The increasing difficulties in mathematics among secondary school students in particular and citizens in general are known by all. This gap damage the basis for the exercise of active citizenship called for by the Recommendations of the European Parliament and the Council of the European Union. Already at the beginning of the 20th century, the greatest mathematicians of the time attributed these difficulties to a penalising view of the discipline, seen only as a one-way transmission of techniques and results. To bring students to a more correct view of the discipline and promote a positive attitude towards the subject, we propose a path of workshop meetings on the PBL model (Problem-Based Learning).

There will be 5 meetings of 3 hours each.

We propose a path of workshop meetings on the PBL model (Problem-Based Learning). Students will have the opportunity to live actively the experience of the ‘researcher’: in each meeting, students will be asked to identify themselves in the role of the "mathematician", working in groups on an assigned problem, under the supervision of teachers/tutors. After this phase of active discovery, at the end of the meeting each group will report, in the presence of an experienced mathematician, on their own solution to the problem. In this final phase, a large group discussion will be promoted to compare possible different solutions by the groups.

It will be possible for the school tutors to recommend mathematical areas to be preferred in the choice of these problems. When the topic of the workshop will be identified, a university lecturer will be identified to function as an "expert" for the project.

Code: B.TEC/SCIE.21

Duration: 15 hours

Project Manager: Marina Cazzola

Meetings to prepare for the study of university mathematics. The aim is not to prepare for the ‘entry tests’, but to familiarise students with the language, logical tools and symbolism of mathematics, with the dual purpose of familiarising them with the study method they will encounter in the first years of a degree programme in Mathematics, Physics or Statistics, and to help them overcome any previous gaps in the study method (and not necessarily in contents) that might hinder their future path.

Cycles of lessons/exercises will be proposed on:

• how to study a maths book (this is not preparation for entry tests)
• understanding a definition
• studying a demonstration, verifying it on examples
• analysing different classes of reasoning and distinguish a completely wrong argument from one that has a useful idea and can be translated into a correct demonstration.

Code: B.TEC/SCIE.22

Duration: 15 hours

Project Manager: Giona Veronelli

The same scientific result can be communicated and perceived in essentially different ways; therefore the importance of a basic mathematical and statistical education and honest scientific communication is evident. We will take common examples (orders of magnitude and their perception, ways of describing the variation of a quantity, the concept of probability, statistics), focusing on both the mathematical concept and the way it is communicated, graphically and verbally.

Topics

• Scientific communication: what it is, what is it for and what it requires
• Orders of magnitude: what they are and how they are used, their role in scientific communication
• Percentages and proportions: how to describe the increase and decrease of a quantity, problems in the common perception of these descriptions
• Conceptual basis of probability and statistics: various descriptions of probability, common mistakes and misconceptions, conditional probability, what statistics does, what is a test, how to interpret the results, how easy it is to misunderstand what they tell us
• Basic concepts of scientific communication with graphs (and infographics)

The course will be mainly in lecture mode, but there will also be group exercises and discussions on examples taken from current events.

Code: B.TEC/SCIE.24

Duration: 8 hours (extendable to 15)

Project Manager: Samuele Mongodi

We will discuss what a mathematical model is, what is it for, what is not for, why it works and when it doesn't work. In particular, I will focus on three types of modelling (flows, time-dependent systems, graphs) and their applications in some areas (pollution, ecosystems, viability, economic production), trying to understand why one type of model is chosen over another, what information can be acquired and for which questions a certain model is useless.

Topics

• What is a mathematical model, how and when it works
• Flows, causal models, feedback phenomena
• Successions by recurrence and growth models
• Predator models and SIR model; qualitative study
• Graphs, graph search algorithms and social networks

The course will alternate moments of theoretical explanation with moments of numerical experimentation and discussion of the use of mathematical models in decision-making processes.

Code: B.TEC/SCIE.25

Duration: 6 hours (extendable to 15)

Project Manager: Samuele Mongodi