Tools for Thought: The Case of Mathematics

The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced

Teaching Environmental Management Competencies Online: Towards “Authentic” Collaboration?

Environmental Management (EM) is taught in many Higher Education Institutions in the UK. Most this provision is studied full-time on campuses by younger adults preparing themselves for subsequent employment, but not necessarily as environmental managers, and this experience can be very different from the complexities of real-life situations. This formal academic teaching or initial professional development in EM is supported and enhanced by training and continuing professional development from the major EM Institutes in the UK orientated to a set of technical and transferable skills or competencies expected of professional practitioners. In both cases there can be a tendency to focus on the more tractable, technical aspects of EM which are important, but may prove insufficient for EM in practice. What is also necessary, although often excluded, is an appreciation of, and capacity to deal with, the messiness and unpredictability of real world EM situations involving many different actors and stakeholders with multiple perspectives and operating to various agendas. Building on the work of Reeves, Herrington and Oliver (2002), we argue that EM modules need to include the opportunity to work towards the practice of authentic activities with group collaboration as a key pursuit. This paper reports on a qualitative study of our experiences with a selected sample taken from two on-line undergraduate EM modules for second and third year students (referred to respectively as Modules A and B) at the Open University, UK where online collaboration was a key component. Our tentative findings indicate that on-line collaboration is difficult to ensure as a uniform experience and that lack of uniformity reduces its value as an authentic experience. Whilst it can provide useful additional skills for EM practitioners the experience is uneven in the student body and often requires more time and support to engage with than originally planned

INVESTIGATING USER PREFERENCES FOR SERVICES IN RURAL AREAS OF SCOTLAND: A TERRITORIAL APPROACH

Territorialisation of rural policies requires moving from a sectoral approach to service provision, and policies that focus exclusively on health and education, for example, to an understanding of overall service provision and quality, differentiated by rural area definition, not primarily by sector. An investigation of the expectations of stakeholders in rural Scotland, relating to availability, quality and accessibility of services, revealed that preferences were often different within different areas. The results input to the debate about the need to territorialise rural policy, and provide information for allocation decisions relating to resources aimed at creating sustainable rural communities in Scotland.Services, participatory methods, Scotland, user preferences, territorial rural policies, Community/Rural/Urban Development,

Parsing Argumentation Structures in Persuasive Essays

In this article, we present a novel approach for parsing argumentation structures. We identify argument components using sequence labeling at the token level and apply a new joint model for detecting argumentation structures. The proposed model globally optimizes argument component types and argumentative relations using integer linear programming. We show that our model considerably improves the performance of base classifiers and significantly outperforms challenging heuristic baselines. Moreover, we introduce a novel corpus of persuasive essays annotated with argumentation structures. We show that our annotation scheme and annotation guidelines successfully guide human annotators to substantial agreement. This corpus and the annotation guidelines are freely available for ensuring reproducibility and to encourage future research in computational argumentation.Comment: Under review in Computational Linguistics. First submission: 26 October 2015. Revised submission: 15 July 201

The uses of qualitative data in multimethodology:Developing causal loop diagrams during the coding process

In this research note we describe a method for exploring the creation of causal loop diagrams (CLDs) from the coding trees developed through a grounded theory approach and using computer aided qualitative data analysis software (CAQDAS). The theoretical background to the approach is multimethodology, in line with Minger’s description of paradigm crossing and is appropriately situated within the Appreciate and Analyse phases of PSM intervention. The practical use of this method has been explored and three case studies are presented from the domains of organisational change and entrepreneurial studies. The value of this method is twofold; (i) it has the potential to improve dynamic sensibility in the process of qualitative data analysis, and (ii) it can provide a more rigorous approach to developing CLDs in the formation stage of system dynamics modelling. We propose that the further development of this method requires its implementation within CAQDAS packages so that CLD creation, as a precursor to full system dynamics modelling, is contemporaneous with coding and consistent with a bridging strategy of paradigm crossing

Untangling Knots: Embodied Diagramming Practices in Knot Theory

The low visibility and specialised languages of mathematical work pose challenges for the ethnographic study of communication in mathematics, but observation-based study can offer a real-world grounding to questions about the nature of its methods. This paper uses theoretical ideas from linguistic pragmatics to examine how mutual understandings of diagrams are achieved in the course of conference presentations. Presenters use shared knowledge to train others to interpret diagrams in the ways favoured by the community of experts, directing an audience’s attention so as to develop a shared understanding of a diagram’s features and possible manipulations. In this way, expectations about the intentions of others and appeals to knowledge about the manipulation of objects play a part in the development and communication of concepts in mathematical discourse

A practitioner's guide to 'Imagine', the systemic and prospective sustainability analysis

The purpose of the Mediterranean Action Plans Coastal Area Management Programme is to help Mediterranean countries implement a sustainable management process for their coastal areas. This in particular implies thinking collectively about possible futures by taking into account past developments and the present situation of the area in question. To do so and right from the very start, the Blue Plan has assisted teams involved in the CAMPs to use the systemic and prospective approach so as to highlight priorities, forecast negative developments and suggest action to be taken to establish sustainable development in the Mediterranean's coastal areas. What do we mean by sustainable development? The Blue Plan adheres to a definition that is a blend of what you find in the Bruntland Report and at the FAO, 'sustainable development is one that respects the environment, is technically appropriate, economically viable and socially acceptable, making it possible to meet the needs of present generations without jeopardising the ability of future generations to meet their own needs'. In this framework the 'Imagine' analysis of systemic and prospective sustainability now proposes a set of tools and methods (a methodological corpus) to describe, assess and examine the level of sustainability of an eco-socio system in the past, present and future by means of indicators and a participatory process that considers local actors to be experts at their level

Drawing off the page: How new 3D technologies provide insight into cognitive and pedagogical assumptions about mathematics

Mathematics has a history of being a two-dimensional inscribing practice. We describe the potential evolution in doing, thinking, and learning mathematics with the emergence of a technological innovation that enables real-time 3D virtual and material interactions. Using the 3D drawing pen as a simple and recently available technology, we highlight how it helps re-think long-standing assumptions and dichotomies in mathematics education including, for example, the material distinction between diagram and manipulative, the semiotic distinction between icon and index, and the developmental progression of action-icon-symbol. We then speculate on the future possibilities of the shift in technological infrastructure that 3D pens and similar technology may give rise to