Symbolizing as a Constructive Activity in a Computer Microworld

1996 ◽  
Vol 14 (2) ◽  
pp. 113-138 ◽  
Author(s):  
Leslie P. Steffe ◽  
John Olive
Keyword(s):  
Mathematical Activity ◽  
Constructivist Teaching ◽  
Guiding Principle ◽  
Computer Microworld ◽  
Mathematical Symbols ◽  
Teaching Episode ◽  
Numeral Systems ◽  
Mental Operations

In the design of computer microworlds as media for children's mathematical action, our basic and guiding principle was to create possible actions children could use to enact their mental operations. These possible actions open pathways for children's mathematical activity that coemerge in the activity. We illustrate this coemergence through a constructivist teaching episode with two children working with the computer microworld TIMA: Bars. During this episode, in which the children took turns to partition a bar into fourths and thirds recursively, the symbolic nature of their partitioning operations became apparent. The children developed their own drawings and numeral systems to further symbolize their symbolic mental operations. The symbolic nature of the children's partitioning operations was crucial in their establishment of more conventional mathematical symbols.

Design and Use of Computer Tools for Interactive Mathematical Activity (TIMA)

2002 ◽  
Vol 27 (1) ◽  
pp. 55-76 ◽  
Author(s):  
Leslie P. Steffe ◽  
John Olive
Keyword(s):  
Teaching Experiment ◽  
Mathematical Activity ◽  
Constructivist Teaching ◽  
Learning Tools ◽  
Computer Tools ◽  
Guiding Principle ◽  
Teacher Researcher ◽  
Drill And Practice ◽  
Mathematical Operations

Our guiding principle when designing the TIMA was to create computer tools that we could use to achieve our goals when teaching children. The design of the TIMA took place in the context of a constructivist teaching experiment with 12 children that extended over a three-year period. Three different TIMA were designed and used in the teaching experiment: Toys, Sticks, and Bars. These tools were designed to provide children contexts in which they could enact their mathematical operations of unitizing, uniting, fragmenting, segmenting, partitioning, disembeding, iterating and measuring. As such, they are very different from the drill and practice or tutorial software that are prevalent in many elementary schools. We provide examples of how the TIMA were used by children to engage in cognitive play and, through interactions with a teacher/researcher and other children, transform that play into independent mathematical activity with a playful orientation. The role of the teacher in provoking perturbations that could lead eventually to accommodations in the children's mathematical schemes was critical in the use of the TIMA as learning tools.

Creating Microworlds for Exploring Mathematical Understandings in the Early Years of School

2002 ◽  
Vol 27 (1) ◽  
pp. 77-92 ◽  
Author(s):  
Nicola Yelland
Keyword(s):  
Mathematics Curriculum ◽  
Early Years ◽  
Mathematical Activity ◽  
Learning Context ◽  
Computer Supported Collaborative Learning ◽  
Construction Of Knowledge ◽  
Computer Microworld ◽  
High Level ◽  
Active Exploration ◽  
Computer Tasks

This article will describe the strategies and interactions of pairs of Year 2 children (average age 7 years 4 months) while they worked on novel tasks in a computer microworld embedded in a mathematics curriculum. The curriculum encouraged the active exploration of ideas in both on and off computer tasks, which complemented each other. Observations of the children supported the notion that the active construction of knowledge in a computer supported collaborative learning context, enabled the children to engage with powerful ideas and use metastrategic strategies. Further their spontaneous comments and persistence with tasks indicated a high level of interest and enthusiasm for these tasks in preference to those that traditionally characterize mathematical activity.

Do Event-Related Brain Potentials Reflect Mental (Cognitive) Operations?

2002 ◽  
Vol 16 (3) ◽  
pp. 129-149 ◽  
Author(s):  
Boris Kotchoubey
Keyword(s):  
Cognitive Processes ◽  
Point Of View ◽  
Internal Variables ◽  
Brain Potentials ◽  
Cognitive Operations ◽  
External Variables ◽  
Series Of Experiments ◽  
Mental Operations ◽  
A Chain ◽  
Processing Mechanisms

Abstract Most cognitive psychophysiological studies assume (1) that there is a chain of (partially overlapping) cognitive processes (processing stages, mechanisms, operators) leading from stimulus to response, and (2) that components of event-related brain potentials (ERPs) may be regarded as manifestations of these processing stages. What is usually discussed is which particular processing mechanisms are related to some particular component, but not whether such a relationship exists at all. Alternatively, from the point of view of noncognitive (e. g., “naturalistic”) theories of perception ERP components might be conceived of as correlates of extraction of the information from the experimental environment. In a series of experiments, the author attempted to separate these two accounts, i. e., internal variables like mental operations or cognitive parameters versus external variables like information content of stimulation. Whenever this separation could be performed, the latter factor proved to significantly affect ERP amplitudes, whereas the former did not. These data indicate that ERPs cannot be unequivocally linked to processing mechanisms postulated by cognitive models of perception. Therefore, they cannot be regarded as support for these models.

