Francesco Saverio TORTORIELLO | COMPLEMENTARY MATHEMATICS II

cod. 0512300031

COMPLEMENTARY MATHEMATICS II

	0512300031
	DEPARTMENT OF MATHEMATICS
	EQF6
	MATHEMATICS
	2024/2025

PERCORSO SHARED STUDY PATHWAY

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2018
	SPRING SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/04	6	48	LESSONS	OPTIONAL SUBJECTS

PROFESSORS

FRANCESCO SAVERIO TORTORIELLO T Curriculum

	Objectives
	MIGLIORARE LA PREPARAZIONE IN CAMPO MATEMATICO/GEOMETRICO DEGLI STUDENTI ATTRAVERSO LO STUDIO DI QUESTIONI DI BASE SU CUI È COSTRUITA LA MATEMATICA IN VISTA DEL SUO INSEGNAMENTO NELLA SCUOLA PRIMARIA. CONOSCENZA E CAPACITÀ DI COMPRENSIONE: -CONOSCENZE DI BASE DI CARATTERE PREVALENTEMENTE GEOMETRICO; -CONOSCENZA DELLE PRINCIPALI RICERCHE IN DIDATTICA DELLA MATEMATICA IN TALE AMBITO. CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE: -SVILUPPARE NEGLI STUDENTI CAPACITÀ NELL’AFFRONTARE PROBLEMI SIGNIFICATIVI PER L’INSEGNAMENTO DELLA GEOMETRIA E DI LIBERARSI DALLE NUMEROSE MISCONCEZIONI CHE NE INQUINANO LA FORMAZIONE

MIGLIORARE LA PREPARAZIONE IN CAMPO MATEMATICO/GEOMETRICO DEGLI STUDENTI ATTRAVERSO LO STUDIO DI QUESTIONI DI BASE SU CUI È COSTRUITA LA MATEMATICA IN VISTA DEL SUO INSEGNAMENTO NELLA SCUOLA PRIMARIA.
CONOSCENZA E CAPACITÀ DI COMPRENSIONE:
-CONOSCENZE DI BASE DI CARATTERE PREVALENTEMENTE GEOMETRICO;
-CONOSCENZA DELLE PRINCIPALI RICERCHE IN DIDATTICA DELLA MATEMATICA IN TALE AMBITO.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE:
-SVILUPPARE NEGLI STUDENTI CAPACITÀ NELL’AFFRONTARE PROBLEMI SIGNIFICATIVI PER L’INSEGNAMENTO DELLA GEOMETRIA E DI LIBERARSI DALLE NUMEROSE MISCONCEZIONI CHE NE INQUINANO LA FORMAZIONE

