Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.
Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.
For historians of mathematics and those interested in the history of science, 'A Discourse Concerning Algebra' provides an new and readable account of the rise of algebra in England from the Medieval period to the later years of the 17th century. Including new research, this is the most detailed study to date of early modern English algebra, which builds on work published in 1685 by John Wallis (Savilian Professor of Geometry at Oxford) on the history of algebra. Stedall's book follows the reception and dissemination of important algebraic ideas and methods from continental Europe (especially those of Viéte) and the consequent revolution in the state of English mathematics in the 17th century. The text emphasises the contribution of Wallis, but substantial reference is also provided to other important mathematicans such as Harriot, Oughtred, Pell and Brouncker.
The book reports a comparative research project about algebra teaching and learning in four countries. Algebra is a central topic of learning across the world, and it is well-known that it represents a hurdle for many students. The book presents analyses built on extensive video-recordings of classrooms documenting the first introduction to symbolic algebra (students aged 12 to 14). While the content addressed in all classrooms is variables, expressions and equations, the teaching approaches are diverse. The chapters bring the reader into different algebra classrooms, discussing issues such as mathematization and social norms, the role of mediating tools and designed examples, and teacher beliefs. By comparing classrooms, new insights are generated about how students understand the algebraic content, how teachers instruct, and how both parties deal with difficulties in learning elementary algebra. The book also describes a research methodology using video in search of taken-for-granted aspects of algebra lessons.
This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.
For the past decade reform efforts have placed importance on all students being able to participate in collaborative and productive mathematical discourse as an essential component for their learning of mathematics with deep conceptual understandings. In this book our intent is to support mathematics education researchers, teacher educators, teachers and policy makers in providing positive solutions to the enduring challenge in mathematics education of enabling all participants including diverse students to equitably access mathematical discourse. By diverse learners we mean learners who are minoritized in terms of gender, disability, or/and social, cultural, ethnic, racial or language backgrounds. We aim to increase understanding about what it means to imagine, design and engage with policy and practice which enhance opportunities for all students to participate in productive mathematical discourse. In widening the lens across policy and practice settings we recognize the interplay between the many complex factors that influence student participation in mathematics. The various chapters tell practical stories of equitable practices for diverse learners within a range of different contexts. Different research perspectives, empirical traditions, and conceptual foci are presented in each chapter. Various aspects of diversity are raised, issues of concern are engaged with, and at times conventional wisdom challenged as the authors provide insights as to how educators may address issues of equitable access of minoritized learners to the mathematical discourse within settings across early primary through to high school, and situated in schools or in family and community settings.
Through theoretical and methodological frameworks, researchers from writing studies, communication disorders, communication studies, applied linguistics, anthropology, and education, argue for a new dialogic approach to multimodality as a question of semiotic practices as well as multimodal artifacts.
This book explores the connection between the ways people speak in mathematics classrooms and their opportunities to learn mathematics. The words spoken, heard, written and read in mathematics classrooms shape students’ sense of what mathematics is and of what people can do with mathematics. The authors employ multiple perspectives to consider the means for transformative action with respect to increasing opportunities for traditionally marginalized students to form mathematical identities that resonate with their cultural, social, linguistic, and political beings.
