Mathematics teaching and workshop (2019/2020)

Course code
Name of lecturers
Enrico Gregorio, Andrea Albiero
Enrico Gregorio
Number of ECTS credits allocated
Academic sector
Language of instruction
II semestre dal Mar 2, 2020 al Jun 12, 2020.

Lesson timetable

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Learning outcomes

The course aims to analyze problems in mathematics teaching from a general point of view, but also going deeper in some specific themes. The components of the “indicazioni nazionali” will be examined and traditional and alternative methods for teaching will be illustrated. The workshop aims to furnish the main theoretical and methodological elements for planning and analyzing laboratory sessions in secondary school classes. The course will provide • critical analysis of the main methodologies for teaching developed in the research on didactics of mathematics, also with reference to the specific role of the teacher and to the conceptual, epystemologic, linguistic and didactic nodes in mathematics teaching. • design and development of mathematics teaching methodologies; illustration of principles and methods for building learning activities and a curriculum consistent with the objectives stated in the national indications for liceo and in the guidelines for technical and professional schools; • study of the teaching and learning processes of mathematics, with particular attention to the new technologies; analysis of the potential and of the critical aspects connected with the usage of technologies; • main theoretical frames developed in didactics of mathematics for teaching activities centered on the usage of new technologies along with an analysis of learning through them. At the end of the course the students will be at hand with various didactic techniques for different theoretical topics. Knowledge and understanding: the students will know relevant didactic aspects of mathematics and will be able to examine textbooks with consciousness. Applying knowledge and understanding: the students will be able to organize didactic experiences and to apply the techniques they learned in different situations. Making judgements: the students will be able to choose among various techniques the one more apt to the topic at hand. Communication skills: the students will be able to properly deliver a lecture. Learning skills: the students will be able to widen their knowledge starting from what they learned."


Mathematics laboratory for constructing mathematical meanings
Mathematics laboratory: historical and pedagogical roots.
Mathematics laboratory in the Italians standards for mathematics.
Theoretical frameworks for the mathematics laboratory: instrumental approach, theory of semiotic mediation, multimodal approach.
Students' processes in mathematics laboratory: exploring, conjecturing, argumentations and proving.
Teacher's processes in mathematics laboratory.
Didactical analysis of teaching experiments with physical artifacts as the mathematical machines (for geometrical transformations, conics sections and perspective drawing) and digital artifacts as dynamic geometry software (DGS).

Reference books
Author Title Publisher Year ISBN Note
George Polya Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume I Ishi Press 2009 978-4-871-87831-9
George Polya Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume II Ishi Press 2009 978-4-87187-832-6

Assessment methods and criteria

The examination consists in an oral interview about the planning of a teaching experience.

Criteri di valutazione:

• Knowledge and understanding: understanding of the chosen topic and knowledge of didactic techniques.

• Applying knowledge and understanding: ability to apply didactic techniques to a new topic.

• Making judgements: ability to synthesize from various sources.

• Communication skills: language clarity and appropriateness.

• Learning skills: ability to read texts chosen in autonomy