Mathematical ideas and indigenous languages

The article deals with the investigation of fundamentals and present state of multyparadigmal analyses of language units representing the system of coordinates of communication in the Ukrainian, Russian and English languagess. Coordinates of communication are presented in the work as a deictic start-point of communication “I – here – now”, defined by K. Buhler in his “Language Theory” as well as the related language units of the same semantics and functions in the languages. The specifics of these words and word combinations is in their possibility to express different types of reference changing them in frames of a certain context of communication act. Multy-paradigmality is described in the present article as a basis of complex methodology of modern researches on linguistics, in particular, contrastive linguistics and linguistics of translation. Many works of modern linguists have been done based on semantic or / and structural aspects of linguistic and pragmatic analyses of the system of communication coordinates at all or its particular representations (see works by Yu. Apresyan, N. Arytyunova, K. Buhler, K. Brugman, J. Lions, N. Kirvalidze, Ch. Fillmore, etc.). But there has not been done any complex multy-paradigmal researches of communication coordinate system before. Works of such a kind (see the ones by M. Avdonina, N. Zhabo, S. Terekhova, etc.) mainly characterize allomorphic and isomorphic features of the analyzed language units in Russian, English, French, and Ukrainian. This article represents roots, origin and patterns of multy-paradigmality of the characterized language units which are important for the future development of both contrastive linguistics and translation theory. It describes the procedure of multyparadigmal analyses of language units that is appropriate for the above mentioned fields of science. Lexical centric approach and textual centric one, being involved in the investigation, contain complex methodology of functional and semantic categories study that is appropriate for such language categories as deixis, reference, anaphor, etc. It contains complex, multy-paradigmal analyses of units of different language levels denoting “place or direction in space”, “time” and “person” indication. Multy-paradigmal approach provided in the research includes the following stages: 1) conceptual / logical and semantic analyses; 2) language units analyses (including structural, lexical and grammatical, functional and semantic ways of analyses); 3) psycholinguistic analyses (in particular, free associative experiment and its verifying). The results of the above mentioned procedure are supplied additionally with some extra-lingual facts complementing it. They essentially help to simplify the correct comprehension, understanding and learning of communication coordinates representations in speech for foreigners. The tendency to complex analyses of language units of different types has become regular for modern researches on contrastive linguistics as well as linguistics of translation for the last decades, although multyparadigmal investigations are yet less regular than other ones nowadays. The methodology and procedure of multy-paradigmal analyses can be varied partially in accordance with the material and purpose of the research however the principles of multy-paradigmality of both the above mentioned fields of science are out of changes, they are universal for Indo-European languages. The further investigations of multy-paradigmality in languages and translation appear in functional semantics, cognitive linguistics, language and culture studies, sociolinguistics, psycholinguistics, especially if they are developed based on the contrastive analyses.

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The Parietal Cortex in Sensemaking: The Dissociation of Multiple Types of Spatial Information

Computational Intelligence and Neuroscience ◽

10.1155/2013/152073 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14 ◽

Cited By ~ 3

Author(s):

Yanlong Sun ◽

Hongbin Wang

Keyword(s):

Parietal Cortex ◽

Spatial Information ◽

Mathematical Thinking ◽

Hierarchical Organization ◽

Levels Of Abstraction ◽

Perceptual Analysis ◽

Different Types ◽

Sensemaking Process ◽

Network Simulations ◽

Different Levels

According to the data-frame theory, sensemaking is a macrocognitive process in which people try to make sense of or explain their observations by processing a number of explanatory structures called frames until the observations and frames become congruent. During the sensemaking process, the parietal cortex has been implicated in various cognitive tasks for the functions related to spatial and temporal information processing, mathematical thinking, and spatial attention. In particular, the parietal cortex plays important roles by extracting multiple representations of magnitudes at the early stages of perceptual analysis. By a series of neural network simulations, we demonstrate that the dissociation of different types of spatial information can start early with a rather similar structure (i.e., sensitivity on a common metric), but accurate representations require specific goal-directed top-down controls due to the interference in selective attention. Our results suggest that the roles of the parietal cortex rely on the hierarchical organization of multiple spatial representations and their interactions. The dissociation and interference between different types of spatial information are essentially the result of the competition at different levels of abstraction.

