Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Communication and transformation through collaboration: Rethinking drawing activities in early childhood.

This article is a study of the arts in early childhood as a way of learning, for both children and their teachers. The author suggests that drawing can be a powerful tool for collaborative approaches to pedagogy. When teachers draw with children, pathways of communication can be opened, and the collaborative exercise can trigger processes of transformation for both adult and child. In order to present challenges to more traditional, hands-off pedagogical practices in arts education, this article is an account of reflexive arts pedagogies, and how they can work to improve communication and understandings between adults and children. Within the educational contexts of Australian preschooling and primary schooling, the author examines the process of collaborative drawing, and how this can enable a process of transformation. Her analysis, and the accompanying examples of reflexive practices, combine complementary lenses, socio-cultural and postmodern, that she sees as working in harmony to produce new possibilities, in arts education in particular, and, more broadly, in early childhood education.

Inter-sector leader transitions and organisation transformation : a research agenda

Faced with the need for strategic change, structural and cultural realignment, innovation and value-adding, many public sector organisations are tapping into a wider senior leadership talent pool and attracting successful leaders from other sectors (Flynn and Thompson, 2009). Leadership renewal has resulted, in some cases, in the external recruitment of whole senior leadership teams (Hockridge, 2008), raising issues about the influence of context on leader success (Pawar and Eastman, 1997) and potential leader transition failure, a costly outcome for leaders and organisations (Howard, 2001). There is little research on inter-sector leader transitions, which is surprising given the significant costs associated with leader acquisition and failure(Conger, 2010; Day and Halpin, 2004). For example, it is not clear what organizations do (or do not do) to ensure the outcomes of their significant investment in inter sector transitions are realised. In addition, it is not clear how the individual leader manages the challenging transition into a new leadership context and how their approach to leadership facilitates or inhibits successful transition (Avolio, 2010). Leader assimilation programs have been developed to assimilate new leaders (Manderscheid, 2008); however, assimilation is not necessarily a desired organisational outcome (Denis and Pineault, 2000). In this paper we critically review the limited literature on inter-sector leader transitions and transformational change outcomes and argue for a mutual accommodation approach. We draw on our own initial empirical work to propose the elements of a program for achieving this outcome from the perspective of the public organisation and the inter-sector appointee.

A profluorescent azaphenalene nitroxide for nitroxide-mediated polymerization

A novel nitroxide-mediated polymerization (NMP) control agent; 1,1,3,3-tetramethyl-2,3-dihydro-2-azaphenalen-2-yloxyl (TMAO), was used in the free-radical polymerization of styrene. The conversion of styrene during NMP was studied using FT-Raman spectroscopy and the effectiveness of TMAO as a NMP control agent was assessed by GPC analysis. Fidelity of the TMAO-alkoxyamine end-group on the synthesized polymers was confirmed by GPC, UV-Vis and fluorescence spectroscopic analyses. Comparison to the well known NMP control agent, TEMPO was made. TMAO showed control of molecular weight approaching that of TEMPO. Attempts to improve the properties of TMAO as an NMP control agent by synthesizing an analogue with bulkier substituents around the nitroxide did not generate the target molecule but demonstrated some of the interesting chemistry of the azaphenalene ring system

Economic development, enlightenment and creative transformation : creative industries in the New China

This paper examines some of the implications for China of the creative industries agenda as drawn by some recent commentators. The creative industries have been seen by many commentators as essential if China is to move from an imitative low-value economy to an innovative high value one. Some suggest that this trajectory is impossible without a full transition to liberal capitalism and democracy - not just removing censorship but instituting 'enlightenment values'. Others suggest that the development of the creative industries themselves will promote social and political change. The paper suggests that the creative industries takes certain elements of a prior cultural industries concept and links it to a new kind of economic development agenda. Though this agenda presents problems for the Chinese government it does not in itself imply the kind of radical democratic political change with which these commentators associate it. In the form in which the creative industries are presented – as part of an informational economy rather than as a cultural politics – it can be accommodated by a Chinese regime doing ‘business as usual’.

Workplace mobbing : expulsion, exclusion, and transformation

The issue of workplace bullying has received considerable attention in recent times in both the academic literature and in the print and electronic media. The stereotypical bullying scenario can be described as the “bully boss” model, where those in more senior positions tend to bully the staff they supervise. By way of contrast, this paper presents the findings of a three year exemplarian action research study into the lesser known phenomenon of workplace mobbing. Consistent with grounded theory methods, the findings are discussed in the context of emergent propositions in relation to the broader social, cultural, and organisational factors that can perpetuate workplace mobbing in the public sector.

Glycosaminoglycan and growth factor mediated murine calvarial cell proliferation

Understanding the complex mechanisms underlying bone remodeling is crucial to the development of novel therapeutics. Glycosaminoglycans (GAGs) localised to the extracellular matrix (ECM) of bone are thought to play a key role in mediating aspects of bone development. The influence of isolated GAGs was studied by utilising in vitro murine calvarial monolayer and organ culture model systems. Addition of GAG preparations extracted from the cell surface of human osteoblasts at high concentrations (5 microg/ml) resulted in decreased proliferation of cells and decreased suture width and number of bone lining cells in calvarial sections. When we investigated potential interactions between the growth factors fibroblast growth factor-2 (FGF2), bone morphogenic protein-2 (BMP2) and transforming growth factor-beta1 (TGFbeta1) and the isolated cell surface GAGs, differences between the two model systems emerged. The cell culture system demonstrated a potentiating role for the isolated GAGs in the inhibition of FGF2 and TGFbeta1 actions. In contrast, the organ culture system demonstrated an enhanced stimulation of TFGbeta1 effects. These results emphasise the role of the ECM in mediating the interactions between GAGs and growth factors during bone development and suggest the GAG preparations contain potent inhibitory or stimulatory components able to mediate growth factor activity.