The technological mediation of mathematics and its learning

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools – physical, virtual, cultural – in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We begin with an appraisal of the role of digital technologies, and our rationale for focusing on them. We present four categories of digital tool-use that distinguish their differing potential to shape mathematical cognition. The four categories are: i. dynamic and graphical tools, ii. tools that outsource processing power, iii. new representational infrastructures, and iv. the implications of highbandwidth connectivity on the nature of mathematics activity. In conclusion, we draw out the implications of this analysis for mathematical epistemology and the mathematical meanings students develop. We also underline the central importance of design, both of the tools themselves and the activities in which they are embedded

Pedagogical tools in an online teacher education programme: A sense of belonging and social presence

This thesis presents the findings from a study that explores in what ways the pedagogical tools in an online teacher education programme can facilitate a sense of belonging and social presence. In particular it explores the individual contribution of pedagogical online tools in relation to this. The research data was gathered using a mixed methodology. Qualitative data was gathered from questionnaires sent to six participants of the online teacher education programme that were then analysed to identify common themes, patterns and difference in participants perspectives. Quantitative data was collected by analysing the contributions of each of the six participants in specific computer mediated communication forums using Garrison and Anderson’s (2004) social presence and indicators framework across two papers of this online programme. There are two key findings evident in the data of this study. The first is that pedagogical online tools can facilitate a sense of belonging and afford social presence in an online community of learners. However, each tool has different affordances. The effectiveness of their use depends on the way they are supported and used by the lecturer. Secondly, each participant had a different perspective on the affordances of each individual tool in their usefulness for fostering a sense of belonging and social presence. This was of particular interest as it indicates that one tool can afford a diversity of factors that may have a particular resonance with individual participants. The findings highlight the importance of lecturers needing to take into account the different affordances of online tools and the different ways that students might use them. Therefore, this study is in a position to inform the development of this and other online teacher education programme

Re-designing an MA module to foster agency, engagement and production in online social software

This article describes the process of re-designing a module on the MA in Media, Culture and Communication at the Institute of Education (IOE), University of London. This process took place as part of the “Pedagogic Research to Embedded E-Learning” (PREEL) project at the IOE and involved moving a module largely concerned with offline production of teaching resources into online engagement with Internet culture. Course participants were encouraged to think about issues around production in social software in ways which were relevant to their professional and personal activity online. The early stages of the re-design process were recorded in a course tutor blog and there were further attempts to reflect on the process using two evaluations, one in the middle of a pilot version of the course and the other at the end. The article concludes with a series of lessons learned which can be taken forward during the revalidation process

A literature review of the use of Web 2.0 tools in Higher Education

This review focuses on the use of Web 2.0 tools in Higher Education. It provides a synthesis of the research literature in the field and a series of illustrative examples of how these tools are being used in learning and teaching. It draws out the perceived benefits that these new technologies appear to offer, and highlights some of the challenges and issues surrounding their use. The review forms the basis for a HE Academy funded project, ‘Peals in the Cloud’, which is exploring how Web 2.0 tools can be used to support evidence-based practices in learning and teaching. The project has also produced two in-depth case studies, which are reported elsewhere (Galley et al., 2010, Alevizou et al., 2010). The case studies focus on evaluation of a recently developed site for learning and teaching, Cloudworks, which harnesses Web 2.0 functionality to facilitate the sharing and discussion of educational practice. The case studies aim to explore to what extent the Web 2.0 affordances of the site are successfully promoting the sharing of ideas, as well as scholarly reflections, on learning and teaching

Analytic frameworks for assessing dialogic argumentation in online learning environments

Over the last decade, researchers have developed sophisticated online learning environments to support students engaging in argumentation. This review first considers the range of functionalities incorporated within these online environments. The review then presents five categories of analytic frameworks focusing on (1) formal argumentation structure, (2) normative quality, (3) nature and function of contributions within the dialog, (4) epistemic nature of reasoning, and (5) patterns and trajectories of participant interaction. Example analytic frameworks from each category are presented in detail rich enough to illustrate their nature and structure. This rich detail is intended to facilitate researchers’ identification of possible frameworks to draw upon in developing or adopting analytic methods for their own work. Each framework is applied to a shared segment of student dialog to facilitate this illustration and comparison process. Synthetic discussions of each category consider the frameworks in light of the underlying theoretical perspectives on argumentation, pedagogical goals, and online environmental structures. Ultimately the review underscores the diversity of perspectives represented in this research, the importance of clearly specifying theoretical and environmental commitments throughout the process of developing or adopting an analytic framework, and the role of analytic frameworks in the future development of online learning environments for argumentation

Ballet Pedagogy as Kinesthetic Collaboration: Exploring Kinesthetic Dialogue in an Embodied Student-Teacher Relationship

