What is Computational Transposition

This chapter reviews conceptual elements expanding study of recent theoretical frameworks for analyzing online courses for mathematics teaching and learning. A critical analysis is conducted about the peculiarities of the current online teaching and learning courses called Massive Open Online Courses (MOOC) available for supporting teachers in the teaching of mathematics with technologies. Analysis is based on the extension and implementation of key concepts of the didactic theory of mathematics, namely didactic transposition and teaching contract. Theory extensions, as computational transposition and epistemological and didactic validity, support reflections of online professional development of mathematics teachers from results of innovative experiences in distance education. The overall analysis highlights problems associated with the physical distance between actors involved in online educative modalities related to teaching and learning of mathematics with technologies and the virtual character of educational Internet resources and its impact on the type of acquired knowledge.