We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should address the epistemological, ontological, semiotic-cognitive, educational-instructional, ecological, and instruction optimization problems. OSA assumes anthropological, pragmatic and semiotic principles to approach all these types of problems, as well as embraces sociocultural principles to face the educational-instructional problem. The notion of didactic suitability has been introduced as a systemic criterion to address the problem of optimization of mathematical instruction processes.