	Prerequisites
	YOU NEED ONLY BE AWARE OF BASIC CONCEPTS OF ALGEBRA, GEOMETRY AND ANALYSIS

	Contents
	NUMBERS NATURAL NUMBERS AND THEIR REPRESENTATION IN BASE TEN. ADDITION AND SUBTRACTION BETWEEN NATURAL NUMBERS. OPERATIONS WITH NATURAL NUMBERS. OWNERSHIP OF OPERATIONS. POWERS AND PROPERTIES. THE PRIME NUMBERS. EUCLID'S THEOREM ON PRIME NUMBERS; FERMAT'S CONJECTURE; PERFECT NUMBERS; THE FRIENDLY NUMBERS. MULTIPLICATION AND DIVISION BETWEEN NATURAL NUMBERS. EUCLIDEAN DIVISION ALGORITHM; MCD AND MCM; DECIMAL NUMBERS AND FRACTIONS. EQUIVALENT FRACTIONS. POSITIONAL WRITING OF NATURAL AND DECIMAL NUMBERS. OPERATIONS BETWEEN DECIMAL NUMBERS. OWNERSHIP OF OPERATIONS. MEANING OF BRACKETS IN SEQUENCE OF OPERATIONS. PROPERTIES OF NATURAL NUMBERS: PREVIOUS NEXT, ODD EVEN, DOUBLE, HALF ...). OPERATIONS WITH WHOLE NUMBERS. PRIME NUMBERS. MULTIPLES AND DIVIDERS. SPACE AND FIGURES INTRODUCTION TO EUCLIDEAN GEOMETRY. EUCLID'S ELEMENTS. DIVISION OF BOOKS. EUCLID AND THE ELEMENTS. THE POSTULATES, THE AXIOMS, ANGLES OPPOSITE THE VERTEX; CONGRUENCE CRITERIA, THE PONS ASINORUM THEOREM, INVERSE OF THE PYTHAGOREAN THEOREM. PROPERTIES OF THE ISOSCELES TRIANGLE. NOTABLE POINTS OF TRIANGLES; CENTER, CENTER OF GRAVITY, CIRCLE CENTER; EULER'S THEOREM; THE CIRCUMFERENCE, LENGTH OF AN ARC OF CIRCUMFERENCE; CIRCULAR SECTOR AREA; ROPE THEOREM; TANGENT THEOREM; SECANT AND TANGENT THEOREM; SECANT THEOREM; CORNERS AT THE CENTER AND CORNERS AT THE CIRCUMFERENCE. EQUIVALENCE BETWEEN FIGURES. COMPOSITION AND DECOMPOSITION OF FIGURES. ELEMENTS OF SIMPLE FIGURES OF SPACE (VERTICES, EDGES, ...). UNIT OF MEASURES OF LENGTHS, AREAS AND VOLUMES. PERIMETER OF POLYGONS. POLYGON AREAS. SUM OF THE ANGLES OF A TRIANGLE AND POLYGONS. PYTHAGOREAN THEOREM. TRANSLATIONS, ROTATIONS AND SYMMETRIES. SCALE REPRODUCTIONS: EXTENSIONS AND REDUCTIONS. LENGTH OF THE CIRCUMFERENCE AND AREA OF THE CIRCLE. EUCLID'S THEOREMS. THALES' THEOREM, THE SIMILARITY CRITERIA. SOLVING GEOMETRIC PROBLEMS WITH FIRST AND SECOND DEGREE EQUATIONS ARTIFACTS USE OF GEOGEBRA PRIM FOR THE STUDY OF GEOMETRY. USE OF NEPERO STICKS FOR MULTIPLICATION RELATIONSHIPS AND FUNCTIONS INTRODUCTION TO ANALYTICAL GEOMETRY. DISTANCE BETWEEN TWO POINTS, MIDPOINT OF A SEGMENT, CENTER OF GRAVITY OF A TRIANGLE; AREAS AND PERIMETERS. THE STRAIGHT LINE IN THE CARTESIAN PLANE; STRAIGHT FOR TWO POINTS AND STRAIGHT FOR A KNOWN POINT THE ANGULAR COEFFICIENT; PARALLEL LINES AND PERPENDICULAR LINES. INTERSECTION OF STRAIGHT LINES. LINEAR SYSTEMS: SUBSTITUTION METHOD. THE CIRCUMFERENCE IN THE CARTESIAN PLANE; CIRCUMFERENCE FOR THREE POINTS; STRAIGHT LINES AND CIRCUMFERENCES. NOTIONS OF MATHEMATICAL LOGIC: SETS AND QUANTIFIERS, REPRESENTATIONS OF A SET, SUBSETS, INTERSECTIONS OF SETS, UNION; MEASUREMENT, DATA AND FORECASTS ELEMENTS OF COMBINATORIAL CALCULATION: SIMPLE DISPOSITIONS SIMPLE PERMUTATIONS AND WITH REPETITION; THE TARTAGLIA TRIANGLE. EXAMPLES OF DIDACTIC ACTIVITIES FOR PRIMARY SCHOOL WITH COMBINATORICS

Contents

NUMBERS
NATURAL NUMBERS AND THEIR REPRESENTATION IN BASE TEN. ADDITION AND SUBTRACTION BETWEEN NATURAL NUMBERS. OPERATIONS WITH NATURAL NUMBERS. OWNERSHIP OF OPERATIONS. POWERS AND PROPERTIES. THE PRIME NUMBERS. EUCLID'S THEOREM ON PRIME NUMBERS; FERMAT'S CONJECTURE; PERFECT NUMBERS; THE FRIENDLY NUMBERS. MULTIPLICATION AND DIVISION BETWEEN NATURAL NUMBERS. EUCLIDEAN DIVISION ALGORITHM; MCD AND MCM; DECIMAL NUMBERS AND FRACTIONS. EQUIVALENT FRACTIONS. POSITIONAL WRITING OF NATURAL AND DECIMAL NUMBERS. OPERATIONS BETWEEN DECIMAL NUMBERS. OWNERSHIP OF OPERATIONS. MEANING OF BRACKETS IN SEQUENCE OF OPERATIONS. PROPERTIES OF NATURAL NUMBERS: PREVIOUS NEXT, ODD EVEN, DOUBLE, HALF ...). OPERATIONS WITH WHOLE NUMBERS. PRIME NUMBERS. MULTIPLES AND DIVIDERS.
SPACE AND FIGURES
INTRODUCTION TO EUCLIDEAN GEOMETRY. EUCLID'S ELEMENTS. DIVISION OF BOOKS. EUCLID AND THE ELEMENTS. THE POSTULATES, THE AXIOMS, ANGLES OPPOSITE THE VERTEX; CONGRUENCE CRITERIA, THE PONS ASINORUM THEOREM, INVERSE OF THE PYTHAGOREAN THEOREM. PROPERTIES OF THE ISOSCELES TRIANGLE. NOTABLE POINTS OF TRIANGLES; CENTER, CENTER OF GRAVITY, CIRCLE CENTER; EULER'S THEOREM; THE CIRCUMFERENCE, LENGTH OF AN ARC OF CIRCUMFERENCE; CIRCULAR SECTOR AREA; ROPE THEOREM; TANGENT THEOREM; SECANT AND TANGENT THEOREM; SECANT THEOREM; CORNERS AT THE CENTER AND CORNERS AT THE CIRCUMFERENCE. EQUIVALENCE BETWEEN FIGURES. COMPOSITION AND DECOMPOSITION OF FIGURES. ELEMENTS OF SIMPLE FIGURES OF SPACE (VERTICES, EDGES, ...). UNIT OF MEASURES OF LENGTHS, AREAS AND VOLUMES. PERIMETER OF POLYGONS. POLYGON AREAS. SUM OF THE ANGLES OF A TRIANGLE AND POLYGONS. PYTHAGOREAN THEOREM. TRANSLATIONS, ROTATIONS AND SYMMETRIES. SCALE REPRODUCTIONS: EXTENSIONS AND REDUCTIONS. LENGTH OF THE CIRCUMFERENCE AND AREA OF THE CIRCLE. EUCLID'S THEOREMS. THALES' THEOREM, THE SIMILARITY CRITERIA. SOLVING GEOMETRIC PROBLEMS WITH FIRST AND SECOND DEGREE EQUATIONS
ARTIFACTS
USE OF GEOGEBRA PRIM FOR THE STUDY OF GEOMETRY. USE OF NEPERO STICKS FOR MULTIPLICATION
RELATIONSHIPS AND FUNCTIONS
INTRODUCTION TO ANALYTICAL GEOMETRY. DISTANCE BETWEEN TWO POINTS, MIDPOINT OF A SEGMENT, CENTER OF GRAVITY OF A TRIANGLE; AREAS AND PERIMETERS. THE STRAIGHT LINE IN THE CARTESIAN PLANE; STRAIGHT FOR TWO POINTS AND STRAIGHT FOR A KNOWN POINT THE ANGULAR COEFFICIENT; PARALLEL LINES AND PERPENDICULAR LINES. INTERSECTION OF STRAIGHT LINES. LINEAR SYSTEMS: SUBSTITUTION METHOD. THE CIRCUMFERENCE IN THE CARTESIAN PLANE; CIRCUMFERENCE FOR THREE POINTS; STRAIGHT LINES AND CIRCUMFERENCES.
NOTIONS OF MATHEMATICAL LOGIC: SETS AND QUANTIFIERS, REPRESENTATIONS OF A SET, SUBSETS, INTERSECTIONS OF SETS, UNION;
MEASUREMENT, DATA AND FORECASTS
ELEMENTS OF COMBINATORIAL CALCULATION: SIMPLE DISPOSITIONS SIMPLE PERMUTATIONS AND WITH REPETITION; THE TARTAGLIA TRIANGLE. EXAMPLES OF DIDACTIC ACTIVITIES FOR PRIMARY SCHOOL WITH COMBINATORICS

