1º Ano | 2º Semestre
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
- 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
- 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
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%)
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