Probability and Statistics in Mathematics Education
Objectives
It is intended to adjust the student’s prior knowledge of mathematics to the didactic teaching practice requirements of the Secondary Education. The recent reforms in the curriculum point to a pedagogical practice grounded in the scientific rigor. Thus, it is required, from the future mathematical teachers, a greater mathematical fluency. Accordingly, at the end of this course, the students should have acquired the following knowledge’s and capabilities:
- teach with confidence the topics of Probability and Statistics presented in the Mathematics Program;
- distinguish valid didactic approaches from those that do not fulfill the objectives listed in the Mathematics Program;
- being able use the calculator and the computer on the implementation of different statistical techniques.
General characterization
Code
11525
Credits
6.0
Responsible teacher
Filipe José Gonçalves Pereira Marques
Hours
Weekly - 5
Total - 42
Teaching language
Português
Prerequisites
Good knowledge of the mathematical analysis concepts, in particular of the topics: functions of several variables, series and calculation of primitives and integrals.
Bibliography
- Guimarães e Cabral (1997). Estatística. McGraw-Hill.
- Montgomery e Runger (2002). Applied Statistics and Probability for Engineers. Wiley.
- Mood, Graybill e Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
- Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2007). Introdução à Estatística, 2ª edição. McGraw-Hill
- Paulino e Branco (2005). Exercícios de Probabilidade e Estatística. Escolar Editora.
- Pestana, D. e Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian, Lisboa.
- Rohatgi (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley.
- Tiago de Oliveira (1990). Probabilidades e Estatística: Conceitos, Métodos e Aplicações, vol. I, II. McGraw-Hill.
Teaching method
Theoretical and practical lectures with oral exposition of the different topics complemented with examples and resolution of problems. In particular the discussion and reflection of the different topics will be promoted in order to create bases and critical capacity; fundamental features so that students, in the future, are able to transmit in a rigorous and motivating way the concepts in the program of Mathematics for Secondary Education. Calculators and computers will be used as supporting tools for the consolidation and exploration of the different concepts.
Evaluation method
If you require any further information, please feel free to contact regent (Prof. Inês Jorge Sequeira).
Continuous evaluation:
Continuous evaluation will be done in three different moments:
- first evaluation: theoretical and practical written work and respective presentation, rated 0-20 (T1), counting 30% of the final grade.
- second evaluation: written test, rated 0-20 (T2), counting 30% of the final grade.
- third evaluation: theoretical and practical written work and respective presentation, rated 0-20 (T3), counting 40% of the final grade.
The student obtains approval if 0.3T1 +0.3T2 +0.4T3 is greater than or equal to 9.5. If a student does not attend to one of the evaluations he is evaluated with zero in the respective evaluation.
Resource examination:
Is made a written exam in the only date provided for this evaluation. The exam is ranged from 0 to 20. The student obtains approval if its grade is greater than or equal to 9.5.
Subject matter
1. Descriptive Statistics in Secondary Education
2. Problems solving in combinatorial analysis in the Secondary Education
3. Theory of probability and probability distributions in Secondary Education.
4. A didactic approach to Statistical Inference
5. Linear regression in the Secondary Education