Modern computer systems routinely present information to the user as a combination of text and diagrammatic images, described as "graphical user interfaces". Practitioners and researchers in Human-Computer Interaction (HCI) generally believe that the value of these diagrammatic representations is derived from metaphorical reasoning; they communicate abstract information by depicting a physical situation from which the abstractions can be inferred. This assumption has been prevalent in HCI research for over 20 years, but has seldom been tested experimentally. This thesis analyses the reasons why diagrams are believed to assist with abstract reasoning. It then presents the results of a series of experiments testing the contribution of metaphor to comprehension, problem solving, explanation and memory tasks carried out using a range of different diagrams. The results indicate that explicit metaphors provide surprisingly little benefit for cognitive tasks using diagrams as an external re...

ABSTRACT. This paper suggests that from a cognitive-evolutionary perspective, computational media are qualitatively different from many of the technologies that have promised educational change in the past and failed to deliver. Recent theories of human cognitive evolution suggest that human cognition has evolved through four distinct stages: episodic, mimetic, mythic, and theoretical. This progression was driven by three cognitive advances: the ability to “represent ” events, the development of symbolic reference, and the creation of external symbolic representations. In this paper, we suggest that we are developing a new cognitive culture: a “virtual ” culture dependent on the externalization of symbolic processing. We suggest here that the ability to externalize the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need those specialized skills.

Abstract. In this paper, we argue that this distinction between CSCL and HCI is based on a particular understanding of the relationship between humans and computers—and more generally between humans and their tools in activity systems. We draw on work by Shaffer and Kaput (1999), Clark (2003), and Latour (1996a; 1996b; 1996c) to conduct a thought experiment, extending the analytical reach of activity theory (Nardi, 1996b), mediated action (Wertsch, 1998) and distributed cognition (Pea, 1993) by adopting a stronger form of the concepts of distribution and mediation in the context of cognitive activity. For rhetorical purposes, we posit this stronger form of the distribution of intelligence across persons and objects as a theory of distributed mind. Our purpose in describing a theory of distributed mind as an extension of (but not replacement for) extant sociocultural theories on this 10 th anniversary of the International Conference on Computer Supported Collaborative Learning is to problematize for the field its current focus on human collaboration as supported by computers. We are concerned that a field focusing on the interactions of humans will overlook the ways in which meaningful cognitive (and therefore pedagogical) activity is distributed among human and non-human agents within activity systems. We argue that all computer-supported learning is fundamentally collaborative—whether or not the computer is supporting the interaction of persons in the learning process. The consequences of such a move are a call for a tighter integration of the fields of CSCL and HCI, and a more powerful framework to help guide pedagogical choices in an age marked by rapid expansion of powerful cognitive technologies.

Abstract. Recent work by the evolutionary psychologist Merlin Donald (1991) argues that human cognition has developed across evolutionary time through a series of four distinct stages, each growing out of its predecessor and yielding its own cultural form. They began with episodic (ape-like) memory and passed through mimetic (physical-action-based), mythic (spoken), and theoretical (written) transformations. In the chapter it is argued that we are entering, via computational media, a fifth stage of cognitive development leading to a virtual culture, which will replace the writing-based theoretic culture and which will support and be supported by a new hybrid mind, just as each of the predecessor stages subsumed its prior stage (Shaffer & Kaput, in press). Additional support for this claim is provided by the recent work of Terrence Deacon (1997), who argues that the development of human linguistic competence needs to be viewed in a new way, through the co-evolution of brain and language, and where the major defining features of real human language are its embodiment of a relatively small number of recombinable (syntactical) elements and symbolic reference, features not shared by communication devices used by other species. It is suggested that the evolutionary perspective needs to complement mathematics educators ’ other ways of understanding the learning and use of mathematics, especially the semiotic side of the subject. It turns out that mathematics has played a critical role in the development of both writing and computational media, each the means by which a new stage of cognition was reached. Further, our understanding of language, especially its referential nature and its relationship to brain function, has implications for how we understand the symbolic aspects of mathematics and how they may be learned. In the first part of the chapter the Merlin Donald analyses is recounted. Afterwards the coevolution of writing and the earliest mathematics is examined, and this is followed by a description of the new stage into which we are emerging. 1.