Lectures, group exercises, and in-class assessments.
BASIC MATHEMATICS FOR PRIMARY AND CHILDHOOD SCHOOL
Academic Year 2025/2026 - Teacher: LUCIA MARIA MARINOExpected Learning Outcomes
The course is aimed at enabling students to acquire fundamental knowledge of arithmetic, elementary algebra, plane and solid geometry, logic, and probability, which are essential for approaching the study of mathematics and its applications with awareness.
In particular, the course intends to provide both theoretical and practical tools for understanding and applying concepts such as equations and systems, Cartesian representations, geometric properties, and logical reasoning.
Specifically, the expected learning objectives are:
DD1. Knowledge of mathematical language and the deductive method; mastery of arithmetic tools (number systems, powers, roots, fractions, and decimals) and the ability to use literal calculus to solve equations and first-degree systems.
DD2. Ability to determine areas and volumes of the main geometric figures, using properties, theorems (in particular the Pythagorean Theorem), and elementary constructions (including solids of rotation). Ability to recognize and describe basic properties of plane figures.
DD3. Students will be encouraged to independently deepen their knowledge and practice exercises on the topics covered. By the end of the course, they will be able to autonomously develop solutions to the main problems addressed in the course, selecting the most appropriate strategy based on the results learned. Constructive peer-to-peer discussion and continuous interaction with the instructor will also be strongly encouraged so that students can critically monitor their own learning process.
DD4. Attendance of lectures and reading of recommended texts will help students become familiar with the rigor of mathematical language and acquire the specific terminology of linear algebra and geometry. Through constant interaction with the instructor, students will learn to communicate the knowledge acquired with rigor and clarity, both orally and in writing. By the end of the course, students will have understood that mathematical language is a valuable tool for clear communication in scientific contexts.
DD5. The course aims to provide students with the forma mentis and logical rigor necessary for the teaching of mathematics.
Course Structure
Required Prerequisites
No specific prerequisites are required for attending the course.
Attendance of Lessons
Attendance at lectures is not mandatory, but it is strongly recommended for passing the exam.
Detailed Course Content
Elements of Logic and Set Theory:
Elements of logic. Propositional logic. Elements of set theory. Operations on sets. Operations and algebraic structures.
Algebra and Arithmetic:
Number sets (natural numbers, integers): historical aspects, notes on constructions, elementary properties, division and remainder classes. Rational numbers (fractions), use and manipulation, proportions, percentages. Real numbers. Literal calculus.
Probability and Statistics:
Basic concepts of probability (finite case). Applications and problem solving. Elementary notions of statistics.
Euclidean Geometry:
In the plane: Euclid’s postulates (overview), polygons (general properties, convexity and concavity, angles). Triangles (criteria of congruence, Pythagoras’ Theorem), notable quadrilaterals and their properties. Regular polygons. The circle. Rigid transformations of the plane, symmetries of figures.
In space: Polyhedra, pyramids and prisms. Regular polyhedra. Solids of revolution.
Analytic Geometry:
Use of Cartesian coordinates on the line, in the plane, and in three-dimensional space. The Cartesian plane: equations of lines (parallelism, perpendicularity), graphs. Cartesian coordinates in space (introduction).
Textbook Information
The reference textbook for the course is:
A. Gimigliano, L. Peggion: Elementi di Matematica, UTET Università (Novara), 2022 (Second Edition).
The presentation of the topics in this textbook follows the same structure adopted in the course; therefore, its use is strongly recommended (both for attending and non-attending students).
