Overall objectives:

O1 - Be aware of the Nature of Mathematics by discussing different perspectives of Mathematics as a Science and its educational implications.
O2 - Be aware of the role of error in the creation and learning of Mathematics
O3 - Recognise that the purposes of Mathematics Teaching involve several dimensions and identify the consequences of these in curriculum development, in the learning process and in the social role that Mathematics plays.
O4 - Recognise the implications for Mathematics Teaching of the introduction of problem solving and investigative activities in classroom practice.
O5 - Analyse and reflect on teaching-learning situations and problems of professional practice, through the mobilization of acquired knowledge and construction of new knowledge.

Syllabus:

1 - Nature of Mathematics.
1.1 - Perspectives on Mathematics as a Science and its educational implications;
1.2 - Stages in the evolution of Mathematics;
1.3 - Role of error in the creation and learning of Mathematics.
2 - Problem solving and investigative activities.
2.1 - Problem solving in math class;
2.2 - Investigative activities in math class;
2.3 - Tasks for math class with problem solving and investigative activities.
3 - The Mathematics Class: Planning and Conducting.
3.1 - Structure of a class based on problem solving and investigative activities;

Literature/Sources:

Abrantes, P. , 1985 , Planificação no ensino da Matemática. ,
National Council of Teachers of Mathematics (NCTM) , 2007 , Princípios e normas para a matemática escolar , APM
Ponte, J. P. , 2005 , O professor e o desenvolvimento curricular , APM
Abrantes, P. , 1999 , Investigações matemáticas na aula e no currículo , APM
Precatado, A., Lopes, A. V., Baeta, A., Loureiro, C., Ferreira, E., Guimarães, H. M., Almiro, J., Ponte, J. P., Reis, L., Serrazina, L., Pires, M. V.,Teixeira, P. & Abrantes, P.. , 1998 , Matemática 2001: Diagnóstico e recomendações para o ensino e aprendizagem da Matemática , APM
Davis, P. & Hersh, R. , 1995 , A experiência matemática , Gradiva
Garnica, A. V. M. , 2002 , As demonstrações em educação matemática: Um ensaio , BOLEMA
Polya, G. , 2006 , A arte de resolver problemas: um novo aspecto do método matemático , Rio de Janeiro: Interciências
APM , 1994 , Normas Profissionais para o Ensino da Matemática , Lisboa: APM/IIE
APM , 1991 , Normas para o Currículo e Avaliação em Matemática Escolar (tradução dos Standarts do NCTM) , APM/IIE
Matos, J. M., Serrazina, M. L. , 1996 , Didáctica da matemática , Lisboa: Universidade Aberta
Ponte, J. P., Brocardo, J., e Oliveira, H. (Orgs.) , 2003 , Investigações matemáticas na sala de aula , Belo Horizonte, Brasil. Autêntica Editora
NCTM , 1991 , Normas para o currículo e a avaliação em matemática escolar , APM/IIE

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Classes include theoretical and practical moments, dedicated to the introduction, development or synthesis of the subjects studied, and others of a practical nature. Assessment is continuous, with an emphasis on the formative aspect, allowing to integrate the different performances of the students, at different moments, in relation to different problems. For the assessment, the following elements and respective weights will be considered: two group assignments (20% each); an individual written work (30%) and a written test (30%). Only the test mark can be improved in the resit exam. Students that obtain a final grade higher than or equal to 9.5 pass the subject.