In many educational settings, manipulative materials (such as Cuisenaire Rods and Pattern Blocks) play an important role in children’s learning, enabling children to explore mathematical and scientific concepts (such as number and shape) through direct manipulation of physical objects. Our group at de MJT Media Lab has developed a new generation of “digital manipulatives”-computationallyenhanced versions of traditional children’s toys. These new manipulatives enable children to explore a new set of concepts (im particular, “systems concepts ” such as feedback and emergence) that have previously been considered “too advanced ” for children to learn. In this paper, we discuss four of our digital manipulatives-computationallyaugmented versions of blocks, beads, balls, and badges.

Developmental psychology and developmental neuropsychology have traditionally focused on the study of children. But these two fields are also supposed to be about the study of change, i.e. changes in behavior, changes in the neural structures that underlie behavior, and changes in the relationship between mind and brain across the course of development. Ironically, there has been relatively little interest in the mechanisms responsible for change in the last 15–20 years of developmental research. The reasons for this de-emphasis on change have a great deal to do with a metaphor for mind and brain that has influenced most of experimental psychology, cognitive science and neuropsychology for the last few decades, i.e. the metaphor of the serial digital computer. We will refer to this particu-

Standard conceptions of how the environment influences the person are constrained by the dominant view of representation - and, therefore, perception, cognition, and language - as fundamentally consisting of encodings. I argue that this encoding view is logically incoherent. An alternative view of representation is presented, interactivism, and shown to avoid the incoherencies of encodingism. The interactivist model of representation provides accounts for standard presumed encoding phenomena, and highlights processes and forms of influence of the environment on the person that are obscure or entirely absent from the encoding account. The multiplicity and complexity of the processes of environmental influence acquire a theoretically coherent organization and development from within the interactive perspective.

Over the past several years, a community of researchers has been using and refining a particular framework for research and curriculum development in undergraduate mathematics education. The purpose of this paper is to share the results of this work with the mathematics education community at large by describing the current version of the framework and giving some examples of its application. Our framework utilizes qualitative methods for research and is based on a very specific theoretical perspective that is being developed through attempts to understand the ideas of Piaget concerning reflective abstraction and reconstruct them in the context of college level mathematics. Our approach has three components. It begins with an initial theoretical analysis of what it means to understand a concept and how that understanding can be constructed by the learner. This leads to the design of an instructional treatment that focuses directly on trying to get students to make the constructions cal...

Computer programming environments for learning should make it easy to create worlds of responsive and autonomous objects, such as video games or simulations of animal behavior. But building such worlds remains difficult, partly because the models and metaphors underlying traditional programming languages are not particularly suited to the task. This dissertation investigates new metaphors, environments, and languages that make possible new ways to create programs -- and, more broadly, new ways to think about programs. In particular, it introduces the idea of programming with "agents" as a means to help people create worlds involving responsive, interacting objects. In this context, an agent is a simple mechanism intended to be understood through anthropomorphic metaphors and endowed with certain lifelike properties such as autonomy, purposefulness, and emotional state. Complex behavior is achieved by combining simple agents into more complex structures. While the agent metaphor enables...

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The Beatbugs are hand-held percussive instruments that allow the creation, manipulation, and sharing of rhythmic motifs through a simple interface. When multiple Beatbugs are connected in a network, players can form large-scale collaborative compositions by interdependently sharing and developing each other’s motifs. Each Beatbug player can enter a motif that is then sent through a stochastic computerized "Nerve Center ” to other players in the network. Receiving players can decide whether to develop the motif further (by continuously manipulating pitch, timbre, and rhythmic elements using two bend sensor antennae) or to keep it in their personal instrument (by entering and sending their own new motifs to the group.) The tension between the system’s stochastic routing scheme and the players ’ improvised real-time decisions leads to an interdependent, dynamic, and constantly evolving musical experience. A musical composition entitled “Nerve ” was written for the system by author Gil Weinberg. It was premiered on February 2002 as part of Tod Machover’s Toy Symphony [1] in a concert with the Deutsches Symphonie Orchester Berlin, conducted by Kent Nagano. The paper concludes with a short evaluative discussion of the concert and the weeklong workshops that led to it.

We propose that connectionism and dynamic systems theory are strong contenders for a general theory of development that holds true whatever the content domain. We illustrate, through our own career narratives, the origins of these theories in motor and language development. We situate connectionism and dynamic systems among other classic and contemporary theories and conclude that, although there are meaningful differences, these differences pale in relation to the shared assumptions about the fundamental processes and mechanisms of change.

It is argued that theoretical approaches to the nature of the influence of early experience on personality development have been vitiated by incorrect metaphysical assumptions, of a sort historically characteristic of immature sciences. In particular, mind and mental phenomena are construed in terms of various sorts of substances and structures, instead of in terms of process ontologies. We show that these underlying metaphysical assumptions have prevented the most central problems of the influence of early experience from being addressed, and, therefore, from being answered as well. These aporia seriously infect such contemporary approaches as object relations theory, attachment theory, and cognitive behavioral theory. We outline an alternative process ontology of mind and intentionality — specifically, a process-functional ontology for representation — and explore the form of early influence offered within this new perspective. The Influence of Early Experience

Music today is more ubiquitous, accessible, and democratized than ever. Thanks to technologies such as high-end home studios, audio compression, and digital distribution, music now surrounds us in everyday life, almost every piece of music is a few minutes of download away, and almost any western musician, novice or expert, can compose, perform and distribute their music directly to their listeners from their home studios. But at the same time these technologies lead to some concerning social effects on the culture of consuming and creating music. Although music is available for more people, in more locations, and for longer periods of time, most listeners experience it in an incidental, unengaged, or utilitarian manner. On the creation side, home studios promote private and isolated practice of music making where hardly any musical instruments or even musicians are needed, and where the value of live