Complements of Arithmetic and Geometry

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1. To consolidate the ideia of number sense and the understanding of numbers and operations;

2. To develop flexible strategies for mental calculation by applying different algorithms;

3. To consolidate one's spacial sense, with emphasis on visualization and understanding of the properties of geometric figures in the plane and in space;

4. To make estimates and determine measurements, and relate different units of measurement;

5. To develop the ability to solve problems, to reason and communicate in various mathematical contexts related to the topics under study;

6. To develop the ability to conduct research and to use creativity and autonomy in solving given tasks;

7. To explore the diversity of available resources in arithmetic and geometry.


1. Construction of mathematical structures

1.1. The construction of the concept of number: from activities of pre-numerical nature to the building of the concept of number and the application of algorithms

1.2. The construction of topological-geometrical concepts: the child and space - from topology to geometry

2. Exploratory tasks in Arithmetic and Geometry

2.1. The development of the sense of number, the application of algorithms and the use of manipulatives

2.2. The use of dynamic geometry software in the teaching and learning of Mathematics

2.3. Games and ludic activities

3. Problems of Arithmetic and Geometry in different contexts

Teaching Methodologies

Theoretical-practical lessons and Tutorial Sessions – The topics of this course will be discussed and explored in detail by solving problems and exercises, which will use diverse resources whenever necessary.

The course will benefit from the use of Moodle, the learning management platform available at the University of the Azores, thus enhancing the performance of asynchronous activities.


Aharoni, R. (2008). Aritmética para pais: um livro para adultos sobre a matemática das crianças. Gradiva.

Breda, A. et al. (2011). Geometria e Medida no Ensino Básico. ME-DGIDC.

Damas, E. et al. (2010). Alicerces da Matemática. Areal Editores.

Fayol, M. et al. (2010). Fazer contas ajuda a pensar? Fundação Francisco Manuel dos Santos.

Haylock, D. (2006). Mathematics Explained for Primary Teachers. Sage Publications.

Jensen, G. (2003). Arithmetic for Teachers with Applications and Topics from Geometry. American Mathematical Society.

Long, C. & DeTemple, D. (2006). Mathematical Reasoning for Elementary Teachers. Pearson Education.

Palhares, P. (Coord.) (2004). Elementos de Matemática para Professores do Ensino Básico. Lidel–Edições Técnicas.

Palhares, P., Gomes, A. & Amaral, E. (Coord.) (2011).



ECTS Credits



  • Orientação Tutorial - 18 hours
  • Teórico-Práticas - 60 hours

Evaluation Methodology

  • Frequency: 70%
  • Group work: 20%
  • Individual work: 10%