Sciences and Teaching of Natural Systems

ANNALISA CUSI

Knowledge and understanding: At the end of the course, students will be familiar with fundamental topics and issues in the field of mathematics education. They will have acquired some basic knowledge of the role of the main theoretical tools that research in mathematics education offers future teachers for the design and analysis of teaching practice. They will be familiar with dynamic geometry software and know how to use it in teaching.
Apply knowledge and understanding: Students will be able to compare different approaches to teaching mathematics and identify the most appropriate approaches for the different teaching-learning contexts in which future teachers may find themselves working. They will be able to apply the teaching and pedagogical knowledge developed during the course in the design of teaching materials and activities aimed at implementing approaches focused on the co-construction of knowledge, also with the support of digital tools.
Critical and judgemental skills: Students will have developed an approach to teaching mathematics based on critical reflection on practice, shared within working groups. They will be able to critically address issues in mathematics education based on reflection on the mathematical contents covered in the course. They will be able to discuss the role of softwares in mathematics teaching.
Communication skills: Students will be able to present the content in oral exams and explain what they have learned to others.
Learning skills: Students will be able to independently analyse research articles on mathematics teaching with the aim of identifying ideas for lesson planning. They will be able to develop meta-reflections on their own and others' approaches to new mathematical contents and issues related to mathematics teaching. They will be motivated to explore scientific topics and those specific to educational design and to take a critical approach to the teaching materials and various sources of information available to them in their professional career.

At the end of the course, the student will be able to deal with topics concerning the teaching of the mathematics in secondary schools, with a specific focus on geometry and calculus and on the use of resources in teaching.
The course is aimed at making students reach the following specific aims:

Knowledge and understanding:
By the end of the course, the student will have acquired basic knowledge of theoretical frameworks for the study of teaching-learning processes in geometry and calculus and, more generally, of processes supported by the use of technologies, both digital and non-digital. Furthermore, he/she will have learnt to refer to this knowledge for the analysis of these processes.

Applying knowledge and understanding:
The student will be able to reflect on and compare different didactic approaches for the teaching of specific contents examined during the course. He/she will also be able to use his/her knowledge for the planning of laboratorial activities, for the design of teaching resources and for the implementation of research-action processes. He/she will be familiar with digital resources for teaching mathematics and will be able to use them in teaching.

Critical and judgmental skills:
The student will have learnt to integrate their knowledge and deal with complexity in order to reflect on mathematics teaching-learning processes, to design teaching resources (also digital) and to use them in the Mathematics teaching practice.

Communication skills:
The student will be able to argue his or her point of view and share with other interlocutors (specialists and non-specialists) his/her reflections, possible solutions to the didactic problems discussed during the course and the criteria that guided the design of didactic activities and resources.

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 introduced at lower and upper secondary school level.

Theoretical frameworks for the analysis of teaching-learning processes in geometry and arithmetics/early algebra and for reflection on the role of digital resources in supporting cognitive and metacognitive processes in the teaching-learning of mathematics.
Teaching methods: laboratorial approach to the teaching of Mathematics and use of resources (digital or not) for teaching, with a focus on the role of the teacher.
Argumentation and proof in mathematics, with a focus on geometry and arithmetics/early algebra.
Didactic elements for the teaching pf geometry and arithmetics/early algebra.

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

No textbook is adopted.

During the course, dialogue-based lessons will alternate with group work and collective discussions.
The students will also be involved in the reading of research papers in Mathematics Education to reflect on the relationship between theory and practice in the teaching of Mathematics, in the design of laboratorial activities and of teaching resources, which will be discussed during the lessons.
Students will find the slides and teaching materials useful for exam preparation on the e-learning platform.

Course attendance is optional, but recommended.

The assessment is carried out by means of an oral examination, aimed at certifying knowledge of the main aspects covered during the course and the skills developed in relation to the ability to analyse teaching processes and design teaching resources.
Both attending and non-attending students will be required to work on the design of a teaching laboratory or teaching resources.
Sufficient knowledge of the content covered and a correspondingly sufficient competence in the analysis of teaching processes and the design of teaching resources is required for passing the examination with a pass mark (18/30). In order to achieve a mark of 30/30 with distinction, the student must also demonstrate excellent knowledge of the topics covered in the course and the ability to refer to this knowledge in order to develop in-depth reflections on these topics and for the design of resources to support teaching processes.

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 a laboratorial activity or of a didactical resource for secondary school classes, with the aim of fostering the reflection on the possible connections with issues faced during the course.

• Theoretical frameworks for analysing teaching and learning processes in geometry (12 hours, spread across the first part of the course).
  • Books: Slides and other materials (research papers, worksheets) shared during the course.


• Theoretical frameworks for analysing teaching and learning processes in arithmetic/early algebra (4 hours, spread across the second part of the course).
  • Books: Slides and other materials (research papers, worksheets) shared during the course.


• Theoretical frameworks for reflection on the role of digital resources in supporting cognitive and metacognitive processes in mathematics teaching and learning (4 hours distributed throughout the second part of the course).
  • Books: Slides and other materials (research papers, worksheets) shared during the course.


• Teaching methodologies: laboratory teaching and use of resources (digital and non-digital) for teaching, with a focus on the role of the teacher (12 hours distributed throughout the course).
  • Books: Slides and other materials (research papers, worksheets) shared during the course.


• Arguing and proving in mathematics, with a focus on geometry and arithmetic/early algebra (8 hours spread throughout the course).
  • Books: Slides and other materials (research papers, worksheets) shared during the course.


• Elements of geometry and arithmetic/early algebra teaching (8 hours spread throughout the course).
  • Books: Slides and other materials (research papers, worksheets) shared during the course.