The twenty-first century ballet class often retains traditional organization, beginning with the barre work, continuing with the centre practice, adage, pirouettes, and allegro. However, the pedagogical demands on teachers have evolved within that framework due to critical questioning of how factors such as patriarchal underpinnings of class structure, the students lived experience, and the efficacy of newly added pedagogical strategies influence dance education. Employing ethnographic methods, in the form of two separate studies, this research addresses how embodied student-teacher relationships based on multisensory perception can create kinesthetic dialogue, which facilitates the transmission of embodied knowledge. The purpose of this dissertation is to explore how an embodied student-teacher relationship manifests itself in the ballet studio, highlighting whether kinesthetic dialogue facilitates the transfer of bodily knowledge. The questions driving the research were: What combination of verbal and non-verbal communication is observed between the teacher and the students in each environment? Do instances within this communication illustrate the pedagogical tool of kinesthetic dialogue? Do moments within this pedagogical dialogue appear to trigger previously developed body memory in the students, based on their reactions to instructions, as well as in their performance of the material? Ethnographic data collection techniques included: participant observation, teacher interviews, student email interviews, student focus groups as well as student surveys. Results are reported using both a priori themes as well as themes that emerged from the data. The data interpretation across both studies is reported using two overarching pedagogical themes: the application of traditional pedagogical strategies with their accompanying ideologies, and the incorporation of innovative techniques that facilitated a progressive approach to learning. Literature demonstrates that the student-teacher relationship is saturated with a patriarchal history, hierarchical constraints and external aesthetic expectations. However, critical analysis by scholars and educators regarding institutionalization, the body, and pedagogy are shifting the foundations of traditional ballet for future generations. This research indicates that bringing ballets well-established pedagogical tools to consciousness has the potential to create more effective learning situations. An understanding of kinesthetic dialogue can facilitate the conscious application of a reciprocal mode of kinesthetic communication that ballet teachers have intuitively employed for centuries

Models for Learning (Mod4L) Final Report: Representing Learning Designs

The Mod4L Models of Practice project is part of the JISC-funded Design for Learning Programme. It ran from 1 May – 31 December 2006. The philosophy underlying the project was that a general split is evident in the e-learning community between development of e-learning tools, services and standards, and research into how teachers can use these most effectively, and is impeding uptake of new tools and methods by teachers. To help overcome this barrier and bridge the gap, a need is felt for practitioner-focused resources which describe a range of learning designs and offer guidance on how these may be chosen and applied, how they can support effective practice in design for learning, and how they can support the development of effective tools, standards and systems with a learning design capability (see, for example, Griffiths and Blat 2005, JISC 2006). Practice models, it was suggested, were such a resource. The aim of the project was to: develop a range of practice models that could be used by practitioners in real life contexts and have a high impact on improving teaching and learning practice. We worked with two definitions of practice models. Practice models are: 1. generic approaches to the structuring and orchestration of learning activities. They express elements of pedagogic principle and allow practitioners to make informed choices (JISC 2006) However, however effective a learning design may be, it can only be shared with others through a representation. The issue of representation of learning designs is, then, central to the concept of sharing and reuse at the heart of JISC’s Design for Learning programme. Thus practice models should be both representations of effective practice, and effective representations of practice. Hence we arrived at the project working definition of practice models as: 2. Common, but decontextualised, learning designs that are represented in a way that is usable by practitioners (teachers, managers, etc).(Mod4L working definition, Falconer & Littlejohn 2006). A learning design is defined as the outcome of the process of designing, planning and orchestrating learning activities as part of a learning session or programme (JISC 2006). Practice models have many potential uses: they describe a range of learning designs that are found to be effective, and offer guidance on their use; they support sharing, reuse and adaptation of learning designs by teachers, and also the development of tools, standards and systems for planning, editing and running the designs. The project took a practitioner-centred approach, working in close collaboration with a focus group of 12 teachers recruited across a range of disciplines and from both FE and HE. Focus group members are listed in Appendix 1. Information was gathered from the focus group through two face to face workshops, and through their contributions to discussions on the project wiki. This was supplemented by an activity at a JISC pedagogy experts meeting in October 2006, and a part workshop at ALT-C in September 2006. The project interim report of August 2006 contained the outcomes of the first workshop (Falconer and Littlejohn, 2006). The current report refines the discussion of issues of representing learning designs for sharing and reuse evidenced in the interim report and highlights problems with the concept of practice models (section 2), characterises the requirements teachers have of effective representations (section 3), evaluates a number of types of representation against these requirements (section 4), explores the more technically focused role of sequencing representations and controlled vocabularies (sections 5 & 6), documents some generic learning designs (section 8.2) and suggests ways forward for bridging the gap between teachers and developers (section 2.6). All quotations are taken from the Mod4L wiki unless otherwise stated

Learning design – making practice explicit

New technologies have immense potential for learning, but the sheer variety possible also creates challenges for learners in terms of navigating through an increasingly complex digital landscape and for teachers in terms of how to design and support learning interventions. How can learners and teachers make informed decisions about what technologies to use in the design and support of learning activities? This presentation will consider this question and present a new methodology for design – 'learning design', which aims to shift the creation and support of learning from what has traditionally been an implicit, belief-based practice to one that is explicit and design based. Learning design research at the Open University, UK has included the development of a set of conceptual design views, a tool for visualising designs (CompendiumLD) and a social networking site, for sharing and discussing learning and teaching ideas and designs (Cloudworks). An overview of this work will be provided, along with a discussion of the perceived benefits of this new approach to educational design

What would learning in an open world look like? A vision for the future

The pace of current technological advancement is phenomenal. In the last few years we have seen the emergence of ever more sophisticated gaming technologies, rich, immersive virtual worlds and new social networking services that enable learners and teachers to connect and communicate in new ways. The pace of change looks set to continue as annual Horizon reports testify (http://www.nmc.org/horizon). Clearly new technologies offer much in an educational context, with the promise of flexible, personalised and student-centred learning. Indeed research over the past few years, looking at learners' use of technologies, has given us a rich picture of how learners of all ages are appropriating new tools within their own context, mixing different applications for finding/managing information and for communicating with others (Sharpe and Beetham, forthcoming)