Menù principale
B024296 - BASIC MATHEMATICS(I)
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2022-23
Coorte 2022 - 5-years Single Cycle Degree in PRIMARY TEACHER EDUCATION
Course year
First year - First Semester
Belonging Department
Education, Languages, Intercultures, Literatures and Psychology (FORLILPSI)
Course Type
Single education field course
Scientific Area
MAT/03 - GEOMETRY
Credits
6
Teaching Hours
36
Teaching Term
12/09/2022 ⇒ 02/12/2022
Attendance required
No
Type of Evaluation
Final Grade
Course Content
show
Course program
show
Lectureship
- Last names A-L DOLCETTI ALBERTO
- Last names M-Z PEDICONI FRANCESCO
Teaching Language - Last names A-L
Italian
Teaching Language - Last names M-Z
Italian
Course Content - Last names A-L
Review on the concepts and on the language of elementary arithmetic and geometry.
The structures of the systems of natural numbers, of integers, of rationals and basic facts or real numbers.
Basic topics of geometry in the plane and in the space.
The structures of the systems of natural numbers, of integers, of rationals and basic facts or real numbers.
Basic topics of geometry in the plane and in the space.
Course Content - Last names M-Z
Basics of Logic and Naive Set Theory.
Basics of Euclidean Geometry in 2 and 3 dimensions.
Basics of Arithmetic.
Basics of Euclidean Geometry in 2 and 3 dimensions.
Basics of Arithmetic.
Suggested readings - Last names A-L (Search our library's catalogue)
Main reference:
GIMIGLIANO A., PEGGION L., Elementi di matematica, Seconda edizione, UTET – De Agostini, Novara, 2021.
Additional arguments from:
SABENA C., FERRI F., MARTIGNONE F., ROBOTTI E., Insegnare e apprendere matematica nella scuola dell'infanzia e primaria, Mondadori Università, Firenze, 2019.
Notes provided by the teacher.
A complete and updated bibliography will be indicated at the beginning of the course.
GIMIGLIANO A., PEGGION L., Elementi di matematica, Seconda edizione, UTET – De Agostini, Novara, 2021.
Additional arguments from:
SABENA C., FERRI F., MARTIGNONE F., ROBOTTI E., Insegnare e apprendere matematica nella scuola dell'infanzia e primaria, Mondadori Università, Firenze, 2019.
Notes provided by the teacher.
A complete and updated bibliography will be indicated at the beginning of the course.
Suggested readings - Last names M-Z (Search our library's catalogue)
(Main textbook) A. Gimigliano, L. Peggion, Elementi di Matematica, Seconda edizione, UTET Università - De Agostini, Novara, 2021
(Further reference) C. Sabena, F. Ferri, F. Martignone, E. Robotti, Insegnare e apprendere matematica nella scuola dell'infanzia e primaria, Mondadori Università, Firenze, 2019.
(Further reference) C. Sabena, F. Ferri, F. Martignone, E. Robotti, Insegnare e apprendere matematica nella scuola dell'infanzia e primaria, Mondadori Università, Firenze, 2019.
Learning Objectives - Last names A-L
- developing a positive attitude towards mathematics, identifying and overcoming misconceptions in a conscious way;
- developing awareness of the importance of mathematical education in the formation of girls and boys and for a development of their aware citizenship in a complex society;
- developing a correct, original and creative mathematical thinking regarding the topics of the course and in particular in view of the effects on teaching-learning processes in the age range 3-11 years;
- understanding some results of current research on mathematics education relating to the development of basic mathematical concepts in the age range 0-11 years;
- acquiring the basic knowledge and the skills to understand mathematical concepts and to know how to use and to apply them in solving exercises and problems and in proposing simple mathematical models for problem-situations at various levels of complexity;
- acquiring competences in producing correct argumentation, formulating hypotheses, discussing the assumed hypotheses and drawing consequences, and in recognizing the validity of an argument;
- understanding the value of arguing, conjecturing, posing and solving problems both individually and in a relational context, also for the purposes of teaching-learning implications;
- being able to organize basic mathematical knowledge in a hypothetical-deductive way and being able to place hierarchically definitions, sufficient conditions, necessary conditions, characterizations, properties;
- being able to distinguish between definitions and descriptions of mathematical objects in relation to mathematical knowledge in the age range 3-11 years;
- acquiring communication skills, using mathematical language correctly, both in discussion with peers and simulating teaching-learning situations;
- showing good ability to learn autonomously and to deepen the topics developed in the course.
- developing awareness of the importance of mathematical education in the formation of girls and boys and for a development of their aware citizenship in a complex society;
- developing a correct, original and creative mathematical thinking regarding the topics of the course and in particular in view of the effects on teaching-learning processes in the age range 3-11 years;
- understanding some results of current research on mathematics education relating to the development of basic mathematical concepts in the age range 0-11 years;
- acquiring the basic knowledge and the skills to understand mathematical concepts and to know how to use and to apply them in solving exercises and problems and in proposing simple mathematical models for problem-situations at various levels of complexity;
- acquiring competences in producing correct argumentation, formulating hypotheses, discussing the assumed hypotheses and drawing consequences, and in recognizing the validity of an argument;
- understanding the value of arguing, conjecturing, posing and solving problems both individually and in a relational context, also for the purposes of teaching-learning implications;
- being able to organize basic mathematical knowledge in a hypothetical-deductive way and being able to place hierarchically definitions, sufficient conditions, necessary conditions, characterizations, properties;
- being able to distinguish between definitions and descriptions of mathematical objects in relation to mathematical knowledge in the age range 3-11 years;
- acquiring communication skills, using mathematical language correctly, both in discussion with peers and simulating teaching-learning situations;
- showing good ability to learn autonomously and to deepen the topics developed in the course.
