Mathematics Elements

Ficha de unidade curricular - Ano letivo 2017/2018

Teaching language

Portuguese

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

- Understand, in a depth way, and mobilize concepts and procedures related with the fundamental themes of mathematics such as:
Geometry and Measurement
Number theory
Statistics and Probabilities
- Connect ideas, concepts and mathematical procedures
- Solve geometric problems, using models to spatial visualization and geometric knowledges of the shapes
- Use properly, concepts, tools and formulas to determine measurements, mobilizing knowledge about systems and measurement processes
- Solve numerical problems, mobilizing knowledge of numbers theory
- Know and apply, in a critical way, tools and statistical techniques in the resolution of the real problems
- Determine and use probabilities to model real situations and solve problems.

Syllabus

-Geometry and Measurement
Visualization And representation
   Planning and building models
   Representations of two and three dimensional
   Calculation of volumes and areas
Geometric transformations
   Isometries in the plane
   Dilations and similarities

Numbers theory
   Construction of the natural numbers (Axiomatic Peano)
   Construction of integers, rational and real numbers from the natural numbers
   real numbers
   Definition and properties of the operations

-Statistics and Probabilities
   Sampling Techniques
   Analysis, representation and data reduction
   sample characteristics: location and dispersion measures
   Two-dimensional distributions
   Linear regression
   Definitions probability
   Conditional probability
Normal probability model

Demonstration of the syllabus coherence with the UC intended learning outcomes

This course aims to understand, in depth, and mobilizing concepts and procedures relating to subjects of Geometry and Measurement, Number Theory and Statistics and Probability. The concepts will be addressed including numerous and varied experiences of problem solving. Is through of the problems solve that this curricular unit contributes to the development of the ability to think mathematically and for the understand and the deepen of different mathematical topics above mentioned.

Teaching methodologies

The work to be undertaken in this course will focus on the active participation of students in individual work and in group work, with the aim to develop the skills refered above. The sessions will be organized taking into account the reading, discussion and analysis of texts and the resolution and discussion of problems that allows to approach the contents of this curricular unit and carry out preparatory work for the design of a statistic investigation.

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

The active participation of students, individually or in groups, aims to contribute to the deepening of the themes of this curricular unit. The classroom sessions will focused on the problem solving and the production of the respective reports. With a view to understanding the statistical techniques in the reality problem solving, students will be involved in a statistical study around issues associated with the course of Family and Community Service, that includes various activities which are the phases of a statistical investigation.

Assessment methodologies and evidences

The evaluation will be an ongoing process which will include retroactive adjustment moments of individual work and group activities and oral and written expression.

The students must have an attendance of 75% of the classroom sessions (except for students with special status) and (i) participate in carrying out the proposed activities in class (30%), (ii) realize an individual written test, whose contents relate to themes Geometry and Measurement, Number Theory and Probability (40%) and (iii) develop, in group, a statistical study (30%).

Attendance system

Taking into account the specificity of training and the high percentage of technical training of this curricular unit, the students must have an attendance of 75% of the classroom sessions (except for students with special status).

Bibliography

Caraça, B. J. (1998). Conceitos fundamentais da Matemática. Lisboa: Gradiva.
Enzensberger, M. H. (2000). O diabo dos números. Porto: Edições ASA.
Graça Martins, M. E. & Cerveira, A. (1998). Introdução às probabilidades e estatística. Lisboa: Universidade Aberta.
Graça Martins, M. E., Loura, L. & Mendes, F. (2007). Análise de Dados. Lisboa: Editorial do Ministério da Educação.
Jacobs, H. (2003). Geometry. New York: W. H. Freeman and Company.
Murteira, B., Ribeiro, C. S., Silva, J. A. & Pimenta, C. (2010). Introdução à Estatística. Lisboa: Escolar Editora.
Palhares, P. (coord.) (2004). Elementos de Matemática. Lisboa: Lidel.
Veloso, E. (1998). Geometria: Temas actuais. Lisboa: Instituto de Inovação Educacional.
Veloso, E. (2012). Simetria e transformações geométricas. Lisboa: Associação de Professores de Matemática.