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Verbs of falling and their argument structure in Circassian languages

Acta Linguistica Petropolitana ◽

10.30842/alp2306573716122 ◽

2020 ◽

Vol XVI (1) ◽

pp. 723-756

Author(s):

I. Bagirokova ◽

◽

D. Ryzhova ◽

◽

Keyword(s):

Argument Structure ◽

Cognitive Linguistics ◽

Initial Point ◽

Surface Expression ◽

Special Importance ◽

Vertical Orientation ◽

Caucasian Family ◽

Different Types ◽

Corpus Data ◽

Initial Source

This paper describes the semantics of falling in Adyghe and Kuban Kabardian from a typological perspective. The analysis is based on corpus data, accompanied by the results of elicitation. Although they represent the same Circassian branch of the Northwest Caucasian family, Adyghe and Kabardian still demonstrate some differences in the way their predicates of falling are lexicalized: while in Adyghe we have a distributive system which includes special lexical means for different types of falling (verbal root -fe- for falling from above, wəḳʷerejə- for losing vertical orientation, -zǝfor detachment, and verbs from adjacent semantic domains such as -we- ‘beat’ for destruction), there is only one dominant (-xwe-) and several peripheral predicates in the Kabardian language. What is peculiar about these languages, when compared to the available typological data, is that the parameter of orientation to the initial (Source) vs. final point (Goal) of movement is of special importance in lexicalizing cases of falling. In Circassian languages, simultaneous surface expression of Source and Goal of movement within a clause is prohibited for morphosyntactic reasons, and the lexemes denoting falling are divided into Source- vs. Goal-oriented ones. For some verbal roots, this orientation is an intrinsic semantic property (cf. -zǝ- which is always Source-oriented); in other cases, it is marked with specifi c affi xes (cf. a locative combination je-…-xǝ ‘down’ which marks re-orientation to the Source of falling of the initially Goal-oriented Adyghe verb -fe-). Thus, our analysis of the material may not only help to contribute to the general typology of falling but may throw light on such a phenomenon in cognitive linguistics as the emphasis on the fi nal point of movement in opposition to the initial point, also known as goal bias

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ETHNOMATHEMATICS THOUGHT AND ITS INFLUENCE IN MATHEMATICAL LEARNING

MaPan ◽

10.24252/mapan.2020v8n2a3 ◽

2020 ◽

Vol 8 (2) ◽

pp. 205-223

Author(s):

Andi Saparuddin Nur ◽

◽

Kartono Kartono ◽

Zaenuri Zaenuri ◽

S B Waluya ◽

...

Keyword(s):

History Of Mathematics ◽

Local Culture ◽

Field Of Study ◽

Mathematical Learning ◽

Research Results ◽

Formal Knowledge ◽

Cultural Activities ◽

Learning Mathematics ◽

Formal Mathematics ◽

History Of

Mathematics is a symbol of rationality and the highest intellectual achievements of human civilization. Mathematics has always been seen as abstract and formal knowledge. However, in the last few decades, the idea has emerged that mathematics is a knowledge that develops in human cultural activities. The concept of mathematics in culture is widely known as ethnomathematics. This paper aims to briefly describe the history, criticism, and challenges of ethnomathematics, the thoughts of ethnomathematics experts, and their influence in learning mathematics today. The development of ethnomathematics gave rise to a field of study covering aspects of anthropology and the history of mathematics, non-formal mathematics practice, traditional mathematics, and multicultural learning. Various research results indicate that ethnomathematics contributes to improving school mathematics. Although culture has an important role in learning mathematics, to integrate it requires comprehensive efforts to overcome various obstacles. Teachers need to improve competencies related to understanding local culture to maximize the transformation of ethnomathematics learning in the classroom.

