Methodology of Mathematics

Recommended Prerequisites

2 semestres of Analysis,  Álgebra,  Geometry, and Probability and Statistics.

Teaching Methods

Presentations by the professor, lecture and discussion of texts. Observation of portuguese classes and of recorded classes from other countries.

Learning Outcomes

Analyze the place of mathematics education in the school curriculum of primary and secondary, reflecting on the different mathematical paths in Portugal and other countries. Reflection on the nature and methods of the mathematical work: experiment-conjecture-proof-generalization. Pathways to integration of mathematics and educational sciences and the role of didactics of mathematics. The issue of assessment, of national examinations and of international comparative studies. Commented readings of relevant authors. Reflection on the role of the introduction to teaching practice and the challenges of the early career of the young math teacher.     

Work Placement(s)

No

Syllabus

1. The present math curriculum in Portugal and other european, asian and american countries.

2. The work of the mathematician and of the math teacher.

3. Methods from mathematics; proof.

4. Mathematical modeling and applications

5. The teaching of Probability and Statistics.

6. Educational Sciences and the role of the mathematics teacher.

7. Didactic(s).

8. Assessment in mathematics; national examinations; international studies.

9. Reference authors: Polya, Bento Caraça, Davis e Hersch, Stewart, Devlin, Sebastião e Silva.

10. The internship and the induction year.

11. Failure in Mathematics. 

Head Lecturer(s)

Helena Maria Mamede Albuquerque

Assessment Methods

Assessment
Research work: 20.0%
Synthesis work: 20.0%
Project: 30.0%
Laboratory work or Field work: 30.0%

Bibliography

A Philip Davis, Reuben Hersh - A experiência Matemática, Gradiva, 1995

M. Paula Serra de Oliveira (coord.) - Teias Matemáticas, Gradiva/Imprensa da Universidade de Coimbra, 2004

G. Polya - Como resolver problemas, Gradiva, 2003

John Allen Paulos - Notícias e Matemática, Publicações Europa-América, 1997

João Pedro da Ponte e outros - Reflectir e investigar sobre a prática profissional, APM, 2002

C. Sagan, Biliões e Biliões, Gradiva, 2013

A. Aczel, O último teorema de Fermat, Gradiva, 1997

Bento de Jesus Caraça - Conceitos Fundamentais da Matemática, Gradiva. Lisboa, 1998

Keith Devlin - Matemática - a ciência dos padrões, Porto Editora. Porto, 2003

Ian Stewart - Deus joga aos dados?, Gradiva, 1991

João Pedro da Ponte e outros - Histórias de investigações matemáticas, IIE, 1998

R. Brown, T. Poter, The Methodology of Mathematics, Mathematics and Knots, 1989

Elon Lages Lima, Matemática e Ensino, col. Temas de Matemática, Gradiva, 2004

Lobo Vilela, Métodos da Matemática, Fig. da Foz, 1938.