# Mathematical Applications

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### Objectives

1. To understand the scope of Mathematics and its applications, its role in the progress of civilization and its relevance in contemporary society;

2. To appreciate the beauty of Mathematics through the understanding of its processes and characteristics as a science;

3. To develop the ability to research, creativity and autonomy;

4. To relate the topics studied with mathematical content in the guidelines for Preschool Education and in the curriculum of the First Cycle of Elementary Education;

5. To apply strategies for problem solving and mathematical modelling in situations of everyday life;

6. To consolidate scientific knowledge in numbers and operations; geometry and measurement; logic and set theory; algebra; probability and statistics;

7. To combine theoretical knowledge and practical applications;

8. To explore the feasibility of using some material resources appropriate to the tasks at hand.

### Program

1. Maths in Preschool and Primary Education

2. Problem solving. Pólya's prescription for solving problems. Problem solving strategies. Mathematical modeling

3. Introduction to Probability. The concept of probability. Problems with permutations and combinations. The Pascal triangle.

4. Introduction to Statistics. The statistical method. Tables and graphs. Measures of central tendency and dispersion. The spreadsheet

5. Modular Arithmetic. Modular addition, subtraction, multiplication and division. Identification Numbers and Check Digits. Secret Codes: An Introduction to Cryptography

6. Sequences and regularities. Examples, properties and applications. Pictorial sequences. Arithmetic and geometric progressions

7. Right triangle trigonometry. The Pythagorean. Theorem Trigonometric ratios

8. Applications for the Preschool and Basic Education. Symmetry groups in Art and Nature. Tessellations Games and math manipulatives. Origami. The Fibonacci numbers.

### Teaching Methodologies

Theoretical-practical sessions – The topics of this course will be discussed and developed by studying concrete applications and by solving problems and exercises. The topics will be presented using electronic means, when appropriate. The course will benefit from the use of Moodle, the online learning platform available at the University of the Azores, thus enhancing the performance of asynchronous activities.

### Bibliography

Breda, A. et al. (2011). Geometria e Medida no Ensino Básico. MEC.

Cascalho, J., Nogueira, R. & Teixeira, R. (2012). O jogo e o desenvolvimento do raciocínio lógico-matemático: explorações no jardim-de-infância. Jornal de Mathemática Elementar 298, 5-12.

Hull, T. (2006). Project Origami: Activities for Exploring Mathematics.A. K. Peters.

Long, C. & DeTemple, D. (2006). Mathematical Reasoning for Elementary Teachers. Pearson Education.

Martins, M. et al. (2007). Análise de Dados: Texto de apoio para os professores do 1º ciclo. MEC.

Picado, J. (2001). A álgebra dos sistemas de identificação. Boletim daSPM 44, 39-73.

Ponte, J. P. et al. (2009). Álgebra no Ensino Básico. MEC.

Posamentier, A. (2007). The Fabulous Fibonacci Numbers. PrometheusBooks.

Teixeira, R. (2012). Jogos ecológicos: uma experiência de matemática recreativa com alunos de Educação Básica. Jornal de Mathemática Elementar 296, 15-20.

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### Classes

• Orientação Tutorial - 18 hours
• Teórico-Práticas - 60 hours

### Evaluation Methodology

• Group assignment with a oral presentation and a digital component: 50%
• Individual assignments : 50%