Didactics of Geometry

Assessment consists of a written examination, an optional practical laboratory test (mandatory only for students who have attended less than 70% of the laboratory sessions), and an oral examination.

The written examination lasts two hours and consists of exercises and problem-solving tasks covering the topics addressed during the course. Students will be provided with a list of the propositions contained in the first four books of Euclid's Elements and the axioms of Hilbert's plane geometry. Students are required to bring a ruler and a compass.

The practical laboratory test with GeoGebra consists of carrying out geometric constructions and proofs using the GeoGebra software. Students who attend at least 70% of the laboratory sessions are exempt from this practical test.

The oral examination consists of the submission and discussion of a teaching unit focused on the topics addressed during the course, designed in accordance with the Italian National Guidelines for the first cycle of education (lower secondary school) or the second cycle of education (upper secondary school).

The course examination is considered passed only if all required components have been successfully completed (written and oral examinations or, for students who have not met the laboratory attendance requirement, the written examination, the practical laboratory test, and the oral examination).

The final grade is awarded on a 30-point scale and will be communicated immediately after the oral examination.

The purpose of the written examination is to assess whether students are able to use technical tools (primarily the GeoGebra software, but also physical instruments such as a ruler and compass) to solve problems, construct mathematical proofs in Euclidean plane geometry, and address tasks related to the historical introduction of analytic geometry. Assessment criteria include the ability to apply the disciplinary knowledge acquired during the course accurately and effectively by connecting theory and practice, the conceptual and logical correctness of the solutions, the efficiency of the solution strategy, and the appropriate use of technical mathematical language.

The practical laboratory test aims to assess whether students have acquired the technical knowledge and skills required to use GeoGebra effectively in mathematics teaching. Assessment criteria include knowledge of the software commands and the ability to use the software independently and effectively to produce geometric constructions typical of Euclidean geometry. Since these skills are essential for meaningful participation in the laboratory activities, the practical test is required only for students who have not fulfilled the minimum laboratory attendance requirement.

The oral examination aims to assess students' ability to design a teaching unit that integrates disciplinary content coherently and effectively with the educational context and with theoretical and methodological perspectives derived from research in mathematics education, including a structured and reflective approach to assessment. Assessment criteria include the overall coherence of the teaching unit (e.g., the alignment between learning objectives and assessment methods), its consistency with the Italian National Guidelines, its suitability for the intended educational context, its feasibility for classroom implementation, the appropriateness of the theoretical and methodological frameworks adopted, and the effectiveness with which these are employed in both the design and discussion of the project. Students' autonomy of judgement, communication skills, and capacity for independent learning will also be assessed through their ability to identify and incorporate appropriate autonomous in-depth studies that enrich the proposed teaching unit.