Modelling neural locations of elementary mental operations

1997 ◽  
Author(s):  
Lawrence M. Parsons ◽  
Peter T. Fox ◽  
Jack L. Lancaster ◽  
Jinhu Xiong
Keyword(s):  
Mental Operations

Enlightening Symbols

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
Sixteenth Century ◽  
Number System ◽  
Psychological Effects ◽  
Mathematical Notation ◽  
Rhetorical Style ◽  
The Past ◽  
Mathematical Symbols ◽  
Before And After ◽  
New Ideas ◽  
Different Cultures

While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the fascinating history behind the development of our mathematical notation system. It shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, the book looks at how historians have disagreed over the origins of the number system for the past two centuries. It follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. It also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

Preface to the special issue, CMAM 2011, no. 3.

2011 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Ivan Gavrilyuk ◽  
Boris Khoromskij ◽  
Eugene Tyrtyshnikov
Keyword(s):  
Separation Of Variables ◽  
Numerical Algorithms ◽  
Multilevel Methods ◽  
High Dimensional ◽  
Special Issue ◽  
High Dimensions ◽  
Guiding Principle ◽  
Tensor Methods ◽  
Closed World ◽  
The One

Abstract In the recent years, multidimensional numerical simulations with tensor-structured data formats have been recognized as the basic concept for breaking the "curse of dimensionality". Modern applications of tensor methods include the challenging high-dimensional problems of material sciences, bio-science, stochastic modeling, signal processing, machine learning, and data mining, financial mathematics, etc. The guiding principle of the tensor methods is an approximation of multivariate functions and operators with some separation of variables to keep the computational process in a low parametric tensor-structured manifold. Tensors structures had been wildly used as models of data and discussed in the contexts of differential geometry, mechanics, algebraic geometry, data analysis etc. before tensor methods recently have penetrated into numerical computations. On the one hand, the existing tensor representation formats remained to be of a limited use in many high-dimensional problems because of lack of sufficiently reliable and fast software. On the other hand, for moderate dimensional problems (e.g. in "ab-initio" quantum chemistry) as well as for selected model problems of very high dimensions, the application of traditional canonical and Tucker formats in combination with the ideas of multilevel methods has led to the new efficient algorithms. The recent progress in tensor numerical methods is achieved with new representation formats now known as "tensor-train representations" and "hierarchical Tucker representations". Note that the formats themselves could have been picked up earlier in the literature on the modeling of quantum systems. Until 2009 they lived in a closed world of those quantum theory publications and never trespassed the territory of numerical analysis. The tremendous progress during the very recent years shows the new tensor tools in various applications and in the development of these tools and study of their approximation and algebraic properties. This special issue treats tensors as a base for efficient numerical algorithms in various modern applications and with special emphases on the new representation formats.

PEDAGOGICAL CONDITIONS OF THE COMMON CULTURAL POTENTIAL OF THE COURSE UNIT CONTEMPORARY CONCEPTS OF NATURAL SCIENCE// Academy Journal No.4(16), 2019/ Chief Editor Susan Belih /OEAPS Inc.(Open European Academy of Public Sciences). Tallinn, Estonia. 09.04.2019: OEAPS Inc., 2019. - pp. 15-18

2019 ◽  
Author(s):  
Raisa Nikolaevna Afonina
Keyword(s):  
Clinical Psychology ◽  
Natural Science ◽  
Professional Training ◽  
Chief Editor ◽  
Educational Process ◽  
Professional Competencies ◽  
European Academy ◽  
The Common ◽  
Science Academy ◽  
Mental Operations

The content of the course unit Contemporary Concepts of Natural Science is of great importance in the common cultural and common professional training of a Clinical Psychology specialist. Conceptual bases of the educational process realization of the course unite Contemporary Concepts of Natural Science reflect modern scientific beliefs about its essence, content and specificity. The theory of gradual formation of mental operations and notions is to the most extent appropriate for the formation of common cultural and common professional competencies.

Restoring Damaged Relationships Through the Art of Invitation: Application with Addicted Incarcerated Women

2019 ◽  
Vol 46 (3) ◽  
Author(s):  
Katti J. Sneed ◽  
Debbie Teike
Keyword(s):  
Human Services ◽  
Addiction Treatment ◽  
The United States ◽  
Incarcerated Women ◽  
Relationship Building ◽  
Health And Human Services ◽  
Guiding Principle ◽  
Faith Based ◽  
Department Of Health ◽  
Complementary Approach

This article presents a description of Art of Invitation as a complementary approach to traditional addiction treatment through the alignment of Art of Invitation (AOI) with Substance Abuse and Mental Health Services Administration (SAMHSA) Ten Guiding Principles for Recovery.  AOI is a faith based relationship building approach that combines key Judeo/Christian teachings with relationship building tools, skills, and concepts for those seeking to build and restore relationships.  SAMHSA, as the leading agency within the U.S. Department of Health and Human Services, spearheads public health efforts to advance behavioral health within the United States.  Each Guiding Principle is presented along with a description of how AOI is shared with incarcerated women, an often neglected population, participating in an inpatient treatment program housed in a community corrections facility.

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