Jesús Gallardo Romero, José Luis González Marí y Verónica Aurora Quintanilla Batallanos
Abstract: We show the advances obtained in the configuration of a developing model for the interpretation of mathematics understanding. Such a model links the cognitive approach of mathematics interpretation with the semiotic approach through a process of integration, which shows an operative way to move from the students’ activity to their mathematical understanding. The fundamental principles which define this model are divided in two dimensions, the phenomenon-epistemological and the hermeneutical. The first one includes a method for the identification and organization of task with which the mathematical activity of the students can be registered. The second one comprises an interpretative plan which grants the access to the students’ understanding in terms of the given uses to the mathematical knowledge. The effectiveness of this model can be proved with some evidences obtained when interpreting a pair of secondary students when they solve an elementary arithmetic problem.
Keywords: interpretation, understanding in mathematics, phenomenological and epistemological analysis, hermeneutics, multiplication algorithm.
