How Language Informs Mathematics

In How Language Informs Mathematics Dirk Damsma shows how Hegel’s and Marx’s dialectics allow us to understand the structure and nature of mathematical and capitalist systems. Knowledge of such systems allows for an innovative approach to economic modelling.

The book emerges from several contemporary concerns in mathematics, language, and mathematics education. However, the book takes a different stance with respect to language by combining discussion of linguistics and mathematics using examples from each to illustrate the other. The picture that emerges is of a subject that is much more contingent, much more relative, much more subject to human experience than is usually accepted. Another way of expressing this, is that the thesis of the book takes the idea of mathematics as a human creation, and, using the evidence from language, comes to more radical conclusions than most writers allow.

This book considers some of the outstanding questions regarding language and communication in the teaching and learning of mathematics – an established theme in mathematics education research, which is growing in prominence. Recent research has demonstrated the wide range of theoretical and methodological resources that can contribute to this area of study, including those drawing on cross-disciplinary perspectives influenced by, among others, sociology, psychology, linguistics, and semiotics. Examining language in its broadest sense to include all modes of communication, including visual and gestural as well as spoken and written modes, it features work presented and discussed in the Language and Communication topic study group (TSG 31) at the 13th International Congress on Mathematical Education (ICME-13). A joint session with participants of the Mathematics Education in a Multilingual and Multicultural Environment topic study group (TSG 32) enhanced discussions, which are incorporated in elaborations included in this book. Discussing cross-cutting topics it appeals to readers from a wide range of disciplines, such as mathematics education and research methods in education, multilingualism, applied linguistics and beyond.

Educators increasingly recognize the importance of disciplinary literacy for student success, beginning as early as the primary grades. This cutting-edge volume examines ways to help K–12 students develop the literacy skills and inquiry practices needed for high-level work in different academic domains. Chapters interweave research, theory, and practical applications for teaching literature, mathematics, science, and social studies, as well as subjects outside the standard core--physical education, visual and performing arts, and computer science. Essential topics include use of multimodal and digital texts, culturally responsive and sustaining pedagogy, and new directions for teacher professional development. The book features vivid classroom examples and samples of student work.

Here is a whole new way of looking at math that liberates math phobes from their anxiety, enables business people to do their jobs more effectively, challenges and informs math buffs, and provides educators with the tools to teach math easily and effectively. How can it do all that? By reuniting numbers and meaning, two subjects that should never have been separated in the first place. Entertaining, anecdotal, and immensely practical, this extraordinary book offers a revolutionary way of looking at math as a language, something that we've all heard before but which has never made sense until now. Mathsemantics is that rare book that will change the way you look at the world—and provide the most sensible and inspiring answer yet to the problem of American innumeracy. "Eye opening . . . a good antidote to innumeracy."—Library Journal

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.

This text explores a set of key concepts in Marxist theory as developed and read by Lacan, demonstrating links and connections between Marxist thought and Lacanian practice. The book examines the complexity of these encounters through the structure of a comprehensive vocabulary which covers diverse areas, from capitalism and communism to history, ideology, politics, work, and family. Offering new perspectives on these concepts in psychoanalysis, as well as in the fields of political and critical theory, the book brings together contributions from a range of international experts to demonstrate the dynamic relationship between Marx and Lacan, as well as illuminating "untranslatable points" which may offer productive tension between the two. The entries trace the trajectory of Lacan’s appropriation of Marx’s concepts and analyses how they were questioned, criticized, and reworked by Lacan, accounting for the wide reach of two thinkers and worlds in constant homology. Each entry also discusses psychoanalytic debates relating to the concept and seeks to refine the clinical scope of Marx’s work, demonstrating its impact on the social and individual dimensions of Lacanian clinical practice. With a practical and structured approach, The Marx through Lacan Vocabulary will appeal to psychoanalysts and researchers in a range of fields, including political science, cultural studies, and philosophy.

The combined impact of linguistic, cultural, educational and cognitive factors on mathematics learning is considered in this unique book. By uniting the diverse research models and perspectives of these fields, the contributors describe how language and cognitive factors can influence mathematical learning, thinking and problem solving. The authors contend that cognitive skills are heavily dependent upon linguistic skills and both are critical to the representational knowledge intimately linked to school achievement in mathematics.

Teacher Education and Practice, a peer-refereed journal, is dedicated to the encouragement and the dissemination of research and scholarship related to professional education. The journal is concerned, in the broadest sense, with teacher preparation, practice and policy issues related to the teaching profession, as well as being concerned with learning in the school setting. The journal also serves as a forum for the exchange of diverse ideas and points of view within these purposes. As a forum, the journal offers a public space in which to critically examine current discourse and practice as well as engage in generative dialogue. Alternative forms of inquiry and representation are invited, and authors from a variety of backgrounds and diverse perspectives are encouraged to contribute. Teacher Education & Practice is published by Rowman & Littlefield.

Language and culture play a critical role in the teaching of mathematics and this role intensifies when considering the teaching of mathematics in dual language classrooms. This book unpacks lessons learned from socio-cultural theory being applied to research of the teaching of mathematics to Emergent Bilinguals with the end of informing practice. Utilizing a socio-cultural lens, authors present the possibilities and limits of the teaching of mathematics in dual language programs (90/10; 50/50 models). Themes of translanguaging, disciplinary literacy instruction, and culturally responsive instruction are leveraged to test the potential of these constructs to assist Spanish/English Emergent Bilinguals access rigorous mathematics content. Authors also present limits to these models, as often they can overshadow the mathematics learning. We embrace a stance where language and literacy are seen as tools for content area learning and not as ends unto themselves.