# Comunicação Matemática

Teacher Responsible: Rui João Teles da Silva Ramalho

1º Ano | 2º Semestre

**Learning objectives**

Mobilize knowledge and competences required to develop an integrated curriculum, that promotes and develops mathematical communication
Communicate findings, ideas and math procedures using a correct and clear language, fitted both to oral and written situations
Distinguish characteristics of different types of language
Apply correctly the math language in oral and/or written activities
Execute intellectual activities involving mathematical judgments
Recognize that the validity of a statement is related with the consistence of a logical used argumentation and not with any exterior authority.
Develop logical arguments when justifying conclusions
Define strategies of communication fitted to the different periods of logical-mathematician knowledge construction
Respect the rules defined for the development of activities

**Syllabus**

Languages
- Types of language
- Mathematician language
Logic of propositions
- Notion of proposition. Logical value of a proposition
- Logical operations. Definition and proprieties
- Logistic syllogism and Polysyllogisms
Conditions and sets logical systems
- Condition notion. Condition classification.
- Math operations between conditions. Quantifiers
- Set forms and element. Cardinal of a set.
- Representation of sets
- Sets relationship and operations. Proprieties
Relationship between operations with conditions and sets and with arithmetic operations
Binary relationship.
- Notion of binary relationship. Representation of binary relationships.
- Applications. Binary relationships defined in a single set: equivalent and order binary relationships

#### Teaching methodologies (including evalution)

Strategies and resources to be used
Explanation
Individual work
Team work
Problems
Description:
In the theoretical classes the contents presented will be applied ,debated and systematized later on within the theoric-practical classes mingling moments of individual work with those of team work aiming at solving problematic situations and their description in proper language.
Evaluation Forms and due classification:
2 written individual tests (50% + 50%)
Description:
The evaluation of knowledge inherent to the activities of mathematic communication- concerning concepts, representation, procedures and arguments- and progress of learning done along this unit, will be based in the acquisition of competences displayed by each student in written individual tests.#### Essential Bibliography (including ISBN)

BÍVAR, A. et al (2013). Programa e Metas Curriculares de Matemática: ensino básico. Lisboa: MEC
CARAÇA, B. J. (2000). Conceitos Fundamentais da Matemática. Lisboa: Gradiva. ISBN 978-972-662-616-9
LIPSCHUTZ, S. (1994). Teoria de Conjuntos. Lisboa: McGraw-Hill.
MUSSER, G., BURGER,W. (1997). Mathematics for elementary teachers: a contemporary approach. New Jersey: Prentice Hall. ISBN 0-13-246182-X