BERGAMO
Overview
Date/time interval
Syllabus
Course Objectives
At the end of the course, students will have acquired basic knowledge of the fundamentals of Euclidean geometry in two and three dimensions. At the end of the course, students will have revisited and explored in greater depth the main topics related to space and shapes that are covered in primary school. The aim is therefore to achieve knowledge and awareness of these contents from an educational point of view. This should allow for an initial reflection on the teaching-learning processes that will be explored in depth in mathematics courses in subsequent years. The National Guidelines for the first cycle of education serve as a reference in relation to the objectives and goals to be achieved in the course and their close link with the objectives and goals at the end of primary school. The laboratory hours attached to the course, offered in collaboration with the motor skills module teacher, will allow for an initial in-depth study of mathematics teaching, encouraging reflection on the points of contact/overlap/reinforcement between geometry and motor skills in both nursery and primary school.
Course Prerequisites
Foundational notions of geometry and manipulation of algebraic formulas at high school level.
Teaching Methods
The course will be structured methodologically with:
- Lectures and discussions
- Geometry workshop activities
- Individual and group exercises
- Individual and group work on regulatory documents (National Guidelines), textbooks, etc.
- Ancillary geometry and motor skills workshop to be held during motor skills lessons.
Assessment Methods
The Geometry and Motricity exam is held on a single date and includes both modules.
The written test with a total duration of 1h 30' consists of:
- 13 multiple-choice and 1 open-ended geometry question;
- 10 multiple-choice and 1 open-ended question of motricity.
The questions will cover the course content and the reflective-critical skills that it is hoped students will also achieve through the proposed laboratory activities. Open-ended questions will be valued at 4 points each, while multiple-choice questions will be valued at 1 point. Depending on the CFUs of the two modules, the score will therefore be distributed as follows: 17 points for the geometry exam (sufficient evaluation equal to 10/17) and 14 points for the motricity exam (sufficient evaluation equal to 8/14) for a total of 31/30ths. The exam will be considered passed only if the grades for both modules are sufficient, and, in that case, the two grades will be added together.
Laude will be awarded, at the discretion of the teachers, as an additional point for those who show excellent proficiency in the open-ended questions and/or achieve the full mark of 31/thirty.
Contents
Introduction to geometry: presentation of historical aspects of the evolution of geometry, axiomatic structure, existence of non-Euclidean geometries, presence of geometry in the school curriculum with particular reference to the National Guidelines.
The specific contents of the course will be as follows:
- Knowing, comparing and manipulating definitions and properties (angles, axes of symmetry, diagonals, etc.) of the main plane figures (triangles, quadrilaterals, regular polygons, circles) and representing them using appropriate tools (ruler, set square, compass, protractor), dynamic geometry software (GeoGebra) and software for exploring geometric concepts (virtual GGBot)
- Recognise similar plane figures in various contexts and reproduce an assigned figure to scale.
- Determine the area of simple figures by breaking them down into elementary figures, such as triangles, or by using the most common formulas.
- Estimate the area of a figure bounded by curved lines, both by default and by excess.
- Know the number π, calculate the area of a circle and the length of its circumference, knowing the radius, and vice versa.
- Know and use the main geometric transformations and their invariants.
- Represent points, segments and figures on the Cartesian plane.
- Introduction to spatial geometry: calculate the area and volume of the most common solid figures and give estimates of everyday objects.
An introduction to the teaching of geometry will be provided in all lessons and will be explored, with PerContare guide in more depth in the workshop attached to the course.
Online Resources
More information
The course will be mainly based on the slides and handouts provided by the professor and other materials uploaded to the moodle page.
Possible further study texts:
Insegnare e apprendere matematica nella scuola dell'infanzia e primaria. Sabena, Ferri, Martignone & Robotti, ISBN: 9788861845626, 2019, Mondadori Università
Matematica per scienze della formazione primaria, Cazzola, 2017, Carrocci Editore.
ATTIVAZIONE - Laboratori di matematica per la scuola del primo ciclo. Castellini, Giberti, Lemmo & Maffia, 2023, Libreria Universitaria