The teacher’s activity under a phenomenological lens

According to phenomenological perspectives, students must be educated to see and focus things in ways coherent with the mathematical notions to learn: for example to see the mathematical properties of a function in a graph representing a certain situation. We refer to Rota’s account of mathematical thinking as “disclosure”, and give a phenomenological interpretation of the cognitive processes related to graphical modelling activities, and of the role of the context therein. We contrast the classroom discussions of the same task in two different grades (9 and 11), and show how the teacher uses suitable didactic techniques to promote different “layers” of students’ disclosures of Calculus concepts.