BERGAMO
Overview
Date/time interval
Syllabus
Course Objectives
Upon completion of the course, students will possess foundational knowledge regarding the principles of Euclidean plane and solid geometry. Furthermore, students will have reviewed and deepened their understanding of the key topics related to the "Space and Shapes" (Spazio e Figure) domain, as addressed in kindergarten and primary school. The primary objective is to achieve a deep understanding and awareness of these topics from a pedagogical perspective. This foundation will enable an initial reflection on teaching and learning processes, which will be further expanded upon in mathematics courses during subsequent academic years. The National Guidelines for the First Cycle of Education (Indicazioni Nazionali) will serve as the core reference framework for the goals and targets to be achieved during the course, highlighting their strong connection with the learning objectives expected at the end of primary school. The laboratory hours accompanying the course will facilitate an initial, in-depth exploration of mathematics education. Specifically, these sessions will foster reflection on the intersections, overlaps, and mutual reinforcements between the geometric domain and the motor/kinesthetic domain, focusing on applications for both kindergarten and primary school settings.
Course Prerequisites
Teaching Methods
Methodologically, the course will be structured using the following instructional approaches:
Interactive lectures (combining direct instruction with classroom dialogue)
Geometry laboratory activities (hands-on practical learning)
Individual and group exercises
Individual and group work focusing on national regulatory documents (National Guidelines), textbooks, and related educational materials
An accompanying geometry laboratory
Assessment Methods
The examination for the Mathematics and Motor Education (Matematica e Motricità) course is held on a single date and covers both modules.
The written exam has a total duration of 1 hour and 30 minutes and consists of:
- 13 multiple-choice questions and 1 open-ended question for the Geometry module;
- 10 multiple-choice questions and 1 open-ended question for the Motor Education module.
The questions will focus on the course content and the critical-reflective skills that students are expected to have acquired, including through the proposed laboratory activities.
The points for the questions will be awarded as follows:
Open-ended questions: 4 points each
Multiple-choice questions:
Correct answer: 1 point
No answer provided: 0 points
Incorrect answer: -0.25 points
Based on the ECTS credits (CFU) assigned to the two modules, the maximum score is allocated as follows:
17 points for the Geometry module (minimum passing grade: 10/17)
14 points for the Motor Education module (minimum passing grade: 8/14)
This results in a maximum total score of 31/30.
The examination is considered passed only if the student achieves a passing grade in both modules. If this condition is met, the scores from the two modules are added together to determine the final grade.
Honors (cum laude) may be awarded at the instructors' discretion as an additional recognition for students who demonstrate excellent competencies in the open-ended questions and/or achieve the maximum full score of 31/30.
Contents
This section presents the historical evolution of geometry, its axiomatic structure, the existence of non-Euclidean geometries, and the role of geometry in the school curriculum, with particular reference to the National Guidelines (Indicazioni Nazionali).
The specific contents of the course will include:
2D Shapes: Knowing, comparing, and manipulating the definitions and properties (angles, axes of symmetry, diagonals, etc.) of primary two-dimensional shapes (triangles, quadrilaterals, regular polygons, circles). Representing them using appropriate tools (straightedge, set square, compass, protractor), dynamic geometry software (GeoGebra), and educational software for exploring geometric concepts (virtual GGBot).
Recognizing similar 2D shapes in various contexts and reproducing a given figure to a specified scale.
Determining the area of simple figures by decomposing them into elementary shapes (e.g., triangles) or by applying standard formulas.
Estimating the area of figures, including those with curved boundaries, by determining lower and upper bounds.
Understanding the number π, calculating the area of a circle and the circumference given the radius, and performing the inverse operations.
Understanding and applying the main geometric transformations and their invariants.
Representing points, segments, and shapes on the Cartesian coordinate system.
Calculating the surface area and volume of the most common 3D solids and estimating the measurements of everyday real-world objects.
All lectures will maintain a strong focus on geometry education for kindergarten and primary school settings, with prospective glimpses into lower secondary school.
Throughout the course, educational tools and strategies will be provided based on the approach of the "PerContare" guides. Furthermore, various pedagogical and practical aspects will be explored in depth during the accompanying laboratory sessions.
Online Resources
More information
The course will primarily rely on the lecture slides and materials provided by the instructor, alongside all additional resources made available on the course Moodle page.
Special emphasis will be placed on the geometry activities outlined in the teaching guides of the "PerContare" project (www.percontare.it).