	Teaching Methods
	THE COURSE AIMS TO PROVIDE SOME BASIC KNOWLEDGE OF MATHEMATICS, FRAMING THEM IN THE HISTORICAL CONTEXT OF ORIGIN AND DEVELOPMENT. IN PARTICULAR, IT IS INTENDED TO PROVIDE A KNOWLEDGE OF THE FOUNDATIONAL ASPECTS OF MATHEMATICS BY FOCUSING ATTENTION ALSO ON THE RELATIONSHIP BETWEEN MATHEMATICS, HISTORY AND DIDACTICS OF MATHEMATICS. THE COURSE IS ORGANIZED IN FRONTAL LESSONS HELD BY THE TEACHER (2 CFU- NUMBERS; 2 CFU SPACE AND FIGURES, 2 CFU REPORTS AND FUNCTIONS, 1 CFU MEASUREMENT, DATA AND PRECISIONS), AND LABORATORY (1 CFU - ARTIFACTS).

Teaching Methods

THE COURSE AIMS TO PROVIDE SOME BASIC KNOWLEDGE OF MATHEMATICS, FRAMING THEM IN THE HISTORICAL CONTEXT OF ORIGIN AND DEVELOPMENT. IN PARTICULAR, IT IS INTENDED TO PROVIDE A KNOWLEDGE OF THE FOUNDATIONAL ASPECTS OF MATHEMATICS BY FOCUSING ATTENTION ALSO ON THE RELATIONSHIP BETWEEN MATHEMATICS, HISTORY AND DIDACTICS OF MATHEMATICS. THE COURSE IS ORGANIZED IN FRONTAL LESSONS HELD BY THE TEACHER (2 CFU- NUMBERS; 2 CFU SPACE AND FIGURES, 2 CFU REPORTS AND FUNCTIONS, 1 CFU MEASUREMENT, DATA AND PRECISIONS), AND LABORATORY (1 CFU - ARTIFACTS).

	Verification of learning
	THE ASSESSMENT AND FINAL EVALUATION WILL CONSIST OF: A WRITTEN EXAM TO AN ORAL INTERVIEW.

	Texts
	PAOLA MAGRONE, ANA MILLA'N GASCA I BAMBINI E IL PENSIERO SCIENTIFICO CAROCCI EDITORE, 2018 ANNA MAZZITELLI, ANA MILLA'N GASCA L'ABC DELLA MATEMATICA CAROCCI FABER, 2021 R.NATALINI, A. BACCAGLINII FRANK, P, DI MARTINO, G. ROSOLINI DIDATTICA DELLA MATEMATICA MONDADORI

Lessons Timetable

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2025-03-26]

Francesco Saverio TORTORIELLO | COMPLEMENTARY MATHEMATICS II