Mathematics, Culture and Reality

Scholar Year: 2018/2019 - 2S

Courses

Head Teacher Responsability Maria de Fátima Pista Calado Mendes Head

Weekly workload Hours/week T TP P PL L TC E OT OT/PL TPL O S Type of classes Lectures Type Teacher Classes Hours Contact hours Totals 1 4,00 Joana Brocardo   2,67 Joana Filipa Oliveira Cabral   1,33

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

- Understand the history and nature of mathematics and recognize its impact on society
- Mobilize knowledge about the foundation, evolution and nature of mathematics and the ability to communicate clearly and coherently
- Use conceptual and methodological tools to analyze situations that involve information of a mathematical
- Identify, formulate and solve problems, balancing risks and benefits in decision making
- Critically analyze theoretical and empirical data to solve problems and make appropriate decisions
- Mobilize adequate mathematical knowledge to the questioning and interpretation of emerging issues in the contemporary world

Syllabus

Mathematics, Culture and Reality
Error detection systems
Graphs and applications
Four-color theorem
Linear and exponential growth
Powers of ten base and scientific notation
Geometry, Culture and Reality
Euclidian geometry
Non-Euclidean geometries
Spherical geometry
Taxicab geometry
Number as language
Numeration systems
Characteristics of numeration systems
Organization and potentialities of positional numeration systems
Numbers and regularities

Demonstration of the syllabus coherence with the UC intended learning outcomes

This CU aims to mobilize and to understand some aspects of history and nature of mathematics, beyond recognition of the impact of this science on society. Furthermore, the proposed tasks will help students to know topics such as number systems and non-Euclidean geometries, as well as error detection systems and graph theory to show the impact of this science on society The proposed tasks will also help students to develop their ability to clearly and consistently communicate by mobilizing mathematical knowledge adequate to the questioning and interpretation of emerging issues of the contemporary world.

Teaching methodologies

The work to be developed in this CU will focus on active student participation, whether in individual or in group work, looking for the deepening of knowledge related to the topics of the program. The sessions will be organized taking into account the reading and discussion of texts, presentation made by the teacher or by the students of the program topics, problem solving and mathematical investigations. The tutorial support, individual support or group support consists in the orientation and organization of the student study to deepen the themes and answering questions posed by students and can be done in person or at distance.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

The expected learning are located at four levels: (a) know some aspects of the history of mathematics that illustrate how this science has developed; (B) identify key aspects of mathematical activity; (C) mobilize adequate mathematical knowledge to the interpretation of emerging issues of the contemporary world; (D) solve problems and develop small researchs by identifying and explaining strategies and reasoning used. Thus, the activities to develop include (i) reading and discussion of scientific and technical texts, (ii) preparation of abstracts and commentaries, (iii) exploration and discussion of problems, (iv) to search relevant information for the deepening of the themes of this unit, and (v) oriented discussion of these themes.

Assessment methodologies and evidences

The evaluation will focus on the work throughout the CU. Will be taken into account (i) attendance, (ii) the realization of a written test (65%) and (iii) the realization of a working group on a topic of UC (35%). In order to complete the CU in continuous assessment mode you must have a minimum of 70 points in the test, a total of 200. Students who do not opt for continuous evaluation or do not obtain positive mark there, will do a final exam.

Attendance system

To take advantage of the mode of continuous assessment, each student has to attend 75% (50% for working students) of classroom sessions. If this does not occur the students have to perform an examination.

Bibliography

Benarroch, M. (1993). Grafos y Redes. Colección: Matemáticas: Cultura y Aprendizaje.
Buescu, J. (2001) O Mistério do bilhete de identidade e outras histórias – crónicas das fronteiras da Ciência. Lisboa: Gradiva.
Buescu, J. (2003) Da falsificação de Euros aos pequenos mundos – novas crónicas das fronteiras da Ciência. Lisboa: Gradiva.
Buescu, J. (2007) O fim do mundo está próximo? Lisboa: Gradiva.
Crato, N. (2007). Passeio aleatório. Pela ciência do dia-a-dia. Lisboa: Gradiva.
Crato, N. (2008). A Matemática das coisas. Lisboa: Gradiva.
Crato, N., SANTOS, C. & TIRAPICOS, L. (2006). A espiral dourada. Lisboa: Gradiva.
Devlin, K. (2002). Matemática. A ciência dos padrões. Porto: Porto Editora.
Farmer, D. & Stanford, T. (2003). Nós e superfícies. Lisboa: Gradiva.
Gardner, M. (2002). As Últimas recreações. Lisboa: Gradiva.
Guillen, M. (1983). Pontes para o infinito. Lisboa: Gradiva.
Haylock, D. (2001). Mathematics explained for primary teachers. London: Paul Chapman Publishing.
Jacobs, H. (1974). Geometry. San Francisco: Freeman.
Jacobs, H. Mathematics: a human endeavour. San Francisco: Freeman.
Morrison & Morrison (2002). Potências de Dez. O Mundo às várias escalas. Porto: Porto Editora.
Palhares, P. (coord.). (2004). Elementos de Matemática. Lisboa: Lidel.
Palhares, P.; Gomes, A. & Amaral, E. (coord.) (2011). Complementos de Matemática para professores do Ensino Básico. Lisboa: Lidel.
Sites
http://www.atractor.pt/
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/
http://www.powersof10.com/