Iconicity in mathematical notation: Commutativity and symmetry

Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects – those which visually resemble in some way the concepts they represent – offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd’s hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance.

Arabic and Roman Numbers as Part of Chinese Semiotic System

The role of Roman and Arabic numbers in the Chinese semiotic system was analyzed. It was found that the use of Roman numbers in the Chinese language is extremely restricted: they only occur in official documents executed in accordance with the Western traditions and in some educational editions, which is due to the fact that the functions of Roman numerals are commonly carried out by the Chinese characters belonging to the traditional Heavenly Stems and Earthly Branches sets. On the contrary, Arabic numbers are widespread. They originated in India and penetrated into China at the third attempt in the early 20th century. The failures of the first two attempts are explained by such fundamental differences of the Chinese writing system from the Western one as the direction of the text (down from the top and right to left) and the multiplicity of writing. With the Chinese language reforms, Arabic numbers were introduced in Mandarin. Having penetrated into the Chinese semiotic system, Arabic numbers became so widespread that a state standard was produced to regulate their co-existence with the traditional Chinese characters of numbers. Besides, Arabic numbers have acquired another important function in the Mandarin semiotic system over the last twenty years: they replace characters in the sphere of Internet and mobile-phone interaction. However, in contrast to other numbers in Mandarin, Arabic numbers, as mathematical signs, are devoid of the status of lexical units. Therefore, despite their extensive use, the functions of Arabic numbers in Mandarin are strictly limited.

PSYCHOLOGICAL IMPACT OF QUANTIFIERS IN ADVERTISEMENTS

The article is devoted to comparative investigation of advertisements of one cosmetic company written in different languages, in particular, we analysed quantifiers in English and Ukrainian Avon brochures on the grounds of their polycode nature. The analysis of recent publications allowed us to notice that the investigations of both advertisements and the category of quantitativity are based on different theoretical and practical principles. Being guided by already existing classifications of quantifiers in English and Ukrainian by S. O. Shvachko, V. M. Kondratiuk, O. S. Ananieva, we displayed morphological, structural and combinatory possibilities of quantifiers, textual modifications of numeral combinations in English and Ukrainian advertisements. We suggested main models of quantifiers, emphasizing an important role and functions of units which express definite and indefinite quantity. Morphologically quantifiers are represented not only by numerals, but also by nouns, pronouns, adjectives, adverbs, verbs, their situational and idiomatic combinations, and even mathematical signs. The study of structural and combinatory possibilities of quantifiers also showed morphemes-quantifiers, the usage of quantifiers with specifiers, qualifiers and rhematizers, the structures like n-в-1 (n-in-1), where n>1, as well as word-combinations and phrases synonymic to this structure. All described morphological, structural and combinatory possibilities of quantifiers have a rather significant psychological impact in advertisements, emphasizing the advantages of some cosmetic goods and calling for trust to them. Besides, language means are supplemented by visual, graphic and sometimes sensory (olfactory) ones, which strengthen the influence on the consumer.

TAPS HEXAGONAL EN EL DESARROLLO DEL PENSAMIENTO LÓGICO

TAPS HEXAGONAL EN EL DESARROLLO DEL PENSAMIENTO LÓGICO TAPS HEXAGONAL IN THE LOGICAL THOUGHT'S DEVELOPMENT Ivan Rojas DOI: https://doi.org/10.33017/RevECIPeru2008.0008/ RESUMEN El juego consiste en armar los taps hexagonal con números y usar los signos matemáticos de las operaciones básicas, intermedias y avanzadas según el nivel de que se encuentre. El alumno debe tratar de formar 5 a más ecuaciones en poco tiempo con los taps hexagonales. En el presente proyecto hemos elegido los hexagonales que se adaptan mejor a nuestros intereses y abarcar los ámbitos de las matemáticas ya que hay trabajos que no se dedican a los niveles de transferencia y las dimensiones sociales. Palabra Clave: Juegos Matemáticos, Matemática Recreativa. ABSTRACT The game consists of arming the taps hex numbers and using mathematical signs of the core operations, intermediate and advanced levels as it is. The student must try to form 5 to more equations in a short time with taps hexagonal. In this project we chose the hexagonal that are better suited to our interests and cover the fields of mathematics as there are jobs that are not dedicated to the levels of transfer and the social dimensions. Keyword: Mathematical Games, Mathematical Recreativa.

Aspectos matemáticos (y conceptuales) de la economía de Piero Sraffa. Desarrollos.

Aspectos matemáticos (y conceptuales) de la economía de Piero Sraffa. Desarrollos. Matematical and conceptual aspectsof the economy of Piero Sraffa. Abstract: Although the author of this work has published many works on the Piero Sraffa ́work, this long article is dedicated specifically to the mathematics contained in his capital book, throughout his book, chapter by chapter. Such an effort can be justified because there is nothing similar in Spanish language and because, as we will see, it may be allow us to clarify, to rectify and to develop, although limitedly, the mathematical content. The purpose is that it serves for the reading of Production of commodities by means of commodities, for to be able to enjoy its analytical economic content and also not to get lost with, sometimes, the disguised mathematical ramblings, sometimes also, of economic reasonings of the great turinés. Although the opposite is normal, the economist Italian's effort to build an economics book where mathematics seems to remain hidden is extraordinary. Of course, the particular use of Sraffa is updated to the current mathematical signs. In the present text, we have tried to be as original as possible so as not to repeat the inevitable partial aspects of previous works. In particular, this has been the case about the fixed capital and partially with the issues of reducing capital to dated work and joint production. On the rest has been tried to find some original elements. Hovewer the previuos comments, some of the conceptual contents have inevitable been included. The reason for this is that without understanding, critizing or devoloping them, the formal aspects can not be understood. Keywords:Sraffa, economy, analysis

Brief Report: What You See Is What You Get? Sign Language in the Mathematics Classroom

This Brief Report addresses the fundamental role that sign language plays in the mathematics classroom of deaf and hard-of-hearing (DHH) students. Selected findings are gathered from an ongoing study of signs and gestures used by DHH students and their teachers when encountering and communicating mathematical ideas at a German special-needs school that focuses on hearing and communication. The focus rests primarily on iconic aspects of mathematical ideas as reflected in the gestural–somatic modality of sign language. A categorization of iconicity in mathematical signs as used by the students is presented and used to reconstruct a case of meaning making in a Grade 5 geometry classroom. Insights gained from these observations lead beyond the DHH mathematics classroom by providing new perspectives on the interplay between language and communication, individual experience, and shared conceptualization.

The role of gestural polysigns and gestural sequences in teaching mathematical concepts

In this paper, we examine the conceptual pedagogical value of representational gestures in the context of teaching halving to first graders. We use the concept of the ‘polysign’ as an analytical tool and introduce the notion of a ‘mathematics gesture sequence’ to assess the conceptual role gestures play in explicating mathematical concepts. In our study of four teachers each teaching a lesson on halving, they produced representational polysign gestures that provided multiple layers of information, and chained these gestures in mathematical gestural sequences to spatially represent the operation of halving. Their use of gestures and their ability to use gestures accurately to convey mathematical concepts varied. During the lesson, learners, whose teachers used few representational gestures or used gestures that were conceptually incongruent with the mathematical concept, expressed more confusion than learners whose teachers used conceptually appropriate gestures. While confusion can be a productive part of the learning process, our analysis shows that producing conceptually appropriate gestures may be important in mediating concepts and the transition from concrete and personal symbolic processes to institutional mathematical signs.