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

- Bartolini Bussi, M.G. (1998). Verbal interaction in mathematics classroom: A Vygotskian analysis. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in mathematics classroom (pp. 65–84). Reston, VA: NCTM.
- Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer.
- Brousseau, G. (2003). Glossaire de quelques concepts de la théorie des situations didactiques en mathématiques. Retrieved from http://dipmat.math.unipa.it/~grim/Gloss_fr_Brousseau.pdf.
- Indicazioni Nazionali per il Curricolo, 2012 http://www.indicazioninazionali.it/documenti_Indicazioni_nazionali/indicazioni_nazionali_infanzia_primo_ciclo.doc
- https://invalsi-areaprove.cineca.it/
- Rally Matematico Transalpino, http://smfi.unipr.it/it/orientamento/rally-matematico-transalpino-pr
- Vergnaud, G. (1988). Theoretical frameworks and empirical facts in the psycology of mathematics education. Plenary address in, Ann & Keith Hirst (Eds.) Proceedings of ICME 6, pp. 29-47
- Vergnaud, G. (1998). A Comprehensive Theory of Representation for Mathematics Education. Journal of Mathematical Behaviour, 17 (2), pp. 167-181
- Vergnaud, G. (2009). The Theory of Conceptual Fields. Human Development, 52, pp. 83-94
- Vergnaud, G. (2013). Conceptual development and learning. Revista Qurriculum, 26, pp. 39-59

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