Mathematics

ANNALISA CUSI

General aims: The successful student will be able to deal with arguments concerning the teaching of the mathematics in secondary schools.

Specific aims:
Knowledge and understanding: The successful student will have acquired basic notions about didactical theories and will know possible different approaches to specific mathematical topics. The successful student will know a suitable framework for the main concepts of several mathematical topics, having caught up a good familiarity with fundamental aspects, as the connection between various fields of the mathematics.

Applying knowledge and understanding: The successful student will be able to discuss traditional didactic choices. S/he will be able to prepare lectures and exercises to teach mathematics taking in due account some solutions to several teaching problems. S/he will be able to use a dynamic geometry software in an education context.

Critical and judgmental skills: The successful student will be familiar with mathematical methods. S/he will have reflected on known mathematical contents; s/he knows how to tackle questions about the teaching of mathematics in a critical way. S/he will be able to discuss the role of software at an educational level.

Communication skills: The successful student will be able to present subjects and arguments in the oral test, and to explain to other people what s/he learned.

Learning skills: The acquired knowledge will allow to study more specialized subjects. The student will be motivated to extend his/her knowledge.

The successful student will be able to deal with arguments concerning the teaching of the mathematics in secondary schools.

The course is aimed at making students reach the following specific aims:

Knowledge and understanding: The successful student will have acquired basic notions about didactical theories and will know possible different approaches to specific mathematical topics. The successful student will know a suitable framework for the main concepts of several mathematical topics, having caught up a good familiarity with fundamental aspects, as the connection between various fields of the mathematics.

Applying knowledge and understanding: The successful student will be able to discuss traditional didactic choices. S/he will be able to prepare lectures and exercises to teach mathematics taking in due account some solutions to several teaching problems. S/he will be able to use a dynamic geometry software in an education context.

Critical and judgmental skills: The successful student will be familiar with mathematical methods. S/he will have reflected on known mathematical contents; s/he knows how to tackle questions about the teaching of mathematics in a critical way. S/he will be able to discuss the role of software at an educational level.

Communication skills: The successful student will be able to present subjects and arguments in the oral test, and to explain to other people what s/he learned.

Learning skills: The acquired knowledge will allow to study more specialized subjects. The student will be motivated to extend his/her knowledge.

The mathematical contents that are taught at lower and upper secondary school.

Classical models of learning: transmissive model, radical constructivism, social constructivism.
Classical theoretical frameworks of mathematics education: theory of didactical situations, semiotic mediation, metacognition and affective factors.
Institutional aspects: national curriculum, INVALSI, OECD-PISA.
Methodological elements for the teaching of mathematics: role of the teacher, mathematical laboratory, mathematical discussion, assessment.
Studies on mathematical thinking: problem-solving, argumentation and proof, defining, modeling.
Didactic elements for specific mathematical contents: arithmetic/algebra, probability, calculus.

The slides of the lessons and teaching materials will be shared on the e-learning page of the course.

The teaching methodology adopted for the Mathematics course will be characterized by interactive lessons and moments devoted to working group activities and collective discussions, focused on the analysis of activities for secondary school classes, students’ protocols and excerpts that document teaching-learning processes.
Students will also be involved in the design of activities and educational paths, which will be discussed during the lessons.
The student will find on the e-learning platform the slides and the teaching materials useful for the preparation of the exam.

Course attendance is optional, but recommended.

The assessment of the course is carried out through an oral examination, aimed at certifying the knowledge related to the main aspects introduced during the course and the skills developed in relation to the ability of analyzing teaching activities and teaching-learning processes, referring to the theoretical lenses provided by mathematics education research.
Both attending and non-attending students will also be required to work on the design of an educational activity for secondary school classes, which will be discussed both during the lessons (in the case of attending students) and during the exam.
Sufficient knowledge of the contents covered and a corresponding sufficient competence in the analysis of teaching materials and teaching-learning processes and in the planning of activities for the classes is required for passing the exam with the minimum grade. To achieve a score of 30/30 cum laude, the student must also demonstrate that he/she has acquired excellent knowledge of the contents introduced during the course and the ability to refer to such knowledge to develop in-depth reflections on teaching-learning processes and to effectively design activities for classes.

It is not possible to identify "frequently asked questions or tasks", since, during the exam, questions will be formulated starting from the product of students' design of an educational activity for secondary school classes, with the aim of fostering the reflection on the possible connections with issues faced during the course.