Teaching code

4S006126

Credits

9

Coordinator

Michele Picotti

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/02 - ALGEBRA
MAT/03 - GEOMETRY

Erasmus students

Not available

Courses Single

Not Authorized

Moodle Seminars 0

The teaching is organized as follows:

Learning objectives

PRE-SCHOOL
1. Knowledge and Understanding
At the end of the course the student will have to:
- Learn about the necessary steps to develop an educational path for the development of basic mathematical skills in the 3-6 years band;
- know the main theoretical models concerning the curricular programming and the evaluation of the learnings for the age range 3-6 years;
- know how to frame the evolution of the main aspects of mathematical thought;
- Know the logical connectives and the related truths tables; Know the properties of logical operations;
- know the concept of relation, order and equivalence relation;
- Know how to work with sets;
- Know the characteristics of numeric sets, operations on them, and their properties;
- The positional notation of numbers also in bases other than base ten;
- Understand the sense of mathematical formalisms and know how to build algorithms for modeling simple problems taken mainly from real contexts.
2. Applying Knowledge and Understanding
At the end of the course, future teachers will be able to:
-propose reflections and discussions on the daily experiences of children or on activities especially prepared for them to acquire the ability to count objects or events,
-to be familiar with numbers and with the structure of the first operations,
- to gradually reach the early processes of abstraction, the use of simple symbols and an early idea of operation.
Future teachers will be able to propose reflections and discussions aimed at acquiring the capacity to construct sets, to establish the belonging or not to a whole, to relate objects according to the criteria indicated, to identify the possible relation between two sets, knowing how to sort objects in a collection.
3. Making Judgements
At the end of the course students will have a critical and analytical attitude that enables them to question their beliefs and spontaneous ideas.
4. Communication skills
At the end of the course students will have to know how to use a rigorous and appropriate language for discipline.
5. Learning skills
At the end of the course students will have to Be able to independently find the teaching material valid and useful for building learning pathways.

PRIMARY SCHOOL
1. Knowledge and Understanding
At the end of the course the student will have to:
- know the necessary steps to develop an educational and formative project for the primary education band for the development and consolidation of basic mathematical competences;
- know how to frame the evolution of the main aspects of mathematical thought;
- Know the logical connectives and the related truths tables;
- Know the properties of logical operations;
- know the concept of relation, order and equivalence relation;
- Know how to work with sets;
- Know the characteristics of numeric sets, operations on them, and their properties;
- know the positional notation of numbers also in bases other than base ten;
- To know the main theoretical models concerning the introduction of natural numbers for the primary schooling band;
- Understand the sense of mathematical formalisms and know how to build algorithms for modeling simple problems taken mainly from real contexts.
2. Applying Knowledge and Understanding
At the end of the course the future teachers will be able:
-to propose to the children learning pathways introducing natural, integers and decimals numbers, and the operations on them, their comparison and their representation on the line, and on different numbering systems.
Future teachers will propose activities aimed at stimulating the conscious use of techniques and procedures of arithmetic calculation with natural and decimal numbers, written and mental, also with reference to real contexts so that children know how to derive implicit and explicit information from problematic situations and know how to choose and compare solution strategies.
-They will also be able to use new technologies to enrich the didactic proposal.
3. Making Judgements
At the end of the course students will have a critical and analytical attitude that enables them to question their beliefs and spontaneous ideas.
4. Communication skills
At the end of the course students will have to know how to use a rigorous and appropriate language for discipline.
5. Learning skills
At the end of the course students will have to Be able to independently find the teaching material valid and useful for building learning pathways.

Prerequisites and basic notions

Conoscenze e competenze livello 12 EQF

Program

Introduzione alla logica formale in prospettiva didattica

Breve analisi storica

Il concetto di vero e falso; le proposizioni e i connettivi “e” , “o” , “non”, “se… allora…” , “se e solo se” con relative tavole di verità.

Distribuzioni equivalenti di verità; proprietà dei connettivi logici.

Analisi di un ragionamento: schemi validi e ragionamenti corretti.

La logica dei predicati; proposizioni aperte, quantificatori; insieme soluzione e sue rappresentazioni: estensiva, per proprietà caratteristica, diagrammi di Venn.

Insiemi e sottoinsiemi.

Congiunzione, disgiunzione e negazione di enunciati aperti: intersezione, unione e complementare di un insieme. Proprietà delle operazioni tra insiemi.

I sillogismi.

Le relazioni e la loro rappresentazione; relazioni binarie definite su un insieme; proprietà delle relazioni: riflessiva, antiriflessiva, simmetrica, antisimmetrica, transitiva.

Le relazioni di equivalenza e sue rappresentazioni grafiche.

Partizione di un insieme in classi di equivalenza; equipotenza.

Relazioni d’ordine; insiemi ordinati.

Funzioni.

Il concetto di numero e gli insiemi numerici

Riferimenti storici.

Strutture algebriche.

Il contare.

Notazione posizionale in base n.

I numeri naturali e relative operazioni. Ordinamento di N.

I numeri primi (dimostrazione dell’infinità dei numeri primi); scomposizione di ogni numero in fattori primi, MCD e mcm.

I numeri interi; relazione d’ordine; valore assoluto; le operazioni nell’insieme dei numeri interi.

I numeri razionali; definizione di frazione; frazioni equivalenti; frazioni ridotte ai minimi termini.

Definizione di numero razionale (assoluto).

Operazioni con le frazioni; I numeri decimali; I numeri periodici; trasformazioni da frazioni a numeri decimali e viceversa.

Le proporzioni e le varie proprietà.

Le percentuali.

La misura.

Introduzione ai numeri reali.

Dimostrazione dell’irrazionalità di 2–√
. L’approssimazione; errori assoluti e relativi.

Definizione assiomatica di Z e Q.

Didactic methods

Lezione frontale partecipata

Learning assessment procedures

Written exam divided into three parts: 1. closed-ended test; 2. exercises; 3. open-ended questions.

Evaluation criteria

The evaluation of learning will take place through a written test consisting of solving closed-ended tests, exercises and open-ended questions on the theoretical topics of the course, with proposals for didactic activities relating to the questions in the school of competence. For the laboratory part, the compilation of forms relating to the design of didactic paths on the topics covered in the specific module is required. Students will have to demonstrate that they: - understand the mathematical concepts covered - know how to offer children exploratory activities related to the mathematical concepts covered - know how to use correct, appropriate and rigorous language

Criteria for the composition of the final grade

12 punti per i test
12 punti per gli esercizi
8 punti per i quesiti
[33 punti = 30 Lode]

Exam language

Italiano