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.

The Language of Mathematics: How the Teacher’s Knowledge of Mathematics Affects Instruction introduces the reader to a collection of thoughtful works by authors that represent current thinking about mathematics teacher preparation. The book provides the reader with current and relevant knowledge concerning preparation of mathematics teachers. The complexity of teaching mathematics is undeniable and all too often ignored in the preparation of teachers with substantive mathematical content knowledge and mathematical teaching knowledge. That said, this book has a focus on the substantive knowledge and the relevant pedagogy required for preparing teachings to enter classrooms to teach mathematics in K-12 school settings. Each chapter focuses on the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. Chapter One opens the book with a focus on the language and knowledge of mathematics teaching. The authors of Chapters Two-Nine present field-based research that examines the complexities of content and pedagogical knowledge as well as knowledge for teaching. Each chapter offers the reader an examination of mathematics teacher preparation and practice based on formal research that provides the reader with insight into how the research study was conducted as well as providing the findings and conclusions drawn with respect to mathematics teacher preparation and practice. Finally, Chapter 10 presents an epilogue that focuses on the future of mathematics teacher preparation.

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.

This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable. The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and information on alternative presentations. The work ends with an excursion on infinite sets, principally a discussion of the mathematics of Axiom of Choice and often very useful equivalent statements. Contents:SetsMappingsProperties of MappingsFamiliesRelationsOrdered SetsCompletely Ordered SetsInduction and RecursionThe Natural NumbersFinite SetsFinite SumsCountable SetsSome Algebraic StructuresThe Real Numbers: Complete Ordered FieldsThe Real Number SystemThe Real Numbers: ExistenceInfinite Sets Readership: Undergraduate and graduate students in mathematics; Mathematicians. Key Features:Comprehensive and rigorous in its coverageProvides alternative insights on concepts and definitionsProvides a list of sections with some unusual but insightful approachesKeywords:Sets;Mappings;Families;Order;Natural Numbers;Inductive Proofs;Recursive Definitions;Real Numbers

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.