Scienze della Formazione Primaria | BASIC MATHEMATICS AND MATHEMATICS EDUCATION

cod. 4461000050

BASIC MATHEMATICS AND MATHEMATICS EDUCATION

	4461000050
	DIPARTIMENTO DI SCIENZE UMANE, FILOSOFICHE E DELLA FORMAZIONE
	EQF7
	PRIMARY TEACHER EDUCATION
	2019/2020

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2016
	ANNUALE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
1	MATEMATICA DI BASE
	MAT/04	6	36	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
2	DIDATTICA DELLA MATEMATICA
	MAT/04	6	36	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	CRISTINA COPPOLA2 T Curriculum
	GEMMA CAROTENUTO1 Curriculum

	Objectives
	IT IS A CHARACTERISING TEACHING, DIVIDED INTO 2 MODULES: BASIC MATHEMATICS, MATHEMATICS EDUCATION. THE MAIN AIM OF THE FIRST MODULE IS TO PROVIDE MATHEMATICAL KNOWLEDGE, ANALYSED FROM AN HIGHER POINT OF VIEW, IN ORDER TO TEACH SUCH DISCIPLINE BOTH IN PRIMARY SCHOOLS AND IN KINDERGARTEN. THE SECOND MODULE AIMS TO PROVIDE PEDAGOGICAL AND METHODOLOGICAL TOOLS USEFUL FOR DESIGNING MATH ACTIVITIES AND FOR UNDERSTANDING THE MAIN ISSUES RELATED TO TEACHING / LEARNING PROCESSES OF THIS SUBJECT. KNOWLEDGE AND UNDERSTANDING: THE MAIN KNOWLEDGE, ACQUIRED BY THE STUDENTS, WILL BE: MODULE BASIC MATHEMATICS: BASIC KNOWLEDGE OF ARITHMETICS, GEOMETRY, MATHEMATICAL LOGIC, PROBABILITY THEORY. MODULE MATHEMATICS EDUCATION: THE MAIN RESEARCHES IN MATHEMATICS EDUCATION AND THE DIFFERENT METHODOLOGIES IN THIS FIELD, IN PARTICULAR THE ONES REGARDING THE USE OF ARTIFACTS IN LABORATORY ACTIVITIES. APPLYING KNOWLEDGE AND UNDERSTANDING: THE MAIN SKILLS, ACQUIRED BY THE STUDENTS, WILL BE, ON THE ONE HAND TO APPLY THE ACQUIRED KNOWLEDGE IN THE ELABORATION AND RESOLUTION OF SIMPLE PROBLEMS, MEANINGFUL FOR MATHEMATICS TEACHING IN PRIMARY SCHOOL AND IN KINDERGARTEN. BESIDES, ON THE OTHER ONE, STUDENTS, THROUGH THE MODULE MATHEMATICS EDUCATION, STARTING FROM THE UNDERSTANDING OF THE RESULTS OF THE RESEARCHES IN MATH EDUCATION AND FROM THE LABORATORY EXPERIENCES, CARRIED OUT DURING THE COURSE, BECOME ABLE TO APPLY IN A CRITICAL WAY, IN THEIR FUTURE TEACHING ACTIVITY, THE KNOWLEDGE ACQUIRED IN THE MODULE BASIC MATHEMATICS.

IT IS A CHARACTERISING TEACHING, DIVIDED INTO 2 MODULES: BASIC MATHEMATICS, MATHEMATICS EDUCATION. THE MAIN AIM OF THE FIRST MODULE IS TO PROVIDE MATHEMATICAL KNOWLEDGE, ANALYSED FROM AN HIGHER POINT OF VIEW, IN ORDER TO TEACH SUCH DISCIPLINE BOTH IN PRIMARY SCHOOLS AND IN KINDERGARTEN. THE SECOND MODULE AIMS TO PROVIDE PEDAGOGICAL AND METHODOLOGICAL TOOLS USEFUL FOR DESIGNING MATH ACTIVITIES AND FOR UNDERSTANDING THE MAIN ISSUES RELATED TO TEACHING / LEARNING PROCESSES OF THIS SUBJECT.

