Didactics of Geometry (first part)
A.Y. 2025/2026
Learning objectives
This class will deal with some basic questions on the learning and teaching of middle and high school mathematics, setting the historical and laboratory perspectives in the appropriate theoretical math education frameworks.
Expected learning outcomes
Basic elements of methodologies and technologies for the teaching of geometry useful in forming a perspective math teacher.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Historical and epistemological framework of Euclid's Elements.
Study of selected propositions from the Elements, with a focus on the first four books.
Historical and epistemological framework of plane geometry from Hilbert's perspective and comparison with the Euclidean approach.
Historical and epistemological introduction to analytic geometry, with a focus on conic sections and the problem of tangents.
Study of selected propositions from the Elements, with a focus on the first four books.
Historical and epistemological framework of plane geometry from Hilbert's perspective and comparison with the Euclidean approach.
Historical and epistemological introduction to analytic geometry, with a focus on conic sections and the problem of tangents.
Prerequisites for admission
Theoretical foundations of the Theory of Didactical Situations. Theoretical foundations of semiotics for Mathematics Education. Theoretical foundations related to multimodality and embodiment. Theoretical foundations related to the concepts of argumentation and proof in Mathematics Education
Teaching methods
The course is delivered through lectures (both traditional and interactive), laboratory activities with exercises, group work, and classroom discussions.
The materials for students—including the slides used during lectures, materials used in activities, and supplementary resources—are made available to students on MyAriel.
The materials for students—including the slides used during lectures, materials used in activities, and supplementary resources—are made available to students on MyAriel.
Teaching Resources
For the foundations in Mathematics Education:
D'Amore, B. (2023), Elementi di Didattica della Matematica. Bonomo.
Baccaglini-Frank, A., Di Martino, P., Natalini, R., & Rosolini, G. (2018). Didattica della Matematica. Mondadori Università.
For disciplinary content:
An edition of Euclid's Elements. Alternatively: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html (in English)
Hartshorne, B. (2010). Geometry: Euclid and Beyond. Springer.
D'Amore, B. (2023), Elementi di Didattica della Matematica. Bonomo.
Baccaglini-Frank, A., Di Martino, P., Natalini, R., & Rosolini, G. (2018). Didattica della Matematica. Mondadori Università.
For disciplinary content:
An edition of Euclid's Elements. Alternatively: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html (in English)
Hartshorne, B. (2010). Geometry: Euclid and Beyond. Springer.
Assessment methods and Criteria
Assessment of learning is carried out through a written exam, a possible practical lab test (required only for those who have not attended at least 70% of the lab hours), and an oral exam.
The written exam, lasting 2 hours, consists of exercises and problem-solving tasks related to the course topics. A list of the propositions from the first four books of Euclid and the axioms of Hilbert's plane geometry will be provided. Students must bring a ruler and compass.
The practical lab test with GeoGebra involves performing constructions/proofs using the GeoGebra software (attendance of at least 70% of the lab hours exempts students from the practical test).
The oral exam consists of the submission and discussion of a didactic project focused on the course topics, designed in accordance with the Indicazioni Nazionali (National Curriculum Guidelines) for lower secondary school (first cycle of education) or upper secondary school (second cycle of education).
The exam is considered passed if all components are passed: written and oral exams, or—if lab attendance is insufficient—written, practical lab, and oral exams.
The final grade is given out of 30 and will be communicated immediately at the end of the oral exam.
The goal of the written exam is to assess whether the student is able to use technical tools (primarily GeoGebra, but also a physical ruler and compass) to solve problems and carry out proofs within the domain of Euclidean plane geometry. Evaluation criteria include the correct and effective application of disciplinary knowledge gained during the course, the ability to connect theory and practice, the conceptual and logical accuracy of solutions, the efficiency of the problem-solving strategy, and the use of appropriate technical language.
The goal of the practical lab test is to assess whether the student has acquired the technical knowledge and skills necessary for effective use of GeoGebra in math lessons. Evaluation criteria refer to the knowledge of commands and the effective, autonomous use of the software in geometric constructions typical of Euclidean geometry. As these aspects are essential for effective participation in the lab, the practical test must be taken only in the case of insufficient attendance.
The goal of the oral exam is to assess the student's ability to design a teaching unit that coherently and effectively incorporates disciplinary content, context, and didactic and methodological perspectives from mathematics education research. This includes a structured and reflective approach to assessment. Evaluation criteria will refer to the coherence of the project (e.g., alignment between learning objectives and assessment methods), its adherence to the National Curriculum Guidelines, its suitability for the context, its feasibility in the classroom, the appropriateness of the theoretical and methodological frameworks used, and the effectiveness of their application in both the design and discussion phases. Independent thinking, communication skills, and the ability to learn through appropriate and engaging self-directed study for the classroom context will also be evaluated.
The written exam, lasting 2 hours, consists of exercises and problem-solving tasks related to the course topics. A list of the propositions from the first four books of Euclid and the axioms of Hilbert's plane geometry will be provided. Students must bring a ruler and compass.
The practical lab test with GeoGebra involves performing constructions/proofs using the GeoGebra software (attendance of at least 70% of the lab hours exempts students from the practical test).
The oral exam consists of the submission and discussion of a didactic project focused on the course topics, designed in accordance with the Indicazioni Nazionali (National Curriculum Guidelines) for lower secondary school (first cycle of education) or upper secondary school (second cycle of education).
The exam is considered passed if all components are passed: written and oral exams, or—if lab attendance is insufficient—written, practical lab, and oral exams.
The final grade is given out of 30 and will be communicated immediately at the end of the oral exam.
The goal of the written exam is to assess whether the student is able to use technical tools (primarily GeoGebra, but also a physical ruler and compass) to solve problems and carry out proofs within the domain of Euclidean plane geometry. Evaluation criteria include the correct and effective application of disciplinary knowledge gained during the course, the ability to connect theory and practice, the conceptual and logical accuracy of solutions, the efficiency of the problem-solving strategy, and the use of appropriate technical language.
The goal of the practical lab test is to assess whether the student has acquired the technical knowledge and skills necessary for effective use of GeoGebra in math lessons. Evaluation criteria refer to the knowledge of commands and the effective, autonomous use of the software in geometric constructions typical of Euclidean geometry. As these aspects are essential for effective participation in the lab, the practical test must be taken only in the case of insufficient attendance.
The goal of the oral exam is to assess the student's ability to design a teaching unit that coherently and effectively incorporates disciplinary content, context, and didactic and methodological perspectives from mathematics education research. This includes a structured and reflective approach to assessment. Evaluation criteria will refer to the coherence of the project (e.g., alignment between learning objectives and assessment methods), its adherence to the National Curriculum Guidelines, its suitability for the context, its feasibility in the classroom, the appropriateness of the theoretical and methodological frameworks used, and the effectiveness of their application in both the design and discussion phases. Independent thinking, communication skills, and the ability to learn through appropriate and engaging self-directed study for the classroom context will also be evaluated.
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Laboratories: 24 hours
Lessons: 28 hours
Lessons: 28 hours
Professors:
Asenova Miglena, Rizzo Ottavio Giulio
Professor(s)