# Foundations and Teaching of Mathematics I (2018/2019)

Course code
4S006126
Credits
9
Coordinator
Michele Picotti
Academic sector
MAT/02 - ALGEBRA MAT/03 - GEOMETRY
Language of instruction
Italian
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Lezioni 8 Sem. 1A, Sem. 1B Michele Picotti

Laboratorio [Gruppo 1] 1 Lab. 1A, Lab. 1B Michele Picotti

Laboratorio [Gruppo 2] 1 Lab. 1A, Lab. 1B Maria Mori

Laboratorio [Gruppo 3] 1 Lab. 1A, Lab. 1B Maria Mori

Laboratorio [Gruppo 4] 1 Lab. 1A, Lab. 1B Maurizio Rodegheri

### Learning outcomes

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.

### Syllabus

Propositional and Predicate Logic and sets
Relations and functions

### Assessment methods and criteria

The examination test is written, with theoretical questions and exercises.

 Activity Author Title Publisher Year ISBN Note Lezioni A. Baccaglini Frank, P. Di Martino, R. Natalini, G.Rosolini DIDATTICA DELLA MATEMATICA Mondadori 2018 9788861845503 Lezioni Laura Giovannoni Lingua e logica Francoangeli 1997 Lezioni M. Bergamini G. Barozzi matematica multimediale.blu, vol. 1, Zanichelli Zanichelli 2015 Laboratorio A. Baccaglini Frank, P. Di Martino, R. Natalini, G.Rosolini DIDATTICA DELLA MATEMATICA Mondadori 2018 9788861845503 Laboratorio Bruno D'Amore DIDATTICA DELLA MATEMATICA Pitagora 2001 Laboratorio Laura Giovannoni Lingua e logica Francoangeli 1997 Laboratorio M. Bergamini G. Barozzi matematica multimediale.blu, vol. 1, Zanichelli Zanichelli 2015 Laboratorio Bruno D'Amore Problemi Franco Angeli 1993 8820479265