KNOWLEDGE AND UNDERSTANDING:
THE MAIN KNOWLEDGE, ACQUIRED BY THE STUDENTS, WILL BE:
MODULE BASIC MATHEMATICS: BASIC KNOWLEDGE OF ARITHMETICS, GEOMETRY, MATHEMATICAL LOGIC, PROBABILITY THEORY.
MODULE MATHEMATICS EDUCATION: THE MAIN RESEARCHES IN MATHEMATICS EDUCATION AND THE DIFFERENT METHODOLOGIES IN THIS FIELD, IN PARTICULAR THE ONES REGARDING THE USE OF ARTIFACTS IN LABORATORY ACTIVITIES.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE MAIN SKILLS, ACQUIRED BY THE STUDENTS, WILL BE, ON THE ONE HAND TO APPLY THE ACQUIRED KNOWLEDGE IN THE ELABORATION AND RESOLUTION OF SIMPLE PROBLEMS, MEANINGFUL FOR MATHEMATICS TEACHING IN PRIMARY SCHOOL AND IN KINDERGARTEN. BESIDES, ON THE OTHER ONE, STUDENTS, THROUGH THE MODULE MATHEMATICS EDUCATION, STARTING FROM THE UNDERSTANDING OF THE RESULTS OF THE RESEARCHES IN MATH EDUCATION AND FROM THE LABORATORY EXPERIENCES, CARRIED OUT DURING THE COURSE, BECOME ABLE TO APPLY IN A CRITICAL WAY, IN THEIR FUTURE TEACHING ACTIVITY, THE KNOWLEDGE ACQUIRED IN THE MODULE BASIC MATHEMATICS.

	Prerequisites
	NONE.

	Contents
	TEACHING IS DIVIDED INTO TWO MODULES (36 HOURS FOR EVERYONE). EACH MODULE WILL DEAL WITH DISTINCT CONTENTS BUT CLOSELY RELATED TO EACH OTHER. MODULE BASIC MATHEMATICS WILL DEAL WITH THE FOLLOWING TOPICS: ARITHMETIC. THE CONCEPT OF NUMBER. NATURAL NUMBERS. BASIC OPERATIONS AND RELATED PROPERTIES AND REPRESENTATIONS. PRIME NUMBERS. MULTIPLES AND DIVISORS. DECIMAL POSITIONAL NOTATIONS OF NATURAL NUMBERS. NUMBERS’ REPRESENTATION DIFFERENT FROM THE DECIMAL ONE AND FROM POSITIONAL ONE. INTEGERS. BASIC OPERATIONS, RELATED PROPERTIES AND REPRESENTATIONS. FINITE ARITHMETIC. RATIONAL NUMBERS. REDUCTION TO NORMAL FORM. BASIC OPERATIONS, RELATED PROPERTIES AND REPRESENTATIONS. REAL NUMBERS: IRRATIONALS, PROPORTIONS AND PERCENTAGE. GEOMETRY: BASIC NOTIONS OF EUCLIDEAN GEOMETRY. LOGIC: THE CONCEPT OF SET AND RELATED REPRESENTATIONS. OPERATIONS AMONG SETS. ORDER RELATIONS AND EQUIVALENCE RELATIONS. FUNCTIONS. CARDINALITY OF A SET AND EQUIPOTENCE CONCEPT. FINITE AND INFINITE SETS. HINTS OF PROPOSITIONAL CALCULUS AND OF PREDICATES CALCULUS. THE CONCEPT OF PROOF AND OF AXIOMATIC SYSTEM PROBABILITY: HINTS OF PROBABILITY CALCULUS. MODULE MATHEMATICS EDUCATION WILL DEAL WITH THE FOLLOWING TOPICS: THE MAIN FRAMEWORKS IN MATHEMATICS EDUCATION, USEFUL FOR TEACHING IN KINDERGARTEN AND IN PRIMARY SCHOOL; THEORIES ON THE CONCEPT OF NUMBER’ S DEVELOPMENT IN THE EARLY YEARS OF AN INDIVIDUAL. COMPETENCES IN MATHEMATICS. DIDACTIC CONTRACT. PROBLEMS IN MATHEMATICS. MODELS AND MISCONCEPTIONS. MATHEMATICS AND LANGUAGE. THE MATH LABORATORY. THE THEORY OF SEMIOTIC MEDIATION.

