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 - 4

Total - 60

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

  1. Guimarães e Cabral (1997). Estatística. McGraw-Hill.
  2. Montgomery e Runger (2002). Applied Statistics and Probability for Engineers. Wiley.
  3. Mood, Graybill e Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
  4. Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2007). Introdução à Estatística, 2ª edição. McGraw-Hill
  5. Paulino e Branco (2005). Exercícios de Probabilidade e Estatística. Escolar Editora.
  6. Pestana, D. e Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian, Lisboa.
  7. Rohatgi (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley.
  8. 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

Attendance

All students are admitted to evaluation.

CONTINUOUS EVALUATION

The continuous assessment will be made through one written work and respective presentation (T1), one test (T2) with minimum grade of 8 points.

Final Grade = 0.5 T1 + 0.5 T2, with T2 >= 8 points.

The student obtains approval to UC if Final Grade is greater than or equal to 9.5 values.

RESOURCE SEASON EVALUATION

The evaluation of Season 2 is made by Exam (E), being valid both for grade improvement and for approval to UC.

The student obtains approval to the UC if Resource Final Grade is greater than or equal to 9.5 values. 

GRADE IMPROVEMENT

Students who intend to take the appeal exam, with a view to improving their grades, must, in advance, request this improvement from academic services.

The works cannot be improved.

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

Programs

Programs where the course is taught: