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267
Constructing scientific knowledge in the classroom
 Educational Researcher
, 1994
"... The online version of this article can be found at: Published on behalf of ..."
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The online version of this article can be found at: Published on behalf of
Digital manipulatives: new toys to think with
 Proc. CHI ’98 Human Factors in Computing Systems
, 1998
"... 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 ..."
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Cited by 76 (6 self)
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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 manipulativescomputationallyaugmented versions of blocks, beads, balls, and badges.
A theoretical analysis of insight into a reasoning task
 Cognitive Psychology
, 1970
"... An informationprocessing analysis of insight into a singularly deceptive and difficult deductive problem is presented. Two models are described. The first represents an economical explanation of the Ss initial responses but is difficult to reconcile with their subsequent responses induced by certai ..."
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Cited by 44 (2 self)
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An informationprocessing analysis of insight into a singularly deceptive and difficult deductive problem is presented. Two models are described. The first represents an economical explanation of the Ss initial responses but is difficult to reconcile with their subsequent responses induced by certain remedial procedures. The second model does take account of such responses and shows how insight into the correct solution is correlated with the awareness that tests for falsification are more appropriate than tests for verification. The relevance of the experimental results and the explanatory model are discussed in relation to wider issues. Previous research on deductive reasoning has usually involved the evaluation of given inferences as valid or invalid, or the making of inferences from given premises. These techniques have been a characteristic feature in studies of syllogistic reasoning, in studies of the effect of personality variables upon the deductive process, and in miscellaneous investigations of logical competence. Such research has increased our knowledge about the interactions between cognitive and affective processes and about the layman’s general logical ability, but it has perhaps been less revealing about the process of reasoning itself. A notable exception is, of course, provided by research on the computer simulation of thinking (e.g., Newell, Simon, & Shaw, 1958; Reitman, 1965.) In the tasks which we shall consider the Ss have neither to make inferences in a direct fashion from premises presented to them, nor to evaluate given conclusions as valid or invalid. They have to choose the conditions which would allow a valid inference to be made. These tasks are structurally simple but deceptively difficult, and the present paper offers a theoretical analysis of the attempts to solve them. THE PROBLEM This is one example of the problem (Wason, 1966). You are presented with four cards showing, respectively, “A, ” “D, ” “4, ” “7, ” and you know
A Framework for Research and Curriculum Development in Undergraduate Mathematics Education
 Research in Collegiate Mathematics Education
, 1996
"... 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 ..."
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Cited by 38 (6 self)
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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...
Technologies for lifelong kindergarten
 Educational Technology Research and Development
, 1998
"... you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact inform ..."
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Cited by 33 (1 self)
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you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Connectionism and the study of change
 Brain Development and Cognition: A Reader
, 1993
"... 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 b ..."
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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 deemphasis 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
How Does the Environment Affect the Person?
"... 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 o ..."
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Cited by 23 (19 self)
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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.
Connectionism and dynamic systems: are they really different?
, 2003
"... 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 ..."
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Cited by 20 (0 self)
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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.
Cognitive growth in elementary and advanced mathematical thinking
 In D. Carraher and L. Miera (Eds.), Proceedings of PME X1X
, 1995
"... This paper addresses the development of mathematical thinking from elementary beginnings in young children to university undergraduate mathematics and on to mathematical research. It hypothesises that mathematical growth starts from perceptions of, and actions on, objects in the environment. Success ..."
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This paper addresses the development of mathematical thinking from elementary beginnings in young children to university undergraduate mathematics and on to mathematical research. It hypothesises that mathematical growth starts from perceptions of, and actions on, objects in the environment. Successful “perceptions of ” objects lead through a Van Hiele development in visuospatial representations with increasing verbal support to visually inspired verbal proof in geometry. Successful “actions on” objects use symbolic representations flexibly as “procepts ” — processes to do and concepts to think about — in arithmetic and algebra. The resulting cognitive structure in elementary mathematical thinking becomes advanced mathematical thinking when the concept images in the cognitive structure are reformulated as concept definitions and used to construct formal concepts that are part of a systematic body of shared mathematical knowledge. The analysis will be used to highlight the changing status of mathematical concepts and mathematical proof, the difficulties occurring in