Given its abstract nature and the highly syntactical competence required by the use of symbolic algebra, research on its teaching and learning must rely on approaches that include semiotic concepts and analyses that recall the history of algebraic ideas, among others. Educational Algebra: A Theoretical and Empirical Approach deals with a theoretical perspective on the study of school algebra, in which both components (semiotics and history) occur. This perspective runs opposite to general theoretical models, since it submits components for the design of local frameworks for theoretical...
Given its abstract nature and the highly syntactical competence required by the use of symbolic algebra, research on its teaching and learning must...
About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block. But the main discovery of Brauer is perhaps the existence of families of infinitely many nonisomorphic groups having a "common block"; i.e., blocks having mutually isomorphic "source algebras." In this book, based on a course given by the author at Wuhan University in 1999, all the concepts mentioned are introduced, and all the...
About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzer...
Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups. In 1978 Alperin and BrouA(c) discovered the Brauer category, and BrouA(c) and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current...
Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one...
This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning." These approaches and others of similar nature lead to a focus on competence rather than a user's activity with mathematical language.
This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allo...
