Fundamentals and applications of elementary mathematics

Objectives

1) Consolidate key concepts to the approach of mathematical topics of the programs and curriculum guidelines for Preschool and Primary Education;

2) Develop a positive attitude toward mathematics and the interest to rediscover relationships and mathematical facts;

3) Reflect on determining factors for the success of mathematics education, such as the importance of investing in the stringency of definitions and mathematical reasoning, in the knowledge of facts and procedures, in an appropriate transition from concrete to abstract, without skip steps, and in the development of mathematical communication and problem-solving strategies, among other aspects;

4) Apply mathematical tools in solving problematic situations within the student´s area of education;

5) Develop the ability to research, creativity and autonomy;

6) Experience teaching resources appropriate to teaching the topics under study.

Program

1. The Mathematics of preschool education
1.1. Properties and classification criteria. Correspondences and associations
1.2. Cardinality, ordinality and the write of numerals. Additions and subtractions
1.3. Figures of the plane and geometric solids. Spatial orientation. Units of measurement
1.4. Construction and interpretation of tables and graphs
1.5. Discovering and building patterns
1.6. The method of Singapore
1.7. Games and manipulatives. Math in children's everyday life
2. Mathematics of primary school
2.1. Numbers and operations. Geometry and measurement. Data organization and processing
2.2. Algebraic reasoning
2.3. Mathematical reasoning, problem solving and mathematical communication. Mathematics as a coherent whole and the promotion of the knowledge of facts and procedures

2.4. Exploration of tasks that promote the articulation of themes among the four years of schooling

2.5. Applications of Elementary Mathematics

Teaching Methodologies

Theoretical-practical classes and Tutorial Sessions– The topics of this course will be discussed and explored in detail by solving problems and exercises, using appropriate resources to each situation.

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.

Evaluation – It will be proposed for each of the two chapters, a written test (50%) and a group assignment (50%); or, alternatively, a final exam.

Bibliography

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.
Long, C. & DeTemple, D. (2006). Mathematical Reasoning for Elementary Teachers. Pearson Education.
Ma, L. (2008). Aprender e Ensinar Matemática Elementar. Gradiva.
Maia, J. S. (2009). Aprender... Matemática do Jardim-de-Infância à Escola. Porto Editora.
Migueis, M. & Azevedo, M. (2007). Educação Matemática na Infância: Abordagens e desafios. Edições Gailivro.
Palhares, P. (Coord.) (2004). Elementos de Matemática para Professores do Ensino Básico. Lidel–Edições Técnicas.
Palhares, P., Gomes, A. & Amaral, E. (Coord.) (2011). Complementos de Matemática para Professores do Ensino
Básico. Lidel–Edições Técnicas.
Pimentel, T. et al. (2010). Matemática nos Primeiros Anos. Texto Editora.
Ponte, J. P. et al. (2009). Álgebra no Ensino Básico. MEC.