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 modeling 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.
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 .TheoremTrigonometric ratios
8. Applications for the Preschool and Basic Education. Symmetry groups in Art and Nature.Tessellations Games
and math manipulatives. Origami. The Fibonacci numbers.
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. Evaluation – Written test (40%), individual assignment (20%) and group assignment (40%); or, instead, a final exam. Concerning the individual assignment, students are asked to conduct a research with data analysis or, alternatively, to participate in some forums in the Moodle platform (discussion, challenges and development of activities for preschool and basic education).The group assignment focuses on the exploration of a topic in chapter 8 of the program (as exemplified in http://sites.uac.pt/mea/iniciativas/am/12-13).
Breda, A. et al. (2011). Geometria e Medida no Ensino Básico. MEC.
Cascalho, J., Nogueira, R. & Teixeira, R. (2012). O jogo e odesenvolvimento do raciocínio lógico-matemático: explorações nojardim-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 forElementary Teachers. Pearson Education. Martins, M. et
al. (2007). Análise de Dados: Texto de apoio para osprofessores 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 MathemáticaElementar 296, 15-20.
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