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Supporting group cognition in an online math community: A cognitive tool for smallgroup referencing in text chat
 Journal of Educational Computing Research (JECR) special
"... cognitive tool for smallgroup referencing in text chat ..."
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cognitive tool for smallgroup referencing in text chat
How are words stored in memory?: Beyond phones and phonemes
, 2007
"... A series of arguments is presented showing that words are not stored in memory in a way that resembles the abstract, phonological code used by alphabetical orthographies or by linguistic analysis. Words are stored in a very concrete, detailed auditory code that includes nonlinguistic information inc ..."
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Cited by 13 (4 self)
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A series of arguments is presented showing that words are not stored in memory in a way that resembles the abstract, phonological code used by alphabetical orthographies or by linguistic analysis. Words are stored in a very concrete, detailed auditory code that includes nonlinguistic information including speaker’s voice properties and other details. Thus, memory for language resembles an exemplar memory and abstract descriptions (using letterlike units and speakerinvariant features) are probably computed on the fly whenever needed. One consequence of this hypothesis is that the study of phonology should be the study of generalizations across the speech of a community and that such a description will employ units (segments, syllable types, prosodic patterns, etc.) that are not necessarily employed as units in speakers’ memory for language. That is, the psychological units of language are not useful for description of linguistic generalizations and linguistic generalizations across a community are not useful for storing the language for speaker use.
Keeping meaning in proportion: The multiplication table as a case of pedagogical bridging tools. Unpublished doctoral dissertation
, 2004
"... ii ..."
Is the Brain a Quantum Computer?
"... We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substant ..."
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We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.
Formal notations are diagrams: Evidence from a production task
"... Although a general sense of the magnitude, quantity, or numerosity of objects is common in both untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but wellspecified situations—to behave formally, that is—are skills unique to people t ..."
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Cited by 9 (3 self)
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Although a general sense of the magnitude, quantity, or numerosity of objects is common in both untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but wellspecified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations typically employ complex, hierarchically embedded structures, which all extant analyses assume are constructed by concatenative, rulebased processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations—in short, that formal notations are a kind of diagram. We examined selfgenerated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we found substantial evidence for spatial representational schemes even in these highly symbolic domains. It is clear that mathematical equations written in modern notation are, in general, visual forms and that they share some properties with diagrammatic or imagistic displays. Equations and mathematical expressions are often set off from the main text, use nonstandard characters and shapes, and deviate substantially from linear symbol placement. Furthermore, evidence indicates that at least some mathematical processing is sensitive to the particular visual form of its presentation notation (Cambell, 1999; McNeil & Alibali, 2004, 2005). Despite these facts, notational mathematical representation is typically considered sentential and is placed in opposition to diagrammatic representations in fields as diverse as education
Mathematics as Reference System of Life: preliminary observations
, 2009
"... We forward hypothesis that all what we refer to as mathematics are cognitive aspects of life, moreover, we have right to refer to mathematics as reference system of life. Mathematics and cognition are not distinguishable between themselves because what we call mathematics refer to the functionality ..."
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Cited by 5 (3 self)
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We forward hypothesis that all what we refer to as mathematics are cognitive aspects of life, moreover, we have right to refer to mathematics as reference system of life. Mathematics and cognition are not distinguishable between themselves because what we call mathematics refer to the functionality by means of what (or via what) we are created by nature, or by God, be it question of our religious persuasion. Thus, according to this hypothesis, mathematics turns out to be considrable more as primary in many points as before, when we attributed to mathematics role of sort of descriptor of nature. When we are going to say that mathematics is reference system of life, we mean that today's mathematics is only some starting state of what might be referred to as mathematics as subject / object of reality.
