OVERVIEW

This unit deals with issues related to mathematical modeling and its teaching in secondary school.

AIMS AND CONTENT

LEARNING OUTCOMES

The unit aims to provide the opportunity to reflect on the complexity of mathematical modeling processes and on the degree of "approximation" and "provisionality" of the methods used and the results achieved, deepening some historical/epistemological and didactic aspects of mathematical modeling, and making some reflections, guided by the reading of scientific works, on the meaning of constructing a mathematical model.

AIMS AND LEARNING OUTCOMES

The unit aims to:

• present scientific results that discuss difficulties, potential, or critical issues in modeling processes within didactic activities for the teaching and learning of mathematics;
• analyze and discuss conceptual, epistemological, and didactical issues in mathematics teaching and learning, with reference to problem-solving activities that may involve modeling aspects;
• provide scientific elements for planning didactic activities on mathematical modeling.

Active participation in the proposed educational activities and individual study will allow the student to:

• understand scientific results that discuss difficulties, potential, or critical issues in modeling processes within didactic activities for the teaching and learning of mathematics;
• analyze problems in order to discuss their potential or critical issues for working on modeling in didactic contexts;
• structure design proposals for teaching activities on mathematical modeling for secondary schools, based on the scientific references covered and discussed in class.

Key competencies for lifelong learning

• Literacy competence: advanced level
• Personal competence: advanced level
• Social competence: advanced level
• Ability to learn to learn: advanced level
• Proficiency in design creation: advanced level

PREREQUISITES

The prerequisites consist of the units from the Bachelor's degree in Mathematics, and the contents of the "Mathematical Education and Dissemination" unit.

TEACHING METHODS

The unit will alternate between expository phases — where national and international research aspects on the topic of modeling will be presented and discussed — and small group work sessions followed by discussions. These sessions will be dedicated to solving and analyzing problems and structuring projects for teaching activities on the subject.

The "think-pair-share" methodology will allow work on basic level literacy competence, basic level personal competences, and basic level social competences.

Problem analysis will allow for work on advanced level literacy competence, advanced level personal competences, and, when carried out in a group, advanced level social competences.

Drafting project proposals for teaching activities will enable work on advanced level literacy competence, advanced level personal competences, advanced level proficiency in design creation, advanced level ability to learn to learn, and, when carried out in a group, advanced level social competences.

Students with certified learning difficulties, disability or other special educational needs are advised to contact the lecturer at the beginning of the unit to arrange teaching in a way that, while respecting the learning objectives, takes into account individual learning patterns and provides suitable compensatory tools.

SYLLABUS/CONTENT

The unit program includes the presentation and discussion of theoretical tools for reflecting on historical/epistemological and didactic aspects of mathematical modeling. In particular, various possible problems will be proposed from which mathematical modeling processes can be initiated. The following topics will also be explored:

1. Different definitions of "model" present in the literature;
2. The view of modeling within the frameworks of national and international standardized tests;
3. National and international studies on difficulties in modeling in didactic activities at various school levels, with particular attention to secondary school, and on possible tools available for the teacher;
4. Reflections on the potential and limitations of known mathematical models.

Additionally, the following will be revisited and discussed in relation to the course's perspective:

• Theoretical frameworks of research in mathematics education for designing teaching activities, such as the theory of semiotic mediation;
• Research on the processes of understanding a problematic situation and constructing a solution;
• Research on mathematical competence.

Finally, students will work on drafting proposals for the design of teaching activities to work on modeling in a classroom setting.

This unit contributes to the achievement of two of the United Nations 2030 Agenda Sustainable Development Goals:

• Goal 4: "Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all"
• Goal 5: "Achieve gender equality and empower all women and girls".

RECOMMENDED READING/BIBLIOGRAPHY

Baccaglini Frank, A., Di Martino, P., Natalini, R., Rosolini, G. (2017). Didattica della Matematica. Mondadori. (recommended reading)

Further readings will be suggested during the lessons and/or will be shared throught Aulaweb.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

The unit is held in the second semester, with lessons starting on February 23, 2026. All class schedules are posted on the EasyAcademy portal.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Preparation of an individual written project proposal for a teaching activity on mathematical modeling for secondary school, and an oral exam.

ASSESSMENT METHODS

The preparation of the project proposal aims to assess the ability to leverage what was learned in the course to structure a teaching activity. This activity should promote the development of mathematical modeling skills in secondary school students. Preparing such a project includes the ability to identify an open and significant mathematical problem, considering its potential to stimulate modeling processes by students, and in terms of mathematical content or ways of thinking potentially involved in the problem-solving process at the target school level.

The project design must also highlight how the characteristics and potential of the problem are exploited within the teaching activity. This involves specifying the methods intended for working on the chosen problem within a hypothetical class at the selected school level (the school level and target class are at the student's discretion). The design choices for the activity should therefore be accompanied by a justification that clearly explains the rationale the student followed for structuring their proposal, including appropriate references to what was covered in class.

The oral examination aims to ascertain the comprehension of the scientific results presented in class, also covering content not necessarily connected to the presented project. The oral exam also aims to assess the ability to argue the design choices of the presented project proposal, referring to what was discussed and covered during the course. In particular, it will be evaluated the ability to highlight the connections between the project and the research presented in class, explicitly detailing any critical issues that may arise within the designed activities and discussing them in relation to the critical aspects highlighted by the results of the scientific research studied.

Active student participation in the proposed activities, the production of problem solutions and analyses during lessons, and working on the formative feedback provided by the lecturer regarding design projects, all serve as assessment methods for achieving the Key Competences for Lifelong Learning. Badges are automatically awarded to all students enrolled in the course.

FURTHER INFORMATION

Attendance is highly recommended.
For taking the exam, contact the teacher.