Learning objectives

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."

Prerequisites and basic notions

Knowledges in algebra, geometry and calculus

Program

The mathematics laboratory for constructing mathematical meanings. The mathematics laboratory: historical and pedagogical roots. The mathematics laboratory in the National Guidelines. Theoretical frameworks for the mathematics laboratory: instrumental approach, semiotic mediation theory, multimodal approach. Student processes in the mathematics laboratory: exploring, conjecturing, arguing, and proving. Teacher processes in the mathematics laboratory. Educational analyses of mathematics laboratory programs with physical artifacts such as mathematical machines (for geometric transformations, conic sections, and perspective) and digital artifacts such as dynamic geometry software.

Bibliography

Didactic methods

Lectures and laboratory activities

Learning assessment procedures

The exam consists of an oral interview on the design of a teaching path with a mathematics laboratory, together with the construction of a verification test

Evaluation criteria

• Knowledge and understanding: understanding of the topic presented and knowledge of teaching techniques. • Applied knowledge and understanding: ability to apply teaching techniques to a new topic. • Independent judgment: ability to synthesize from various sources. • Communication skills: clarity and appropriateness of language. • Learning skills: ability to read selected texts independently.

Criteria for the composition of the final grade

Quality of the presented material: 20/30
Presentation: 10/30

Exam language

Italiano/Inglese