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Mathematics and Theology in the Thought of Nicholas of Cusa

Logica Universalis ◽

10.1007/s11787-019-00232-2 ◽

2019 ◽

Vol 13 (4) ◽

pp. 477-485 ◽

Cited By ~ 2

Author(s):

Roman Murawski

Keyword(s):

Mathematical Knowledge ◽

Mutual Influence ◽

Mathematical Thinking ◽

Physical Reality ◽

Natural Sciences ◽

Mathematical Ideas ◽

Nicholas Of Cusa ◽

Apophatic Theology ◽

The World ◽

Mutual Relations

Abstract Nicholas of Cusa was first of all a theologian but he was interested also in mathematic and natural sciences. In fact philosophico-theological and mathematical ideas were intertwined by him, theological and philosophical ideas influenced his mathematical considerations, in particular when he considered philosophical problems connected with mathematics and vice versa, mathematical ideas and examples were used by him to explain some ideas from theology. In this paper we attempt to indicate this mutual influence. We shall concentrate on the following problems: (1) the role and place of mathematics and mathematical knowledge in knowledge in general and in particular in theological knowledge, (2) ontology of mathematical objects and their origin, in particular their relations to God and their meaning for the description of the world and physical reality, (3) infinity in mathematics versus infinity in theology and their mutual relations and connections. It will be shown that—according to Nicholas—mathematics and mathematical thinking are tools of rationalization of theology and liberating it in a certain sense from the trap of apophatic theology.

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It's a Home Run! Using Mathematical Discourse to Support the Learning of Statistics

Mathematics Teacher ◽

10.5951/mt.101.4.0250 ◽

2007 ◽

Vol 101 (4) ◽

pp. 250-256 ◽

Cited By ~ 2

Author(s):

Kathleen S. Himmelberger ◽

Daniel L. Schwartz

Keyword(s):

Mathematics Classroom ◽

Mathematical Thinking ◽

National Council ◽

Instructional Programs ◽

Group Discussions ◽

Good Communication ◽

Mathematical Ideas ◽

Positive Effects ◽

Procedural Fluency ◽

Learning Mathematics

The Standards developed by the National Council of Teachers of Mathematics (2000) state that instructional programs should enable all students to communicate mathematical ideas. The Standards indicate that good communication includes the ability to express organized and precise ideas as well as the ability to analyze and evaluate the mathematical thinking of others. Learning mathematics goes beyond procedural fluency; it also includes learning to discuss mathematical ideas. For this purpose, small groups have become a frequent configuration in the mathematics classroom. When combined with a suitable exercise, small-group discussions can have positive effects on mathematical understanding.

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Ethnomathematical study on folk dances: focusing on the choreography

Revemop ◽

10.33532/revemop.e202014 ◽

2020 ◽

Vol 2 ◽

pp. e202014

Author(s):

Sara Cristina Magalhães Gomes Ribeiro ◽

Pedro Manuel Baptista Palhares ◽

María Jesús Salinas Salinas

Keyword(s):

