DIDATTICA DELLA MATEMATICA

Academic Year 2026/2027 - Teacher: DANIELA FERRARELLO

Expected Learning Outcomes

The course aims to provide competencies related to the secondary school mathematics teaching profession (for middle and high-schools) through knowledge of theoretical frameworks in mathematics education and concrete experience in instructional design. Specifically, the course pursues the following objectives:

a. Knowledge and Understanding:
- Analyze the main issues in mathematics teaching and learning.
- Gain knowledge of theoretical frameworks in mathematics education.
b. Applying Knowledge and Understanding:
- Design effective instructional pathways for specific schools/classes and topics, simulating their implementation in realistic classroom settings.
- Apply methodologies and educational technologies in mathematics to construct these pathways, anticipating potential student responses, difficulties, and misconceptions.
c. Making Judgements (Autonomy of Judgement):
- Analyze proposed instructional designs in light of the main research frameworks in mathematics education.
d. Communication Skills:
- Learn to communicate mathematical content in a simple manner, highlighting the foundational mathematical meanings.
- Communicate instructional designs effectively with colleagues, including through peer-teaching simulations, to enhance teamwork skills and give/receive constructive feedback.
e. Learning Skills:
- Work effectively both individually and in teams.
- Enhance creative capabilities.
- Learn to design educational activities by adapting topics to the most appropriate pedagogical transposition, even without direct experimental trials.
- Acquire professional skills relevant to the teaching profession.

Course Structure

The course (47 hours) is divided into 35 hours of Frontal Teaching (FT) and 12 hours of Interactive Teaching (IT).

In the first part of the course (approximately 3 hours, FT), the main issues in mathematics teaching and learning will be analyzed (Objective a.)

In the second part (approximately 22 hours, FT), the content related to theoretical frameworks of research in mathematics education and teaching methodologies will be delivered (Objective a.).

In the third part of the course (approximately 6 hours, IT), students will design activities and teaching paths for schools, including through the use of technology and, in particular, artificial intelligence (Objectives b., d., and e.).

In the fourth part of the course (approximately 4 hours, FT), strategies for analyzing teaching experiments will be presented (Objective c.).

In the fifth part of the course (approximately 6 hours, IT), students will simulate, in class and among peers, the teaching activities they have designed (Objectives b., c., and e.).

In the sixth part of the course (approximately 6 hours, FT), the activities designed and simulated will be analyzed in light of the research theories in mathematics education presented during the course (Objective c.).

Should the course be delivered in blended or distance mode, the necessary changes may be introduced with respect to what has been stated above, in order to comply with the program set out in the syllabus.

To ensure equal opportunities and in compliance with current legislation, interested students may request a personal meeting in order to arrange any compensatory and/or exempting measures, based on the learning objectives and specific needs.

Students may also contact the CInAP (Center for Active and Participatory Integration – Services for Disability and/or Specific Learning Disorders) contact professor in our Department.

Required Prerequisites

Knowledge of Italian language. The course is accessible only for Italian-speakers, because students are requested to design teaching/learning activities for italian classes.

Deep knowledge of the mathematical topics of middle and secondary school.

Attendance of Lessons

Class attendance is essential for an optimal use of the course, because students will work with the teacher and their colleagues, to acquire the desired skills (Objectives d. and e.).

Detailed Course Content

Issues in Mathematics Teaching/Learning: Errors and learning difficulties in mathematics; how learning occurs.
Theoretical Frameworks & Teaching Methodologies:
- Mathematics Laboratory methodology
- Dewey’s theory and learning-by-doing
- Collaborative and cooperative learning
- Theory of Multiple Intelligences
- Embodied cognition theories
- Role of visualization in mathematics education
- Use of history of mathematics in teaching
- Critical mathematics education, philosophy & mathematics, and Math-Ethics (Matem-Etica)
- Vygotsky’s theory
- Instrumental genesis
- TPACK framework
- Artificial Intelligence in mathematics education
- Pedagogy for Special Educational Needs (SEN/BES)
Instructional Design: Designing activities and pathways using educational technologies and AI tools.
Analysis Strategies: Analysis of discourse in educational experiments.
Simulations: Peer-teaching simulations of designed activities.
Critical Analysis: Evaluation of mathematical activities using theoretical frameworks.

Textbook Information

The main resource is attendance at the course, during which the didactic paths will be developed. Research papers and lectures' notes will be provided.

Course Planning

	Subjects	Text References
1	Analysis of problematic situation in math learning
2	Theoretical framework in Math Education
3	Design of learning actions
4	Strategies of analysis of teaching experimets
5	Simulation of the designed paths
6	Analysis of designed paths

Learning Assessment

Learning Assessment Procedures

The final exam consists of two parts (totaling 30 points):

Theoretical Knowledge Test (0–18 points): Assessment of theoretical frameworks and methodologies presented during the course.
Lesson Plan Design & Simulation (0–12 points): Preparation and oral defense of a simulated lesson on a topic drawn 2–3 days prior to the exam.
- 4 points: Knowledge of the underlying mathematical content.
- 8 points: Pedagogical design of the lesson path.

During the exam, the lesson will be presented and discussed as a simulation of classroom practice together with didactical design. Students may use slide presentations. A.I. tools may be used during lesson preparation, provided the student can critically explain and justify their pedagogical choices and content during the oral exam.

Breakdown of the 30-Point Scale across Learning Objectives:

a. Knowledge and understanding: 22 points (18 points for theoretical test + 4 points for mathematical content)
b. Applying knowledge and understanding: 2 points (lesson simulation & effective design, also taking into account current guidelines)
c. Autonomy of judgement: 2 points (critical analysis & anticipation of learning difficulties)
d. Communication skills: 2 points (ability to present mathematical concepts clearly and simply)
e. Learning skills: 2 points (general instructional design)
Honors (Lode): Awarded only for exceptional projects and oral presentations.
Online/Remote Assessment: Exams may be conducted online if required by emergency or university regulations. Compensatory/dispensative measures can be requested through the departmental CInAP contact.

Examples of frequently asked questions and / or exercises

Methodology of mathematics' laboratory
TPACK theoretical framework
Cooperative learning models
Vygotsky's theory
Embodiment theory
What teaching theories or methodologies have been applied in this instructional design?
How can student learning be assessed?
What improvements could be made to the proposed activity?

Degree Course in

Mathematics