new grasp of notions such as value,\ud knowledge, complexity, and risk