EMBODIED SPATIAL ARTICULATION: A GESTURE PERSPECTIVE ON STUDENT NEGOTIATION BETWEEN KINESTHETIC SCHEMAS AND EPISTEMIC FORMS IN LEARNING MATHEMATICS
"... Two parallel strands in mathematicseducation research—one that delineates students ’ embodied schemas supporting their mathematical cognition and the other that focuses on the mediation of cultural knowledge through mathematical tools—could converge through examining reciprocities between schemas a ..."
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Cited by 4 (3 self)
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Two parallel strands in mathematicseducation research—one that delineates students ’ embodied schemas supporting their mathematical cognition and the other that focuses on the mediation of cultural knowledge through mathematical tools—could converge through examining reciprocities between schemas and tools. Using a gesturebased methodology that attends to students ’ hand movements as they communicate their understanding, data examples from design research in two domains illustrate students ’ spontaneous spatial articulation of embodied cognition. Such embodied spatial articulation could be essential for deep understanding of content, because in performing these articulations, students may be negotiating between their dynamic imagebased intuitive understanding of a concept and the static formal mathematical formats of representing the concept. Implications for mathematics education are drawn. The growing body of literature on ‘situated cognition ’ and ‘cognition in context ’ (e.g., Lave & Wenger, 1991; Hutchins & Palen, 1998) is informing research in mathematics education. In particular, we are challenged to think of mathematical cognition not as “abstract ” inthehead processes devoid of concrete grounding, but as phenomenologically, intrinsically, and necessarily dwelling in student interactions with objects in their environment (Heidegger, 1962;
Cogito ergo sum
, 2008
"... Pythagorean numbers Let Pythagorean number be triple, with first two elements as projections and third as arrow of where is called projection of distinction and projection of hologram. Pythagorean numbers should be used both as cognitive and mathematical term, but, of course, in different outline. F ..."
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Cited by 4 (4 self)
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Pythagorean numbers Let Pythagorean number be triple, with first two elements as projections and third as arrow of where is called projection of distinction and projection of hologram. Pythagorean numbers should be used both as cognitive and mathematical term, but, of course, in different outline. For Pythagorean number in mathematical outline we may always attribute as its meaning cognitive Pythagorean number, either in trivial sense or as physical interpretation or maybe in some other sense. Taking Pythagorean number in cognitive sense we of course maybe loose possibility to find directly corresponding mathematical pair, but we may assume always its existence as we will soon see. Main element that makes Pythagorean number be Pythagorean number is its arrow: If there exists transform then this transform defines pair as Pythagorean number. Pythagorean number, Arrow of thinking or arrow of cogito. For a Pythagorean number being triple, arrow, if we use Pythagorean number in cognitive sense, we call arrow of thinking or arrow of cogito. We suggest for thinking simple
On Reference System of Life
 Riga, Quantum Distinctions
"... We argue cognition may be considered in new outline, i.e., as functionality of life from within reference system of life. We conjecture that this give us way to consider mathematics as aspect of life from new approach. ..."
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Cited by 4 (2 self)
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We argue cognition may be considered in new outline, i.e., as functionality of life from within reference system of life. We conjecture that this give us way to consider mathematics as aspect of life from new approach.
Stable kernels and fluid body envelopes
 SICE J. Control, Measurement, Syst. Integration
"... Recent advances in robotics leads us to consider, on the one hand, the notion of a kernel, a set of stable algorithms that drive developmental dynamics and, on the other hand, variable body envelopes that change over time. This division reverses the classic notion of a fixed body on which different ..."
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Cited by 3 (2 self)
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Recent advances in robotics leads us to consider, on the one hand, the notion of a kernel, a set of stable algorithms that drive developmental dynamics and, on the other hand, variable body envelopes that change over time. This division reverses the classic notion of a fixed body on which different software can be applied to consider a fixed software that can be applied to different kinds of embodiment. Thus, it becomes possible to study how a particular embodiment shapes developmental trajectories in specific ways. It also leads us to a novel view of the development of skills, from sensorimotor dexterity to abstract thought, based on the notion of a fluid body in continuous redefinition. 1