Mathematical Structure ◽

Autonomous Community ◽

Numerical Schemes ◽

Mathematical Ideas ◽

School Practice ◽

Northern Portugal ◽

Different Types

The investigation in ethnomathematics we are developing aims to analyse the mathematical structure inherent in various elements that constitute folk dances of Northern Portugal and Galicia, which is an autonomous community of Spain, specifically choreography, music and accessories. Focusing on choreography, we intend to represent and describe the movements that dancers perform during dances. Different types of choreography were identified in folk dances based on dispositions that although dancers may not remain fixed through the dance, are those to which they end up returning. In addition, diagrams and numerical schemes were elaborated to represent the successive positions occupied by dancers or pairs through the folk dances. The mathematical ideas and procedures resulting from this ethnomathematical research will then be used for school practice, through the construction of tasks to be applied in the classroom.Keywords: Ethnomathematics. Folk dances. Choreography.Estudio etnomatemático sobre danzas folclóricas: centrándose en la coreografíaLa investigación en Etnomatemática que estamos desarrollando tiene como objetivo analizar la estructura matemática inherente a los diversos elementos que constituyen las danzas folclóricas del norte de Portugal y Galicia, que es una comunidad autónoma de España, a saber, coreografía, accesorios y música. Centrándonos en la coreografía, pretendemos representar y describir los movimientos que realizan los bailarines durante los bailes. Se han identificado diferentes tipos de coreografía en los bailes folclóricos, en función de las disposiciones que, si bien los bailarines no pueden mantener fijos durante los bailes, ellos son a los que finalmente regresan. Además, se elaboraron diagramas y esquemas numéricos para representar las posiciones sucesivas ocupadas por los bailarines o parejas a través de los bailes folclóricos. Las ideas y procedimientos matemáticos resultantes de esta investigación etnomatemática se utilizarán en la práctica pedagógica mediante la construcción de tareas que se aplicarán en el aula.Palabra clave: Etnomatemática. Danzas folclóricas. Coreografía.Estudo etnomatemático sobre danças folclóricas: focando na coreografiaA investigação em Etnomatemática que estamos a desenvolver visa analisar a estrutura matemática inerente aos vários elementos que constituem danças folclóricas do Norte de Portugal e da Galiza, que é uma comunidade autónoma de Espanha, nomeadamente a coreografia, os acessórios e a música. Focando na coreografia, pretendemos representar e descrever os movimentos que os dançarinos realizam durante as danças. Diferentes tipos de coreografias foram identificados nas danças folclóricas, baseados nas disposições que, embora os dançarinos possam não manter fixas ao longo das danças, são aquelas a que eles acabam por retornar. Além disso, foram elaborados diagramas e esquemas numéricos para representar as sucessivas posições ocupadas pelos dançarinos ou pares através das danças folclóricas. As ideias e procedimentos matemáticos resultantes desta investigação etnomatemática serão, então, utilizadas na prática pedagógica, por meio da construção de tarefas para serem aplicadas na sala de aula.Palavras-chave: Etnomatemática. Danças folclóricas. Coreografia.

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Exploring the impact of lesson study through the views of Lao mathematics teacher educators on the needs, learning and difficulties

International Journal for Lesson and Learning Studies ◽

10.1108/ijlls-06-2018-0040 ◽

2019 ◽

Vol 8 (2) ◽

pp. 98-116

Author(s):

Sommay Shingphachanh

Keyword(s):

Mathematics Teacher ◽

Lesson Study ◽

Teacher Educators ◽

Mathematical Thinking ◽

Structured Interview ◽

Current Situation ◽

Content Type ◽

Mathematical Ideas ◽

Mathematics Teacher Educators ◽

The Impact

Purpose The purpose of this paper is to comprehensively explore the current situation of lesson study (LS) implementation and practice among Mathematics Teacher Educators (MTEs) in Teacher Training Colleges (TTCs) across the country in Laos. Moreover, the study investigates MTEs’ professional learning through LS experience, the difficulties they encountered during practicing LS and their urgent needs to deepen their comprehension in the context of LS. Design/methodology/approach Data were collected through semi-structured interview with 45 MTEs from 7 TTCs in February/March 2018 (seven weeks). The study also collected 14 LS reports, 7 LS posters from the respondents and observed one cycle of LS practice in 2 TTCs. The data were systematically analyzed using inductive category formation through the procedure of transcribing and reading the transcription, thematic coding and categorizing and interpreting the meaning of thematic ideas (Mayring, 2015; Merriam, 2009). Licensed software MAXQDA 10 was used for this qualitative study. Findings The study argued based on LS practice in LS model 1 and model 2. MTEs that followed LS model 1 practiced LS in a superficial aspect and quantitatively relied upon the results from the checklists. They majorly satisfied the immediate measurement of teacher teaching’s behavior and student learning’s behavior. Frequently, time constraints, writing LS reports and collaboration were the great challenges. In contrast, MTEs that followed LS model 2 practiced LS in order to deepen understanding of students’ mathematical thinking. Although LS helped them by adjusting appropriate learning task, they encountered difficulty to innovate it effectively. LS also helped them in offering students’ autonomy to explore mathematical ideas, but they failed to understand the values of utilizing students’ mathematical ideas. Research limitations/implications The findings from this study are beneficial for LS practice in the country and similar LS initiatives to find a measure to enhance the effectiveness of LS in schools and TTCs. The study suggested providing clear details of each step, the essential aspect and the core concept of LS to MTEs for successful transposition of LS to a non-Japanese context. Providing LS advisors who have had great experience in conducting LS not just high teaching or working experience only is highly recommended. This study has a limitation in observing LS practices from all seven TTCs. Originality/value Ministry of Education and Sports (MoES) recognizes the significance of implementing LS in TTCs to enhance the quality of teaching-learning, though the progress of LS in those TTCs has not yet been addressed. Current situation of LS revealed in this study is valuable for similar initiatives, MoES and Japan International Cooperation Agency to make an effort in order to move LS forward.

