Numbers have always been used to evaluate and measure a wide range of situations, both qualitative and quantitative, and consequently, they help us make decisions and choices. However, they are not always used correctly: it’s one thing for a scale to use numbers to represent quantities, such as the numbers we learned to count with as children, but it’s quite another to simply use numbers to indicate an order. In this manuscript, starting with medical and geological examples, we will examine some fundamental properties of numbers, so that we can use rating scales critically. In this regard, we would like to offer ideas for showing students practical and interdisciplinary applications of the correct use of mathematics.

This paper deals with problems concerning the planning of mathematics courses in teacher educational pathways to professional qualifications, respectively, A059 - Matematica e Scienze per la scuola secondaria di I grado (Mathematics and Science for lower secondary school) and A049 - Matematica e Fisica (Mathematics and Physics for upper secondary school). It will be shown how the University of Trieste, with the activation of its courses, chose suitable contents and didactical methodologies in the attempt to overcome these problems. The PAS - Percorsi Abilitanti Speciali (Special Qualification Pathways) in the academic years 2013/2014 and 2014/2015 will be discussed and then a comparison will be made with the experience of analogous courses in TFA - Tirocinio Formativo Attivo (Active Educational Training).

Among the various courses offered to the schools of the Friuli Venezia Giulia region by the University of Trieste, for the PNRR project ‘Active orientation in the school-university transition’, within the framework of the National Recovery and Resilience Plan, Mission 4 ‘Education and Research’ Investment 1.6, we proposed a didactic activity in mathematics related to the topic of social sustainability. In this contribution, we present a description of the activity carried out, with various ideas that can be used in the curriculum hours or in complementary activities. The topic presented concerns an introduction to discrete dynamical systems, with a focus on linear and exponential growths. The activity was proposed to several classes in the third, fourth and fifth year of high schools. Naturally, methods and topics were adapted according to the level of the students present. Topics considered more challenging or more advanced are marked with the symbol . The lectures were complemented by various group work and workshops, which we report only in part.

Alcuni capitoli della matematica godono di una brutta reputazione e sono spesso considerati dagli studenti (e non solo) particolarmente aridi, noiosi, astrusi. Il modulo di 10 ore, inserito nell’offerta didattica disciplinare “Didattica dell’analisi e laboratorio” del Tirocinio Formativo Attivo (TFA), classe A049 (Matematica e Fisica), dell’Università degli Studi di Trieste, proponeva di prendere in considerazione, come esempio tra i tanti, quello relativo alla trigonometria.