Search

Este libro recoge un conjunto de estudios escritos en memoria del profesor Fernando Cerdán por compañeros y amigos, sobre lo que fue el tema central de su trabajo profesional: la investigación sobre la enseñanza y el aprendizaje de la resolución de problemas de matemáticas. El libro se abre con un facsímil de un texto suyo,'Acerca del carácter aritmético o algebraico de los problemas verbales', aparecido en 1991, cuya vigencia se examina en el siguiente capítulo, y contiene trabajos que, de una forma u otra, discurren por los caminos que él frecuentó: problemas aritméticos y algebraicos verbales, razón y proporción, heurística y problemas de construcción con regla y compás.

This work focuses on central catadioptric systems, from the early step of calibration to high-level tasks such as 3D information retrieval. The book opens with a thorough introduction to the sphere camera model, along with an analysis of the relation between this model and actual central catadioptric systems. Then, a new approach to calibrate any single-viewpoint catadioptric camera is described. This is followed by an analysis of existing methods for calibrating central omnivision systems, and a detailed examination of hybrid two-view relations that combine images acquired with uncalibrated central catadioptric systems and conventional cameras. In the remaining chapters, the book discusses a new method to compute the scale space of any omnidirectional image acquired with a central catadioptric system, and a technique for computing the orientation of a hand-held omnidirectional catadioptric camera.

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 analysis. The Methodological design allows for the interpretation of specific phenomena and the inclusion, within such interpretative frameworks, of evidence not included in more general treatments. Such is the case of phenomena observed in subjects who are initiating the study of symbolic algebra, involving the production of personal sign systems at the intermediate level or the level previous to the mathematical sign system which is to be learned. Disciplines such as Linguistics, Logic, Psycholinguistics, Semiotics, general Cognitive Psychology, Mathematics Psychology, Mathematics Epistemology, History of Mathematics, and others have carried out research on the same topics approached by Mathematics Education and have redefined their results within the framework of their respective fields. Specifically, theorists in Linguistics, Information Processing and Didactics of Mathematics have done important work on the notion of code. Today, this notion is a key element to interpreting the idea of representation in the new explanatory models of cognitive problems placed by alternative teaching approaches, including those involving a technological environment. Additionally, Psycholinguistics and Artificial Intelligence in procedural models of human abilities have intended to explain how and why users of mathematical language naturally and commonly make mistakes in syntactical procedures. Educational Algebra: A Theoretical and Empirical Approach adds to previous developments with priority given to a pragmatic perspective on'meaning in use'over'formal meaning'. The bulk of these approaches and others of similar nature have lead to a focus on competence rather than on a user's activity with mathematical language. Such a shift in perspective has fundamental implications on the way mathematical language is studied. Essentially, Grammar—the abstract formal system—and Pragmatics—the principles of the use of language—are complementary domains in this volume. Both are related to different teaching models, whether new or traditional, used in helping students to become competent users of Algebra. Because of this, Educational Algebra: A Theoretical and Empirical Approach will be of interest to researchers and practitioners within the mathematics education field.