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Introducing a new tool to navigate, understand and use International Codes of Nomenclature

PeerJ ◽

10.7717/peerj.8127 ◽

2019 ◽

Vol 7 ◽

pp. e8127

Author(s):

Evangelos Vlachos

Keyword(s):

A Priori ◽

Mathematical Structure ◽

Zoological Nomenclature ◽

International Code ◽

Entire System ◽

Different Types ◽

Standard Sets ◽

Linear Text ◽

And Linguistics

Background In order to designate the various concepts of taxa in biology, evolution and paleontology, scientists have developed various rules on how to create unique names for taxa. Different Codes of Nomenclature have been developed for animals, plants, fungi, bacteria etc., with standard sets of Rules that govern the formation, publication and application of the nomina of extant and extinct species. These Codes are the result of decades of discussions, workshops, publications and revisions. The structure and complexity of these Codes have been criticized many times by zoologists. This project aims, using the International Code of Zoological Nomenclature as a case study, to show that the structure of these Codes is better reflected and understood as networks. Methods The majority of the text of the Code has been divided into hundreds of Nodes of different types, connected to each other with different types of Edges to form a network. The various mathematical descriptors of the entire system, as well as for the elements of the network, have been conceptually framed to help describing and understanding the Code as a network. Results The network of the Code comprises 1,379 Nodes, which are connected with 11,276 Edges. The structure of the Code can be accurately described as a network, a mathematical structure that is better suited than any kind of linear text publication to reflect its structure. Discussion Thinking of the Code as a network allows a better, in-depth understanding of the Code itself, as the user can navigate in a more efficient way, as well as to depict and analyze all the implied connections between the various parts of the Code that are not visible immediately. The network of the Code is an open access tool that could also help teaching, using and disseminating the Code. More importantly, this network is a powerful tool that allows identifying a priori the parts of the Code that could be potentially affected by upcoming amendment and revisions. This kind of analysis is not limited to nomenclature, as it could be applied to other fields that use complex textbooks with long editing history, such as Law, Medicine and Linguistics.

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Metafore metatestuali

PARADIGMI ◽

10.3280/para2009-001008 ◽

2009 ◽

pp. 101-117

Author(s):

Maria Josep Cuenca ◽

Josep Ribeira

Keyword(s):

Cognitive Linguistics ◽

Special Cases ◽

Different Types

In this paper, the cognitive importance of metaphor is shown by analysing text deixis, which can be thought of as an operation based on the metaphor text is space. After reviewing the concept of metaphor as found in cognitive linguistics, text deixis is defined and exemplified as a procedure related to both situational deixis and anaphora. The analysis of narrative examples highlights different types of text deixis which can be understood as metaphoric extensions of the above mentioned metaphor basic metaphor. Metaphorically, demonstratives can indicate proximity or distance from a textual, temporal or emotive perspective; in addition, deixis am Phantasma and presentational deixis, which are not related to any linguistic antecedent, are considered as special cases of text deixis. Keywords: Anaphor, Deixis, Demonstratives, Metaphor, Metalinguistic metaphor, Text deixis

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