Discourses On Algebra

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.

Psychoanalytic theory has traditionally taken sexual difference to be the fundamental organizing principle of human subjectivity. White Men Aren’t contests that assumption, arguing that other forms of difference—particularly race—are equally important to the formation of identity. Thomas DiPiero shows how whiteness and masculinity respond to various, complex cultural phenomena through a process akin to hysteria and how differences traditionally termed “racial” organize psychic, social, and political life as thoroughly as sexual difference does. White masculinity is fraught with anxiety, according to DiPiero, because it hinges on the unstable construction of white men’s cultural hegemony. White men must always struggle against the loss of position and the fear of insufficiency—against the specter of what they are not. Drawing on the writings of Freud, Lacan, Butler, Foucault, and Kaja Silverman, as well as on biology, anthropology, and legal sources, Thomas DiPiero contends that psychoanalytic theory has not only failed to account for the role of race in structuring identity, it has in many ways deliberately ignored it. Reading a wide variety of texts—from classical works such as Oedipus Rex and The Iliad to contemporary films including Boyz 'n' the Hood and Grand Canyon—DiPiero reveals how the anxiety of white masculine identity pervades a surprising range of Western thought, including such ostensibly race-neutral phenomena as Englightenment forms of reason.

This collection addresses concepts and theories of change, contexts and functions of reform discourses, and fields of change in educational research. It examines a wide variety of issues such as girls’ education in France, educational neuroscience, the professionalization in Child Protection, and mathematics discourses. It pays attention to the pervasiveness of crisis rhetoric in American Education Research, to the current university climate, and to perspectives for teacher education. The volume presents in-depth studies that integrate the perspective of history and philosophy of education. Educational research has been typically carried out within a discourse of change: changing educational practice, changing policy, or changing the world. Sometimes these expectations have been grand, as in claims of emancipation; sometimes they have been more modest, as in research as a support for specific reforms. This book explores the answers to such questions as: Are these expectations justified? How have these discourses of change themselves changed over time? What have researchers meant by change, and related concepts such as reform, improvement, innovation, progress and the new? Does this teleological and hopeful discourse itself reflect a particular historical and national/cultural point of view? Is it over promising for educational research to claim to solve social problems, and are these properly understood as educational problems? In doing so, it challenges prevailing ideas about the application of philosophy and history of education, and demonstrates the relevance of philosophical and historical approaches for the practice and theory of education and for educational research. This publication, as well as the ones that are mentioned in the preliminary pages of this work, were realized by the Research Community (FWO Vlaanderen / Research Foundation Flanders, Belgium) Philosophy and History of the Discipline of Education: Faces and Spaces of Educational Research.