The following papers present an overview of the OSA theoretical notions, its motivation, and anthropological and semiotic assumptions. The OSA is an emerging theoretical system that attempts to articulate different points of view and theoretical notions about mathematical knowledge, its teaching and learning. It is supported and nurtured by contributions from the various disciplines and technologies interested in human cognition and its development: epistemology, psychology, sociology, semiotics, educational sciences.
In the following papers the notions of institutional and personal meaning of mathematical objects are developed and exemplified, laying the foundations for an anthropological - pragmatic and semiotic conception of mathematical knowledge, both from an institutional (social and cultural) and personal (cognitive) point of view. Likewise, the notions of configuration of practices, objects, processes and relationships (semiotic functions), as analytical tools for institutional and personal mathematical practices are developed and exemplified.
The following papers introduce and exemplify the notions developed in the OSA to analyze and design mathematical instruction processes (teaching - learning of specific contents), taking into account the epistemic, ecological, cognitive, affective, interactional (teaching and teaching roles) and mediational facets.
The didactic suitability of an instructional process is defined as the degree to which the process (or a part of it) meets certain characteristics allowing to be classified as optimal or adequate. This required achieving the adaptation between the students’ personal meanings (learning) and the intended or implemented institutional meanings (teaching), taking into account the circumstances and resources available (environment). The learning optimization can take place locally through a mixed model of instruction that articulates the inquiry, collaboration and transmission of knowledge, a model managed by didactic suitability criteria interpreted and adapted to the context by the teacher. The following articles describe and exemplify the use of this tool.
List of papers in which the concordance and complementarities of the OSA with other theoretical frameworks used in Mathematics Education are studied.
OSA papers with applications to the field of teachers’ education.
OSA papers with applications to the field of algebra.
OSA papers with applications to the field of arithmetics.
OSA papers with applications to the field of calculus.
OSA papers with applications to the field of statistical education.