Symbol as Metonymy and Metaphor: A Sociological Perspective on Mathematical Symbolism

As a social practice, mathematics remains shrouded in mystery and seems inaccessible for outsiders. It comes across as a closed formal system that is largely considered independent of the people who practise it and hence totally impervious to sociological investigation. This article seeks to question these assumptions and is offered as a contribution to an emerging sociology of mathematics and abstraction. The argument unfolds on an ethnographic register and follows the reactions to a particular mathematical symbol in two different contexts. The first stretch of the description tracks the responses to this symbol on an online forum devoted to discussing mathematics and the other draws from a classroom context the author was part of as a participant observer. Thus focussing on just one aspect of mathematical practice, the way in which symbols are handled by practitioners, it attempts to underline the character of mathematics as a distinctive form of sociality. In the process it raises and seeks to address the following questions. What do controversies over and reactions to mathematical symbols tell us about mathematics as a practice? What roles do symbols play in the mathematical discourse? And, can a broader sociological perspective on mathematical symbolism be developed?

THE REPRESENTATION OF EXPERIENCE IN UNDERGRADUATE BUSINESS STUDENTS’ TEXTS: A FUNCTIONAL ANALYSIS OF MULTIMODAL MEANING MAKING RESOURCES IN MARKETING TEXTS

From the Systemic Functional Linguistics (SFL) standpoint, experiential meanings reflect our experience, perceptions, and consciousness. Research on experiential meaningmaking in tertiary contexts has traditionally focused on areas such as mathematics, journalism and media, science and computing, nursing, and history. This paper aims to investigate the experiential multimodal meanings in an undergraduate marketing course. The data comprised three written assignments and the tutor’s two model texts. The study employed a multidimensional approach by Alyousef (2013), which is framed by SFL (Halliday 2014) and O’Halloran’s (2005, 1998, 2008, 1999) multisemiotic framework for the analysis of semiotic codes in mathematics. The results showed that the experiential meanings in the students’ marketing plan texts were primarily construed through material processes and both explicit and implicit relational identifying processes. The findings indicated how mathematical symbolism is encoded in the multisemiotic texts, in the most economical manner, by using grammatical strategies of structural condensation. The results also noted the extent to which the different modes of meaning were integrated in the texts.

A multimodal approach to visual thinking: the scientific sketchnote

There is a growing interest in the use of visual thinking techniques for promoting conceptual thinking in problem solving tasks as well as for reducing the complexity of ideas expressed in scientific and technical formats. The products of visual thinking, such as sketchnotes, graphics and diagrams, consist of ‘multimodal complexes’ that combine language, images, mathematical symbolism and various other semiotic resources. This article adopts a social semiotic perspective, more specifically a Systemic Functional Multimodal Discourse Analysis approach, to study the underlying semiotic mechanisms through which visual thinking makes complex scientific content accessible. To illustrate the approach, the authors analyse the roles of language, images, and mathematical graphs and symbolism in four sketchnotes based on scientific literature in physics. The analysis reveals that through the process of resemiotization, where meanings are transformed from one semiotic system to another, the abstractness of specialized discourses such as physics and mathematics is reduced by multimodal strategies which include reformulating the content in terms of entities which participate in observable (i.e. tangible) processes and enhancing the reader/viewer’s engagement with the text. Moreover, the compositional arrangement creates clear stages in the development of the ideas and arguments that are presented. In this regard, visual thinking is a form of cultural communication through which abstract ideas are translated and explained using a multimodal outline or summary of essential parts by adapting resources (e.g. linguistic resources and mathematical graphs), using new resources (e.g. stick figures and other simple schematic drawings) and maintaining others from the original text (e.g. mathematical symbolic notation), resulting in a congruent (or concrete) depiction of abstract concepts and ideas for a non-specialist audience.

A MULTIMODAL ANALYSIS OF MATHEMATICAL DISCOURSE IN ENGLISH FOR YOUNG LEARNERS

Of multiple discourses where the Vietnamese young learners are increasingly engaged to develop their English profciency, English mathematical discourse (MD) has proved to be more and more popular. This paper explores the materials in this realm from multisemiotic perspective. In particular, it deals with two questions: (1) to what extent each of the three semiotic resources - language, visual images and mathematical symbolism - is represented in the materials of learning mathematics in English (ME) developed for young learners (YL) and (2) how many words the YLs need to know to comprehend the language component of these materials. Data for illustrations and discussions are withdrawn from the printed resources currently accessible in the Vietnamese context. The results offer insights into the functions of other resources in constructing meanings apart from the well-established role of language as well as the vocabulary load of these materials. The paper concludes with a discussion of pedagogical signifcance of this study for material designers, teachers and learners and implications for further research.

What is Mathematics, Really? Who Wants to Know?

Famous physicists, like Einstein and Wigner have been wondering, why mathematical symbolism could play such an effective and decisive role in the development of physics. Since the days of Plato, there have been essentially two different answers to this question. To Plato mathematics was a science of the unity and order of this universe. Since Galilei people came to believe that mathematics does not describe the objective world, it is not a reflection of some metaphysical realism. It is rather a reflection of human activity in this world. Kant, by his “Copernican Revolution of Epistemology” seems to have been the first to realize this. For example, number, or more generally arithmetic, was to the Pythagoreans “a cosmology” (KLEIN, 1985, p. 45), to Dedekind it is a means to better distinguish between things. The paper sketches the transition from an ontological to a semiotic interpretation of mathematics.