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Elements of logic. Propositional logic. Elements of set theory. Operations on sets. Operations and algebraic structures. | Lecturer’s notes and textbook, Chapter 1. |
| 2 | Number sets (natural and integer numbers): historical aspects, notes on constructions, elementary properties, division and remainder classes; rational numbers (fractions), use and manipulation, proportions, percentages; real numbers; literal calculus. | Lecturer’s notes and textbook: Chapters 2–3-4-5--6. |
| 3 | Basic elements of probability (finite case), applications and problem solving, and elementary notions of statistics.E | Lecturer’s notes and textbook: Chapter 7. |
| 4 | Eucidean Geometry. In the plane: Euclid’s postulates (overview); polygons (general properties, convexity and concavity, angles); triangles (criteria of congruence, Pythagoras’ Theorem); notable quadrilaterals and their properties; regular polygons; the circle; rigid transformations of the plane; symmetries of figures. In space: polyhedra, pyramids, and prisms; regular polyhedra; solids of revolution. | Lecturer’s notes and textbook: Chapters 8–9. |
| 5 | Analytic Geometry. Use of Cartesian coordinates on the line, in the plane, and in three-dimensional space; the Cartesian plane: equations of lines (parallelism, perpendicularity), graphs; Cartesian coordinates in space (introduction). | Lecturer’s notes and textbook: Chapter 10. |
Learning Assessment
Learning Assessment Procedures
The exam consists of two tests (the first called Aritmetica Zero and the second called Written Exam) plus an optional Oral Exam.
Aritmetica Zero: This test assesses arithmetic calculation skills that should have been acquired during compulsory schooling. The use of calculators is not allowed. The test must be passed with a positive result (score greater than or equal to 21/30). Only passing is required; the score does not contribute to the final grade. The duration of the test is 30 minutes.
Failure to pass Aritmetica Zero before the date of the written exam results in non-admittance to the written exam. Aritmetica Zero is valid for one academic year. Therefore, if passed in the academic year 202x/2y, it is valid until 30/09/202y.
Written Exam: The written exam is passed with a minimum score of 15/30 and consists of exercises similar to those seen during lessons, as well as more theoretical questions. The duration of the exam is 2 hours, during which the use of textbooks, notes, or handouts is not allowed. Calculators are also not permitted.
Oral Exam: The oral exam is an interview on the course topics (both those covered in class and those present in textbooks, see the syllabus) lasting approximately 20 minutes.
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The oral exam is mandatory for students who obtain a score in the written exam between 15 and 20 (inclusive).
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The oral exam must also be taken in all cases where it is requested by either the instructor or the student.
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For students who obtain a score in the written exam greater than or equal to 27, the oral exam is required to achieve a score higher than 27 (it is understood that an unsatisfactory oral exam can lower the final grade). In practice, if a student scores 28 in the written exam, they may choose to record the grade without taking the oral exam; in this case, a score of 27 will be registered. Alternatively, the student can choose to take the oral exam: depending on its outcome, the score of 28 may be lowered, confirmed, or increased.
Grading Criteria:
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NOT PASSED: the student demonstrates a poor and fragmented knowledge of the subject, shows serious misunderstandings, and is unable to present the subject matter acceptably.
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18-21: the student demonstrates limited knowledge and a basic understanding of the subject, presenting in an unclear and imprecise manner.
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22-24: the student demonstrates acceptable knowledge and an essential understanding of the subject, presenting correctly but not fully structured.
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25-27: the student demonstrates broad knowledge and an adequate understanding of the subject, presenting correctly but not completely.
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28-29: the student demonstrates in-depth knowledge and a solid understanding of the subject, presenting in a clear and structured manner.
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30-30 cum laude: the student demonstrates complete and detailed knowledge and an excellent understanding of the subject, presenting in a clear and structured manner.
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Information for students with disabilities and/or DSA
To guarantee equal opportunities and in compliance with current regulations, interested students can request a personal meeting with the instructor to plan any compensatory and/or dispensatory measures, based on the learning objectives and specific needs.
It is also possible to contact the CInAP (Center for Active and Participatory Integration – Services for Disabilities and/or DSA) departmental coordinator.
Examples of frequently asked questions and / or exercises
Targeted exercises on the properties of operations, powers, roots, and literal calculus; arithmetic problems; problems in plane and solid Euclidean geometry; exercises on the Cartesian plane; exercises on sets and their operations; exercises on probability and logic.