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.

Technology-rich learning environments can serve the pressing need for core curriculum reform in science and mathematics by enabling more diverse students to learn more complex concepts at a younger age. Unfortunately, today’s technology research and development efforts result not in an richly integrated environment, but rather with a fragmentary collection of incompatible software application islands. In this article we ask: how can the best innovations in technology-rich learning integrate and scale up to the level of major curricular reforms? A potential solution is component software architecture, which provides open standards that enable plug and play composition of software tools produced by many different projects and vendors. We describe an exploratory effort in which four research groups produced software components for the mathematics of motion. The resulting prototypes support (a) integration of the separately produced tools into the same windows, files, and interfaces, (b) dynamic linking across multiple representations and (c) drag and drop composition of activities without requiring programming. We also summarize an extended Internet discussion which raised critical issues regarding the future of component software architecture in education, and look ahead to the prospect of scalable integration of components beyond the desktop computer.

This paper discusses the design and development of Smart Tools Builder, an instructional learning environment (ILE) for teaching students about distance, time, and speed calculations. This system is part of a larger project, the Adventures of Jasper Woodbury problem solving series, a video disc based program that focuses on anchored instruction and generative learning, to help students learn to think and reason mathematically about complex and realistic problems. The goals of the Smart Tool Builder are two fold: (i) use a constructivist approach ina multi-representational framework to help students develop a deeper understanding of variables and functional relations, speci cally the relation between distance, rate, and time, and (ii) use this knowledge to build personalized smart tools to help them solve complex problems e ectively and e ciently.

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.

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