Levels of Sophistication in Elementary Students’ Understanding of Polygon Concept and Polygons Classes

This paper reports sophistication levels in third grade children’s understanding of polygon concept and polygon classes. We consider how children endow mathematical meaning to parts of figures and reason to identify relationships between polygons. We describe four levels of sophistication in children’s thinking as they consider a figure as an example of a polygon class through spatial structuring (the mental operation of building an organization for a set of figures). These levels are: (i) partial structuring of polygon concept; (ii) global structuring of polygon concept; (iii) partial structuring of polygon classes; and (iv) global structuring of polygon classes. These levels detail how cognitive apprehensions, dimensional deconstruction, and the use of mathematical language intervene in the mental process of spatial structuring in the understanding of the classes of polygons.

Core Texts of the Sŏn Approach

The book is a study and partial translation of Core Texts of the Sŏn Approach (Sŏnmun ch’waryo), a Korean anthology of key texts foundational to Korean Sŏn (Chan/Zen) Buddhism. This anthology provides a convenient entrée to two fundamental themes of Korean Sŏn: Sŏn vis-à-vis the doctrinal teachings (in which Sŏn is shown to be superior); and the huatou (Korean hwadu) method of practice-work popularized by the Song dynasty Chan master Dahui Zonggao (1089–1163). This method consists of “lifting to awareness” or “keeping an eye on” the huatou or phrase, usually the word wu無‎/No (Korean mu). No mental operation whatsoever is to be performed upon the huatou. The practitioner simply lifts the huatou to awareness constantly, twenty-four hours a day. Core Texts of the Sŏn Approach, which was published in Korea during the first decade of the twentieth century, attempts to encapsulate the entire Korean Sŏn tradition in one convenient volume (and thus functions as a sort of vade mecum). It contains eight Chan texts by Chinese authors and seven Sŏn texts by Korean authors, showing the organic relationship between the parent Chinese Chan tradition and its heir Korean Sŏn. Due to the circumstances of modern East Asian history, Korean Sŏn is much less well-known in the West than Japanese Zen. This book will give readers access to a broad sweep of texts of the Korean branch of this school of East Asian Buddhism.

Mindful Pedagogy: Invocating the Concept of Play Beyond the Confines of Recess

Recess is often a topic overlooked in pedagogical theory due to its presumed simplicity. The essence of recess connects with play as a physical counterpart to a well-rounded education. In this article we explore the relationship play has with recess and well-being and explore its pragmatikos (systematic usefulness) as regards schooling in lieu of deep ecological frameworks of systems (wholism) theory and systemic, nonlinear dynamics. We argue that recess in its current conceptualisation—in contradistinction to work or study—is a counterfeit to metaphysical play based on the writings of Ananda K. Coomaraswamy who sheds light on its spiritual premise. By bringing to the forefront metaphysical Ideas of play we encounter similitudes between the Platonic doctrine of ēdūcere and anamnesis with Buddhist phenomenology, especially regarding the practice of Mindfulness (sati); both extol a “recollection” as opposed to a “memorisation” which arguably occupies much of Westernised curriculum. Finally, in traditional, premodern education, emphasis was placed on Spirit and heartfelt intuition, a remembrance of who we are, our Buddha-nature or Christhood, not on cerebral ratiocination whose mental operation, according to Plato, was tenebrous and illusory. Our aspiration is not an education that includes mindfulness, rather, a mindfulness-based education.

Constructions and creativity

The first principle of cognitive linguistics is to look for the origins of linguistic powers in robust mental operations not specific to language. For millennia, language science has assumed that human beings possess mental operations for unifying, combining, and merging patterns to create expressions, and that, conversely, they can analyze expressions they encounter to recognize patterns that were combined to produce them. The third section of this article reviews some of the literature concerned with these powers to combine patterns into expressions and to analyze expressions into patterns that were blended to create them. Any assumption about such a linguistic power takes out a loan on theory that must be cashed out with a non-language-specific explanation if the theory is to count as cognitive. One can stipulate to the existence of some unexplained power that is needed for linguistic performance, but that stipulation is insubstantial until it is grounded in a demonstrated non-language-specific operation. An assumption or stipulation about a linguistic power is cashed out when we locate and model the non-language-specific cognitive operations that make that linguistic power possible. The first section of this article presents the proposition that the non-language-specific mental operation that accounts for these linguistic powers is blending, otherwise known as conceptual integration. The second section provides a topical review of blending in specific communicative form-meaning pairs and their combination. Blending is the foundation of creativity in communication, or, more specifically, in the creation and combining of form-meaning pairs, also called “constructions.”

Semiotics of the Image: Addressing the Different Types of Mental Operation and Their Sematic Interpretation

Our era is dominated by the prevailing presence of images. The spectator often identifies with the characters and aims to interpret the signs evoked by the objects, since every image is governed by codes. If we look at the history of image semiotics, we observe a cognitive and pragmatic approach. According to Kant, the images we receive from the environment are not simply reproductions but often creative productions based on patterns generated by the imagination. According to recent research in semiotics, we observe that the pragmatic approach is extended by a study of stimuli collected by the environment. On the other hand, Köhler’s theory of Gestalt considers perception as a pre-conscious activity, linking visual semiology with the functional interpretation of perception. In addition, Tardy brings into focus strategies of visual communication by highlighting the semiotic status of represented objects. For this reason, it is essential to deepen the versatility of the field of semantic interpretation of a visual support from different types of mental operations. Finally, the semiological approach to the image with different types of mental operation will be able to generate a plural and original semantic interpretation through the creative exploitation of visual elements.

