On the Nature of Students\u27 Digital Mathematical Performances

In this study I investigate the nature of digital mathematical performances (DMPs) produced by elementary school students (Grades 4-6). A DMP is a multimodal text/narrative (e.g., a video) in which one uses the performance arts to communicate mathematical ideas. I analyze twenty-two DMPs available at the Math + Science Performance Festival in 2008. Assuming a sociocultural/postmodern perspective with emphasis on multimodality, my focus is on the role of the arts and technology in shaping students’ mathematical communication and thinking. Methodologically, I employ qualitative case studies, along with video analysis. I conduct a descriptive analysis of each DMP using Boorstin’s (1990) categories of what makes good films, focusing on surprises, sense-making, emotions, and visceral sensations. I also conduct a cross-case analysis using Boorstin’s categories and the mathematical processes and strands of the Ontario Curriculum. The multimodal nature of DMP is one of its most significant pedagogic attributes. Mathematics is traditionally communicated through print-based texts, but the production of DMPs is an alternative that engages students in conceiving multimodal narratives. The playfulness offers scenarios for students’ collaboration, creativity, and imagination. By making DMPs available online, students share their ideas in a public and social environment, beyond the classrooms. Most of the DMPs only explore Geometry and offer opportunities to experience some surprises, sense-making, emotions, and visceral sensations. The lack of focus on other strands (e.g., Algebra) may be seen as a reflection on what (and how) students are (or not) learning in their classes. The production of conceptual DMPs is a rare event, although I acknowledge that I analyzed only DMPs of the first year of the Festival, that is, students did not have examples or references to produce their DMPs. Some DMPs potentially explore conceptual mathematical surprises, but they appear to have gaps in terms of sense-making. The use of the arts and technologies does not guarantee the mathematical conceptuality of DMPs. This study contributes to mathematics education with an exploratory discussion about how mathematical ideas can be (a) communicated and represented as multimodal texts at the elementary school level and (b) seen through a performance arts lens. The study also points out directions about the pedagogic components for conceiving conceptual DMPs in terms of the performance arts and the components of the Ontario Curriculum

Annotated Bibliography on O.K. Bouwsma Collection

Dr. Ronald Hustwit is the author of O.K. Bouwsma: A Philosophers Journey, Something About O.K. Bouwsma, An Annotated Bibliography of Bouwsma’s works, and an Index of The Bouwsma Collection at The Humanities Research Center, The University of Texas. He has edited five works of O.K. Bouwsma’s papers: Toward a New Sensibility, Without Proof or Evidence, Wittgenstein Conversations, Bouwsma’s Notes on Wittgenstein’s Philosophy and Bouwsma’s Commonplace Book.https://openworks.wooster.edu/bouwsma/1000/thumbnail.jp

Quilts as Visual Texts

I argue that quilts should be considered as visual texts, one to which theories of visual rhetoric and rhetoric in general can be applied. In drawing together the worlds of academia and quilting, I will use a variety of theoretical lens to explore quilts as texts. As a text, quilts contain units of meaning much like words. These units of meaning will be explored in Chapter 2 “Quilt Talks: How Quilts Communicate.” In this chapter I will follow the model of Elsley and propose a semiotics of quilts, one that can then be applied to any quilt. This semiotics is possible because the quilt is a text. Extending the analysis of quilts beyond their surface, Chapter 3 “Quilt Works: Rhetorical Tasks of Quilts” will explore quilts made by quilters who wanted to state a message, one that could be a political position, an encomium, a synthesis, an analysis, or even an argument in Blair’s narrow definition. The act of quilting and its resultant meaning will be explored in Chapter 4 “Embodiment: How the Act of Quilting Makes Meaning,” which will discuss meaning in relation to quilts that in some way memorialize either the quilter, her relationships or her departed loved ones. The chapters begin with the description of a quilt that serves as an icon, illuminating the difficulties of interpretation and the rhetoric of the quilts described therein. In each chapter, I present these attributes as examples of quilts behaving as texts

The interpretation of English noun phrases with particular regard to generic reference

Within a relevance-theoretic inferential framework, the present corpus-based study offers an explanatory account of how English noun phrases are interpreted in discourse with particular regard to generic reference. Relevance pragmatics pays special attention to the process of discovering the proposition expressed by an utterance as a direct speech act and therefore it provides us with tools to explain how the interpretation of noun phrases contributes to the recovery of the proposition, especially how inference is being carried out. Two sets of features developed in this thesis capture the mechanism of interpreting NPs in general and generic reference in particular. One set applies to nominal expressions which belong to a discoursal network, specifying their relations and thereby enabling us to establish the network. When the NP in question is an introductory expression, another set of features, which has therefore become more important, is used to indicate the clues used in establishing a mental representation of its interpretation. With the help of these two feature-based systems, cognitively significant clues to the interpretation of an NP and its discoursal relations can be caught, including those for deciding whether a certain NP is to be interpreted generically or not. This study also investigates the four types of generics discussed in the linguistic literature: member generics, class generics, sub-class generics, and the generic use of pronouns. With the help of the one-million-word ICE-GB and other authentic sources, a comprehensive classification of discoursal relations and types of generic referents is established, which will serve as a basis for future research

Mathematics Education and Language Diversity

This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies. This open access book examines multiple facets of language diversit

A fluctuating, intermediate warp: a micro-ethnography and synthetic philosophy of fibre mathematics

This project explores the inventive worlds of artists who engage with weaving technologies in the production of their work. It aims to understand the mathematical practices of these textile practitioners, without reifying or subsuming their work within a closed teleology. Side-lining approaches to both mathematics and artistic production that fetishize individual genius or the imposition of form on passive matter, I approach both artistic and mathematical activities as making practices. The project draws on the philosophy of Gilbert Simondon to (re)theorise the role of technique and technology in artistic and mathematical creation. This focus foregrounds fibres and looms, diagrams and models as participants in material modes of reasoning. Exploring how the practices of both novice and expert weavers exceed the sovereign subject in ways that open up mathematical and weaverly tools as experimental forms, the project uses a micro-ethnographic analysis to examine how materials, machines, and humans improvise “algorhythmically” – a concept developed to describe both the regulation and excess of creative processes. Three case studies explore how the loom serves as a generative form/ground for engagement with mathematico-weaverly problems. Placing these material experimentations in the context of historical encounters between disciplines, the dissertation attempts to give contours to an emergent field of fibre mathematics