Learning Objectives - Last names M-Z
Providing basic knowledge of Logic, Euclidean Geometry and Arithmetic. Developing logical, argumentative, communicative and autonomous learning skills, also for the purpose of teaching activities.
Prerequisites - Last names A-L
Fundamental prerequisites for understanding the topics developed in the course consist of the basic conceptual and procedural knowledge and the skills usually acquired in the pre-university education, when faced with seriousness and commitment.
Prerequisites - Last names M-Z
Basic concepts of mathematics from secondary school.
Teaching Methods - Last names A-L
Ex cathedra lecture with exercises in the classroom. During the lessons, dialogue is encouraged and all personal contributions from students are welcome; the teacher may ask students to express explicit suggestions and considerations on the topics and to try to solve exercises and to suggest models for simple problem-situations.
By means of student reception, it will be possible to discuss and deepen in a personalized way topics chosen by each student and answer any questions.
By means of student reception, it will be possible to discuss and deepen in a personalized way topics chosen by each student and answer any questions.
Teaching Methods - Last names M-Z
Lessons and exercise hours. Student reception.
Further information - Last names A-L
Although not mandatory, class attendance is strongly recommended, because of the relevance of relational aspects, both among peers and with the teacher, in teaching-learning processes, in particular in order to have the possibility of identifying misconceptions, whose overcoming often requires long times and the guidance of the teacher and in order to build a positive attitude towards the discipline.
The class takes advantage of the MOODLE platform (with mandatory registration for all) and which can be particularly useful for students who have serious and motivated difficulties in attending regularly classes.
Attendance at the student reception is strongly encouraged for any discussion on topics and on exercises / problems, faced in teaching, or for any autonomous personal in-depth study.
The class takes advantage of the MOODLE platform (with mandatory registration for all) and which can be particularly useful for students who have serious and motivated difficulties in attending regularly classes.
Attendance at the student reception is strongly encouraged for any discussion on topics and on exercises / problems, faced in teaching, or for any autonomous personal in-depth study.
Further information - Last names M-Z
Class attendance is strongly recommended.
Students are strongly advised to use the e-learning platform moodle by UniFi.
Students are strongly advised to use the e-learning platform moodle by UniFi.
Type of Assessment - Last names A-L
Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the skills verified in the two modalities, all the skills and the basic knowledge of the topics addressed are mainly verified in the written exam, in particular those of an operational and applicative type useful to solve problems. All competences relating to linguistic and communicative skills and the ability to hierarchically structure the mathematical knowledge learned are mainly verified in the oral exam that will allow to enhance the originality and autonomy of mathematical thinking.
In order to pass the exam, it is necessary at every step to be able to show the acquisition of all the knowledge on elementary contents and basic skills in order to execute the fundamental algorithms, object of teaching-learning in primary school.
After two unsuccessful exam enrollments and before a third enrollment in the same academic year, each student is strongly advised to come to an interview with the teacher to assess the difficulties encountered in studying and passing the exam.
Although it is impossible to make a strict separation between the skills verified in the two modalities, all the skills and the basic knowledge of the topics addressed are mainly verified in the written exam, in particular those of an operational and applicative type useful to solve problems. All competences relating to linguistic and communicative skills and the ability to hierarchically structure the mathematical knowledge learned are mainly verified in the oral exam that will allow to enhance the originality and autonomy of mathematical thinking.
In order to pass the exam, it is necessary at every step to be able to show the acquisition of all the knowledge on elementary contents and basic skills in order to execute the fundamental algorithms, object of teaching-learning in primary school.
After two unsuccessful exam enrollments and before a third enrollment in the same academic year, each student is strongly advised to come to an interview with the teacher to assess the difficulties encountered in studying and passing the exam.
Type of Assessment - Last names M-Z
Written and oral exam.
Course program - Last names A-L
The development of some basic mathematical concepts in the age range 0-11 years.
Review of the concepts and on the language at the basis of elementary arithmetic and geometry.
Numerical structures of natural numbers, of integers, of rationals and basic arguments on real numers: significant problem-situations, theoretical aspects, analysis and comparison of algorithms of computation.
Basic themes of plane and space geometry and geometric transformations: geometry as a theoretical organization and as a representative model.
Review of the concepts and on the language at the basis of elementary arithmetic and geometry.
Numerical structures of natural numbers, of integers, of rationals and basic arguments on real numers: significant problem-situations, theoretical aspects, analysis and comparison of algorithms of computation.
Basic themes of plane and space geometry and geometric transformations: geometry as a theoretical organization and as a representative model.
Course program - Last names M-Z
PART I
- Elements of Logic (1): logic statements; connectives and quantifiers; basics of Naive Set Theory; set operations.
- Plane Euclidean Geometry: angles, convex polygons, circles; Pythagorean Theorem.
- Solid Euclidean Geometry: planes and straight lines in the space; convex polyhedra; solids of revolution.
PART II
- Elements of Logic (2): functions and relations between sets; binary operations and algebraic structures.
- Natural numbers: Peano's axioms; Euclidean division; prime numbers, GCD and lcm, divisibility criteria.
- Other numerical sets: integers; rational numbers; real numbers.
- Elements of Logic (1): logic statements; connectives and quantifiers; basics of Naive Set Theory; set operations.
- Plane Euclidean Geometry: angles, convex polygons, circles; Pythagorean Theorem.
- Solid Euclidean Geometry: planes and straight lines in the space; convex polyhedra; solids of revolution.
PART II
- Elements of Logic (2): functions and relations between sets; binary operations and algebraic structures.
- Natural numbers: Peano's axioms; Euclidean division; prime numbers, GCD and lcm, divisibility criteria.
- Other numerical sets: integers; rational numbers; real numbers.