Skip to main content

IPLUSO 22166

Fundamental Concepts of Mathematics

Primary Education
  • ApresentaçãoPresentation
    This curricular unit aims to understand and deepen the basic concepts considered fundamental in a process of confident mastery of the notions to be discovered, constructed, internalized and applied. The themes will be explored from a problem-solving perspective, considering this as a process from which students have the possibility of relating mathematics to the world around them and, on the other hand, exploring and analysing situations with meaning within mathematics itself. Therefore, the concepts will be approached in a way that includes numerous and varied experiences of solving problems and using diverse materials.
  • ProgramaProgramme
    Numbers • Numerical sets - Sets N, Q, Z and R. - Symbology and concepts of meeting, intersection, complementary, contained, contains, belongs, does not belong, (...). - Representation in diagrams. • Integers - Dividers and multiples - Prime numbers and decomposition of a number into prime factors - Greatest common divisor and least common multiple • Rational numbers - Decimal number system • Operations and their properties Geometry and Measurement • Geometric solids • Volume and capacity • Properties of plane figures • Areas and perimeters • Geometrically equal figures and equivalent figures Algebra and Functions • Regularities and numerical sequences • Symbols and algebraic expressions - Notion of variable - Algebraic expressions • Function families and their representation - Linear - Inverse proportionality Data • Notion of statistical variable • Notion of qualitative and quantitative variables
  • ObjectivosObjectives
    a) Develop the concepts of area and volume and their properties. b) Develop spatial reasoning when solving problems in different contexts c) Develop students' sense of number, with an emphasis on mental calculation and its strategies, and also on understanding the properties of operations. d) Develop an understanding of numbers and operations, as well as the use of this knowledge and skills in solving problems in different contexts. e) Develop algebraic thinking and proportional reasoning in varied contexts. f) Develop mathematical reasoning, specifically, the formulation, testing and demonstration of conjectures, using iconic representations (figures, graphs and diagrams), numerical and algebraic. g) Develop habits of reasoning, problem solving, establishing connections and mathematical communication between different topics, numbers, algebra and geometry.
  • BibliografiaBibliography
    Caraça, B. J. (1998). Conceitos fundamentais da Matemática. Lisboa: Gradiva. Palhares, P. (2009). Elementos de Matemática para professores do Ensino Básico. Editora Lindel. ME-DGIDC (2009). ÁLGEBRA NO ENSINO BÁSICO. Lisboa: Ministério da Educação, Direcção Geral de Inovação e Desenvolvimento Curricular. Haylock, D. (2001). Mathematics explained for primary teachers. London: Paul Chapman Publishing. NCTM (2007). Princípios e Normas para a Matemática Escolar. Lisboa: APM. Vale, T. Pimentel, A. Barbosa, L. Fonseca, L. Santos & P. Canavarro (Orgs.), Números e Álgebra na aprendizagem da Matemática e na formação de professores (pp. 29-48). Lisboa: SEM-SPCE. Jacobs, H. (1974). Geometry. San Francisco: Freeman Musser, G. & Burger, W. (1997). Mathematics for elementary teachers. A contemporary approach. USA: Prentice-Hall.  
  • MetodologiaMethodology
    The work to be developed within the scope of this UC will privilege the active participation of students, whether in individual work or in group work, seeking to deepen knowledge related to different themes under study. The sessions will be organized in a problem-solving context. There will be a presentation by the teacher or students of the aforementioned mathematical topics, the resolution and discussion of mathematical problems and investigations. The process will include problem solving and reporting; presentation and discussion of work; exposure of certain themes; preparation and discussion, in groups, of small works. Each student is expected to carry out the proposed activities and requested assessment products, clearly and rigorously demonstrating the knowledge acquired and engaging in study/preparation for the different activities to be carried out in class, including assessment activities.  
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não