Abstract
This essay deals with the constitutive processes of teaching, having as its guiding axis the adherence between training process, didactic-methodological practices, cognition, learning and human development. It characterizes mathematical practices in multi, inter and transdisciplinary perspectives, differentiating them in the context of teaching in the classroom. It discusses principles and didactic relationships established in the triad teacher, student and mathematical knowledge in the process of teaching mathematics through Problem Solving. It theorizes about the didactic action with educational intentionality as a possibility of cognitive development and significance of the school mathematical knowledge. It reflects on solving algorithms and mathematical understanding in schoolchildren’s learning. It presents examples of teaching projects in mathematics that link didactic and educational aspects in a single and simultaneous process whose approach transcends the disciplinary organization established in the curricular matrices, constituting itself in a transdisciplinary didactic practice.