Didactics of Mathematics

Objectives

1. To reflect on the importance of mathematics and its role in the acquisition of skills and knowledge by children
2. To discuss the didactic approches to mathematical education
3. To understand children's learning processes in order to identify the elements inherent in these processes and the intended learning outcomes
4. To plan didactics sequences in given contexts, based on content from different curricular approches and programs
5. To select materials (structured and nonstructured) and technology in order to facilitate learning.
6. To know how to use oral and written communication to stimulate mathematical reasoning and representation and to give children the opportunity to express their mathematical ideas
7. To solve problems in the classroom using preferentially the Pólya method procedures
8. To use mental calculation strategies as well as tradicional algorithms
9. To report the results of learning experiences demonstrating research skills and individual autonomy.

Program

1. The importance of dydactics in mathematics for learning mathematical skills and clarification of educational objectives.
2. Curriculum guidelines for mathematics in Pre-school and in the first Cycle of Elementary Education according to present educational policy.
3. Different approches to mathematical education.
4. Expetations of children regarding mathematical knowledge.
5. Conceptualization of processes in the learning of mathematics as regards number operation, geometry and mesuarement and the organization and treatement of data.
6. Processes of mathematical communication in the classroom.
7. Problem-solving and problem-solving stages based on the preferential use of the Pólya model in the classroom.

8. Connections between mathematics and other subjet areas.

Teaching Methodologies

The discussion method is used to introduce practical contents relating to the course unit. During the semester, students are asked to read sellect documents relating to teaching practice and to summerize the main ideas reflected in them (20% of the final mark). They will also be required to present a lesson plan and to participate actively in a classroom observation procedure (50% of the final mark). A selection of the work done by students will be discussed in class. A written final test will also be required of students (30% of the final mark).

Bibliography

Barros, M., & Palhares, P. (1997). Emergência da Matemática no jardim-de-infância. Porto: Porto Editora.
Brocardo, J.; Serrazina, M. L. & Rocha, I. (2008). O sentido do número. Reflexões que entrecruzam teoria e prática. Lisboa: Escolar Editora.
De Walle, J. et al. (2010). Elementary & Middle School Mathematics' Teaching Development. Pearson International Edition.
Ministério de Educação e Ciência. (2018). Aprendizagens Essenciais (1.º e 2.º Ciclos do Ensino Básico). Lisboa: Ministério de Educação e Ciência.
Ministério de Educação e Ciência. (2013). Programa e metas curriculares de Matemática do Ensino Básico. Lisboa: Ministério de Educação e Ciência.
National Council of Teachers of Mathematics. (2000). Princípios e Normas para a Matemática Escolar. Lisboa: Associação de Professores de Matemática.
Planas, N., & Alsina À. (Eds.) (2009). Educación matemática y buenas prácticas. Barcelona: Editorial GRAÓ.
Ponte, J., & Serrazina, M. L. (2000). Didática da Matemática do 1.º ciclo. Lisboa: Universidade Aberta.
Silva, I. L.; Marques, L.; Mata, L., & Rosa, M. (2016). Orientações Curriculares para a Educação Pré-Escolar. Lisboa: Ministério da Educação/Direção-Geral da Educação.