Contents

TEACHING IS DIVIDED INTO TWO MODULES (36 HOURS FOR EVERYONE). EACH MODULE WILL DEAL WITH DISTINCT CONTENTS BUT CLOSELY RELATED TO EACH OTHER.
MODULE BASIC MATHEMATICS WILL DEAL WITH THE FOLLOWING TOPICS:
ARITHMETIC. THE CONCEPT OF NUMBER. NATURAL NUMBERS. BASIC OPERATIONS AND RELATED PROPERTIES AND REPRESENTATIONS. PRIME NUMBERS. MULTIPLES AND DIVISORS. DECIMAL POSITIONAL NOTATIONS OF NATURAL NUMBERS. NUMBERS’ REPRESENTATION DIFFERENT FROM THE DECIMAL ONE AND FROM POSITIONAL ONE. INTEGERS. BASIC OPERATIONS, RELATED PROPERTIES AND REPRESENTATIONS. FINITE ARITHMETIC. RATIONAL NUMBERS. REDUCTION TO NORMAL FORM. BASIC OPERATIONS, RELATED PROPERTIES AND REPRESENTATIONS. REAL NUMBERS: IRRATIONALS, PROPORTIONS AND PERCENTAGE.
GEOMETRY: BASIC NOTIONS OF EUCLIDEAN GEOMETRY.
LOGIC: THE CONCEPT OF SET AND RELATED REPRESENTATIONS. OPERATIONS AMONG SETS. ORDER RELATIONS AND EQUIVALENCE RELATIONS. FUNCTIONS. CARDINALITY OF A SET AND EQUIPOTENCE CONCEPT. FINITE AND INFINITE SETS. HINTS OF PROPOSITIONAL CALCULUS AND OF PREDICATES CALCULUS. THE CONCEPT OF PROOF AND OF AXIOMATIC SYSTEM
PROBABILITY: HINTS OF PROBABILITY CALCULUS.
MODULE MATHEMATICS EDUCATION WILL DEAL WITH THE FOLLOWING TOPICS: THE MAIN FRAMEWORKS IN MATHEMATICS EDUCATION, USEFUL FOR TEACHING IN KINDERGARTEN AND IN PRIMARY SCHOOL;
THEORIES ON THE CONCEPT OF NUMBER’ S DEVELOPMENT IN THE EARLY YEARS OF AN INDIVIDUAL. COMPETENCES IN MATHEMATICS. DIDACTIC CONTRACT. PROBLEMS IN MATHEMATICS. MODELS AND MISCONCEPTIONS. MATHEMATICS AND LANGUAGE. THE MATH LABORATORY. THE THEORY OF SEMIOTIC MEDIATION.

	Teaching Methods
	FOR BOTH THE MODULES THERE ARE MULTIMODAL FRONT LECTURES, GUIDED DISCUSSIONS, EXERCISES, GROUP ACTIVITIES, LABORATORY ACTIVITIES.

	Verification of learning
	THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF WRITTEN AND ORAL EXAMINATIONS. THE WRITTEN EXAMINATION IS PRELIMINARY TO THE ORAL INTERVIEW. IT IS POSSIBLE ACCEPT THE VOTE OF WRITTEN EXAMINATION, WITHOUT HOLDING THE ORAL INTERVIEW. THROUGH BOTH THE EXAMINATIONS, IT WILL BE EVALUATED: KNOWLEDGE OF THE MATHEMATICAL CONTENT AND OF THE EDUCATIONAL THEORIES FACED DURING THE COURSE, CAPABILITY TO EXPOSE THEM IN A CRITICAL MANNER AND TO CONTEXTUALISE THEM IN THE FIELD OF MATHEMATICS TEACHING.

Verification of learning

THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF WRITTEN AND ORAL EXAMINATIONS.
THE WRITTEN EXAMINATION IS PRELIMINARY TO THE ORAL INTERVIEW. IT IS POSSIBLE ACCEPT THE VOTE OF WRITTEN EXAMINATION, WITHOUT HOLDING THE ORAL INTERVIEW.
THROUGH BOTH THE EXAMINATIONS, IT WILL BE EVALUATED: KNOWLEDGE OF THE MATHEMATICAL CONTENT AND OF THE EDUCATIONAL THEORIES FACED DURING THE COURSE, CAPABILITY TO EXPOSE THEM IN A CRITICAL MANNER AND TO CONTEXTUALISE THEM IN THE FIELD OF MATHEMATICS TEACHING.

	Texts
	SABENA CRISTINA, FERRI FRANCA, MARTIGNONE FRANCESCA, ROBOTTI ELISABETTA (2019). INSEGNARE E APPRENDERE MATEMATICA NELLA SCUOLA DELL’INFANZIA E PRIMARIA. MONDADORI UNIVERSITÀ. ZAN ROSETTA (2016). I PROBLEMI DI MATEMATICA. DIFFICOLTÀ DI COMPRENSIONE E FORMULAZIONE DEL TESTO. CAROCCI FABER. OTHER DOCUMENTS SUGGESTED OR GIVEN DURING THE COURSE.