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

The Art History Canon and the Art History Survey Course: Subverting the Western Narrative.

Art History enrollments at the college level are declining as students flock to STEM majors and perceive Art History as dated and of little use in today’s modern, scientific world. Yet Art History classes can teach valuable skills. When taught in a broad context, the objects art history studies engage critical thinking and can generate new forms of knowledge. However, the pedagogical structure and content of introductory art history survey course does not always offer students the creative leeway to make these connections. Instructors at the college level often retreat to the methods and content that have been a part of the discipline since its inception in the late 19thcentury; the professor as expert authority on the western canon of objects and the grand narrative of progressive development that accompanies them. As university students are becoming more ethnically and socially diverse, the objects covered in the survey continue to speak to a white, European audience that is no longer the only audience listening. While art history remains useful, its canon of objects has become problematic, and reinforces the othering of the non- western world. This essay will first examine how the modern canon and art history’s pedagogical practices came to be by examining the history of the discipline, and the theories, methods and texts that developed alongside academic art history. It will then take a brief look at how modern philosophy, primarily the conceptual ideas of Deleuze and Guattari, can provide a new framework for examining how the teaching of art history can be globalized and taught in a more meaningful way

Enactivism and ethnomethodological conversation analysis as tools for expanding Universal Design for Learning: the case of visually impaired mathematics students

Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants’ multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device

Webbing and orchestration. Two interrelated views on digital tools in mathematics education

The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of webbing and instrumental orchestration are developed. However, the two seemed to be disconnected, and having different cultural and theoretical roots. In this article, we investigate the distinct and joint journeys of these two theoretical perspectives. Taking some key moments in recent history as points of de- parture, we conclude that the two perspectives share an importance attributed to digital tools, and that initial differences, such as different views on the role of digital tools and the role of the teacher, have become more nuances. The two approaches share future chal- lenges to the organization of teachers'collaborative work and their use of digital resources.Comment: Teaching Mathematics and its Applications (2014) to be complete

Are We “Reading the World”? A Review of Multicultural Literature on Globalization

Given its commitment to “reading” the social context, how is multicultural education accounting for the shifting context of our globalized world? A conceptual review of multicultural journals reveals limited engagement. However, a more sustained analysis could fuel re-articulations and contestations of the purpose of education in the 21st century

The teacher as action researcher : Using technology to capture pedagogic form

The paper argues that we make best use of learning technologies if we begin with an understanding of educational problems, and use this analysis to target the solutions we should be demanding from technology. The focus is to address the issue from the perspective of teachers and lecturers – the 'teaching community', and to consider how they could become the experimental innovators and reflective practitioners who will use technology well. Teachers could become 'action researchers', collaborating to produce their own development of knowledge about teaching with technology. For this to be possible, they must be able to share that knowledge, and the paper proposes the use of an online learning activity management system (LAMS) as a way of capturing and sharing the pedagogic forms teachers design. An action research approach, like all research, needs a theoretical framework from which to challenge practice, and paper shows how teachers could use the Conversational Framework to design and test an optimally effective learning experience. Examples of 'generic' learning designs illustrate how such approach can help the teaching community rethink their teaching, collectively, and embrace the best of conventional and digital methods. In this way they will be more likely to harness technology to the needs of education, rather than simply search for the problems to which the latest technology is a solution

Reinventing learning: a design-research odyssey

Design research is a broad, practice-based approach to investigating problems of education. This approach can catalyze the development of learning theory by fostering opportunities for transformational change in scholars’ interpretation of instructional interactions. Surveying a succession of design-research projects, I explain how challenges in understanding students’ behaviors promoted my own recapitulation of a historical evolution in educators’ conceptualizations of learning—Romantic, Progressivist, and Synthetic (Schön, Intuitive thinking? A metaphor underlying some ideas of educational reform (working paper 8). Division for Study and Research in Education, MIT, Cambridge, 1981)—and beyond to a proposed Systemic view. In reflection, I consider methodological adaptations to design-research practice that may enhance its contributions in accord with its objectives

Digital literacy in religious studies

This article considers the relevance of the concept of ‘digital literacy’ within the context of the discipline of religious studies in higher education and reflects on its potential impact on notions of ‘graduateness’. It contemplates how digital technology can be integrated most effectively in learning design and reflects on the skills students need to be equipped with to recognise the challenges and opportunities of digital technology and understand its impact and role within the study of religions

Gaming capital: Rethinking literacy

This paper is part of the symposium: Gameplay, gameplayers and gaming capital: Exploring intersections between games, education and adolescent subjectivities in virtual worlds PEER REFEREEING REQUIRED In rethinking literacy education in light of unprecedented technological change, this paper reports on adolescent gamers and their accumulation of gaming capital. This is in opposition to more pervasive assumptions about gaming as mindless entertainment, learning simulations, ideological tools and interactive mediums for the masses. We see the need to research the medium of games in their entirety, exploring their uniqueness as a medium--while at the same time--making connections to a wider media ecology (Fuller, 2005) that includes more than the games themselves. This media ecology of videogames is demonstrated in part by the 'paratextual' (Consalvo, 2007) industries that support game play, production and design. The 'paratext' is central to gaming capital in creating individual and group systems of distinction within gaming culture. Because we understand videogames as actions across social fields enacted through the actions of players or 'operators' on software, we also deem it necessary to understand both the operator and machines' diegetic and non-diegetic actions (Galloway, 2006). This distinction allows us to think about games as more than texts, literacy practices and narratives, which highlights games' significance in technoclture as systems (Salen, 2008), procedures (Bogost, 2007), algorithms (Galloway, 2006; Wark, 2007), configurations and code (Lessig, 1999; Manovich, 2001). In conclusion we provide a series of interview questions developed to uncover adolescents' gaming capital. We also propose a heuristic to map a players' total volume of gaming capital to better understand how gaming capital establishes trajectories of exchange between cultural and economic capitals and its implications for literacy education

Versioning RLOs as ‘study skills toolkits’ for different user groups and developing community tools to support sharing and customisation

As patterns of need in twenty-first century higher education change so must the solutions. E-learning solutions, in particular, need to be adaptive to fit a range of teaching and learning situations. eLanguages, a research and development unit at the University of Southampton, develops online toolkits of reusable learning objects (RLOs) in Study Skills that can be versioned for different student user groups. Underpinning them is an approach which seeks to deliver high quality content and be cost-effective. Reusability and versatility are central to this. With the creation of a large base of RLOs has come recognition of the need to manage and customise these resources easily and a suite of tools enabling such actions has been developed. This paper will present the toolkits and the pedagogic design of the RLOs. The web-based tools to support management and customisation of RLOs, and potentially facilitate new toolkit creation, will also be introduced