Ontosemiotic approach in mathematics education

Abstract

This book addresses the dilemmas and contradictions posed by the diversity of theories elaborated to understand the complexity of teaching and learning in mathematics education research. The ontosemiotic approach to mathematical knowledge and education is a modular and inclusive theoretical system that addresses this problem. It comprises four articulated partial theories that address ontological, epistemological, and semiotic questions regarding mathematical knowledge and those related to the design, implementation, and evaluation of educational-instructional processes. These theories serve as the basis for developing a fifth theory on educating mathematics teachers and teacher educators. The book presents the initial assumptions and specific tools of each theory, along with examples of their application to different mathematical contents. It also includes a study of concordances and complementarities with other theoretical frameworks, particularly the theory of didactic situations, the anthropological theory of didactics, realistic mathematics education, APOS theory, objectification theory, and the ethnomathematics program. This book is useful for researchers in mathematics education, teacher educators, and mathematics teachers interested in understanding their professional activities and who want to learn tools to reflect on their practice.