OVERVIEW

The course focuses on mathematical modeling and its teaching and learning on secondary school. 

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims at promoting a reflection on the complex process of mathematical modeling and on the approximate and previsional nature of methods and results.

The course addresses technical aspects of modeling, as well as historical/epistemological and didactical ones.

Students will be led to reflect on the construction of a mathematical model and on the comparison between deterministic and probabilistic models.

Students will also be led to reflect on the required knowledge for a first approach to modeling in school, and on difficulties and potentialities of such a first approach. 

AIMS AND LEARNING OUTCOMES

The course will encompass:

• A preliminary questionnaire on students’knowledge in probability, their intuitive image of modeling and their expectations on the course.
• A historical/epistemological overview on the role of mathematical models and the difference between deterministic and probabilistic models, with a special focus to those aspects that are more related to the teaching and learning of modeling at secondary school
• A review (by means of the study of concrete situations, that relevant in history or the contemporary world) of these basic concepts and methods in probability and statistics that are useful for modeling
• The construction, through examples, of the idea of probabilistic model as a way to represent a complex real phenomenon. This is also aimed at making prospective teachers reflect on the mathematical representation of reality and the shift from certainty to uncertainty
• The analysis of teaching pathways for a first approach to statistical-probabilistic models in secondary school
• The study of elementary differential models in the fields of physics, bioogy, demography, epidemiology, …)
• The study of inferential stocastic processes (Markov chains, differential equations of Markovian stocastic processes, …) and the comparison with the deterministic models
• The analysis of experimental data in order to evaluate whether the models are suitable to represent real situations (linear regression, exponential regression, tests…)

TEACHING METHODS

Lectures, individual work on worksheets, class discussions

SYLLABUS/CONTENT

Mathematical modeling (differential models, stocastic processes) and its teaching and learning in secondary school: from a historical/epistemological reflection on modeling processes to educational design

RECOMMENDED READING/BIBLIOGRAPHY

Costantini D., Monari P., Probabilità e giochi d'azzardo, Franco Muzzio Editore 

Guala E., Dispense di probabilità e statistica Dipartimento di Matematica, Ge

Guala E., Modelli deterministici e modelli probabilistici, Dip.di Matematica, Ge

Israel G. La visione matematica della realtà, Laterza

 Hacking I., L'emergenza della probabilità, Il Saggiatore  

Vajani L., Saggi sui processi stocastici, Giuffré Editore

TEACHERS AND EXAM BOARD

Exam Board

ELDA GUALA (President)

CARLO EUGENIO DAPUETO

FRANCESCA MORSELLI

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

COMPLEMENTARY MATHEMATICS 1

EXAMS

EXAM DESCRIPTION

Written dissertation

ASSESSMENT METHODS

Individual review of all the worksheets.

Written dissertation on a given topic

Exam schedule

FURTHER INFORMATION

The attendance to the lessons is recommended

Enrolment to exams:contact the teacher