Mathematical Organizations Related to the Pythagorean Theorem: Description in Terms of Its Components and Degree of Completion

This paper identifies the components (tasks, techniques, technologies and theories) of the praxeologies or mathematical organizations (MOs) related to the Pythagorean theorem, proposed in a set of 34 school textbooks for secondary school in Argentina. The 201 tasks identified are grouped into 11 types of tasks and these, in turn, into 5 genres of tasks. We conclude in the characterization of MO with a greater preponderance of calculus, centered on the task genre “Calculate”. An attempt is made to provide indications of the degree of completeness of these MOs based on the set of indicators formulated by (Fonseca in Discontinuidades matemáticas y didácticas entre la enseñanza secundaria y la enseñanza universitaria (Tesis doctoral). Universidad de Vigo, 2004). Descriptors are generated for each of them and the conclusion is a low degree of completeness.