On the likelihood of 'encapsulating all uncertainty'

The assignment of personal probabilities to form a forensic practitioner's likelihood ratio is a mental operation subject to all the frailties of human memory, perception and judgment. While we agree that beliefs expressed as coherent probabilities are neither ‘right’ nor ‘wrong’ we argue that debate over this fact obscures both the requirement for and consideration of the ‘helpfulness’ of practitioner's opinayesions. We also question the extent to which a likelihood ratio based on personal probabilities can realistically be expected to ‘encapsulate all uncertainty’. Courts cannot rigorously assess a forensic practitioner's bare assertions of belief regarding evidential strength. At a minimum, information regarding the uncertainty both within and between the opinions of practitioners is required.

КОНЦЕПТУАЛЬНАЯ ИНТЕГРАЦИЯ КАК БАЗОВЫЙ МЕТОДОЛОГИЧЕСКИЙ КОНСТРУКТ В СИСТЕМЕ ЛИНГВОКОГНИТИВНЫХ ИССЛЕДОВАНИЙ

В статье концептуальная интеграция рассматривается в качестве ключевого методологического конструкта в системе лингвокогнитивных исследований. Концептуальная интеграция определяет ментальный процесс конструирования значения, особенности образного мышления, специфику репрезентации структур знания и вербализации концептуальных смыслов. Теория концептуальной интеграции расширяет масштабы модели концептуальной метафоры, основанной на отображении двух концептуальных доменов, и в результате обеспечивает возможность более полного и детального объяснения семантики сложных по структуре и содержанию метафорических конструкций. Мақолада концептуал интеграция лингвокнитив изланишлар тизимидаги асосий методологик конструкт сифатида ўрганилмоқда. Концептуал интеграция маъно ясалишнинг ментал жараёнини, ижодий фикрлашнинг хусусиятларини, билим структураларнинг репрезентацияси ва концептуал маъноларнинг вербализациясини аниқлайди. Концептуал интеграция назарияси икки доменга асосланган концептуал метафора модели миқиёсини кенгайтиради ва натижада тузилиши ва таркиби бўйича мураккаб метафорик конструкцияларни тўлиқ ва тўғри тушунтуришга янги имкониятлар беради. The article reviews the conceptual integration as a basic methodological construct in cognitive linguistics research. Conceptual integration determines the mental operation of meaning construction, reflects the specificity of figurative thinking and representation of knowledge structures, as well as conceptual senses. Conceptual Integration/Blending Theory expands the scope of two-domain model of conceptual metaphor and provides a more detailed explanation of complex metaphorical constructions (expressions).

Towards a Process Model of Sustained Attention Tests

Taking up new approaches and calls for experimental test validation, in the present study we propose and validate a process model of sustained attention tests. Four sub-components were postulated: the perception of an item, a simple mental operation to solve the item, a motor reaction, and the shift to the next item. In two studies, several cognitive tasks and modified versions of the d2-R test of sustained attention were applied in order to determine performance in the proposed sub-components. Their contribution for the prediction of performance in sustained attention tests and tests of higher cognitive abilities was assessed. The sub-components of the process model explained a large amount of variance in sustained attention tests, namely 55–74%. More specifically, perceptual and mental operation speed were the strongest predictors, while there was a trend towards a small influence of motor speed on test performance. The measures of item shifting showed low reliabilities and did not predict test scores. In terms of discriminant validity, results of Study 1 indicated that the postulated sub-components were insufficient to explain a large amount of variance in working memory span tasks, in Study 2 the same was demonstrated for reasoning tasks. Altogether, the present study is the first to disentangle sub-components in sustained attention tests and to determine their role for test performance.

Thinking peculiarities testing and forecasting training success of future drivers

The ergonomic support problem of reliability for the “driver-motor car-traffic situation” system is considered. Factors defining the success in selection and training drivers at driving schools are revealed. A correlation interconnection between a level of mental operation development and a training success at driving schools is proved empirically.

Boolean algebra

Boolean algebra, or the algebra of logic, was devised by the English mathematician George Boole (1815–64) and embodies the first successful application of algebraic methods to logic. Boole seems to have had several interpretations for his system in mind. In his earlier work he thinks of each of the basic symbols of his ‘algebra’ as standing for the mental operation of selecting just the objects possessing some given attribute or included in some given class; later he conceives of these symbols as standing for the attributes or classes themselves. In each of these interpretations the basic symbols are conceived as being capable of combination under certain operations: ‘multiplication’, corresponding to conjunction of attributes or intersection of classes; ‘addition’, corresponding to (exclusive) disjunction or (disjoint) union; and ‘subtraction’, corresponding to ‘excepting’ or difference. He also recognizes that the algebraic laws he proposes are satisfied if the basic symbols are interpreted as taking just the number values 0 and 1. Boole’s ideas have since undergone extensive development, and the resulting concept of Boolean algebra now plays a central role in mathematical logic, probability theory and computer design.