In this paper the authors present a reflection concerning a possible vertical curriculum in Mathematics. It needs to consider epistemological aspects related to the teaching-learning of math and linked to the suggestions of the Italian National Curriculum. In this case the Vergnaud’s Theory of Conceptual Field and the Brousseau’s Theory of Situations could prove to be useful for teachers to provide students with fruitful situations so that, facing them, they can construct mathematical knowledge.
Keywords: Mathematics Vertical Curriculum; Theory of Conceptual field; Theory of Situations; mathematical knowledge; Italian National Curriculum; Role of teacher